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Influence of incoherent twin boundaries on the electrical properties of β−Ga2O3 layers
homoepitaxially grown by metal-organic vapor phase epitaxy
A. Fiedler, R. Schewski, M. Baldini, Z. Galazka, G. Wagner, M. Albrecht, and K. Irmscher
Citation: Journal of Applied Physics 122, 165701 (2017);
View online: https://doi.org/10.1063/1.4993748
View Table of Contents: http://aip.scitation.org/toc/jap/122/16
Published by the American Institute of Physics
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JOURNAL OF APPLIED PHYSICS 122, 165701 (2017)
Influence of incoherent twin boundaries on the electrical properties of b-Ga2O3
layers homoepitaxially grown by metal-organic vapor phase epitaxy
A. Fiedler,a) R. Schewski, M. Baldini, Z. Galazka, G. Wagner, M. Albrecht, and K. Irmscherb)
Leibniz-Institut f€
ur Kristallz€
uchtung, Max-Born-Str. 2, 12489 Berlin, Germany
(Received 30 June 2017; accepted 9 October 2017; published online 23 October 2017)
We present a quantitative model that addresses the influence of incoherent twin boundaries on the
electrical properties in b-Ga2O3. This model can explain the mobility collapse below a threshold
electron concentration of 1 1018 cm3 as well as partly the low doping efficiency in b-Ga2O3
layers grown homoepitaxially by metal-organic vapor phase epitaxy on (100) substrates of only
slight off-orientation. A structural analysis by transmission electron microscopy (TEM) reveals a
high density of twin lamellae in these layers. In contrast to the coherent twin boundaries parallel to
the (100) plane, the lateral incoherent twin boundaries exhibit one dangling bond per unit cell that
acts as an acceptor-like electron trap. Since the twin lamellae are thin, we consider the incoherent
twin boundaries to be line defects with a density of 1011–1012 cm2 as determined by TEM. We
estimate the influence of the incoherent twin boundaries on the electrical transport properties by
adapting Read’s model of charged dislocations. Our calculations quantitatively confirm that the
mobility reduction and collapse as well as partly the compensation are due to the presence of twin
lamellae. Published by AIP Publishing. https://doi.org/10.1063/1.4993748
I. INTRODUCTION
Monoclinic gallium sesquioxide (b-Ga2O3) belongs to the
transparent semiconducting oxides. It is distinguished by its
large band gap of about 4.7 eV,1 which is the reason for a
transparency range extending deep into the ultraviolet and for
a high electrical break down field estimated at 8 MV/cm.
Combined with the feasibility of n-type doping by Sn or Si,2,3
b-Ga2O3 has great potential as a material for solar-blind photodetection4–6 and for power electronics where it might outperform GaN and SiC.7–11 To fully exploit the favorable
properties of b-Ga2O3, single-crystalline material of high
structural perfection and controlled electrical characteristics is
a prerequisite. Usually, this can be accomplished by epitaxial
growth of deliberately doped, crystalline films. An advantage
of b-Ga2O3 over conventional wide band gap semiconductors
is the availability of native substrates obtained from crystals
grown from the melt by edge-defined film-fed growth,12 floating zone technique,13–15 and Czochralski growth.16–19
Homoepitaxial growth of b-Ga2O3 layers on such substrates is
therefore the method of choice and has been performed by
molecular beam epitaxy (MBE),20,21 halide vapor phase epitaxy (HVPE),22 or metal-organic vapor phase epitaxy
(MOVPE).23–25 Using MOVPE, we observed low doping efficiencies and low electron mobilities (10–30 cm2/Vs) for Sn
doped layers grown on (100) oriented substrates.24 Below an
electron concentration n of about 5 1017 cm3, a Hall effect
could not be measured at all, equivalent to a mobility collapse.
Recently, similar electrical behavior was reported for b-Ga2O3
layers heteroepitaxially grown on c-plane sapphire substrates
by low pressure chemical vapor deposition.26 On the other
hand, doped b-Ga2O3 bulk crystals grown from the melt
a)
Electronic mail: andreas.fiedler@ikz-berlin.de
Electronic mail: klaus.irmscher@ikz-berlin.de
b)
0021-8979/2017/122(16)/165701/7/$30.00
exhibit much higher electron mobilities at room temperature:
ln 130 cm2/Vs at n 1018 cm3.27 Such mobility values
are in agreement with theoretical predictions that take account
of the most important mechanisms of phonon and impurity
scattering.28–31 Hence, other mechanisms must be responsible
for the observed reduction of the mobility and its collapse
below a certain electron concentration. Since we showed in
previous studies that layers grown homoepitaxially on (100)
oriented substrates by MOVPE may suffer from a high density
of twin lamellae,24,32 it seems likely that these extended
defects have detrimental effects on the electrical properties.
This assumption is corroborated by our study of Sn and Si
doped layers homoepitaxially grown by MOVPE on (010)
substrates.25 These layers are free of twin lamellae and exhibit
high, bulk-like mobilities and no compensation. In Ref. 32, we
analyzed in detail the formation of twin lamellae and showed
that their formation can be suppressed by defined offorientation from (100), but we did not examine the impact of
the twin lamellae on electrical transport.
In the present paper, we report on the electrical transport
properties of Si doped b-Ga2O3 layers homoepitaxially
grown on (100) substrates of no or only slight offorientation. These layers behave electrically very similar to
the Sn doped layers of Ref. 24 with respect to low mobility
values and mobility collapse below a threshold electron concentration (here, n ¼ 1 1018 cm3) as well as low doping
efficiency. By using transmission electron microscopy
(TEM), we show that the layers contain a high density of
twin lamellae. High resolution scanning transmission electron microscopy (STEM) allows us to analyze the atomic
structure of the twin boundaries, which can be classified into
coherent boundaries parallel to (100) and incoherent ones
parallel to (001). While the former ones preserve the atomic
coordination, this is not the case at the incoherent twin
boundaries (ITBs). Our atomic model of an ITB suggests
122, 165701-1
Published by AIP Publishing.
165701-2
Fiedler et al.
that one dangling bond per unit cell is present. The dangling
bonds are arranged along the ITBs of thin twin lamellae and
may act as acceptor states. This is in analogy to the model of
electrically active dislocations originally suggested by
Read33 and further developed to explain unusual carrier
mobility behavior in highly dislocated GaN.34–36 Here, we
adapt this model to ITBs in b-Ga2O3. Based on the density
and geometry of the ITBs, estimated by TEM measurements,
corresponding calculations quantitatively confirm that mobility reduction and collapse as well as partly the compensation
are due to the presence of twin lamellae.
II. EXPERIMENTAL
b-Ga2O3 layers of about 250 nm thickness were grown
by MOVPE on (100) oriented substrates. The respective
MOVPE growth process is explained in detail in Ref. 24.
Tetraethylorthosilicate (TEOS) was used as the metalorganic
precursor for the n-type doping by Si. The substrates were
wafers of dimensions 5 5 0.5 mm3 prepared from bGa2O3 bulk crystals grown by the Czochralski method.18,19
The surface orientation of the square-shaped substrates was
(100) with unintentional miscut deviations below 0.4 as
determined by atomic force microscopy measurements of the
step heights and widths on epitaxy-ready substrate surfaces.
The edges were parallel to [010] (b-direction) and [001]
(c-direction), respectively. Most of the used substrates were
electrically insulating due to Mg doping of the bulk crystals.
In addition, some conductive substrates were used, which
were sliced from unintentionally n-type doped crystals.
Electrical characterization of the layers on insulating
substrates was performed by resistivity and Hall effect measurements at room temperature using a commercial setup
(Lake Shore HMS 7504) and contacting the samples in van
der Pauw configuration. Point-like contacts were prepared by
applying InGa eutectic in the four corners of the samples.
Current-voltage measurements of these contacts showed
ohmic behavior for all samples under investigation.
In order to detect deep electron traps, we applied deep
level transient spectroscopy (DLTS) to the layers on conductive substrates. Circular Schottky contacts (diameter 0.4 mm
and 0.8 mm) prepared by using a shadow mask and depositing 30 nm Ni by electron beam evaporation served as test
structures. The DLTS measurements were performed in the
temperature range from 100 K to 540 K using a BioRad
DL8000 system with Fourier transform correlation of the
capacitance transients. In this way, electron traps with
energy levels of up to 1.3 eV below the conduction band
edge (i.e., within the upper quarter of the band gap) are
recorded.
The structural properties of the layers were investigated
by transmission electron microscopy (TEM) and high resolution scanning transmission electron microscopy (STEM)
using an aberration corrected FEI Titan 80–300 microscope
operated at 300 kV. The microscope is equipped with a
Fischione high angle annular dark-field detector (HAADF)
and a highly brilliant field emission gun (X-FEG). Details on
the chosen TEM operating parameters and on the preparation
J. Appl. Phys. 122, 165701 (2017)
of cross-sectional TEM samples along the (010) orientation
can be found in Ref. 32.
The Si dopant concentration was determined by secondary ion mass spectrometry (SIMS) performed by RTG
Mikroanalyse GmbH. Calculations of the influence of ITBs
on the electrical transport properties were implemented in
MATLAB.37
III. RESULTS AND DISCUSSION
A. Electrical properties
Conductivity and Hall effect, as well as DLTS measurements, reveal the following electrical properties of the Si
doped b-Ga2O3 (100) layers:
(i)
(ii)
In Fig. 1, the electron Hall mobility l is plotted versus
the electron concentration n. An unambiguous Hall
effect is measurable only in layers with n > 1 1018
cm3. Above this threshold, the mobility decreases
from 30 cm2/Vs to 10 cm2/Vs for an increase in electron concentration by an order of magnitude, a dependence qualitatively consistent with dominant
scattering at ionized impurities. For n < 1 1018
cm3 the layers are still conductive, but a measurement of the Hall effect is impossible which is ascribed
to a sudden drop in electron mobility with decreasing
electron concentration (mobility collapse). A similar
mobility collapse below a critical carrier concentration is observed in GaN and is explained by the presence of a high density of dislocations forming walls
of potential barriers for electron transport.34–36
The four-terminal resistances of the van der Pauw
measurement in the (100) plane of our layers are
strongly anisotropic: the four-terminal resistance
R[001] with current flow along the [001] direction is
about ten times higher than the resistance R[010] with
current flow along [010]. This large difference cannot
be explained by the monoclinic crystal structure of
b-Ga2O3, since its electron transport properties have
turned out to be almost isotropic.14,27,30,31,38 Rather it
suggests that anisotropically arranged, electrically
FIG. 1. Electron Hall mobility as a function of the electron Hall concentration at 300 K for b-Ga2O3 homoepitaxially grown by MOVPE on (100) oriented substrates (black squares). The blue dashed line represents the
calculated bulk mobility. The green dashed-dotted lines represent the calculated mobility due to incoherent twin boundaries of the lowest (1 1011
cm2) and highest (1.5 1012 cm2) density determined by TEM. The redshaded area illustrates the total calculated mobility within these bounds.
165701-3
(iii)
(iv)
Fiedler et al.
active inhomogeneities, such as extended defects, are
present in the layers.
The electron concentration, measurable by the Hall
effect above 1 1018 cm3, is lower by a factor of
3 to 30 than the Si dopant concentration measured by
SIMS in the respective range from 3 1018 cm3 to
2 1020 cm3 as represented in Fig. 2. This indicates
high compensation of the Si donors by acceptors and
possibly, electrically inactive Si incorporation.
Compensating acceptors could be point defects (e.g.,
Ga vacancies) and extended defects rather than impurities in our layers.
In Fig. 3, a typical DLTS spectrum of a layer is compared with that of a conductive substrate. The spectrum
of the substrate is dominated by the DLTS peak of an
electron trap at 0.7–0.8 eV below the conduction band
edge that is omnipresent in melt-grown b-Ga2O3 bulk
crystals in the mid 1016 cm3 concentration range.27,39
This peak shows no broadening due to non- or multiexponential thermal emission. Therefore, the peak should
be due to a point defect. In contrast, the DLTS spectrum of the layer consists of broadened, overlapping
peaks, while the “bulk” peak is strongly suppressed.
This suggests that the underlying defects possess
closely spaced or continuously distributed energy levels as it is usually assumed for extended defects. For
the approximate center of gravity of the broad DLTS
peak distribution, we determine a thermal activation
energy of 0.34 eV. Since we assume that these defects
significantly contribute to the electrical compensation,
the DLTS evaluation of their concentration, maximum
of the peak distribution is at about 1 1016 cm3,
reflects only a small part of their real concentration.
This is because the electron concentration available for
recharging during a DLTS filling pulse, which is given
by the difference between the concentration of shallow
donors and the concentration of compensating deep
level defects, is much smaller in the present case than
the concentration of the deep level defects, leading to
incomplete filling.
FIG. 2. Electron Hall concentration n at 300 K as a function of the silicon
atomic concentration measured by SIMS for b-Ga2O3 layers homoepitaxially grown by MOVPE on (100) oriented substrates (black squares). The
black line marks the upper electron concentration limit in the ideal case of
completely ionized, uncompensated Si donors. The red-shaded area predicts
the electron concentrations in the presence of incoherent twin boundaries
with densities between 1 1011 cm2 and 1.5 1012 cm2.
J. Appl. Phys. 122, 165701 (2017)
FIG. 3. DLTS spectrum of an (100) oriented, conductive b-Ga2O3 substrate
(red dots) and of a layer (black squares) grown by MOVPE on such a substrate. The time window setting of 20 ms used here corresponds to the emission rate in the peak maximum of en,max ¼ 114 s1.
In conclusion, our observations suggest that electrical
transport in the layers is ruled by anisotropically arranged,
extended defects. A structural analysis by TEM, presented in
the subsequent paragraph, will provide direct evidence of
extended defects and their type.
B. Structural analysis
The TEM analysis of the layers reveals the presence of a
high density of planar defects. A typical example is shown in
Fig. 4(a) by a cross sectional dark field image of a 150 nm
thick layer grown on a substrate with a nominal miscut of
0.1 . While the substrate is free of planar defects and shows
only speckled contrast due to unavoidable surface damage
caused by ion milling, the layer contains a high density of
planar defects. These defects turn out to be twin lamellae.
Structural details on the atomic scale of the boundaries of
the twin lamellae are uncovered by Z-contrast STEMHAADF images. Figure 4(b) shows a region of coalescence
of the two possible twin orientations projected along the
[010] zone axis. Since the atomic number of oxygen (Z ¼ 8)
is much smaller than the atomic number of gallium (Z ¼ 31),
the contrast in these images arises from the gallium columns
only. The image has been overlaid with a stick and ball
model of b-Ga2O3. The stacking can be analyzed from the
lozenge-shaped arrangement of the Ga atoms in the b-Ga2O3
along this projection. The boundary in the (100) plane is
marked by the red dashed line. The lattice in this region can
be continued by mirroring at the (100) plane combined with
a translation by a half c lattice parameter along [001]. This
produces a twinned crystal orientation, described by a c/2
glide reflection.
Let us focus on the (100) twin boundary first. The structural model shown in Fig. 4(c), derived from the Ga positions
in Fig. 4(b), shows that all atoms in the boundary are fully
coordinated, i.e., the twin boundary at the (100) plane is
coherent.
We consider now the twin boundary formed by coalescence along [001] of two twinned nuclei marked by I and II
in Fig. 4(b). The boundary (highlighted by a yellow, dotted
line) can be recognized by the different orientation of the
lozenge-shaped arrangement of the Ga atoms. In the stick
165701-4
Fiedler et al.
J. Appl. Phys. 122, 165701 (2017)
FIG. 5. Scheme of the distribution of incoherent twin boundaries (ITBs) as
seen in a cross sectional TEM image. The yellow stripes represent the ITBs
at the (001)-plane. B is the thickness of the layer, A is the width of the
image, L is the thickness of the TEM sample, D is the mean distance
between each two neighboring ITBs, t is the distance between two adjacent
dangling bonds within an ITB, and hi are the heights of the ITBs.
FIG. 4. (a) Cross sectional TEM dark field image of a typical MOVPE
layer. For imaging, we used a g vector parallel to [001]. (b) High resolution
STEM-HAADF image showing a region where two twin orientations coalesce. The red dashed line indicates the (100) twin boundary, while the yellow dotted line represents the (001) twin boundary. (c) Structural model of
the boundaries developed from the STEM image. Bright green and grey
indicating octahedrally bound Ga atoms, and dark green and black correspond to tetrahedrally bound Ga atoms, respectively. Red balls correspond
to oxygen atoms. (d) and (e) represent enlarged models of atomic bonding
at the (001) boundary corresponding to the, respectively, highlighted structural units in (c).
and ball model of Fig. 4(c), the oxygen atoms, invisible in
STEM and TEM images, have been placed based on the
principle of plausibility, i.e., considering their coordination
and the distortion of the bonds. According to this model, the
boundary is formed of two structural units that are
highlighted by violet, dashed and blue, solid rectangles. In
the first structural unit [enlarged in Fig. 4(d)], an oxygen column is coordinated by two octahedral gallium columns and
arranged in a planar geometry. This is very likely an energetically unfavorable configuration and may lead to local lattice
relaxation. The second structural unit [enlarged in Fig. 4(e)]
is formed of two columns of tetrahedrally bound gallium
atoms bound to an oxygen column. The oxygen atoms in this
column are only coordinated by two gallium atoms, i.e., a
single nearest Ga neighbor is missing compared to the corresponding undisturbed lattice site. The (001) twin boundary
thus is an incoherent boundary that exhibits dangling bonds
and local lattice relaxations. It is natural to assume that these
(001) twin boundaries introduce deep states in the energy
gap of b-Ga2O3 which influence the electrical properties of
the layers in a negative way. A corresponding quantitative
model will be developed in Sec. III C. A prerequisite for any
quantitative model is the knowledge of the density of active
defects introduced by these boundaries. Therefore, we measure the dimensions and density of the incoherent twin
boundaries (ITBs), i.e., their average height, lateral extension, and mean distance as sketched in Fig. 5, from TEM
micrographs.
From the analysis of 3566 twins in b-Ga2O3, we find that
their heights hi range from half a unit cell up to several 10 nm
with 96% below 10 nm and an average value of 3.2 nm.
Additionally, we extract the mean distance D ¼ (40 6 20) nm
between each two neighboring ITBs by measuring each distance of related neighboring (001) boundaries. The thickness
of the TEM sample is L 50 nm, which is a lower bound for
the length of the ITBs, because we see no distortion of the
atom columns in the high-resolution STEM-HAADF images
[see Fig. 4(b)]. Since hi D and hi L and the average vertical separation (along a*) is about 10 nm, it is possible to treat
the ITBs as separate line defects. According to our model of
atomic bonding, one dangling bond per unit cell is present in
the ITB. Hence, we can quantify the density of columnar
arranged dangling bonds by
P
i hi
Nitb ¼
;
(1)
A B a sinðbÞ
where i is the index of the ITBs, a ¼ 1.223 nm is the lattice
parameter,40 b ¼ 103.7 is the monoclinic angle,40 A is the
width of the image, and B is the thickness of the layer. The
hereby determined density of ITBs ranges from Nitb ¼ 1
1011 cm2 to Nitb ¼ 1.5 1012 cm2 with the mean value
hNitbi ¼ 6 1011 cm2. The distance t between two dangling
bonds within an ITB is equal to the lattice parameter
b ¼ 0.304 nm,40 since there is one dangling bond per unit
cell.
C. Transport model in the presence of incoherent twin
boundaries
From the structural analysis, we know that the incoherent twin boundaries (ITBs) at the (001) plane contain dangling bonds. These normally form acceptor-like deep states
165701-5
Fiedler et al.
J. Appl. Phys. 122, 165701 (2017)
1
e2 Nd3
Ec Ed ¼ 36:3 meV 1:46
:
4pe0 e
FIG. 6. Scheme of the band bending due to dangling bonds introducing
acceptor states (negative sign in a rectangle) in an n-type semiconductor.
The axis system illustrates the potential energy in the b-c plane in the case
of incoherent twin boundaries (ITBs). Cylindrical space charge regions of
radius R and axis along [010] form around the ITBs. D represents the mean
distance between each two neighboring ITBs.
in an n-type semiconductor.41 Since we investigate moderately to highly n-type doped material, the Fermi level is
located above or pinned by the deep dangling bond state.
Hence, the dangling bond acceptor catches a free electron
and forms a negatively charged region. The valence and conduction band edges are bent and a spherical space charge
region forms around the dangling bond. Since the dangling
bonds are columnar arranged, like line defects, the resulting
space charge region around an ITB has a cylindrical shape
with the radius R and the cylinder axis along [010] as shown
in Fig. 6.
Due to charge neutrality, we can define R in such a way
that the cylinder contains an amount of fixed positive charge
equal to the negative charge at the ITB42
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f
f
;
(2)
pR2 Ndþ Na ¼ ) R ¼
b
pb Ndþ Na
where Ndþ is the density of ionized donors,
þ Na is the density
of ionized acceptors, the difference Nd Na is the electron concentration of an n-type semiconductor without
extended defects, b is the distance between two dangling
bonds within an ITB, and f is the filling factor of the dangling
bonds. Due to Coulomb repulsion, the occupation of the
closely spaced dangling bonds by electrons is limited.
Hence, the filling factor is somewhere between 0 and 1. The
filling of dangling bonds is determined using Read’s minimum energy approximation for line defects given in Ref. 42,
f
0:232 ;
(3)
E ¼ E0 f 3ln
fc
2
e 1
being the energy of the interaction of two
with E0 ¼ 4pe
0e b
electrons in adjacent sites, where e0 e ¼ 10:2e0 is the product
of the absolute dielectric constant and the relative static one,43
1
fc ¼ b p Ndþ Na 3 , and E ¼ ðEc Eitb Þ ðEc Ed Þ is
the thermal activation energy of dangling bonds. Formula (3)
is exact for T ¼ 0 K and gets more inaccurate with increasing
temperature by underestimating the filling of dangling bonds.
Nevertheless, it is an appropriate approximation at 300 K and
gives a lower bound for f. For the ionization energy of the
ITBs, we take Ec Eitb 0:34 eV, the center of gravity of
the broad DLTS peak distribution (Fig. 3), as a reasonable
assumption. The shallow donor ionization energy is calculated
after Ref. 27,
(4)
Assuming a homogeneous distribution of the ITBs, a
periodical electrostatic potential / occurs. For the in-plane
electrical transport through the layer, the electrostatic potential along [001] is crucial (see Fig. 6), since the ITBs form at
the (001)-plane. The potential barrier that an electron has to
overcome when flowing in [001] is the difference between
the potential maximum at the ITB and the potential minimum at half way D/2 between adjacent ITBs. The analytical
calculation of / was done by Krasavin for dislocations in
GaN, which are also columnar arranged,35 and is adopted by
us for the case of ITBs in b-Ga2O3,
4e2 Ndþ Na R3
e2 f
lnð2Þ:
(5)
e/ðR; D; bÞ ¼
3 e0 eD
2bpe0 e
For the current flow between twinned regions, this barrier has to be overcome by thermionic emission, like in polycrystalline or powdered semiconductors.44 Therefore, a twin
boundary can be assumed as a back-to-back Schottky barrier
and it is possible to define an effective resistance for such a
barrier. Using the effective resistance, it is possible to define
a quantity litb, which has the dimensions of a carrier
mobility44
eL
e/ðR; D; bÞ
;
(6)
litb ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp kB T
8kB Tpm
where m* ¼ 0.28m0 is the effective electron mass.38 litb can
be interpreted either in terms of a constant carrier density
associated with a thermally activated mobility or conversely
in terms of a constant mobility and thermally activated carrier density.44 Following Matthiessen’s rule, the total mobility results from
1
1
1
¼
þ
;
ltot lbulk litb
(7)
where lbulk is the bulk mobility of b-Ga2O3 due to normal
scattering processes. The bulk mobility is calculated using
an empirical expression given in Eq. (7) of Ref. 28. To
obtain the dependence of the mobility l on the electron concentration n like in Fig. 1, it is necessary to calculate n by
solving (iteratively) the charge neutrality equation. Since the
dangling bonds within an ITB show acceptor-like behavior,
the charge neutrality equation as well has to be adjusted35
Nitb
:
n ¼ Ndþ Na f
b
(8)
Using the well-known expressions for the density of ionized donors (Ndþ ) and ionized acceptors (Na ) as a function of
the Fermi energy (EF), the temperature and the respective ionization energies, and assuming Boltzmann statistics, one can
calculate the electron concentration n for a certain density of
donors Nd, point defect related acceptors Na, and acceptors
related to ITBs Nitb. For Na, we take 5 1015 cm3, a value
measured by DLTS for layers on (100) substrates off-oriented
165701-6
Fiedler et al.
by about 6 towards [001] which do not contain extended
defects, and hence, we assume that this value accounts for
point defect related acceptors. Furthermore, we assume for the
calculation that all Si atoms are incorporated as electrically
active shallow donors, i.e., Nd is taken equal to the Si atomic
concentration. The resulting mobility due to the presence of
ITBs versus the electron concentration n is plotted together
with the experimental results in Fig. 1. Nearly all experimental values are in the calculated range given by the bounds for
the density of ITBs using the model of homogeneously distributed, charged barriers. The mobility collapse at a critical
electron concentration of about 1 1018 cm3 is also reproduced by our model.
The electron concentration n in the presence of ITBs
versus the Si atomic concentration is plotted together with
the experimental results in Fig. 2. The calculation shows that
the given density of ITBs in the layers account for the strong
compensation, in particular, in the low Si doping range up to
3 1019 cm3. For higher Si atomic concentrations, however, the model fails. Two reasons may be responsible for
this failure: (i) the underestimation of the filling factor f by
Eq. (3) and (ii) our assumption that all Si atoms are incorporated as electrically active shallow donors. In particular, the
latter assumption is probably inapplicable for high Si doping
concentrations since incorporation on electrically inactive
sites, including the formation of defect complexes and gettering of Si at ITBs, may take place.
Finally, we point out that a strong conductivity anisotropy is inherent to our simple model. Since we have regarded
only space charge cylinders expanded in the [010] direction,
the barrier for current flow along [001] has a maximum and
reduces for current flow away from this direction. This
assumption is in accordance with the principal arrangement
of the twin lamellae and explains qualitatively the anisotropy
in the four-terminal resistances measured by the van der
Pauw method (see above). The measured ratio R[001]/R[010]
of about 10 overestimates the actual conductivity anisotropy
which should correspond to a ratio of only 2 according to
Ref. 45. The reason for this unexpectedly low conductivity
ratio may be due to the incoherent twin boundaries, which
form on the (010)-plane when two twinned islands coalesce
and which are not taken into account in the present model.
From atomic force microscopy images of the layers an aspect
ratio of the length of an island in [010] direction to the length
in [001] direction of about 2 is obtained for every island
forming during MOVPE growth.32 This is an indication for
the density of ITBs in [010] direction and might explain a
two-to-one anisotropy in conductivity.
IV. CONCLUSIONS
b-Ga2O3 layers grown homoepitaxially by MOVPE on
(100) substrates of slight off-orientation below 0.4 showed
a low mobility of at most 30 cm2/Vs, a mobility collapse
below a threshold electron concentration of 1 1018 cm3,
as well as low doping efficiency with electron concentrations
being a factor of up to 30 lower than the silicon donor doping
concentration. Combining the structural investigations of
twin lamellae in these layers, in particular, the geometry and
J. Appl. Phys. 122, 165701 (2017)
density of ITBs, with a transport model for charged dislocations in GaN,35 the low mobility and the mobility collapse at
low n-type doping can be well explained. The low doping
efficiency is at least partly described by the model.
Thus, we conclude that point defects like Ga vacancies,
which are considered to be important compensating acceptors in n-type b-Ga2O3,46 play only a minor role for compensation in our samples. Our model may also explain the
electrical behavior of n-type b-Ga2O3 layers grown on sapphire (0001) substrates by low pressure chemical vapor
deposition, where a similar trend in mobility over electron
concentration was reported.26 Such heteroepitaxial growth
results in 60 rotational domains of b-Ga2O3 as we observe
by MOVPE growth on (0001) sapphire and already reported
by Lv et al.47 We expect that the grain boundaries between
these domains behave electrically in a similar way as the
ITBs.
As it has been shown in previous work, twinning
occurs due to possible double positioning of the Ga adatoms on the (100) plane. Hence, twin lamellae form if layer
by layer growth through nucleation of 2D islands prevails
over step-flow growth and their formation can be prevented
if proper combinations of growth parameter and miscut are
chosen.32 Layers, grown on substrates with appropriate
miscut, or on substrate orientations that by symmetry do
not permit double positioning do not show twin lamella and
exhibit an electron mobility similar to the best values
observed in bulk crystals.25
ACKNOWLEDGMENTS
This work was performed in the framework of GraFOx,
a Leibniz Science Campus partially funded by the Leibniz
association. We thank Raimund Gr€uneberg for technical
assistance in MOVPE growth and Christian Palavinskas for
determining the densities of incoherent twin boundaries
during his internship.
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