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Microscopical Structuring of Solids by Molecular Beam EpitaxyЧSpatially Resolved Materials Synthesis.

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Volume 27
Number 5
May 1988
Pages 593-758
International Edition in English
Microscopical Structuring of Solids by
Molecular Beam Epitaxy-Spatially Resolved Materials Synthesis
By Klaus Ploog'
Dedicated to Professor A . Rabenau on the occasion of his 65th birthday
Interfaces and heterojunctions which are incorporated into a crystal in well-defined geometrical and spatial arrangements can lead to a structuring o r engineering of (semiconducting) solids down to atomic dimensions. The electrical and optical properties are then defined locally, and phenomena related to extremely small dimensions ("quantum size effects") become more important than the actual chemical properties of the materials used.
The technique of molecular beam epitaxy allows an atomic layer-by-layer deposition in a
two-dimensional growth process, and crystalline materials in alternating layers of arbitrary
composition and only a few atomic layers thickness are formed. The synthesis of microscopically structured solids by molecular beam epitaxy affords access to a new class of
materials with accurately tailored electrical, optical, magnetic, dielectric, mechanical etc.
properties. The semiconductor and metal superlattices described in this article, which are
made of alternating thin layers of two different materials, symbolize just the beginning of a
new area of materials engineering on a molecular (or atomic) scale. This periodic modulation of the chemical composition normal to the surface imposes an artificial periodicity on
the semiconductor o r metal crystal, a periodicity of one o r two orders of magnitude larger
than its natural lattice spacing. The synthesis of other materials combinations, including
semiconductor/metal, semiconductor/insulator, metal/insulator, polymers, and magnetic
materials, with entirely different properties and for completely different applications will
certainly follow. Finally, a large variety of desired combinations of elements can be selected, and even metastable compounds with novel exciting properties can be synthesized
by molecular beam epitaxy.
1. Introduction
In modern materials science and materials technology
the accurately defined structuring of known solids down to
[*] Dr. K. Ploog
Max-Planck-lnstitut fur Festkorperforschung
Heisenbergstrasse 1, D-7000 Stuttgarr 80 (FRG)
Angew. Chem. lnt Ed. Engf 27 (1988) 593-621
microscopically controlled dimensions is now becoming
more important than the continual search for new chemical compounds. Statistically affected preparation techniques, involving e.g. alloying and diffusion, are being replaced more and more by chemically and physically well
defined methods, as e.g. epitaxy.["] This trend is most obvious in the domain of semiconductor research and development, but it also applies to other materials, e.g. ceramics
0 VCH Verfagsgesellschafr mbH. D-6940 Weinheim, 1986
0570-0833/88/0505-05~3$ 02.50/0
and composites, and in a more general sense even to the
most recent developments in the field of high-temperature
superconductors.[21Semiconductor materials required for
use in devices must be of extreme purity and their crystal
perfection should be as high as possible. Interfaces and accurately defined impurities (“dopants”) have to be incorporated into the crystal intentionally and with high spatial
resolution, in order to define locally the electrical properties and to adjust the desired potential differences. The important consequence of an accurate structuring of solids in
increasingly smaller dimensions is that phenomena related
to these restricted small dimensions (“quantum size effects”) become more important than the chemical properties of the materials used. A striking example for this postulate is the quantum Hall effect.[31The numerical value of
the Hall resistance depends only on fundamental constants, while the compositions and the dimensions of the
crystals become unimportant.
The microscopical structuring of semiconducting solids
down to nanometer dimensions is achieved by heterojunctions (i.e. interfaces between two lattice-matched materials
of different composition) and by p/n doping interfaces
(homojunctions) which are intentionally incorporated into
the crystal with high spatial resolution. This process leads
to the concept of “band-gap engineerir~g”‘~(Fig. I), the
origin of which is already to be found in the patent application for the transitor by Shockley[61and in the later theoretical studies on heterojunctions by Krorner.”] The first experimental confirmation of this concept was accomplished
by the successful fabrication of GaAs/Al.,Ga, -.As heterojunction lased8] which could be operated continuously at
room temperature. The real breakthrough for band gap engineering came with the revitalized development of molecular beam epitaxy of 111-V compound semiconductors at
the Bell L a b o r a t o r i e ~ and
l ~ ~ with the stimulated efforts to
realize artificial semiconductor superlattices in the IBM
Thomas J. Watson LaboratorieslIol at the beginning of the
The concept of semiconductor superlattices”O1 infers
that, by periodic modulation of the chemical composition
(e.g. GaAs/Al,Ga, -,As) in the direction of growth, an artificial one-dimensional periodicity is imposed on the
semiconductor crystal (Fig. Ib). This additional periodicity
is one or two orders of magnitude larger than the natural
spacing of the lattice planes, but it is smaller than the de
Broglie wavelength of electrons, which is about 25 nm in
GaAs. The artificial periodicity, which is superimposed on
the crystal potential, gives rise to the formation of mini- or
sub-bands for electrons and for holes and thus leads to
novel electrical and optical properties of the layered material. For many familiar materials the new structures result
in unusual electronic properties which open u p new technical applications.
The technique of molecular beam epitaxyl’,’’’ made feasible the first reproducible preparation of multilayer heterostructures with atomically abrupt material transitions at
the interfaces and with accurately controlled profiles of
composition and doping over regions only a few nanometers wide. Of particular importance is that the single crystalline pattern of the lattice unit in successive layers continues without disruption or distortion across the inter594
faces between the layers, if lattice matched material systems, such as e.g. GaAs/AIAs, are used.[*’
Table 1. Band gap E, and lattice constant a of binary I l l - V compound semiconductors and of the group 1V element semiconductors Si and G e at room
temperature. The band-structure type is indicated by d (-direct) and i (-indirect). The wavelength ,l is calculated according to A = 1.24/E,.
E, [ev]
1 [wl
a Inml
1.425 (d)
2.16 (i)
1.35 (d)
0.36 (d)
2.26 (i)
0.73 (d)
0.17 (d)
1.65 (if
0 92
1 70
0.566 1
0 6057
0.545 1
0 6479
1.12 (i)
0.66 (i)
1 88
0 5431
The theoretical concept of semiconductor superlattices
and the unique capability of molecular beam epitaxy provided the basis for the successful fabrication of quantum
wells, which represent a section out a of a superlattice and
thereby form a key element of band-gap engineering (Fig.
lc). The quantum wells are formed by embedding a thin
layer of a semiconductor with smaller band gap (e.g.
GaAs) between two semiconductor layers with larger band
Band gap
Band gap
Valence band
Fig. I . Schematic illustration o f t h e concept of band-gap engineering in semiconductor superlattices and quantum wells. a) Scheme of conduction and
valence band edge in an undoped and in an n-doped semiconductor having a
band gap (energy gap) of Ew b) Periodic modulation of conduction and valence band edge in a superlattice, made of two semiconducting materials
with different band gap, and formation of sub-bands for electrons and for
holes. c) GaAs quantum well embedded by two AI,Ga,-,As barriers and
formation of sub-bands for electrons (EtC)as well as for heavy (Elhh)and
light holes (E,,,).
The Ill-V compound semiconductors are particularly suitable for the
fabrication of heterostructures with nearly perfect interfaces because
most of them, including GaAs and AIAs, crystallize in the “zinc blende”
structure. Within the same group of the periodic table of elements the
different constituent elements can be mixed over a wide range, e.g. the
Group 111 elements Al. Ga, In. In this way we can form ternary, quaternary etc. alloy semiconductors without changing the structure type [12].
The lattice constants and the electronic properties of these semiconductors can thus he modified arbitrarily over a wide range simply by the
choice of the alloy composition (Table 1). The hand gap of the ternary
alloy AI,Ga, _,As, e.g., increases from 1.42 eV for GaAs (at 300 K) to
1.91 eV for the mole fraction x=0.4. At higher AI content ( ~ 2 0 . 4 )the
AI,Ga, _,As alloy transforms from a direct into an indirect-gap semiconductor, where the indirect X-minimum (valley) of the conduction band
drops below the direct r-minimum [12]. Therefore, for most applications
of GaAs/ALGa, .As heterostructures the ternary alloy AI,Ga, ,As of
mole fraction x<O.4 is preferred to the binary compound AIAs.
Angew. Chem. Inl. Ed. Engl. 27 (1988) 593-621
gap (e.g. Al,, &ao ,AS). When the thickness of the embedded GaAs layer is comparable to or smaller than the d e
Broglie wavelength for electrons, distinct sub-bands for the
electrons and holes confined in this potential well are
formed. The energy position and the spacing of these subbands depend only on the thickness (width) and on the
depth of the quantum
The depth in turr! is given by
the energy difference between the conduction band edges
(or valence band edges in the case of holes) of the two
semiconductors. These energy differences are also called
band discontinuities. The wavelength or energy, respectively, of the light emitted or absorbed by the 111-V semiconductors in these quantum wells is thus mainly determined by the well width, which is simply a geometric parameter. Similarly to the quantum Hall effect the local
chemical composition of the material becomes less important in these layered structures and quantum size effects
determine the important features. The preparation and investigation of quantum wells made of 111-V semiconductors was crucial for the development of quantum well lase r ~ , [ ’ which
show dramatically improved characteristics
as compared to conventional heterostructure lasers, and
for the development of novel photo detector^.['^^ These two
types of devices are decisive for the new technology of
photonics, which is based on the optical processing of signals. The application of molecular beam epitaxy for the
synthesis of materials with a spatial resolution on an
atomic scale has led to a variety of artificially layered
semiconductors where the motion of electrons and holes is
quantized in the layer plane. An important challenge for
microstructure materials science lies in the fabrication of
quantum wires and quantum dots in which an additional
confinement of the carriers in one or two more dimensions
withrn the layer plane is required.
In the present review paper we start in Section 2 with an
outline of the basic principles of molecular beam epitaxy
applied to the growth of 111-V semiconductors and discuss
the characteristic features of this technique which allow
the spatially resolved synthesis of materials. In Section 3,
four distinct methods for characterizing artificially layered
solids with atomic layer resolution are presented: transmission electron microscopy (TEM), double-crystal X-ray diffraction, luminescence and absorption spectroscopy, and
Hall effect measurements. It is shown that improved methods of materials characterization can have a strong impact
on the future development of the spatially resolved synthesis of materials. In Section 4 we present some selected examples for the microscopical structuring of solids normal
to the crystal surface, and we discuss the exciting electronic properties of the following artificially layered materials: superlattices and quantum well structures made of
111-V semiconductors, spatial separation of electrons from
their ionized parent impurities in selectively doped 111-V
heterostructures, (GaAs)l(AIAs)l monolayer alloys as example for an ordered alloy of composition AlosGaosAs,
monolayer doping in GaAs, combination of a chemical
with a structural periodic modulation in Si/Ge superlattices, and finally metal superlattices. In the closing Section
5 a brief outlook on the future developments of spatially
resolved materials synthesis and microstructure materials
science IS given.
Anyen, Clirm. Int Ed. Engl. 27 (1988) 593-621
2. Fundamentals of Molecular Beam Epitaxy
The controlled fabrication of semiconductor thin films
of high crystal perfection requires the application of epitaxial growth techniques, i.e. oriented layer growth on the
well ordered surface of a host crystal (“substrate”). The arrangement of the lattice units in the growing layers is predetermined primarily by the structure of the host crystal.
Epitaxial growth techniques have been refined dramatically in the past ten years, especially for the 111-V semiconductor layers which are now used in the fabrication of
optoelectronic (photonic) and high-frequency electron devices. Depending on the scientific and technological requirements, one of the three complementary methods of vapor
phase epitaxy, liquid phase epitaxy, or molecular beam
epitaxy is used.[’61
Molecular beam epitaxy (MBE) is a method for the fabrication of extremely thin crystalline films of semiconductors and metals as well as artificially layered structures by
means of atomic or molecular beams.’”
The specific advantages of this sophisticated technique are that artificially
layered solids can be accurately tailored to within atomic
dimensions. Distinct atomic layers of a material can be
manipulated one by one. Figure 2 shows schematically the
basic principle of molecular beam epitaxy for the 111-V
semiconductors GaAs, AI,Ga, -,As, Ga,In, -,As, and
AI,In, -.As. The growth process is based on the reaction of
thermal, non-ionized molecular beams of the constituent
elements with a (001) oriented GaAs or InP substrate surface heated to 500-600°C. At this substrate temperature
the impinging species of the molecular beams can react
with each other and the atoms can migrate sufficiently fast
to their lattice sites so that no defects are formed. The molecular beams are generated by evaporation of the elements Ga, Al, In, and As in small cylindrical effusion cells
having a capacity of about 10-100 cm3. The doping impurities Be for p-type and Si for n-type doping, which are
important for adjusting the electrical properties of 111-V
semiconductors, are incorporated from separate molecular
beams into the growing films. Mechanical shutters are
Fig. 2. Schematic illustration of evaporation and deposition process during
molecular beam epitaxy of I l l - V compounds. RHEED = Reflection HighEnergy Electron Diffraction (see also Fig. 6 ) .
mounted in front of the orifices of the effusion cells. They
allow the molecular beams that are directed onto the substrate to be switched on or off within fractions of a second.
In this way highly refined layered structures with the composition and/or doping changing over a range of just a few
(or even one) atomic layers can be deposited without any
deleterious distortion of the crystal growth. The macroscopic electrical and optical properties of the layered
structures can be accurately tailored as desired simply by
choosing the correct composition and thickness of the constituent layers. In principle, molecular beam epitaxy is a
rather elementary synthetic process, since no foreign atoms
are present at the gas-solid interface and by-products are
not formed.
The basic concepts of the MBE growth process were
first developed in the mid-fifties at the Siemens Research
Laboratories in Erlangen. Using his so-called “Three-Temperature Method”, Giinther“91was able to prepare the first
stoichiometric thin films of the 111-V semiconductors InAs,
InSb, and GaAs on glass substrates. The specific difficulty
for achieving stoichiometry was that the constituent elements of 111-V compounds (i.e. compounds formed from
elements of the third and fifth main groups of the periodic
table) have largely differing vapor pressures so that these
compounds exhibit considerable decomposition at their
evaporation temperature (incongruent evaporation).
Giinther used the Group V-element source oven, kept at a
low temperature T I (e.g. 300°C for As), to maintain a constant vapor pressure in the reaction chamber. The source
oven for the Group 111 element was kept at a much higher
temperature T, (e.g. 950°C for Ga), thus providing a flux
of atoms incident on the substrate that determined the condensation rate of the 111-V compounds. The choice of the
substrate temperature T2 was most crucial. This intermediate temperature had to be kept below the incongruent
evaporation point, so that a condensation of the 111-V
compounds could occur, but it had to be increased to a
value that ensured re-evaporation of the excess Group V
component, which had not reacted, from the substrate surface. The early films prepared by Giinfher were polycrystalline, since they were deposited on amorphous substrates. Furthermore, the vacuum conditions of lo-‘ torr
in the reaction chamber available 30 years ago in the laboratory were not adequate enough for ensuring a reasonable
purity of the films. The molecular beam epitaxy of crystalline semiconductor films followed some ten years later in
the mid-sixties, when Arthurfzo1and Cholgfat the Bell Laboratories studied the fundamental aspects of the interaction
of G a atoms and AsZ molecules with crystalline GaAs surfaces under ultrahigh vacuum (UHV) conditions (base
pressure 10- ’ I torr). In the author’s laboratory, molecular
beam epitaxy has been pursued since 1974.
The most characteristic feature of molecular beam epitaxy is its low growth rate of about one lattice plane o r
monolayer 1i.e. one complete layer of G a plus one complete layer of As o n the (001) surface] per second
( P 0.3 nm/s). The important consequence of this is that the
monocrystalline thin film can be built u p atom by atom in
a highly controlled manner, and atomically flat growth
surfaces are formed. Thus, a high crystal perfection is also
achieved for extremely thin films. Owing to the stringent
Electron diffraction
gun 10-50 keV \
with Shutters
Transfer rod
IM gauge
Fig. 3 . Schematic cross-section of U H V system used for molecular beam epitaxy of I l l - V compounds, including reaction chamber, preparation chamber,
and load-lock chamber. From the preparation chamber the samples can also
be transferred to other processing units or to detailed surface analytical investigations.
Evaporation unit
with effusion ,cells
Continuously rotating
substrate holder
Substrate preparation
and load-lock chambers
Ultrahigh vacuum growth
chamber with LN2 cooled panels
Fig. 4 . Side mew of a system for molecular beam epitaxy of I 1 I-V compounds
constructed in the author’s laboratory.
purity requirements for semiconductors, the film growth
has to be carried out in bakeable UHV systems made of
stainless steel and having a base pressure of l o - ’ ’ torr
(this tolerable residual gas pressure is five orders of magnitude lower than in the regions of space traversed by the
spacelab). Figure 3 shows a schematic cross-section and
Figure 4 a side-view of a three-chamber UHV system for
molecular beam epitaxy installed in the author’s laboratory. The system consists of the following basic components:
- UHV reaction chamber of 45 cm
( G 18 inch) diameter,
internally lined with a liquid-nitrogen (LN,) cooled
- evaporator unit with six to ten effusion cells which are
thermally isolated from each other by an additional
- substrate manipulator for positioning and heating
large-area (up to 75-mm diameter) substrate wafers
- load-lock and preparation chamber to introduce and
exchange the substrate
- measurement system to control the purity of the system, the molecular beam fluxes, the substrate temperature, and the crystal growth.
Angew. Chem. Int. Ed. Engl. 27 (1988) 593-621
Reaction chamber, preparation chamber and load-lock
chamber are isolated from each other by large-diameter
all-metal gate valves and they are pumped independently
of each other. The load-lock chamber is pumped by a
closed-loop He cryopump for rapid pump-down cycles,
and the two other chambers are each pumped by a combination of ion getter pump and Ti sublimation pump. It is
important to make sure that the amount of undesirable hydrocarbons and oxygen-containing compounds in the residual gas of the reaction chamber is kept as low as possible. The substrate wafers mounted on Mo support devices
are transferred by magnetically coupled transfer rods from
one chamber to the other and they are fixed to the respective heater blocks by a bajonet joint. The material fluxes
emerging from the effusion cells are determined by the
temperature of each of the cells and monitored by a movable Bayard-Alpert ion gauge which can be moved into
the position of the substrate (the central portion of the
constituent flux distributions should intersect at this position). The flux measurements by the ion gauge are sufficiently accurate; however, they are not element-specific.
To determine accurately the composition of the residual
gas and to measure the fluxes specific to the constituent
elements, a quadrupole mass spectrometer (QMS) of high
sensitivity can be used. For quantitative flux measurements
the ionization chamber of the QMS placed in the beam
path has to be surrounded by a LN2 cryopanel, and, owing
to material deposits, the spectrometer must be readjusted
continuously. The crystal growth o n the substrate surface
is monitored by electron diffraction under grazing incidence [reflection high-energy electron diffraction
(RHEED)]. Details of this important technique for in-situ
growth control during MBE will be discussed later (see Fig. 6).
The design of high-quality molecular beam sources fabricated from nonreactive refractory materials is the most
important requirement for successful MBE growth. The
evaporation sources have to provide stable high-purity molecular beams of the desired intensity and uniformity, and
they must withstand operating temperatures u p to 1400°C
without themselves contributing to the molecular beams.
Precise temperature stability ( f O . 1 at 1000°C operating
temperature) and reproducibility are essential. For accurate kinetic studies relevant to the growth process,
Knudsen (equilibrium) effusion cells with small orifices
have been used in the past (Fig. 5a) to produce collisionfree thermal energy beams of the constituent elements. The
analytical formulas used to calculate the angular intensity
distribution of molecular beams emerging from Knudsen
cells have been compiled by Herman.'"] Unfortunately,
only very limited experimental data are available to check
the validity of the theoretical approaches. For practical
MBE growth, non-equilibrium (Langmuir-type) effusion
cells with large orifices are used nowadays (Fig. 5b). In addition to the vapor pressure of the starting materials, the
intensity of the molecular beams is also determined by the
evaporation geometry. The crucibles made of pyrolytic
boron nitride (PBN) are of either cylindrical or conical (tapered) shape, and have a length of about 5 to 10 times
greater than their orifice diameter. The crucible capacity of
10 to 100 cm3 for the different starting materials should be
large enough to achieve continuous operating times of sevAngew. Chem Inr. Ed. Engl 27 11988) 593-621
l i
Fig. 5 . Schematic illustration of (a) Knudsen (equilibrium) effusion cell and
(b) non-equilibrium (Langmuir-type) effusion cell used for molecular beam
epitaxy. 9= distribution angle of the molecular beam, L = distance between
cell orifice and substrate, A =diameter of cell orifice, R = substrate radius,
p = a n g l e of impinging molecular beam with respect to substrate normal,
p,=taper of effusion cell wall.
era1 months before recharging is required. The helical Ta
wire to heat the crucible is wound in such a way to avoid
magnetic stray fields deleterious for the operation of the
electron diffraction during growth. Several sheets of thin
crimped Ta foil provide a good thermal isolation to keep
the heating loss as low as possible. The adjustment and
regulation of the temperature is accomplished by continuously operating high-precision regulators having proportional, integral and differential adjustment (PID regulator).
The temperature is measured by a W/Re thermocouple
fixed close to the outside bottom of the cylindrical crucible
(the W/Re thermocouples d o not react with the molecular
beams). It is not important to measure the absolute temperature of the melt in the crucible but to detect the temperature at a fixed location of the thermocouple in a reproducible manner. This relative temperature is then related
to the molecular beam flux arriving at the substrate surface
which is independently determined by the movable ion
gauge or by the thickness of the deposited material. Saito
and Shibatorni'221have recently performed a systematic investigation of the dependence of the uniformity of the molecular beams across the substrate on the geometrical relationship between the Langmuir-type effusion cells and the
substrate. Over a substrate diameter of 75 mm they reduced the variation of the composition of AI,Ga, - .As
layers to less than f 1% by optimizing the following three
geometrical parameters: distance between substrate and
effusion cells, taper qo0
of the conical crucible wall, and
diameter of the cell aperture.
Evaporation of the Group 111 elements of the periodic
table under UHV conditions produces atomic species, i.e.
atomic beams emerge from the respective effusion cells.
Evaporation of the Group V elements, on the other hand,
produces almost exclusively tetrahedrally shaped tetrameric molecules (P4,AS,,, Sb,) by sublimation. For the preparation of phosphides (Gap, InP, etc.) and for some other
special applications dimeric molecules (P2, As2, Sb2) are
required which can be produced by three different methods. First, incongruent evaporation of the binary 111-V
compounds yields dimeric molecules.1231Second, the dimeric species are obtained by thermal decomposition of
gaseous PH3 or ASH^,^^^] which, however, also produces a
large amount of hydrogen in the UHV system. Third, dimers can be generated from the elements by using a twozone effusion cell ("cracker ell").[^^] A flux of tetramers is
first formed in a conventional effusion cell and then
passed through an optically baffled high-temperature stage
where complete conversion to PZrAsz, or Sb2 occurs above
The growth of 111-V semiconductors during molecular
beam epitaxy IS essentially determined by the sticking
coefficient of the atoms and molecules impinging onto the
substrate surface.[z31The substrate temperature is in general chosen to be below the incongruent evaporation temperature of the growing compound. The sticking coefficient of the Group 111 elements Al, Ga, and In is unity on
(001)-oriented GaAs, InP, or GaSb substrates, i.e. each impinging atom sticks. On the other hand, the sticking coefficient of the Group V elements on clean (001) substrate surfaces is zero at the growth temperature. Their condensation occurs only when Al, Ga, or I n adatoms have already
been deposited on the substrate surface. The growth rate of
the films is thus exclusively determined by the arrival rate
of the Group 111 elements. The stoichiometry of most 111-V
semiconductors during MBE growth is self-regulating as
long as excess Group V element molecules are impinging
on the growing surface. In practice a two- to tenfold excess
is used. The excess species of the Group V elements d o not
stick on the heated growth surface. As a result, the crystal
is built layer-by-layer in the [OOl] direction, i.e. first a
monolayer of GaAs (or InP, AIAs, etc.) is nearly completed
before growth of the next monolayer starts. The detailed
growth mechanism of 111-V semiconductors was first established by Foxon and Joyce,L261
who studied the surface
chemical processes by modulated molecular beam spectroscopy, and it has now been confirmed by investigations
of the periodic intensity oscillations of the diffraction features in the RHEED pattern (see Fig. 7).
A good control of the composition of the ternary III111-V alloys AI,Ca, -,As, Ga,In, -,As, etc. can be achieved
by supplying excess Group V species and adjusting the
flux intensities of the impinging Group 111 element beams,
as long as the substrate temperature is kept below the congruent evaporation limit of the less stable of the constituent binary 111-V compounds (e.g. GaAs in the case of
AI,Ga,-.As or InAs in the case of G ~ , I ~ , - . A s ) . [ ~At
higher growth temperatures, however, preferential desorption of the more volatile Group 111 element (1.e. Ca from
AI,Ga, -,As) occurs, so that the final film composition is
not only determined by the added flux intensities but also
by the differences in the desorption rates. To a first approximation we can estimate the rate of loss of the Group
I11 elements from their vapor pressure data. This assumption is reasonable because the vapor pressure of the element over the compound, e.g. G a over GaAs, is similar to
the vapor pressure of this element over its melt.L281
In Table
2 the rates of loss of AI, Ga, and In are compiled for different substrate temperatures. The surface of alloys grown at
Table 2. Approximate rate of loss of Group I l l elements (in monolayers per
second) from the surface of ternary Ill-111-V semiconductors estimated from
vapor pressure data.
T ["CI
high temperatures will thus be enriched by the least volatile Group 111 element. As a consequence, we expect a significant loss of I n in Ga,In, -,As films grown above 550°C
and a loss of G a in AI,Ga, -,As films grown above 650°C.
For accurate adjustments of the effusion cell temperatures
an intermittant calibration based on independently measured film composition, e.g. by X-ray diffraction or photoluminescence measurements (see Section 3), is therefore
required. The lower limit of the substrate temperature during MBE growth was in most cases given by the deterioration of the crystal quality owing to the strong increase of
the defect density, which occurs, e.g., for GaAs below
450°C. However, Horikoshi et al.[291have recently shown
that high quality GaAs and AlAs can be grown at a substrate temperature as low as 300°C, if G a (or Al) and As,
are alternately supplied to the growing surface. In an arsenic-free environment, which exists for a short period, the
surface migration of G a and Al is obviously strongly enhanced.
The growth of ternary 111-V-V alloy films such as, e.g.,
GaP,As, -, by MBE is more complicated, since, in particular in phosphorus-containing compounds, the relative
amounts of the Group V element incorporated in the growing film are not simply proportional to their relative arrival
rates, even at moderate substrate t e r n p e r a t ~ r e s . In
~ ~addi~]
tion, the flux intensity of the Group 111 element arriving at
the growing surface affects the incorporation of the Group
V elements. At present the various factors controlling this
incorporation behavior are not well understood, and it is
difficult to obtain a reproducible composition control of
ternary 111-V-V alloys during MBE growth. For ternary
111-111-V alloys, on the other hand, the simplicity of the
MBE process allows composition control from x=O to
x = 1 in AI,Ca,-,As, Ga,In,-,As, etc. with a precision of
+0.001 and doping control, both n- and p-type, from the
l o T 4to the 10l9 atoms c m - 3 range with a precision of a few
percent. The accuracy is largely determined by the care
with which the growth rate and doping level was previously calibrated in test layers.
In general MBE growth of 111-V semiconductors is accomplished on (001) oriented substrate slices of GaAs,
InP, or GaSb having thicknesses of 300-500 pm. Before introduction into the growth chamber the substrate surface
should be free of crystallographic defects and clean on an
atomic scale, so that the crystal film can indeed be built in
a two-dimensional growth process. Impurities and defects
form nucleation centers for three-dimensional (3D)
growth. The substrate preparation always involves treatment with organic solvents and with oxidizing solutions,
and the final step consists of chemical etching to produce a
Angew Chem. In1 Ed. Engl 27 (1988) 593-621
relatively stable oxide on the substrate surface." I, ' I This
surface oxide protects the substrate against contamination.
After insertion of the substrate into the MBE system the
surface oxide is removed by heating to a temperature just
below the limit of congruent evaporation, and clean crystallographically well ordered substrate surfaces are obtained. Smaller substrate slices are soldered with liquid In
to the circular Mo mounting plate (In becomes liquid at
160°C and it has a high surface tension), and the whole
device is then transferred and heated. Larger substrate
wafers having a constant diameter of 50 or 75 mm (2 or 3
inches) are fixed without In to a special Mo holder designed for direct-radiation substrate heating. After insertion of one of these M o holders with the chemically etched
substrate into the load-lock chamber and evacuation to a
pressure below
torr the substrate is preheated to remove physisorbed gaseous impurities, e.g. H,O and CO.
Then the substrate is transferred to the preparation chamber where the intentionally produced surface oxide is removed by controlled heating. The removal of the surface
oxide can also be accomplished in the reaction chamber, in
order to observe this process by RHEED. The transfer between the chambers is made by trolleys and magnetically
coupled transfer mechanisms. In the growth chamber the
Mo mounting plate holding the substrate wafer is fixed by
a bayonet joint to the Mo heater block which is originally
attached to a special manipulator. This manipulator positions correctly the substrate wafer relative to the evaporation sources, heats it to the required temperature, and continuously rotates it azimuthally for optimum film uniformity.
On using high-purity starting materials ( > 99.9999%),
the purity of the semiconductor films depends crucially on
the residual background impurities in the reaction chamber. Recently, unintentionally doped GaAs with an extremely low residual acceptor concentration of 2 x 10l3
atoms cm-3 was
The residual acceptor is
probably due to carbon impurities from the residual gas of
the reaction chamber. The application of MBE grown
films for fundamental studies as well as in device structures requires the control of the electrical and optical material properties by the deliberate incorporation of small
amounts of impurity (dopant) elements from additional effusion cells. The most common dopants used during MBE
growth of 111-V semiconductors are Be for p-type and Si
for n-type doping. Over a large range of growth conditions
both elements have a sticking coefficient of unity. Abrupt
doping profiles normal to the growth surface can be obtained simply by actuating the shutters in front of the effusion cells. Be substitutes for G a atoms in the GaAs sublattice and forms a nearly ideal shallow acceptor.[321For doping concentrations up to 2 x l O I 9 atoms c m - 3 each incident
Be atom produces one ionized impurity species. By lowering the substrate temperature to 500°C even extremely
high acceptor concentrations u p to 2 x 10'' cm-3 are feasible in Be-doped GaAs with perfect surface morphology.
For (00 I)-oriented substrates, also Si primarily substitutes
for G a atoms i n the GaAs sublattice and forms a shallow
donor.'"] The electrically measured doping concentration
is u p to n = 1 x 10" c m - 3 directly proportional to the dopant arrival rate, provided care is taken to minimize the
background H 2 0 and CO level during growth. At present,
Angew. Chem In!. Ed. Engl. 2711988) 593-621
the origin of the upper limit of 1 x loi9 c m P 3 for the electron concentration in Si-doped GaAs is not exactly clear.
Three mechanisms are discussed, (i) autocompensation by
(ii) adincorporation of Si on As sites or on inter~titials,l~~]
ditional impurities evolving from the Si effusion cell
heated to above 1300°C,[3s1
or (iii) formation of Si-vacancy
complexes acting as acceptors which lead to a compensation in heavily n-doped G ~ A s . [The
~ ~ ]possibility of Si migration or diffusion during MBE growth of AI,Ga,-.As
films at high substrate temperatures and/or with high donor concentration has been the subject of controversial
because of its deleterious effects on the
properties of selectively doped n-AI.,Ga, -.,As/GaAs heterostructures which require abrupt doping profiles. There
is some evidence that a migration of Si in ALGa I - ,As can
only occur at high doping concentration ( > 2 x l o 1 *atoms
cm-') as the result of a concentration-dependent diffusion
process, which is enhanced at high substrate temperatures.
It is finally important to note that the incorporation of Si
atoms on either Ga o r As sites depends significantly on the
orientation of the GaAs substrate.[381In GaAs grown on
(001). ( l I I ) B , (21 l)B, (311)B, (511)A, (51 1)B, and higherindex orientations, Si atoms predominantly occupy G a
sites and act as donors, while they occupy As sites and act
as acceptors on (1 11)A, (21 1)A, and (3 1 l)A orientations.
This different incorporation behavior of Si is now utilized,
e.g., to produce a series of lateral p/n junctions in GaAs on
graded steps of the (001) substrate surface.[391Based on this
method of spatially resolved synthesis during MBE, semiconductors with a few nanometers wide lateral regions of
totally different electrical properties are produced.
Reflection electron diffraction under grazing incidence
(RHEED) is the most important technique for in-situ monitoring of the crystal growth during molecular beam epitaxy.[' The forward scattering geometry with a grazing incidence angle of 1 to 3 " schematically shown in Figure 6a
implies that also a t a primary-beam energy of 10-30 keV
the information (penetration) depth is restricted to the out-
Fig. 6.Geometric arrangement of electron diffraction with grazing-angle I n cidence (RHEED) used as in-situ analytical tool during molecular beam epitaxy: (b) Ewald construction to interpret the diffraction conditions, (c) and
(d) surface unit cell ("mesh") and diffraction patterns of two important reconsfructions during molecular beam epifaxy (not to scale).
ermost atomic layers of the growing crystal. This geometry
makes RHEED fully compatible with the MBE growth
process, and the diffraction pattern can be observed directly on the fluorescent screen (“in-situ”). The diffraction
spots are elongated to characteristic streaks normal to the
shadow edge. The appearance of streaks instead of spots
cannot fully be explained by means of the Ewald construction (Fig. 6b), where in reciprocal space the lattice rods intersect the Ewald sphere tangentially when the diffraction
condition is fulfilled. In addition, we have to assume a specific disorder in certain directions of the growing crystal
The existence of surface reconstructions characteristic for MBE growth (Fig. 6c) leads to additional features in the R H E E D pattern (Fig. 6d) at fractional intervals between the bulk (zinc blende-type) diffraction
streaks.“ ‘I The re-ordering of the surface atoms during reconstruction gives rise to a lowering of the symmetry at the
surface. In most cases the surface unit cell (“mesh”) has a
larger periodicity. This rearrangement at the surface results
from the rehybridization of binding orbitals in order to
minimize the free energy of the surface. The (001) surface
of 111-V semiconductors exhibits a number of different reconstructions during MBE growth which are directly related to the surface stoichiometry. The surface composition, on the other hand, depends crucially on the growth
conditions (substrate temperature, ratio of molecular beam
fluxes, e t ~ . ) . ~Figure
~ ’ ] 6d shows (schematically) the diffraction patterns of the two most important surface reconstructions during MBE growth of GaAs, i.e. the arsenic-stable
(2 x 4)- and the (4 x 4)-reconstruction, taken at different
azimuths. From the occurrence of specific surface reconstructions, identified from the diffraction pattern, we can
in turn derive the actual reaction conditions, and if necessary we can modify them. The monitoring of the RHEED
pattern is of particular importance at the beginning of the
epitaxial growth on the chemically etched and thermally
heated substrate wafer as well as during the preparation of
abrupt material interfaces.
Another characteristic feature of this type of electron
diffraction under grazing incidence is the existence of pronounced periodic intensity oscillations of the specularly
reflected and of the diffracted beams during MBE growth
(Fig. 7, top). The period of these oscillations corresponds
exactly to the time required to deposit a monolayer of
GaAs (or AIAs, Al.,Ga, - , y A ~etc.)
on the (001)
To explain these features we can to a first approximation
assume (Fig. 7, bottom) that the amplitude of the intensity
oscillation reaches its maximum when the monolayer is
just completed (maximum reflectivity). The formation of
the following lattice plane starts with statistically distributed 2D islands having the height of one GaAs monolayer.
The intensity of the diffracted (or reflected) electron beam
decreases with increasing size of the island. The minimum
reflectivity occurs at half-layer coverage (B= 0.5). When
the coverage is further increased the islands coalesce more
and more, and the reflectivity finally reaches a maximum
again at 8= 1. The observed damping of the intensity amplitude is probably due to the fact that the individual surface domains probed by the electron beam are not in
phase. The damping of the RHEED oscillations can be
eliminated when the surface migration of the Group 111
Time (s)
Fig. 7. Top: Periodic intensity oscillation of the specularly reflected electron
beam in the RHEED pattern as a function of time during molecular beam
epitaxy of GaAdAIAs layers. Bottom: Formation o f 2D growth islands o f
monolayer height but different lateral size to illustrate the varying reflectivity
of the incident electron beam from the growing surface (not to scale).
elements is greatly enhanced by short synchronized cessations of the arsenic flux.f431In this case only a few large
domains are formed on the growing surface. The existence
of periodic intensity oscillations in the RHEED pattern is
a conclusive confirmation of the assumption that crystals
are indeed formed in a 2D layer-by-layer growth mode
during molecular beam epitaxy. The RHEED intensity oscillations are now widely used to calibrate and to monitor
absolute growth rates in real time and with monolayer
resolution and to provide direct real-time evidence of the
formation of interfaces on an atomic scale during abrupt
deliberate change of the composition.[441As in the case of
the widely used GaAs/AI,Ga, -,As heterointerface, e.g.,
the sequence of layer growth ternary-to-binary exhibits
considerably different properties (structural and electronic) than the sequence binary-to-ternary, since the G a and
Al atoms have a strongly different surface migration rate at
normal MBE growth conditions. These differences in the
heterointerfaces can be compensated to a certain extent by
the interruption of growth at each interface for a short time
(10i-102s, the value depends on the actual growth conditions).
3. Characterization of Microscopically Structured
The characterization of solids which are microscopically
structured down to atomic dimensions requires analytical
techniques having a high spatial resolution and a high sensitivity and accuracy. The necessity of a detailed characterization stems directly from the historical development of
the semiconductor superlattices. In this field, a sound theory made it first possible to predict the intriguing properties of these microscopically structured semiconducting
materials. Sophisticated measurement systems were then
used to assess the degree to which the predictions have
Angew. Chem. Inr. Ed. Engl. 27 11988) 593-621
been fulfilled. It is important to note that the interface perfection experimentally achievable by MBE is now so high
that conventional methods of depth profiling analysis,
which involve sputtering to section the materiai combined
with some means of composition determination (such as
Auger electron spectroscopy or secondary ion mass spectroscopy) are no longer adequate for the required resolution. Therefore, the continuous development of already existing and of new analytical and measurement techniques
is an unquestionable requirement. Improved techniques
for characterizing materials can in turn also have a strong
impact on the development of spatially resolved materials
In this paper we briefly introduce four methods for
characterizing materials which are routinely used today to
assess the specific properties of microscopically structured
solids, in particular semiconductors: transmission electron
microscopy, double-crystal X-ray diffraction, luminescence and absorption spectroscopy, and Hall effect measurements. In many cases a combination of two or more
methods is necessary.
3.1. Transmission Electron Microscopy
The method of cross-section transmission electron microscopy (TEM) with dark-field and lattice imaging was
first used by P e t r o f j 5 ]to analyze the periodicity, the degree of order at the interfaces, and the composition in
GaAs/ AIAs superlattices. This imaging mode requires that
the incident electron beam is nearly parallel to the layers
of the superlattice, i.e. parallel to the (001) plane in the
[ 1101 direction (see Fig. 8, top). To prepare the thin TEM
specimen, the (001)-oriented substrate with the epitaxiai
layer is first cleaved parallel to the ( 1 10) plane, and the
cleaved fragments are then thinned by chemical etching
and ion beam etching down to a thickness of 10-20 nm.1461
The regular layer sequence A, B, A, B, ... in the epitaxial
film leads to a periodic array of interfaces which in turn
generates a periodic variation of the crystal potential acting as a phase grating for the incident electron beam (provided the coherence length of the electron beam is larger
than the grating periodicity). Thus, in addition to the diffraction spots arising from the diffracting lattice planes of
the layers A and B, we observe characteristic superlattice
spots in the transmission electron diffraction pattern,
which represent a Fourier transform of the phase grating.
Lattice images are formed either in the bright- or darkfield mode by selecting the transmitted or diffracted beam
and one or more of the superlattice diffraction spots with
the objective aperture (Fig. 8, top). The intensity distribution in the resulting lattice image shows a periodicity.
However, this periodicity represents the true distribution
of interfaces in the sample as well as order or disorder at
the interfaces only under very crucial imaging conditions.
The specimen thickness and the defocussing of the objective lens, for example, strongly affect the periodicity observed in the image.
I n Figure 8 (middle and bottom) we show examples for
a cross-sectional dark-field TEM image of a 10-nm GaAs/
10-nm AlAs superlattice and for a high-resolution lattice
image of a 2.8-nm GaAs/2.3-nm AlAs superlattice, respecAngew. C%em. I n f . Ed. Engl. 27 (19881 593-621
Fig. 8. Top: Geometric arrangement of incident electron beam and constiluent layers of a superlattice as well as generation of the imaging conditions
for high-resolution transmission electron microscopy (TEM). Middle and
bottom: Cross-sectional dark-field TEM image and high-resolution lattice
image of GaAs/AIAs superlattices. The TEM micrographs were kindly taken
by Dr. H . Oppolzer, Siemens AG. Munich.
tively. Inspection of the lattice image clearly reveals that
the perfect ordering of the lattice units continues without
distortion also across the interfaces. The two binary components GaAs and AlAs provide the highest contrast at the
interfaces of these superlattices. Suzuki and O k ~ r n o t o [ ~ ’ ~
have recently demonstrated that a high contrast in the lattice plane images can also be obtained for the technologically important GaAs/AI,Ga, -,As superlattices with
x=0.3, if the TEM specimens are cut out of the epitaxial
layer in (001) orientation so that the electron beam is incident in the [IOO] direction. However, the specimen preparation for this orientation is rather elaborate because a
(100) cleavage plane does not exist for the 111-V semiconductors. When the periodicity of the superlattice is larger
than several lattice planes it becomes difficult for a microscope of lower resolution to form a dark field image from
the superlattice spots, as these spots are then located too
60 1
close to the main lattice reflections. But since the G a and
Al atoms have significantly different scattering factors, the
periodic layer sequence can still be imaged as shown in
Figure 8 (bottom). In this micrograph the dark bands are
GaAs and the light bands are AIAs. It is evident, however,
that the resolution is not adequate enough to define the
interfaces on an atomic scale.
3.2. Double-Crystal X-Ray Diffraction
Transmission electron microscopy is a destructive analytical method for the wafer, and it calls for an elaborate preparation of suitable specimens. Double-crystal X-ray diffraction, on the other hand, is a non-destructive method
and it requires far less experimental effort. X-ray diffraction was already used in the early seventies for the characterization of semiconductor s ~ p e r l a t t i c e sbut
l ~ ~it~ soon lost
importance because of its analytical limitations at that
time. For about three years the method has experienced a
renewed widely spread application, which was initiated by
the significantly improved theoretical analysis of the experimentally determined diffraction ~urves.1~~1
In a semiconductor superlattice the lattice parameter as well as the
scattering power are subject to a one-dimensional periodic
modulation in the direction of the layer sequence. As a
consequence, the diffraction pattern consists of a series of
satellite reflections located symmetrically around the respective Bragg reflection. Figure 9 shows schematically the
diffraction geometry of an epitaxial layer grown on a crystalline substrate and the basic principle of a double-crystal
X-ray diffractometer operating in a non-dispersive antiparallel Bragg arrangement. A dislocation-free G e crystal
is used as monochromator and collimator to produce a collimated monochromatic X-ray beam. The appropriate
choice of the asymmetry factor of the collimator crystal
minimizes the angular divergence of the beam incident on
the specimen. In our case the divergence is about 2.35 seconds of arc, and we obtain a very high resolution with such
an in~trument.1~~1
The small difference in the lattice constants between the
Al,Ga, - ,As epitaxial layer and the GaAs substrate crystal
gives rise to a slight distortion of the unit cell of the epitaxy crystal. This distortion of the unit cell can be determined by measuring two reflection curves, one from the
lattice planes parallel to the (001) crystal surface and one
from lattice planes inclined to the crystal surface. Our
measurements have conclusively shown that for this materials system a change of the lattice constant parallel to the
(001) surface does not exist, while the change of the lattice
constant perpendicular to the epitaxial layer surface, i.e. in
the [OOl] direction, depends linearly on the chemical composition of the AI,Ga,-,As layer, i.e. on x. The relative
change of the GaAs and AlAs lattice constants perpendicular to the crystal surface amount to A a =
1.583 x
nm and for a relaxed lattice to (Aa)relax
0.72 x
nm. After conversion of Aa to ( A U ) , ~ using
the elastic stiffness constants we can thus determine the
composition of the epitaxial AI,Ga, -,As layer very accurately. The thickness of the epitaxial layer can be deduced
from the angular spacing of pendellosung fringes,“] if its
total thickness is less than 2 pm ( G X-ray extinction
When very thin layers (thickness <100nm) or when
layered structures are studied, the diffraction maxima of
the epitaxial layer and of the substrate crystal are in general not exactly distinguished, and an unambiguous assessment of lattice distortion and crystal thickness can no
longer be made. In this case it is necessary to perform a
theoretical treatment of the reflection behavior of the
whole crystal (epitaxial layer). We have used a semi-kinematical approach of the dynamical theory of X-ray diffraction for distorted c r y ~ t a 1 s . IThe
~ ~ ~theoretical fit of the experimental diffraction curves yields detailed information
on the strain profile (lattice distortion), the chemical composition, and the thickness of heterostructures. In Figure
10 we show the comparison between measured and calculated diffraction curves for a ten-period GaAs/AlAs superlattice recorded in the vicinity of the symmetric (004)
CuKol,reflection. The average Al concentration of the entire superlattice is determined from the angular spacing between the substrate peak and the main epitaxial-layer peak
(zeroth-order peak). The angular distance (A@), I between
the zeroth-order (“0”) peak and the satellite peak “ 1”
(or “ - 1”) yields the superlattice periodicity T according
to the relation
Epitaxial layer
Reflect I ng’lo Rice plane
x D2
Fig. 9. Schematic illustration of X-ray diffraction from a crystalline epitaxial
layer deposited a n a crystalline substrate (top) and basic principle of a double-crystal X-ray diffractameter in non-dispersive anti-parallel Bragg arrangement (bottom).
where ,
Iis the X-ray wavelength atld 8, is the diffraction
angle of the zeroth-order peak. Also the thickness of the
constituent GaAs and AlAs layers can be determined accurately from these data. The position, the intensity, the halfwidth, and the number of the satellite peaks are crucial criteria for the layer thickness, the composition, periodicity
fluctuations, the inhomogeneity of composition and the in-
[*] Pendellosung fringes = oscillations of the X-ray diffraction curve due to
interferences a f waves scattered at different depths of the epitaxial layer.
Angew Chem. inf Ed Engl. 2711988) 593-621
height of one monolayer (&lattice plane) are formed
which lead to a disorder and thus broadening of the interfaces in the order of a lattice constant ( 20.56 nm). The
growth interruption of 10s is sufficient to smooth the
growth surface and to produce abrupt material transitions
and extremely sharp interfaces. This result is in accordance
with the investigations of the RHEED intensity oscillations.143. 441
1 0 2 0 "'1
Fig. 10. Experimental (dashed line) and theoretical (solid line) X-ray diffraction curves of a (GaAs),,(AIAs)a, superlattice taken in the vicinity of the
(004) reflection with CuKnlradiation.
terface quality. Figure 11 shows an example for the investigation of interface homogeneity and broadening in
GaAs/AlAs superlattices. The diffraction curves were recorded in the vicinity of the quasi-forbidden (002) reflection, because in this geometry the satellite peaks are more
pronounced and therefore more sensitive to interface effects. For the (002) reflection the structure factor of AlAs is
ten times larger than that of GaAs. The existence of interface disorder (broadening) manifests itself in an increase
of the halfwidth and in a decrease of the intensity of the
satellite peaks. The two GaAs/AIAs superlattices whose
results are depicted in Figure 1 1 were grown under the
same growth conditions and their periodicity is exactly the
same, i.e. the maxima of the satellite peaks have the same
angular spacing from the zeroth-order peak. The differences between the two superlattices are the following:
During growth of sample A the growth was stopped for
10 s at each GaAs/AIAs and AlAs/GaAs interface, while
sample B was grown continuously by sequentional opening and closing of the G a and Al shutters. A detailed quantitative analysis of the diffraction curves in Figure 11 reveals that during continuous growth 2D islands with a
The quantitative analysis of the interface quality by
X-ray diffraction becomes even more important when the
lattice parameters of the epitaxial layers have to be
matched to those of the substrate by appropriate choice of
the layer composition, as for Ga,In, -,As with x=O.47 and
Al,In,-,As with x=0.48 on InP substrates. Therefore, in
Ga,Inl -,As/AI,In, -,As superlattices also the chemical
composition of the constituent layers has to be evaluated
accurately. Deviations of more than one percent from the
ideal value cause strain effects which give rise to significant changes in the electronic properties of the material. I n
some cases the semi-kinematic approach of the dynamical
diffraction theory is not sufficient to analyze the measured
diffraction curves quantitatively, and the more elaborate
dynamical theory must be applied.1501In Figure 12 (top) we
show a comparison between the measured and the calculated diffraction curve of a Ga,In, -.,As/AI,In, -,As superlattice. The capability of both the epitaxial growth
method and of the characterization method follows directly from a comparison of data compiled in Table 3 for
four superlattices of this type. Finally, it should be pointed
out that in an ideally lattice-matched Gao4,,Ino 5 3 Z A ~ /
5 2 3 Asuperlattice
on InP substrate the satellite
peaks have almost disappeared, as shown in Figure 12
(bottom). The low residual intensity and the pendellosung
fringes are caused only by the periodicity of the structure
factors in the superlattice. A high intensity of the satellite
peaks thus indicates a periodic variation of the strain in
0 lrnradl
Substrate "0"
10' 0 1-1
Fig I I . X-ray diffraction curves o f two (GaAs),l(A1As)r2 superlattices taken
in the vicinity of the quasi-forbidden (002) reflection with CuKa, radiation.
Sample A was prepared with and sample B without growth interruption at
the heterointerfaces.
Anqew Chrm Int Ed. Engl 27(1988) 593-621
0 [mradl
Fig. 12. X-ray diffraction curves of Ga,ln,_,As/Al,ln, _ , A s superlattices on
InP substrate taken in the vicinity of the (004) reflection with CuKr,,radiation. Top: From multilayer sample prepared by molecular beam epitaxy
( . . . . experiment, -theory). Bottom: Calculated curve for ideally lattice4771nosz3Assuperlattice.
matched Gao4681no53ZA~/AI0
Table 3. Structural parameters of four different Ga,In, - ,As/Al,ln, - ,As superlattices determined by double-crystal X-ray diffraction measurements using C u K n ,
Thickness of
Ga, I n , As
Thickness of
AI,In, _,As
10 2
Average lattice
mismatch of
b l
Lattice strain
in G a , l n , _ , A s
10 - 4 ~ , ~
+ 6.0
+ 9.5
+ 0.0
- 3.5
3.3. Luminescence and Absorption Spectroscopy
For many 111-V semiconductors the specific optical
propertiesil2]play an important role for their application in
optoelectronic devices. Methods to evaluate these optical
properties are thus ideally also employed for a detailed
characterization of microscopically structured solids composed of these materials. The measurement of the luminescence energy of bound excitons (electron-hole pair) Eo (x)
in the ternary AI,Ga, -,As alloy at 4 K, which shifts to
higher energy with increasing x according to
1.515 eV+x(1.247 ev)
[for O<x<O.45]
has for long been used to determine the A1 content (in
GaAs, i.e. x = O , the temperature dependent band gap decreases from 1.515 eV at 4 K to 1.424 eV at 300 K). In the
introduction we have already pointed out that the confinement of electrons and holes in the GaAs quantum wells
gives rise to the existence of distinct energy levels (sub- or
mini-bands) in the conduction and valence bands. The energy spacing between the sub-bands in the conduction and
valence bands determines the spectral (energy) position of
the light emission (photo- and electroluminescence) and
the optical absorption characteristic^.['^^ In Figure 13a we
Mole fraction x
in G a , l n , _ , A s
- 15.0
Mole fraction x
in AI,In,_,As
- 8.0
- 14.0
strained-layer superlattices. However, when the lattice
strain of the constituent Ga,In, -,As and AI,In, -,As
layers are of the same magnitude, the satellite peaks also
exhibit a weak intensity (see Fig. 12 (top) and Table 3).
Lattice strain
in AI,In,_,As
10 -4z2,
show schematically the process to create electron-hole
pairs by the absorption of photons and the recombination
mechanism of electrons and holes, which results in light
emission (luminescence). The energy position of the subbands depends primarily on the width (thickness) L, and
to a lesser extent on the depth Vo of the quantum well. The
energy for the confinement of electrons, i.e. the spacing between the bottom of the conduction band and the n-th subband, assuming infinitely deep wells is to a first approximation given by[’31
E , = (n2nh2)/(2m:L:)
with m,*= effective mass of conducting electrons[’] and
271. (For more accurate
calculations the finite depth of the quantum well has to be
taken into account. The allowed sub-bands for the electrons and holes are then given by solutions of the Schrodinger equation normalized by the boundary condition
that the wave functions and their derivatives are continuous at the GaAs/AI,Ga, -,As interface.) From Equation
( 3 ) it follows that the energy spacing between the allowed
sub-band and the band edge is directly proportional to
l/L:. Consequently, the “optical” band gap which is relevant for luminescence depends primarily on the width of
the GaAs quantum well; it becomes larger when the quantum well becomes narrower. This expectation is confirmed
h = Planck’s constant divided by
Growth sequence of GaAslAixGa,-xAs QWH-
L-inrnl 150
1 ’ 1
g (E)
Fig. 13. Schematic illustration of (a) radiative electron-hole transitions during emission or absorption of light in a GaAs quantum well and (b) energy
dependence of the density of states g ( E ) in a homogeneous semiconductor
(dotted line) and in a quantum well (solid line).
1 70
E IeVl
GaAs AI,Gol.,As
Fig. 14. Photoluminescence spectra of GaAs quantum wells of different well
With decreasing well width a strong blue-shift (i.e. to higher enerwidths t,.
gy) of the luminescence is observed. Int. = intensity in arbitrary units.
In semiconductors m: is used instead of the electron mass me to account
for the influence of the crystal lattice on the conduction electrons (“effective mass approach”).
Angew. Chem. In!. Ed. Engl. 27 (1988) 593-621
This discussion emphasizes the importance of actuating
by the photoluminescence measurements on GaAs quanthe shutters of the effusion cells always at the maximum of
tum wells of different widths, the results of which are
shown in Figure 14. The luminescence energy ( h ~ is) ~ ~the R H E E D intensity oscillations.
In the photoluminescence spectra one generally obgiven by the energy of the transition between the n = 1
serves electron-hole transitions only between the lowest
electron sub-band E l , and the n = 1 heavy-hole sub-band
sub-bands El, and E l h h(or Ell,,,resp.), because the inE Il,h minus the exciton binding energy E,x,lsll according
jected carriers relax extremely fast to these levels. Higher
sub-band transitions, on the other hand, can be best observed by optical absorption measurements (see Fig. 13a).
The absorption spectra of a Gal).,,Ino 53A~/AI04xIno.szAs
( E g = band-gap energy of GaAs). When the photolurninessuperlattice taken at 4 K and at 300 K are shown in Figure
cence measurements are performed at low temperatures
16.IS4]The steplike behavior of the absorption coefficient
(4 K), also the phenomena arising from defects and impurities and the influence of the interface “roughness” can be
studied in detail. The origin of the interface roughness are
the 2 D growth islands with a height of one monolayer
(a,,/2 = 0.283 nm) discussed before, which have different
lateral extensions. As shown schematically in Figure 15,
these islands give rise to different widths of the quantum
wells and consequently to different luminescence ener-
E lev1
t[lOOl Growth direction
Lz af2
When the lateral extension Wof the growth islands
is larger than twice the Bohr radius of the exciton f f B , i.e.
2 a B larger than 30 nm (see also Section 4.2), then several
peaks appear in the photoluminescence spectrum at different energies corresponding to the distinct islands. However, when w becomes less than 2 f f B for smaller growth islands, then the exciton “senses” different widths of the
quantum well and a spectral broadening A ( ~ W ) of
~ , the
luminescence occurs,[s31given by
In the experiments a n increase of the linewidth with decreasing width of the GaAs quantum well was observed,
because the relative influence of growth islands of constant height (ao/2 = 0.283 nm) becomes larger. This undesired roughness caused by the small islands ( W < 2 a B ) can
be reduced quite markedly by the interruption of growth at
the interfaces.‘”’ Also an enhancement of the surface migration of the Group 111 elements results in an expansion
of the larger islands at the expense of the smaller ones.
Anyen,. Cllum In,. Ed. Engl. 27 11988) 593-621
Fig. 16. Absorption spectra of a Ga,,471n,,,,As/Al,,,xlni,srAs
taken at 4 K and 300 K. The dotted line indicates the steplike behavior of the
two-dimensional density of states g ( E ) . Abs. = absorption in arbitrary units
(logarithmic scale).
Fig. 15. lnlluence of the different lateral size of the 2D growth islands at the
GaAs/ALGa,-,As interface on the effective width L, of the quantum well
and on the localization of excitons.
A ( ~ U ) =~(,h ’ / m : ) ( A L , / L : )
as a function of energy is clearly seen. It is caused by the
modified density of states in quasi-2D systems. In addition, the absorption edge is shifted by a few meV to lower
energies, and distinct excitonic absorption peaks appear
(see also Section 4.1.2). For the radiative electron-hole
transitions between the higher sub-band levels the selection rule An = O holds, i.e. the quantum number n does not
The quantization of the wave functions for electrons and
for holes in one direction (i.e. in the quantum well) also
results in a distinct modification of the energy dependence
of the density of states g ( E ) , i.e. the number of the allowed
states per energy interval, which now assumes a steplike
(staircase) form (Fig. 13b).[I3I In bulk semiconductors
where the minimum of the characteristic lengths is much
larger than the mean free path of an electron, the g ( E )
curve always exhibits a parabolic shape and it is equal to
zero at the minimum energy, i.e. at the band edge. In the
case of semiconductor crystals consisting of different elements only the curvature of the parabolic g ( E ) curve
changes. In contrast to bulk material, the steplike g ( E )
curve of quasi-2D systems has a finite non-zero value of
the density of states even at the minimum energy. In addition, the distinct shape of the steplike curve can be adjusted (“tailored”) by appropriate choice of the well width
L, and the potential barrier Vo. The artificial arrangement
of the constituent atoms leads to a completely different
shape of the g ( E ) curve even for materials made of the
most familiar semiconductor crystals, like GaAs and AIAs.
To the concept of band-gap engineering mentioned in the
introduction we can now add the concept of density-ofstates modification. Inspection of Figure 13b further re605
veals that the size quantization also lifts the degeneracy of
the light and the heavy holes in GaAs, i.e. two bound states
E,,,,,, and En,,, with different energies exist in quantum
For the measurements of the optical absorption of epitaxial layers the substrate must either be a transparent substrate, as is the case for InP in Gao4,1n,,53As/A10481n052As
super lattice^,'^^^ or it must be removed by selective etching,
as in the case of the GaAs substrate used to deposit GaAs/
AI,Ga, - ,As super lattice^."^^ The selective removal of the
substrate is difficult, and during this treatment strain can
be induced in the epitaxial layers. Therefore, instead of absorption measurements, photoluminescence excitation
measurements are now frequently used to acquire information on the excitonic resonances and on the energy dependence of the density of states. In this technique the luminescence intensity is measured at a fixed energy (wavelength) while the exciting laser energy is varied across the
energy range of interest. Figure 17 shows such a photoluminescence excitation spectrum of a GaAs double quantum well structure. The transitions to higher subbands,
which are also observable in the absorption spectrum, are
clearly seen.
in t
Fig. 17. Photoluminescence excitdlion spectrum of a 9-nm wide GaAs quantum well taken at 4 K. The dotted curve indicates the position of the photoluminescence line. Int. = luminescence intensity in arbitrary units.
The proportionality factor RH, denoted Hall constant o r
Hall coefficient, is given by
where e is the electronic charge (negative sign) and n is the
electron (carrier) concentration per cm3. An analogous relation holds for the holes.
Measurement of the Hall coefficient R H enables determination of the carrier concentration n, which represents a
characteristic quantity of semiconducting materials. When
electrons as well as holes contribute to the carrier transport
in the sample, the Hall coefficient depends also on the respective mobilities. The mobility p is the proportionality
factor in the relation between the drift velocity u of electrons (or holes) in a semiconducting crystal and an applied
external electric field E. As long as the average drift velocity is small compared to the thermal velocity, the simple
is valid.
The Hall coefficient and the conductivity (or resistivity,
respectively) of semiconducting thin films are measured by
a method developed by van der Pauw.[561
The reciprocal of
the mobility determined in this way is a direct measure of
the retardation of the free-carrier drift by the influence of
the crystal lattice. At low temperatures the scattering of
electrons (holes) by ionized donors (acceptors) and by lattice imperfections, such as dislocations, grain boundaries,
interstitials, etc., dominates. At higher temperatures, e.g. at
room temperature, numerous lattice vibrations are excited
so that a strong scattering by lattice vibrations (“phonons”) is added to this. The various scattering mechanisms
exhibit a different temperature dependence.[”I Further-
3.4. Hall Effect Measurements
The feasibility of doping semiconductors intentionally
with donors (to create free electrons) and with acceptors
(to create free holes) and thus to form p/n junctions (or
diodes) within a crystal is one of the most important basic
requirements for the technical applications of these materials. The measurement of the conductivity (or resistivity, respectively) and of the Hall effect are the most important
methods for determining the concentration, the mobility,
and the carrier type (electrons or holes) in a semiconductor
thin film. When free carriers passing through a crystal are
subject to a transverse magnetic field,a phenomenon called
the Hall effect appears.[”] Under these conditions an electric field is produced whose direction is perpendicular to
the current direction and to the magnetic field vector. The
transverse o r “Hall” voltage V , induced by the electric
field is proportional to the current I and the magnetic field
B and inversely proportional to the thickness of the sample
d, as given in equation (6).
! lo5-
[crn*V s I
I // //
Bulk GaAs
104 -
T [KI-
Fig. 18. Dependence of electron mobility on temperature for three different
sample configurations determined by Hall effect measurements. The distinct
behaviour of each curve indicates a different influence of the various scattering mechanisms in the samples. 2DEG = two-dimensional electron gas.
N,, = concentration of dopant atoms.
Angew. Chem. Inr. Ed. Engl. 27 (1988) 593-621
more, electrons and holes behave differently in the various
scattering processes. As a consequence, we often observe a
complicated relationship between mobility and sample
temperature. Figure 18 shows the dependence of the electron mobility on temperature for three different sample
configurations. The highest mobility at low temperatures is
obtained from a microscopically structured selectively
doped GaAs/Al,Ga, -,As heterostructure. The layer sequence and the properties of this artificially layered structure are described in detail in Section 4.2.
4. Selected Examples for Microscopical Structuring
Normal to the Crystal Surface
In the original concept of semiconductor superlattices”O1
Esaki and Tsu in particular elaborated the theoretical possibilities of a carrier transport perpendicular to the constituent layers. They proposed the existence of extremely fast
so-called Bloch oscillations due to Bragg reflections at the
boundaries of the mini Brillouin zone and predicted a negative dynamic conductivity associated with the transfer of
electrons into regions of negative mass of the mini Brillouin zone. As yet, however, the Bloch oscillations have
never been observed experimentally and today it is anticipated that at the high electric fields required intersubband
transitions of the electrons rather than Bragg reflections
will occur.1s81A negative differential resistance in the current-voltage characteristics perpendicular to the layers can
also be obtained from semiconductor superlattices with
thicker barriers owing to “resonant” tunneling phenomena
of electrons between adjacent quantum wells. This process
requires matching of the energies of the ground state (first
sub-band) and of the excited state (second sub-band) in
the next well at a certain value of the applied external electric field, i.e. the sub-band levels are in “resonance” (see
Fig. 19a for illustration). The first experiments related to
this phenomenon, performed in the early seventies,[591were
not unequivocal, because at that time the material quality
of the artificially layered structures did not meet the requirements. In particular, the fluctuations of the layer thickness within each quantum well, which are due to the
growth islands of monolayer height discussed in Section
3.3 (see also Fig. 15), resulted in fluctuations of the subband energy levels of the quantum wells as well as in a
destruction of the coherence between the interfering electron waves reflected at the two interfaces. Therefore, fifteen years ago other intriguing properties of the periodically layered semiconductor structures came into the forefront which had not been discussed in the original concept,
i. e. the optical (excitonic) properties and the carrier transport parallel to the constituent layers (quasi-2D electron
and hole systems). The microscopically structured semiconductors used for the investigation and device application of these phenomena are in general comprised of one
or more quantum wells which are isolated from each other
by rather thick ( > 5 nm) barriers. Theoretical calculations
have shown that to a good approximation these multiquanturn well heterostructures can be treated as if each constituent layer contributes its characteristic electronic properties to the entire
Anyen. Chem Int. Ed. Engl. 27 11988) 893-621
a’ Ec
Undoped GaAs
Fig. 19. Schematic illustration of resonant tunneling (1.e. vertical transport
perpendicular to the layers) of electrons in GaAs/AI,Ga, -,As superlattices
and quantum wells. a) Sequential resonant tunneling in a superlattice occurring when the potential drop across a superlattice period is equal to the energy spacing between a first excited state and ground state or between second
excited state and ground state. b) Schematic layer sequence of GaAs/
AI,Ga, ,As double-barrier diode for investigating resonant tunneling. c)
Process of resonant tunneling in the double-barrier diode and plot of the
measured current-voltage characteristics (not to scale).
Before some selected examples for the exciting optical
and electrical properties of quasi-2D electron systems will
be presented, ist should be pointed out that in the last five
years the improvement of the crucial interface quality has
inspired a revival of investigations related to resonant tunneling phenomena in microscopically structures semiconductors.[“] The double-barrier structures schematically depicted in Figure 19b are particularly promising for application of the resonant tunneling effect in microwave devices
with extremely high switching frequencies. The operating
principle of these resonant-tunneling diodes follows directly from the illustrations of Figure 19c. Electrons can
tunnel through the double barrier only when the potential
(Fermi) energy of the injecting (left) side coincides (is in
resonance) with the sub-band energy E l , in the quantum
well between the two AI,Ga, -,As barriers by applying an
external voltage. The resonant transmission of electrons
gives rise to a current maximum in the I / V characteristics
at an external voltage of V = 2 E , e-I (the applied voltage is
split into two equal voltage drops at each barrier). When
the applied voltage is further increased, the current drops
steeply (“negative differential resistance”), since the extremely sharp resonance condition is detuned. The potential successful operation of microwave diodes based on the
resonant tunneling effect even at room temperature, imposes stringent requirements, upon the interface quality
which can be met only by the application of RHEED intensity oscillation features combined with growth interruption during the spatially resolved synthesis of materials by
molecular beam epitaxy.["21This procedure makes feasible
the fabrication of amplifiers and oscillators operating in
the submillimeter range with a response time of less than
l o - " s. The frequency limit of these diodes is given by the
electron tunneling time of z =
s, which in turn derives from the ultimate limit of the uncertainty relation according to z < h / A E ( A E = energy broadening of the tunneling state).
4.1. Optical (Excitonic) Properties of Quasi-2D Electron
and Hole Systems
4. I . I . Quantum Well Heterostructure Lasers
In conventional GaAs/AI,Ga, - .As double-heterostructure lasers having a 0.1-0.2 pm thick active layer the energy of the emitted laser light is primarily determined by
the band gap of the material forming the active layer
( E 1.42 eV for GaAs at 300 K).[I2] In addition, impurities
(or dopants, respectively) of the GaAs layer significantly
affect the light emission. The emission energy is always
slightly reduced as compared to the band-gap energy, because this "extrinsic" luminescence dominates in doped
material. The radiative electron-hole transitions responsible for luminescence change their nature drastically when
the thickness of the active GaAs layer is reduced to below
30nm. At these dimensions the formation of quantum
wells with sub-bands for electrons and for holes commences (see Fig. 13). The electrons and holes can still
move freely along the layers (i.e. in x- and y-direction),
while perpendicular to the layers the impulse, the energy,
and the wave function are quantized. It has already been
shown in Section 3.3 that under normal excitation conditions the luminescence in these quasi-2D systems is given
by the radiative recombination of electrons populating the
lowest conduction sub-band E , , with heavy holes populating the uppermost valence sub-band E l h h(transitions from
higher populated sub-bands retaining the quantum number selection rules of An=O are observable only under
high excitation conditions). As a consequence, this "intrinsic" luminescence dominates in (undoped) quantum wells.
Since the energy of the sub-bands for electrons and for
holes depends primarily on L, [see Eq. (3)], we have the
possibility of adjusting the energy of the emitted light arbitrarily between 1.42 eV (for GaAs) and approximately the
band-gap energy of the &Gal -,As barriers (or cladding
layers) by matching the appropriate choice of the well
width during MBE growth, which is a simple geometric
parameter (see Fig. 14).
I n addition to the adjustable (or tunable) wavelength of
the emitted light, the strongly modified density of states
g ( E ) of these quasi-2D systems was the other important
motivation for the development of quantum well laser
structures whose layer sequence is schematically shown in
Figure 20a. Depending on the requirements for the performance of the laser diode, different configurations of the
Fig. 20. Schematic layer sequence of quantum well heterostructure laser. a)
Layer sequence of a modified multi quantum well (MMQW) laser and realspace energy band diagram. b) Various configurations (layer sequences) of
the active region of quantum well lasers illustrated by means of the distinct
real-space energy band diagrams (QW = quantum well, MQW = multi QW,
SCH Q W = separate confinement heterostructure QW, G R I N SCH Q W =
graded index separate confinement heterostructure QW).
active region are chosen (see Fig. 20b), which result in a
modification of the electrical and optical confinement of
the injected carriers and of the light, respectively. The
simultaneous electrical and optical confinement is only
possible because of the reciprocal behavior of direct band
gap and refractive index in these semiconductors. However, single quantum wells often do not provide sufficient
optical confinement for operation of the laser. Therefore,
in the so-called separate confinement heterostructures
(SCH), a separate electrical (in the quantum well) and optical confinement (in the superimposed double heterostructure) is accomplished (see Fig. 20b).
The general advantages of quantum well heterostructure
lasers can be summarized as follows:L631
The steplike energy dependence of the density of states
g ( E ) in quasi-2D systems gives rise to a narrow bandwidth of the optical gain and a high peak value as compared to the parabolic g ( E ) behavior in conventional
3 D systems. The population inversion required for laser
operation is thus achieved at a much lower driving current, and threshold current densities can be obtained
which are three to five times lower than in conventional
The characteristic temperature To, which is a criterion
for the temperature sensitivity of the threshold current
I , has a much higher value.1641The temperature dependence of the threshold current for semiconductor lasers is
given by the empirical relation
The steplike function of the density of states g ( E ) leads
to a reduced sensitivity of the energy distribution of the
carriers. The resulting decreased temperature sensitivity
of the emission wavelength is of particular importance
Angew. Chem. Int. Ed.
Engl. 27 (1988) 593-621
for G a , l n , _ , P , A s I _ , / l n P a n dGa,ln,-,As/Al,In,_,As
lasers which operate in the long-wavelength range of
1.3- 1.65 pm.
3. The qdantum well lasers oscillate more easily in a single
longitudinal mode (single wavelength oscillation). The
device can thus be operated under direct current modulation up to a very high frequency limit, i.e. at very high
bit rates.[”s1
4 Quantum well lasers are especially well suited for
monolithic integration with other active and passive
components on a common substrate,[661since the absorption coefficient of the non-excited part of the quantum well structure is three to five times lower at the
wavelength of the emitted laser light than in conventional laser structures.
At present the best characteristics for GaAs laser diodes
are achieved with the parabolic shape of the band edges
depicted in Figure 20b 0.
The parabolic shape is obtained
by an appropriate grading of the Al concentration in the
Al,Gal -,As barriers. These so-called GRIN SCH (derived
from “Graded Index Separate Confinement Heterostructure) lasers can be operated with threshold current densities as low as 150 A / c ~ ’ . [ ~The
~ ] accurately controlled variation of the composition and of the doping as a function
of layer thickness to obtain the symmetric parabolic shape
of conduction and valence band edges in these G R I N
SCH structures imposes stringent requirements on the spatially resolved materials synthesis.
The wavelength range of minimum optical loss in glass
fibers has been shifted from previously 0.85 pm via 1.3 pm
to 1.55 pm today. Therefore laser diodes made of
Ga, I n , - ,P, As, -, /InP and Ga,In, -,As/A1,Inl _,As lattice-matched to InP substrate as well as GaSb/AI,Ga, -,Sb
are now used for optical communication systems designed
for long distances. The composition of the ternary and
quaternary materials and the widths of the quantum wells
have to be adjusted accurately such that the lasers emit in
the desired wavelength range. The field of application of
GaAs quantum well laser diodes is shifting more and more
to optical data storage and processing as well as to information transmission and processing in local networks (including computer networks).
4.1.2. Excitonic Phenomena
An important consequence of the confinement of electrons and holes is that the excitonic effects have a distinct
impact on the optical properties of these microscopically
structured semiconductor^.^^^^^^^ Excitons are bound electron-hole pairs with a small binding energy, e.g. 4 meV in
GaAs; they are created during the absorption of photons.
In most homogeneous materials the “fragile” excitons are
therefore observable only at low temperatures. The confinement of excitons in quantum wells prevents any dissociation induced by thermal energy, so that excitonic phenomena become observable even at and above room temperature.16y1These effects are now exploited in novel optoelectronic and photonic devices. The enhancement of the
binding energy associated with the confinement of the exA n p w Clwm. In,.
Ed. Engl. 2711988) 593-621
citons can be understood from the illustrations depicted in
Figure 21. The 3D exciton in GaAs has a Bohr radius of
about 14 nm. In a quantum well with a width of less than
28 nm the exciton has to shrink and it is squeezed into an
elliptic form to fit to the well. The increased interaction
between electron and hole induced by the confinement results in an increase of the exciton binding energy by a facIn nartor of four in a 5-nm wide GaAs quantum
rower quantum wells and in short-period superlattices the
exciton wave function partly penetrates the barriers. The
volume of the elliptic exciton thus increases and its binding energy decreases again.
Fig. 21. Schematic illustration of the confinement of excitons In quantum
wells of different widths L,.
As a consequence of the stability of the exciton up to
room temperature and higher temperatures, the semiconductor quantum wells and superlattices exhibit pronounced noniinearities for the absorption coefficient as
well as for the refractive
A saturation of the excitonic absorption is already observed at a very low intensity
of the incident radiation because of the screening of the
excitons by free carriers. A small increase in the incident
light intensity can result in an instantaneous strong increase of the re-emitted intensity.[721These very pronounced nonlinear optical properties make feasible the application of microscopically structured semiconductors as
active elements in photonic circuits used in all-optical
The confinement in quantum wells makes excitons also
stable against ionization in an electric field. However,
when the electric field is applied perpendicular to the
layers, a strong red shift (i.e. shift to lower energy) and a
slight decrease in intensity of the excitonic resonances in
the absorption and emission spectra is observed.[741As
shown in Figure 22, this electric field in the order of 10 mV
per I0 nm (corresponding to several lo4 V/cm) gives rise
to a strong polarization of the electron and hole wave
functions in opposite directions towards the interfaces.
The electric field pulls the electron-hole pair apart, while
the potential barriers hold the two sufficiently close together to remain bound and thus prevent ionization. The
ionization can only occur when the electric field is large
enough to surmount the confinement energy and the particles can tunnel out of the
It is, therefore, possible
to apply fields about 50 times larger than the classical ionization field and still observe excitonic resonances. In this
without field
with field
Bulk Ga As
16 nm
Fig. 22. Opposite polarization of electron and hole wave functions in a GaAs
quantum well subject to an external electric field perpendicular to the layers.
CB = conduction band edge, VB =valence band edge, g, and Qhh= wave
functions for electrons and heavy holes, respectively.
way a red shift of the absorption peak in these structures
corresponding to 2.5 times the exciton binding energy is
obtained even at room temperature. The pronounced optical nonlinearities and the distinct red shift of the excitonic
absorption have provided a basis for the development of
extremely fast (131 ps) optical modulators[761and of selfregulating electro-optical devices (SEED, derived from
Self-Electrooptic Effect
The latter are promising for application as optical gates requiring a very low
switching power, as self-linearized modulators, and as optical switching register.
The red shift of the excitonic features in microscopically
structured semiconductors upon application of an electric
field is observed not only in absorption but also in emission. The field-induced shift of the excitonic emission energy is particularly pronounced at low temperatures. According to the theory developed by Brum and Bastard,"81
the low-energy shift AE,, of the lowest conduction subband in a perpendicular electric field of strength E is given
Fig. 23. Shift of the photoluminescence to lower energy (red shift) observed
in GaAs quantum wells of different widths L, subject to a perpendicular
electric field. The red shift is most pronounced for the larger L, values.
valid because of the deformation of the wave function in
the electric fiefd, and thus parity-forbidden transitions
with An f 0 also become possible. These forbidden transitions, in particular, provide the unique possibility of gaining a deeper insight into the energy structure of sub-bands
in quantum wells and superlattices. At the close of this section it should be pointed out that the described fieldinduced effect is comparable to the well-known Stark effect which is observed for atoms in an electric field. Therefore, this effect is now called the quantum confined Stark
effect (QCSE).
2 1 0 0 [ 1.7
i.e. it is most pronounced in wide GaAs quantum wells.
This assumption is fully confirmed by the experimental results shown in Figure 23. Therefore a compromise must be
found between the desired large energy shift in the electric
field and the necessary confinement when choosing the
width of the quantum well. An accurate analysis of the
shift of the absorption spectra in a perpendicular electric
field provides detailed information on the energy structure
of the valence sub-bands. This structure is extremely complicated and at present not well understood because of the
L,-dependent partial mixing of sub-bands of heavy and
light holes. The method of photocurrent spectroscopy has
turned out to be extremely successful, as shown by the
data in Figure 24. The observed variation of the photocurrent as a function of energy of the incident light at different electric fields yields a direct replica of the real optical absorption ~pectrum."~]
The change in the photocurrent can be measured with higher accuracy than the
change in the absorption coefficient. The results in Figure
24 demonstrate that the quantum-number selection rules
for the radiative electron-hole transitions are no longer
A Inml-
Fig. 24. Photocurrent spectra of a GaAs/Al,, ,Ga,,,As superlattice with
L,=8.5 nm subject to different electric fields perpendicular to the layers. For
clarity each spectrum is shifted by 150 pA on the vertical axis. At the lefthand side the individual numerical voltage values are indicated.
Angew. Chem. Int. Ed. Engl. 27 (1988) 593-621
4.2. Spatial Separation of Free Carriers and Ionized
Impurities in Selectively Doped Heterostructures
The unusual electrical properties of quasi-2D electron
and hole systems were exploited in an impressive manner
in the investigation of the quantum Hall effect and in the
development of high electron mobility transistors, both
made from selectively doped GaAs/Al,Ga, -.As heterostructures. The fabrication of these microscopically structured semiconductors requires that the abrupt change in
composition is synchronized with the abrupt change in
doping. The spatially resolved material synthesis during
molecular beam epitaxy ensures that only the material with
the larger band gap (here: AI,Ga,-,As) is selectively
doped with Si donors (or acceptors) in an accurately defined region and with a well defined concentration, while
the material having the smaller band gap (here: GaAs) is
left undoped and is of extreme purity.[8o1In Figure 25 we
scattering process, selectively n-doped heterostructures exhibit a n electron mobility enhanced by a factor of
4x105k 1986
1 .lo2
5 10
50 100
. . . .I
, . . I
50 100
. . . I
5 10
T K -
Fig. 26. lmprovement of the Hall mobility of electrons (left) and of holes
(right) as a function of temperature T in selectively doped GaAs/
AI,Ga, _,As heterostructures since 1978.
big 25. Schematic plot of conduction and valence band edge in a selectively
n-doped CaAs/AI,Ga, - ,As heterostructure where only the AI,Ga, -,As is
intentionally doped with Si donors. At the interface a quasi two-dimensional
accumulation channel for electrons is formed in the GaAs.
show that in this case the free electrons arising from the
shallow Si donors are transferred to the energetically more
favorable conduction sub-band E l in the adjacent GaAs
(in an analogous way the holes coming from the shallow
Be acceptors would be transferred to the uppermost valence band). The n-AI,Ga,-,As is thus depleted at the interface, while in the GaAs close to the interface a quasi-2D
accumulation channel for electrons is formed (a strong
band bending towards the interface also exists of course in
the GaAs). The band edge discontinuity existing at the
GaAs/AI,Ga, -, interface has thus led to a spatial separation of the free carriers from their parent ionized impurities confined to the n- (or p-) AI,Ga, -,As. As a result, the
ionized impurity scattering for the free carriers confined to
the 2D channel in the GaAs is strongly reduced, and extremely high mobilities are observed as compared to homogeneously doped GaAs having an equivalent 3 D carrier
concentration of about 2 x I O l 7 cm-3, particularly at low
temperatures (see Figs. 18 and 26). But even at room temperature, where thermal phonon scattering is the dominant
Angen'. Chem I n [ . Ed. Engl 27 11988) 593-621
In Figures 18 and 26 we demonstrate the characteristic
feature of the Hall mobility ,u of the 2 D electron gas (2
DEG) as a function of temperature for different samples.
With decreasing temperature, a very steep increase in the
mobility is observed down to 77 K and then a less pronounced increase further down to liquid-He temperature
(4.2 K). The sheet carrier concentrations of the 2 DEG are
typically in the range n,=(2 to 6)x 10" cm-* at 4.2 K, so
that only the lowest sub-band in the triangular potential
well at the interface is populated (see Fig. 25). Also the
continuous increase in the carrier mobility down to very
low temperatures is a characteristic feature of selectively
doped heterostructures (GaAs/AI,Ga, -,As, Ga,In, -,As/
InP, Ga,In, -,As/Al,In, -.As, etc.) with 2 DEG, and it is a
direct consequence of the absence (or strong reduction) of
scattering at ionized impurities which represents the dominant scattering process in homogeneously doped material
at low temperatures. Ever since the first application of selective (or modulation) doping in heterostructures and superlattices by Dingle et a1.1811
in 1978, every year has seen
new records of electron and hole mobilities being reported
(Figure 26). This continuous improvement of the carrier
mobility has been achieved through taking the following
measures during sample preparation:
The originally employed superlattice,1811in which only
the AI,Ga, -,As barriers were doped, was replaced by a
simple heterostructure having just one heterojunction,
as shown in Figure 25.
A thin (10-30 nm) undoped AI,Ga,-,As layer ("spacer") was interspersed between the interface and the
doped AI,Ga, -,As region,[*'I in order to increase the
spatial separation between the free carriers in the 2 D
accumulation channel and their parent ionized impurities.
The growth conditions during molecular beam epitaxy
were refined such that the residual impurity concentration of the GaAs with the 2 DEG is now in the low I O l 3
range and that the GaAs/Al,Ga, -,As interface
61 I
is, as far as possible, free of defects.[831When selecting
the design parameters of the heterostructure (layer
thicknesses, Al composition, and doping concentration)
care must be taken that the AI,Ga,-,As layer is totally
depleted and all free carriers are confined to the 2
Inspection of Figure 26 reveals that the highest mobility
achieved at present for electrons is in the order of 5 x lo6
cm2 V - ’ s-’. The mobilities of holes are about one order
of magnitude lower because of their larger effective mass.
The selectively doped GaAs/AI,Ga, -,As heterostructures described above are now used worldwide in many research and development laboratories in order to fabricate
electron devices having extremely high switching speeds
and low power consumption (HEMT, GaAs IC)[841and to
investigate the quantum Hall effe~t.[~.*~l
The minimized devices of integrated circuits (ICs) are often based on the
field-effect transistor (FET) principle, the arrangement of
which is schematically shown in Figure 27. At present,
there is a strong demand for shorter and shorter switching
times, i.e. for higher frequency limits. The realization of
short switching times requires short gate lengths
( L , < I pm) and high electron mobilities in the active
channel, which exist in particular in selectively doped heterostructures. Switching speeds per gate as low as 10 ps at
300 K and 5 ps at 77 K have been obtained from test circuits (ring oscillators) equipped with two series of high
electron mobility transistors (HEMTs).IS6l These values are
comparable to switching speeds previously only reached
by the fastest switching Josephson elements which, however, had to be operated at much lower temperatures
(4.2 K). The evolution of heterostructures with high-mobility holes and electrons makes feasible the application of a
complementary transistor logic based on GaAs. At present
the primary applications of transistors and circuits fabricated from selectively doped heterostructures are extremely fast processor units for supercomputers, extremely
fast operating digital-analog and analog-digital converters,
as well as low-noise analog amplifiers for microwave techn o l ~ g y . [ The
~ ~ ’ latter ones are now commercially available
from various manufacturers.
sistance and of Sommerfeld’s fine structure constant, a, res p e c t i ~ e l y [but
) for fundamental areas of experimental and theoretical solid state physics (localization, Wigner
lattice, electron-electron correlation, many body effects,
A strong magnetic field ( 5 < B < 20T) is applied
perpendicular to the 2 DEG plane at low temperatures
(T<4.2 K) in order to measure these macroscopic quantum phenomena. Under these conditions the electron system is completely quantized. In addition to the electrical
quantization of the motion perpendicular to the interface,
the magnetic quantization of the motion parallel to the interface is imposed on the carriers; this leads to the formation of the familiar Landau levels, whose energy is characterized by the Landau quantum numbers. Each Landau
level can accommodate only a limited number of electrons,
and this number depends only on e/b and B. Macroscopic
quantum phenomena, as e.g. the relative extrema in the
electrical resistance of the sample, always occur under the
condition that the Fermi level EF crosses a Landau level.
In selectively doped heterostructures having a constant
carrier density such quantum oscillations can thus be observed when the transverse magnetic flux density (induction) B is varied continuously from 0 to 20 T. With increasing flux density the Landau levels move across the Fermi
level, which on average remains constant, and we observe
oscillations in the magnetoresistance (i.e. the longitudinal
resistance) R,, (see Fig. 28), which are known as Shubnikov-de Haas oscillations.1571The measured Hall voltage
UH of the 2 DEG is given by UH = RH I B [see also Eq. (6)],
where the Hall constant RH of the 2 D carrier system depends only on the (constant) carrier density and on the
(constant) elementary charge. When we now introduce the
Hall resistance as RH,&= MH, / I and measure this quantity
under the condition that only a certain number i of Landau
levels is completely filled, i.e. at certain B values, this gives
rise to a quantization of the Hall resistance in rational fractions of ( W e 2 ) .
Figure 28 shows characteristic plots of the magnetoresistance R,, and of the Hall resistance R H , measured on a
selectively doped GaAs/Al,Ga, -,As heterostructure at a
Fig. 27. Schematic configuration of a field-effect transistor (“HEMT”) with
the active region composed of a selectively doped GaAs/AlxGa,_,As heterostructure.
6 [TI-
The quantization of the Hall resistance in quasi-2D electron and hole systems is of great importance not only for
metrology (determination of the unit of the electrical re612
Fig. 28. Hall resistance R H and magneto- (“longitudinal”) resistance R,, of a
selectively doped GaAs/AI,Ga, -,As heterostructure as a function of the
magnetic flux density B. The configuration of the Hall-bar is schematically
shown in the upper inset.
Angew. Cheni. lnr. Ed. Engl. 27 (1988) 593-621
temperature of 1.3 K.13]The curve of the magnetoresistance
clearly displays the well-known Shubnikov-de Haas oscillations. Always when a certain number i of Landau levels
is completely filled at a well defined magnetic flux density,
the Fermi level EF is just located in the range of the energy
gap between two Landau levels and the conductivity cXx
goes to zero with decreasing temperature (since free states
in the vicinity of EP d o not exist, a scattering cannot occur). The individual Landau levels are labeled in Figure 28
by the corresponding quantum numbers n. The additional
structure for n 1 2 is caused by the additional spin splitting. For magnetic fluxes of B 2 3 T t h e minima of the magnetoresistance are considerably broadened, and in the RH.i
curve we observe pronounced regions (plateaus) of constant resistance. These resistance plateaus always appear at
values of h/iez and they are totally independent of the specific geometry of the Hall bar and on the design parameters of the heterostr~cture.’’~~
The Hall plateaus are extremely flat, and they can therefore be measured with high
accuracy. The values of the rational fractions of the quantized Hall resistance are not only independent of the sample employed, but also appear at exactly the same values
for many other materials. Thus, the chemical properties of
the materials play only a minor role in the existence of
these macroscopic quantum phenomena. The explanation
for the occurrence of these plateaus is based on the assumption that localized states between the discrete Landau
levels exist which are generated by defects or residual impurities in the
As a consequence, in samples
with higher electron mobility @ > 2 x 10’ cm2 V-’ s-’ ) the
Hall plateaus are observed at lower magnetic flux densities; however, the width of the plateaus decreases drastically in these samples having a lower residual impurity
concentration. For fundamental investigations of the quantum Hall effect we have recently incorporated a certain
amount of impurities into the 2 D E G region of selectively
doped heterostructures with a high spatial resolution.’ss1
Based on the results described previously, the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig has
performed precision measurements of the quantized Hall
An accuracy and reproducibility has been
obtained for different samples which had never been
reached before. The Hall resistance at the step i = 2 was
determined as RH.Z=12906.403 (1 f 2 . 7 x
Ohm, from
which a value of a - ’ = 137.035992 (1 f 2 . 7 x
for the fine structure constant. During a longer measuring
period a standard deviation as low as s=4.6x lo-’ was
obtained for the ratio of the Hall resistance at the step i = 2
to a conventional reference (standard) resistor having
nearly the same numerical resistance value. This extremely
high precision makes feasible the application of the quantized Hall resistance as a reference resistor for the maintenance of the Ohm preserved in the various national standard laboratories.
4.3. GaAsIAIAs Monolayer Alloys
The control of spatially resolved materials synthesis by
molecular beam epitaxy has now reached a standard that
makes feasible the reproducible fabrication of periodically
Angew. Cliem. Inf. Ed. Engl. 27 11988) 593-621
layered structures composed of 111-V compound semiconductors o r of group-IV-elements whose periodicities are
equal to o r less than the lattice constant of the components
of the s u p e r l a t t i ~ e . [Figure
~ ~ ~ 29 shows schematically the
Fig. 29. Schematic arrangement of constituent atoms i n a (GaAs),(AIAs), superlattice (“monolayer alloy”) which represents an ordered ternary alloy of
composition Alo sCao5As.
arrangement of the atoms in the (GaAs),(AlAs), superlattice, which is composed of alternating (001) GaAs and
(001) AIAs monolayers. The (GaAs),(AlAs), superlattice is
therefore also called monolayer solid solution or monolayer alloy. It has the same composition as the ternary al~ can thus be considered as an ordered
loy Alo sGao5 A and
alloy.[”] The motivation for the fabrication of these
(GaAs),(AlAs), superlattices with (m, n) < 5 were careful
considerations to substitute the ternary AI,Ga, -.As alloy,
where the A1 and G a atoms are statistically distributed on
the lattice sites of the Group I11 elements and which exhibits some detrimental structural, electrical, and optical
properties. First, the Al, sGao,As is an indirect-gap semiconductor[’’] and the radiative electron-hole recombination requires the assistance of a phonon. Second, the electrical properties of n-type Al,Ga,_,As for x>O.2 are controlled by a deep donor (“DX center”) in addition to the
hydrogen-like shallow donor due to the peculiar band
structure of the alloy.[9z1The concentration of the deep donor increases with x and it is the origin of the persistent
photoconductivity effect. Third, the interface roughness
for growth of binary GaAs o r AlAs on the ternary alloy
due to the differences in the G a and A1 surface migration
yields inferior excitonic and transport proper tie^.'^^.^^]
During growth of (GaAs),,(AlAs),, superlattices with
(rn,n)<5 by molecular beam epitaxy the growth rate and
the interface formation were accurately controlled by monitoring the RHEED intensity oscillations.[901The growth
temperature was lowered to 500°C to prevent the interdiffusion of Ga and A1 across the interfaces, and the growth
rate was reduced to one monolayer per 5 s to facilitate the
build-up of the crystal atom by atom.[”] At each interface
the growth was interrupted for 5 s to produce an atomically flat growth surface before the next monolayer was
deposited. Excellent UHV conditions in the MBE system
were the most crucial requirements in order to accomplish
these growth parameters. The well-ordered periodic layerby-layer arrangement of Ga and A1 atoms on the ap613
propriate lattice sites in the [OOl] direction in the
(GaAs),,,(AIAs),, superlattices with m = n and m = I , 2, 3
manifests itself in the appearance of distinct satellite peaks
around the Bragg reflections of the X-ray diffraction patterns shown in Figure 30.[9'1As expected, these shortperiod superlattices exhibit a slight tetragonal distortion in
2.1 2.0
EleVI1.9 1.8
IAl As),lGaAs),
AlnmlFig. 31. Low-temperature photoluminescence spectra taken from the shortperiod (GaAs),,,(AIAs),,, superlattices with m = 1, 2, 3. Int.,,, =luminescence
intensity in arbitrary units (linear scale).
Fig 30. X-ray diffraction patterna o f three ahort-period (GaAs),,,(AIAs),,,
superlattices with m = I , 2, 3 taken with CuKoradiation.
the z-direction. The important structural parameters of the
(GaAs),,,(AIAs),,, superlattices compiled in Table 4 were
obtained from the position of the satellite peaks and from
the angular spacing A& between the Bragg reflection of
the epitaxial layer and the substrate (not shown in Fig. 30)
in a similar manner as described in Section 3.2. The results
of Table 4 indicate that the periodicity of the rn = 1 superlattice is about 8% larger than the ideal value of 0.566 nm.
However, this deviation does not have any influence on
the unique optical properties of this sample.
Table 4. Structural properties of ultrathin-layer (GaAs),,,(AIAs),,, superlattices
obtained from X-ray diffraction measurements using CuKnradiation.
Al content x
Satellite peak
position ["I
(AIAs),(GaAs), -9.27
( A I A S ) ~ ( G ~ A S )-9.27
(AIAs)3(GaAs), -8.81
Period T / n
8.43 23.49 24.8
0.6117 1.08
11.83 19.87 28.45 37.88 1.135 2.01
13.73 18.55 30.25 36.73 1.714 3.03
This naturally poses the question of the actual differences in the electronic properties between these short-period (GaAs),,,(AlAs),, superlattices and the ternary
Al, =,Ciao=,As alloy having the same composition. To answer
this question we have compared the photoluminescence
spectra obtained from these samples; the results are compiled in Figure 31 and in Table 5.I9l1 The luminescence
(indirect-gap semiconspectrum of the Alo &ao 5 A alloy
ductor) consists of three bands having approximately the
same intensity (the two lower energy lines arise from phonon-assisted transitions), while the (GaAs),,,(AIAs),,, super614
Table 5. Variation of photoluminescence peak energy as a function of period
length observed in ultrathin-layer (AIAs),,,-(GaAs),,, superlattices kept at 2 K.
For comparison, the energy of the bound-exiton luminescence detected in
the ternary AI,Ga,_,As alloy is also listed.
Al content x
peak energy [ e y
AI,Ga, - ,As alloy
1 968
lattices with 1 t r n < 4 exhibit only one broad line which
strongly shifts in energy as a function of periodicity. It is
important to note that the luminescence energy is highest
at m=3 but then decreases significantly for m < 3 and
m>3. According to calculations of the bound states in
quantum wells and superlattices, the low-energy shift for
m > 3 is expected, whereas the observed red shift of the luminescence from rn = 3 via m = 2 to rn = 1 is in contrast to
this simple approximation. We can no longer describe the
electronic properties of these short-period superlattices
with m= 1, 2, and 3 by the simple assumption that each
constituent layer contributes its characteristic properties to
the whole system. The shift of the luminescence from the
(GaAs),(AIAs), monolayer alloy by 146 meV to lower energy as compared to the Alo szGao4 8 A ternary
alloy clearly
indicates the existence of a new artificial synthetic material. Calculations of the energy band structure of shortperiod superlattices thus require the treatment of the superlattice crystal as a whole. Recent theoretical calculations performed on this basis are in good agreement with
our experimental luminescence results obtained from
(GaAs),,(AIAs),,, superlattices with m = 1, 2, 3, 4.1931
the electrical properties of the (GaAs),(AIAs), monolayer
alloy are possibly of special interest. A pronounced reduction in the alloy scattering is anticipated in doped samp l e ~ . This
[ ~ ~ additional
scattering mechanism results in a
significant reduction of the carrier mobilities in random
ternary and quaternary alloys.
Angew. Chem. In,. Ed. Engl. 27 (1988) 593-621
The short-period superlattices with periodicities down
to monolayer alloys have been fabricated not only from
lattice-matched components such as GaAs/AIAs, but also
from components which exhibit considerable differences
in the lattice constants, e.g. GaAsAnAs (7% lattice mismatch)'"'' and Si/Ge (4% lattice mismatch).[961In all cases,
successful fabrication was accomplished by spatially resolved synthesis during molecular beam epitaxy.
4.4. Monolayer Doping in GaAs
The concept of monolayer doping, also called delta (6)
o r atomic-plane doping and schematically shown in Figure
32, was originally proposed to improve the doping profiles
Fig. 32. a ) Illustration of the concept of monolayer (delta) doping in GaAs.
b) Formation of a V-shaped potential well for electrons by Si monolayer
doping (not to scale).
of Ge-doped n-type GaAs layers.[971We have employed the
implementation of monolayer doping profiles with Si donors and Be acceptors in GaAs to generate symmetric, Vshaped potential wells with a quasi-2D carrier gas and to
create a new sawtooth doping superlattice having a significantly reduced effective energy gap.[981The dopant atoms
are located in an atomic monolayer parallel to the surface
of the (OOl)-oriented GaAs host material, and the ionized
Si donors (or Be acceptors) provide a continuous sheet of
positive (or negative) charge. The fractional occupation of
the available G a sites in the (001) plane by dopant atoms
can reach several percent. The impurity charge distribution
No can mathematically be described by the Dirac-delta
function according to No=N$06(z), where NkD is the 2 D
donor concentration. The positive sheet of charge creates a
V-shaped potential well. Due to the electrostatic attraction,
the electrons remain close to their parent ionized donors
and form a quasi-2D electron gas with quantized energy
levels (sub-bands) in the narrow potential well. Direct evidence for the existence of a quasi-2D electron system was
provided by magnetotransport measurements.[991
The monolayer doping profiles were obtained during
molecular beam epitaxy by interrupting the growth of the
GaAs host crystal at the desired position by closing the
shutter in front of the Ga effusion cell and leaving the arsenic shutter open. The shutter of the respective dopant effusion cell is opened for a certain time interval (depending
Angrw Clwm. Inr Ed Engl 27 11988) 593-621
on the required doping level u p to several minutes). After
the intended doping level has been reached, the effusion
cell shutter is closed, and the crystal can continue to grow
without distortion by opening of the shutter of the G a
source. When the growth temperature is kept below 550°C
the distribution of the dopant atoms is indeed restricted to
one (001) monolayer. In this way high doping densities of
more than 1 x
cm-' in GaAs can easily be achieved
with Si as well as with Be dopants. These high densities
locally exceed the solubility limit of the respective impurities in GaAs. But nevertheless almost all donors (or acceptors) are ionized and the measured free-carrier concentrations give a realistic picture of the intentionally incorporated impurity atoms.["81Due to the close proximity of the
ionized impurities, the mobilities of the electrons (holes)
confined to the V-shaped potential well are comparable to
homogeneously doped material, and they are thus much
lower than in the selectively doped heterostructures described in Section 4.2.
The concept of monolayer doping during molecular
beam epitaxy makes feasible the spatially resolved incorporation of a sheet of electrons and/or holes confined to
one lattice plane into a semiconductor crystal. For the
reader it is important to note that even at a doping density
of 5 x 10" cm-2 not more than one out of one hundred G a
atoms on the (001) plane is replaced by an impurity atom.
This explains the crucial purity requirements during
growth of the epitaxial layer. We present here two examples for the application of a high-density sheet of electrons
in GaAs confined to one (001) monolayer: (i) non-alloyed
ohmic contacts having a low contact resistance'"'] and (ii)
field effect transistors (FETs) having a high transconductance.['"'I When the lattice plane doped by an amount of
1 x l o i 3c m P 2 impurity atoms is located just 3 nm beneath
the (001) crystal surface, the electrons (or holes) can virtually tunnel without any potential barrier between a metal
electrode deposited on the surface and the quasi-2D carrier system. This arrangement thus represents an ohmic
contact between the deposited metal and the underlying
semiconductor, which exhibits a low specific contact resistance of less than
R cm-' without the necessity of
alloying (i.e. heating for a short time to 400°C in a stream
of hydrogen gas). A (001) GaAs lattice plane having
N h D = 4 - 6 x l o t 2 cm-' carriers and positioned 25 nm beneath the crystal surface can be employed as current-conducting sheet in a field-effect transistor. Detailed investigations of the HEMTs described in Section 4.2 have demonstrated that, in addition to the enhanced electron mobility, primarily the confinement of the electrons to a quasi-2D channel is responsible for the highly improved characteristics of this device. In the monolayer-doped FET
(6-FET) the electrons are confined to the V-shaped potential well and, thus, during pinch-off below the gate they
cannot escape to the undoped semiconductor region. In
this way, high transconductances can be achieved in this
transistor. In addition, electron densities as high as 6 x 10''
cm-' can be realized in the 6-FET, which are larger by a
factor of three than in the HEMT. This higher electron
density more than compensates for the lower electron mobility, and the 6-FET exhibits excellent device characteristics.
the GaP/GaAs materials system, Mathews and Blakeslee['031had recognized already at the beginning of the seventies that semiconductor superlattices almost free of dislocations at the interfaces can be fabricated also from components with a large lattice mismatch, if the constituent
layer thicknesses d o not exceed a certain critical value of,
e.g. 10 nm. Under these conditions the lattice mismatch is
totally accommodated by coherent elastic strain and no
misfit dislocations are formed at the interfaces. The procedure to build u p strained-layer superlattices is schematically shown in Figure 34. The early studies on this subject,
which were almost ignored at that time, were revived again
at the beginning of the eighties, and today strained-layer
superlattices have become the subject of intensive investigations. As a characteristic example of strained-layer superlattices for this review paper we have selected the Si/
G e system, because it is of particular importance for device appIication.[Io4'
Fig. 33. a) Schematic configuration of a GaAs sawtooth doping superlattice
which is composed of a periodic sequence of alternating n- and p-doped
monolayers interspersed by undoped GaAs. b) Periodic variation of the doping profile in the direction of layer sequence. c) Sawtooth-shaped modulztion of conduction and valence band edge. Also indicated is the radiative
electron-hole recombination between the lowest electron and hole subbands.
The layer sequence of GaAs sawtooth doping superlattices is schematically shown in Figure 33a. The structure
consists of a periodic sequence of alternating n- and p-type
monolayers equally spaced by 5-20 nm undoped GaAs regions.""' The doping profile (Fig. 33b) can be described
by a periodic train of &functions. The periodic variation
of the positive and negative space charge in the z-direction
gives rise to a sawtooth-shaped modulation of conduction
and valence band edges (Fig. 33c). In this superlattice the
electron-hole recombination important for the emission of
light occurs between the lowest electron and hole subbands, E , e and E I h h , in adjacent potential wells. The "optical" band gap given by
Unit cells enlarge as they are
grown with more In content
Lattice constant
Defects in
graded layers
, ,
- Compressive
I I,
i i r
Nodefects in
strained layers
is thus smaller than the band gap E l of the homogeneous
material. In Equation (ll), q denotes the elementary
charge and VZ=~(q/&)NzDz,the amplitude of the bandedge modulation (z, = periodicity of the superlattice and
E = permittivity of the semiconductor). The effective band
gap of GaAs sawtooth doping superlattices can thus be
shifted by several hundred meV to lower energies by appropriate choice of the monolayer doping density and of
the periodicity. We have used this effect to fabricate light
emitting diodes and lasers operating in the wavelength
range ,
> 900 nm. As a result, we have produced a new material with accurately tailored optical properties by the
spatially resolved incorporation of donor- and acceptorrich lattice planes into a GaAs crystal.
4.5. Strained Si/Ge Superlattices
In the lattice-matched semiconductor superlattices described previously, the lattice constants of the components
differ by less than 0.5%. The ordering of the energy band
edges at the interfaces is therefore mainly affected by the
discontinuity in electron affinity across the heterojunction.
However, the strain of the constituent layers in GaSb/AlSb
superlattices having a lattice mismatch of only 0.7% can
already affect the ordering of the electronic bands.[Iz1For
larger lattice mismatches the strain increases, and it can
produce a complete new ordering of the energy band
edges. During their investigations of superlattices made of
Fig. 34. Schematic illustration of the formation of strained layer superlattices, e.g. GaAs/Ga,In, _,As with ~ ~ 0 . 3 .
According to Vegard's law the lattice mismatch vo between Si and Si,Ge,-, is given by ~ O = ( a s , c e - a s , ) / a s ,
= O.O42x, where a,, and aSIGe
are the respective lattice constants. The successful fabrication of Si/Si,Gel - 1: superlattices over the whole composition range was accomplished
only after the substrate temperature was reduced during
MBE growth to below 600°C (the Si source material is
evaporated by electron beam evaporation owing to the
high crucible temperature required). In these experiments
it has been shown that the upper critical layer thicknesses,
at which the formation of misfit dislocation begins, are
considerably larger than predicted by the theoretical
model of van der M e r ~ e . " ~ ~ ]
The aspect of particular importance in strained-layer superlattices is the possibility of modifying the distribution
of the strain of the whole epitaxial film on the constituent
layers arbitrarily by appropriate choice of the substrate or
of the buffer layer (see Fig. 35 for illustration). In this
manner the ordering of the conduction and valence band
edges across the heterojunctions can be deliberately adjusted."051 The tetragonal strain existing in the Si/Ge system induces a splitting of the sixfold degenerate conducAngew. Chem. lnt. Ed. Engl. 27 (198%)593-621
Si S u b s t r a t e
Si Substrate
layers with Sb donor impurities (Fig. 37). A selective ntype doping of the Si layers of the superlattice does not
yield a mobility enhancement. On the other hand, also a
quasi-2D hole gas of enhanced mobility in the Si layers
can be formed by selective doping of the constituent
Sio.5Geo layers with G a acceptor impurites."O"l The significantly enhanced carrier mobilities in these selectively
doped Si/Si, Ge, - . ~superlattices are of great current interest for application in high-speed transistors which operate
according to the same principle as the HEMT described in
Section 4.2.
1Misfit dlslocatian
Fig. 35 Schematic illustration of the distribution of the strain of the entire
epitaxial film on the constituent superlattice layers by appropriate choice of
the buffer layer or of the substrate (for details see text).
tion band into twofold and fourfold degenerate valleys.
When the Si/Sio5Ge,, superlattice is grown on a Si substrate or buffer layer, as shown in Figure 35a, the constituent Si layers of the superlattice are not strained, whereas
the constituent Sio.SGeo.slayers have to accommodate the
total (compressive) strain. This strain, however, can be distributed symmetrically on the two constituent layers when
the superlattice is grown on a thick Sic 75Geo2s buffer layer
whose lattice constant is between that of Si and that of
Sio.5Ge,,s(see Fig. 35b). In this case the two constituent
layers are strained by the same smaller amount, but in opposite directions (i.e. tensile strain in Si and compressive
strain in Si, &eo 5). These two possibilities of strain distribution result in a completely different position of the energy band edges relative to each other, as schematically
shown in Figure 36.
It is important to note that the conduction band edge of
the wider-gap material Si can be Iower in energy than that
of SiOsGe,,, when a Sio7sGeo.2s buffer Iayer is employed.['"51As a consequence we can obtain a quasi-2D
electron gas with considerably enhanced mobility in the Si
layers by selective doping of the constituent Sio.5Ceo.5
Substrote ; Buffer Superlattice
Fig. 36. Variation of the energy positron of the band edges in Si/Sio.sGeos
superlattices with respect to each other as a function of the distinct distribution of the total strain on the constituent layers by the selection of two different buffer layers.
Angew Chem Int. Ed Engl 27(1988) 593-621
[ crn 'V'
s-I I
Fig. 37. Temperature dependence of the Hall mobility ,u in selectively ndoped strained Si/Siu &eU
superlattices deposited on Si,, ,<Ge,,2 \ buffer
layers for three samples with dtfferent positions of the Sb dopant atoms (Vs
75: center of the Si layer, Vs 82: center of the Si,,<Ge,, layer, Vs 83. edge of
the Si,,sGe,,, layer). I n the upper inset the observed variation of the Hall
mobility p at 20 K as a function of the position of the Sb dopant atoms x is
In the strained-layer superlattices a structural periodic
modulation exists in addition to the chemical modulation
in the direction of the layer sequence. This coexistence
provides a new degree of freedom to adjust the intriguing
custom-tailored electronic properties of these materials. In
this field we have just arrived at the very beginning of an
exciting stage of development, because the possibilities of
combining different materials are far more abundant than
in the case of the lattice-matched materials systems.
In metallic materials systems, there are no rigid, directed
covalent bonds as in semiconductors. Therefore, the constituent elements for the formation of artificial superlattices always have to be chosen very carefully such that the
expected periodic modulation of the chemical composition
in the growth direction remains stable at the required
growth temperature. Research activities in the field of metal superlattices were very few until 1980, when S~hullerl'~''
successfully fabricated a Nb/Cu superlattice. The constituent elements of this superlattice exhibit totally different
crystal structures, and they show large differences in their
lattice constants. The cubic body-centered N b grows in the
[ 1 101 direction in this superlattice. Since that time the metal superlattices can roughly be devided into two groups:
In group 1 superlattices, the two constituent elements have
the same crystal structure and they form a continuous series of solid solutions. The periodic modulation of the
composition, which is produced during growth, is intrinsically unstable. Examples include the combinations Cu/Ni,
Ag/Pd, Nb/Ta, and Gd/Y. In group 2 superlattices, the
two constituent elements have a different crystal structure,
and their miscibility is rather limited. Therefore, the periodic modulation of the composition in the direction of
layer growth exhibits a higher stability. Examples include
Nb/Cu, Nb/AI, and Mo/Ni. To a first approximation,
geometrical considerations can be taken into account in
order to select the two constituent elements suitable for a
group 2 superlattice and their orientation with respect to
The most common situation for their orientation is that lattice planes of such orientation preferably
grow one on top of the other where the packing density of
atoms in the plane (atoms per nm2) is maximized and similar for both elements.
Metal superlattices of group 1 have in general been fabricated by molecular beam epitaxy. Carefully synthesized
monocrystalline samples, e.g. Nb/Ta superlattices['oyland
Gd/Y superlattices,[""] exhibit a coherence length of several hundred nanometer in the periodic modulation, and
the broadening at their interfaces amounts to only a few
atomic layers. The periodicity of (Gd),,,(Y),, superlattices
could be reduced to 10 atomic layers, i.e. (m,
n ) is equal to
5 . The superlattices of group 2, on the other hand, have as
yet been mainly prepared by sputtering techniques,"' 'I
where rather high residual gas concentrations are present
in the reaction chamber. It is well established that many
metals are excellent getter materials for a number of residual gas constituents. However, at present, any systematic
investigations on the influence of impurities on the properties of these artificial multilayer structures d o not exist. It
is thus most probable that in many cases incoherent periodic multilayer structures were actually obtained or that at
least the coherence length was extremely small. In the field
of metal superlattices further efforts with respect to preparative aspects are necessary in order to provide a more realistic basis for the numerous investigations of the structural and elastic properties as well as of the electrical and
magnetic properties and their correlation to each other.
5. Final Remarks and Future Prospects
Interfaces or heterojunctions, respectively, are incorporated spatially resolved into the crystal. This leads to a microscopical structuring of semiconducting solids. The resulting local discontinuities of conduction and valence
band edges provide a basis for the concept of band-gap (or
wave-function, o r band-structure, respectively) engineering
in semiconductors. The electrical and optical properties
are locally defined, and phenomena in extremely small dimensions (quantum size effects) become more important
than the chemical properties of the employed materials.
The microscopical structuring yields novel electronic properties in otherwise familiar semiconducting materials.
The technique of molecular beam epitaxy makes it feasible to build up crystals atom-by-atom to an extremely perfect arrangement. Based on the 2D growth mode the crystal is stacked lattice plane by lattice plane, and atomically
flat surfaces are produced. The low growth rate of approximately one monolayer per second allows the accurately
controlled regulation of the layer thickness down to one
monolayer and the deposition of crystalline materials of
arbitrary composition in alternating sheets of only a few
atomic layers thick. The comparatively low growth temperature of several hundred "C prevents the interdiffusion of
the constituent materials, and extremely abrupt and clean
interfaces are formed. The specific advantages of this sophisticated crystal growth technique lie in the unique possibilities to structure solids arbitrarily down to atomic dimensions. In this way superlattices are created by exactly
defined periodic modulation of the chemical composition
perpendicular to the growth surface. An artificial periodicity in the direction of growth is superimposed on the crystal potential, which is by one or two orders larger than the
natural lattice spacing.
The synthesis of periodically modulated structures by
molecular beam epitaxy has opened up access to a new
class of solids with accurately custom-tailored electrical,
optical, magnetic, dielectric, etc. properties. The semiconductor and metal superlattices described in Section 4 constitute just the beginning. The materials combinations
semiconductor/metal, semiconductor/insulator, metal/insulator, and magnetic materials having totally different
properties and with as yet unpredictable potential applications will certainly follow. It is important to note, however,
that in future the materials scientists (chemists) will become engaged more and more in the most profound questions of solid state physics and quantum theory. For example, for the effective prediction of the electronic properties
of periodically modulated semiconductor structures, it is
not sufficient to be merely aware of the bulk properties of
the constituent layers; the electronic phenomena arising
from the interfaces must also be understood and explicitly
taken into account.
The concept of band-gap engineering is currently seeing
significant extension, as evidenced, inter alia, by the first
reported efforts to make the locally defined discontinuities
of the energy bands adjustable or even tunable by external
action. An example for the adjustability of the conduction
and valence band discontinuities has already been mentioned with the strained Si/Si,Ge, -, superlattices described in Section 4.5. In this case the various possibilities
to distribute the total strain on the constituent layers in a
locally well defined manner leads to completely different
energy positions of the band edges with respect to each
other. A further possibility of adjusting or tuning the band
discontinuities locally arises when a fraction of or a monolayer of impurity material is epitaxially incorporated in the
vicinity of or directly at the interface. This intermediate
layer leads locally to a significant modification of the band
discontinuities.[''2JFinally, in the case of the third possibility, ultrathin ionized donor and acceptor sheets are incorporated by monolayer doping within a few nanometers of
both sides of the heterojunction interface. The electrostatic
potential of this double layer of ionized donors and acAngew. Chem. Inr. Ed. Engl. 27 11988) 593-621
ceptors (“dipole layer”) is either added to or substracted
from the potential of the band discontinuity depending on
the polarity.“‘31When the distance between the sheets of
positive and negative charge is in the order of the d e Broglie wavelength, the electrons crossing the heterointerface
“experience” a new band discontinuity AE,? eA(q5),
where Aq5 is the potential of the double layer. These new
possibilities of spatially resolved band-gap engineering
add a powerful degree of freedom to the investigation and
separate tuning of the properties of electrons and holes in
accurately defined microscopical regions. These features
will certainly establish new electronic functions for electronic and photonic devices which are based on electrical
and optical signal processing, respectively.
The application of molecular beam epitaxy to spatially
resolved materials synthesis now makes feasible the routine fabrication of a large variety of microscopically structured solids exhibiting a (periodic) modulation in chemical
composition perpendicular to the crystal surface down to
atomic dimensions. In such artificially layered quasi-2D
semiconductors the motion of free charge carriers is quantized within the layer plane. Theoretical considerations
have indicated that quantum size effects in low-dimensional semiconductors are significantly enhanced when the
dimensionality of the system is further reduced. In order to
study the electronic properties of quasi-one-dimensional
( 1 D) and zero-dimensional (OD) systems experimentally,
the motion of electrons and holes has to be confined
(quantized) not only to within the plane but also perpendicular to the plane, i.e. the carriers must be confined to a
quantum wire or to a quantum box whose relevant dimensions are smaller than one of the characteristic lengths of
the carriers. Depending on the properties to be investigated the characteristic lengths can be the d e Broglie wavelength of the electron, the elastic scattering length, or the
inelastic diffusion length. Although selectively doped
GaAs/AI,Ga, - ,As heterostructures with electron mobilities of 10’-106 cm2 V - ’ s - ’ at 4 K exhibit comparatively
large values of 5 pm for the inelastic diffusion length and
of 500 nm for the elastic scattering length, little progress
was hitherto made in the fabrication of quantum wires and
quantum boxes. Starting from artificially layered quasi-2D
semiconductors the following two methods are now preferentially used for lateral patterning in the nanometer
a) Optical holography or electron beam lithography combined with reactive ion beam or plasma etching for the
distinct local removal of appropriate materials.i”41
b Selected-area (laterally defined to within a few tens
of nanometers) enhanced interdiffusion in GaAs/
AI,Ga, -,As quantum wells induced by finely focussed
( < 50 nm) G a ion implantation and subsequent rapid
thermal annealing.” ’’I
In addition, attempts are being made to achieve the supplementary confinement of carriers by application of appropriately structured substrates or arbitrarily off-axis
oriented substrates during MBE growth.
With respect to the electrical properties, strongly enhanced electron mobilities have been predicted in the case
of quantum
whereas the quantum boxes should
A n g e u Ciirm. In! Ed. Engl. 27 11988) 593-621
be insulating. The optical properties should also be fundamentally affected, both by the new quantum confinement
of excitons and by the modified density of states [in a
quantum box, g ( E ) becomes a periodic sequence of 6-functi on^].""^ The energy of the sub-bands for electrons and
holes, the relaxation of excited carriers, and the interaction
of carriers should change drastically. The lower dimensional structures will significantly modify the formation of
excitons, the localization of carriers, possible crystallization effects of the electrons, and the saturation of optical
absorption. Recently, Hirayama et al.L’lS1
were able to confirm the modification of the density of states and the additional quantization, respectively, by the observation of several additional lines in the photoluminescence spectra of
GaAs/AI,Ga, -.As quantum wires.
The reproducible fabrication of microscopically structured (semiconducting) solids having quasi- 1D and quasiOD electronic properties remains one of the major challenges in spatially resolved materials synthesis and, moreover, in the entire field of microstructure materials science.
Methods must be developed which will enable the removal
of materials atom-by-atom or lattice plane-by-lattice plane,
respectively, in well-defined spatial and geometrical arrangements without causing any damage to the crystal surface. The etching techniques developed so far are not suitable for this purpose. The necessity for the development of
methods and techniques to manipulate the atoms in a crystal one-by-one (growth, removal,
can be
justified by a few simple considerations directed far into
the future. In today’s most advanced commercially available semiconductor memory, the 4 Mbit DRAM (Dynamic
Random Access Memory), about l o i 3Si atoms are used for
a 1 bit memory cell. I n the 1 Gbit DRAM, planned for the
end of the nineties, about 10” to 1OI2 Si atoms will be
needed for the 1 bit memory. On the other hand, the recently proposed concept of molecular electronics assumes
that the molecular or “bio” memory requires only about
lo’ atoms per 1 bit memory. When in the future we also
have to try to adopt some important biological principles
in (inorganic) semiconductor design in order to further
miniaturize the information-processing circuits, the mere
diminution of the physical size of materials (or linewidths)
will no longer suffice. Totally different operating principles must be realized for transistors and information processing and storage by exploiting “exotic” effects. The imprinting of multifunctional atomic structures onto the
(semiconducting) crystal should make it feasible to accomplish the processing of information with a definite selectivity, imitating to a certain degree the unique stereoselectivity of the large biomolecules. Microstructure materials
science techniques must be developed for the fabrication
and processing of these (inorganic) materials, whose “active” region is shrinking in physical size from micron to
subnanometer dimensions.
In conclusion, it is must be emphasized that the aforementioned activities in the field of microstructure materials science represent important contributions to a major
branch of chemistry. This field of research should also
have its established position in the universities, and should
not be left almost exclusively to the engineering and physics departments-as was often the case in the past. This
fascinating field of materials science pursues the addition
or removal of appropriate materials in accurately defined
geometrical and spatiaI arrangements ; it is concerned with
the microscopic mechanisms of growth or removal of
atoms, ions or molecules, which is essential for developing
new materials and new (alternate) processing technologies;
it is concerned with the properties of metals, semiconductors, dielectrics (insulators), magnetic materials, ceramics,
polymers, and their composites in restricted dimensions ;
and finally, it is concerned with the interfaces between
these materials. With the ever decreasing physical sizes being dealt with, down to subnanometer dimensions, there
should ultimately emerge an answer to the fundamental
question at which size an agglomeration of a few atoms
(“cluster”) begins to develop the characteristic properties
of crystalline s o l i d ~ . ~ ’ ” ~
The author would like to thank his colleagues who were
very actively committed to the development of the technique
of molecular beam epitaxy and the specijk field of microstructure materials science described here, including A .
Fischer, H . Fronius, Dr. K . Fujiwara, M. Hauser, Dr. Y. Horikoshi, Dr. T. I S M , Dr. H . Jung, J . Knecht, Dr. H. Kunzel,
Dr. J . Nagle, Dr. E. F. Schubert, Dr. L. Tapfer, Dr. S. Tarucha, and Mrs. H. Willerscheid. The continuous support of
thepresent research by Prof. Dr. A . Rabenau, Prof. Dr. H . J .
Queisser, and Prof. Dr. K. von Klitzing is gratefully acknowledged. The author appreciates the preparation of the
line drawingsfor the figures by Mrs. E. Klasmeier, the typing of the manuscript by Mrs. I. Zane, and the critical reading of the manuscript by Dr. 1. Maier. Finally, the financial
support of the Bundesministerium fur Forschung und Technologie (BMFT) and of the Stiftung Volkswagenwerk is acknowledged. It is through their grants that the author has
been able to develop his research in this area.
Received: August 5 , 1987 [A 669 IE]
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