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Silicon-based passives for integrated microwave and infrared applications

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SILICON-BASED PASSIVES FOR INTEGRATED MICROWAVE
AND INFRARED APPLICATIONS
A Dissertation
Submitted to the Graduate School
of the University of Notre Dame
in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
by
Zhuowen Sun
_________________________________
Patrick J. Fay, Director
Graduate Program in Electrical Engineering
Notre Dame, Indiana
April 2006
3318073
2008
33318073
SILICON-BASED PASSIVES FOR INTEGRATED MICROWAVE
AND INFRARED APPLICATIONS
Abstract
by
Zhuowen Sun
An investigation of Si-based passive components in microwave and infrared
frequencies has been undertaken. Coplanar wavegudies (CPWs) with electrodes in direct
contact with moderately doped Si substrates were characterized at microwave frequencies.
A new nonlinear circuit model applicable for CPW lines on both direct metalsemiconductor contacts and SiO2/Si MOS-like substrates has been developed and verified
experimentally using bias-dependent s-parameter measurements from 100 MHz to 10
GHz. In contrast to conventional R-L-C-G models, the proposed model replicates
dispersive effects due to finite substrate resistivity by including nonlinear frequencyindependent junction capacitances and conductances. The modeled junction capacitances
and conductances show excellent scalability with line geometry and substrate doping
concentration. Capacitance-voltage and current-voltage measurements have been
performed to investigate the model's substrate doping type dependence (both n- and ptype). Analysis of the model indicates that a full back-to-back metal-semiconductor
Zhuowen Sun
junction contact model is required for CPWs on n-type substrates, while the higher
Schottky barrier height of typical metal contacts to p-type Si permits a simpler one-sided
junction model for CPWs on p-type substrates.
For infrared detector applications, dipole antennas backed by a dielectric-filled
cavity were also explored to increase air-side directive gain for antenna-coupled diode
detectors. The proposed antenna schemes are designed to be compatible with
conventional IC fabrication processes. A parametric study of antenna design reveals that
a 10 dB boresight gain can be achieved when the cavity dimensions are properly chosen
to excite predominantly TE10 mode aperture fields. The dipole resonant frequency is
found to decrease with increasing dipole length and its input impedance is sensitive to the
dipole position within the cavity.
K-band scale models of the antenna were fabricated and measured at 28.3 GHz to
conclusively evaluate the performance of the antenna designs. The antennas
demonstrated 10 dB directivity and –25 dB cross-polarization at boresight. The crosspolarization was limited by the dipole feed and misalignment. Measured antenna
radiation efficiency was better than 70% throughout the interested frequency range. The
power loss was attributed to filling dielectric and metallic sidewall loss. The measured sparameters and radiation pattern showed good match to 3-dimensional electromagnetic
simulations using HFSS.
CONTENTS
TABLES………………………………………………………………………………... v
FIGURES………………………………………………………………….……………vi
ACKNOWLEDGEMENTS…………………………………………….……………….xiii
CHAPTER 1. INTRODUCTION…………………………………………………………1
1.1 Coplanar waveguide for integrated RF/microwave applications..……………4
1.2 Cavity-backed dipole antennas for infrared detection..……………...………..8
1.3 Thesis outline..…………………………..………………………….……….16
CHAPTER 2. MODELING OF SILICON COPLANAR WAVEGUIDES…….……….17
2.1 A physics-based generic circuit model..……………..………………………17
2.2 Fabrication and measurement..…………..………….………….……………21
2.3 Results and discussion..………………………………………....…………...23
2.3.1 Scattering parameters..……………..……………..………..………23
2.3.2 Waveguide geometry and substrate doping concentration..……….24
2.3.3 Substrate doping type..……………………………….……………30
ii
CHAPTER 3. DESIGN OF CAVITY-BACKED DIPOLE ANTENNAS……...……….33
3.1 Dipole-cavity structure and design rules..………………………..…………..33
3.2 Parametric study of design parameters..……………..………………………37
3.2.1 Cavity parameters..……………..……………..…………………..…37
3.2.1.1 Cavity aperture size..…………………………………..…37
3.2.1.2 Cavity depth..……………..……………..……………….44
3.2.1.3 Cavity sidewall slant angle..……………..………………47
3.2.1.4 Filling dielectric permittivity..……………..…………….51
3.2.2 Dipole parameters..……………………....……………..……………54
3.2.2.1 Dipole length..……………..……………..………………54
3.2.2.2 Dipole width..……………..……………..…………….…57
3.2.2.3 Dipole position..……………..……………..…………….60
3.2.2.4 Metal loss..……………..…………….………………..…64
CHAPTER 4. ANTENNA EXPERIMENTAL VALIDATION…………………..…….68
4.1 Scale model experiments…………..………………..…………………68
4.1.1 Scale model design…………..………………..…………...68
4.1.2 Antenna feed design…………..………………..…………..71
4.1.3 Prototype fabrication…………..………………..………….76
4.2 Results and discussion…………..………………..…………...……….79
4.2.1 Cavity geometry…………..………………..………………79
4.2.2 Dipole length…………..…………………………………...85
iii
4.2.2 Dipole length…………..…………………………………...85
CHAPTER 5. SUMMARY………………………………………………..…………….89
APPENDIX A1. INFRARED DETECTORS…………………….………..…………….92
APPENDIX A2. DIODE NON-LINEARITY…………………………..……………….94
APPENDIX A3. ANTENNA EFFECTIVE AREA………………………….…………..96
APPENDIX A4. DETECTOR SENSITIVTY AND BANDWIDTH……………………98
APPENDIX A5. DETECTOR SIGNAL-TO-NOISE RATIO ………………………...105
APPENDIX A6. METAL LOSS AT INFRARED…………………………..…………111
REFERENCES…………………………..……………………………………………..114
iv
TABLES
TABLE 1: SUBSTRATE SPECIFICATIONS…………………………………………22
TABLE 2: LAYOUT GEOMETRIES OF CPW LINES………………………………..22
TABLE 3: MODEL PARAMETERS FOR CPW LINES “C”…………………………..26
TABLE 4: DIPOLE AND CAVITY GEOMETRIES WITH DIFFERENT FILLING
DIELECTRICS……………………………………………………………..…….……...52
v
FIGURES
Fig. 1.1
Perspective view of Schottky-contact CPW lines on Silicon...…………..3
Fig. 1.2
Illustration of a typical antenna-coupled diode detector. The incident
radiation power is collected by an antenna (a dipole in the figure) and the induced voltage
at the antenna terminals will be rectified by the diode for detection....……………….…..3
Fig. 1.3
(a) Perspective view of MOS-contact CPW line (b) Schottky- contact
CPW lines on Silicon. (b) An equivalent circuit of an incremental section of MOScontact CPW lines on Silicon substrates. Full transmission lines are composed of
concatenated identical sections of this form....…………………………………………....7
Fig. 1.4
(a) A dipole at the air-dielectric interface (b) Ratio of the radiated power
on the dielectric side (θ=180o) to the air-side (θ=0o) for a dipole. The theoretical analysis
uses results from [30].....………………………………………………………………....11
Fig. 1.5
(a) Microstrip dipole radiation in a ray-tracking picture. (b) Computed
boresight gain and resonant resistance of a microstrip dipole (L/W=1.75/0.05 µm) on a
dielectric (εr=2.7) as a function of substrate thickness....…………………..…………....12
Fig. 1.6
Computed radiation pattern of a microstrip dipole (L/W=1.75/0.05 µm) on
a 1.8 µm thick dielectric (εr=2.7) substrate at 29.27 THz.....…………………………….15
Fig. 1.7
Cross-sectional view of a cavity-backed dipole receiving structure. A low-
εr dielectric, benzocyclobutene (BCB, εr=2.7), is assumed in this illustration…………..15
Fig. 2.1
(a) Cross-sectional schematic view of a CPW on Si substrate. The
semiconductor depletion region is shown schematically as a shaded region. (b) Wide-
vi
band quasi-TEM equivalent circuit model for an incremental length of Si-based CPW.
The full model is composed by concatenating many identical sections of this form……18
Fig. 2.2
Computed series resistance and inductance of a CPW line (s=30 µm,
w=18 µm, g= 147 µm) composed of 40nm Ti/200nm Al. See Fig. 2.1a for an illustration
of CPW geometries………………………………………………………………..…….20
Fig. 2.3
Comparison between measured and modeled s-parameters of a typical line
with geometry “C” on substrate “II” with no applied dc bias.…………………………..24
Fig. 2.4
Comparison of (a) measured and modeled attenuation and (b) slow-wave
factor for line with geometry “C” on Si (n-type, ρ=1~2 Ω-cm).…………..…………….25
Fig. 2.5
Comparison among the measured and modeled equivalent junction
capacitances, Ceq, for lines of different geometries on substrate “II” as a function of bias
voltage..…………..…………….…………..………………….………….……………...29
Fig. 2.6
Comparison of the measured and modeled equivalent junction capacitance
for Line "A" on two substrates with different doping concentrations (see Table I)……..29
Fig. 2.7
Measured current-voltage characteristics for typical lines with geometry
“C” on n-type (II) and p-type (IV) substrates. Inset: the simplified equivalent circuit
model for CPWs on p-type Si or MOS substrates with low junction conductances……..31
Fig. 2.8
Comparison among measured and modeled Ceq for different lines on p-
type substrate “IV” as a function of bias voltage.….…………….……….……………...32
Fig. 3.1
(a) Illustration of a dipole antenna backed by a dielectric-filled cavity (b) a
cross-sectional view of a cavity-backed dipole antenna with slanted cavity sidewall......34
vii
Fig. 3.2
Illustration of a microstrip dipole antenna on Silicon substrate………....36
Fig. 3.3
Simulated gain at 28.3 THz for a dipole (L = 1.75 µm) on BCB-filled
cavities with different aperture sizes (X and Y) and a fixed depth (H=1.8 µm). High gain
(~ 10dB) is achieved when X/Y = 12/8 µm.……………………………………..………38
Fig. 3.4
Simulated (a) radiation pattern and (b) electric field distribution of a
dipole (L/W = 1.75/0.05 µm) backed by a cavity (X/Y/H = 12/8/1.8 µm). The dipole is
centered at the coordinate origin and aligned to the y-axis.……………………..………39
Fig. 3.5
Simulated directive gain and E-plane beamwdith at 28.3 GHz of a dipole
(L/W = 1.75/0.05 µm) backed by cavities (X//H = 12/1.8 µm) with different lengths (Y).
The inset shows schematically the definition of the beamwidth.………………………..40
Fig. 3.6
Simulated (a) radiation pattern and (b) aperture electric field distribution
of a dipole (L/W = 1.75/0.05 µm) backed by a cavity (X/Y/H = 12/9.5/1.8 µm). The
dipole is centered at the coordinate origin and aligned to the y-axis.……………………42
Fig. 3.7
Simulated (a) magnitude and (b) phase distribution of the aperture electric
field's y-component at 28.3 THz (λ0=10.6µm) for the antenna shown in Fig. 3.6. Notice
two regions with equal magnitude but 180-degree phase difference. The center distance
of these two regions is ~Y/2=4.9 µm, close to λ0/2.…………………………………..…43
Fig. 3.8
Simulated resonant resistance and boresight gain of a dipole (L/W =
1.75/0.05 µm) backed by cavities (X/Y = 12/8 µm) as a function of cavity depth.……..45
Fig. 3.9
(a) E- and (b) H-plane radiation pattern of a dipole (L/W = 1.75/0.05 µm)
backed by BCB-filled cavities (X/Y = 12/8 µm) with different depth (H). Notice a lower
boresight gain for smaller depth cavity and stronger sidelobes for larger depth cavity…46
viii
Fig. 3.10
Simulated (a) s-parameters and (b) boresight gain and 3-dB E-plane
beamwidth of a dipole (L/W = 1.75/0.05 µm) backed by cavities (X/Y/H = 12/8/1.8 µm)
with different slant angle.………………………………………………………………..48
Fig. 3.11
Simulated (a) antenna effective area and (b) peak effective and detector
bandwidth of a dipole (L/W = 1.75/0.05 µm) backed by cavities (X/Y/H = 12/8/1.8 µm)
with different slant angle.………………………………………………………….…….50
Fig. 3.12
Simulated (a) s-parameters and (b) boresight gain at 28.3 THz and
resonant resistance of different cavity and dipole geometries (see Table V). The resonant
1
ε +1 −
resistance shows a ( r ) 2 dependence.………………………………………………..53
2
Fig. 3.13
Simulated boresight gain at 28.3 THz and resonant frequency of different
dipoles (fixed W=50 nm) backed by a BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The
resonant frequency from simulation shows a 1/L dependence, as expected.…………….55
Fig. 3.14
Simulated (a) input impedance (resistance R and reactance X) at 28.3 THz
and (b) resonant resistance and boresight gain of dipoles as a function of length (W=50
nm) backed by a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).……………………………56
Fig. 3.15
S-parameters of dipoles of different widths (L = 1.75 µm) backed by a
BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The impedance bandwidth increases for wider
dipoles.…………………………………………………………………………………...58
Fig. 3.16
Simulated (a) antenna effective area and (b) peak effective area and
detector bandwidth of dipoles (L = 1.75 µm) backed by a cavity (X/Y/H = 12/8/1.8 µm)
as a function of dipole width.………………………………………………….…………59
ix
Fig. 3.17
Simulated boresight gain at 28.3 GHz of a dipole (L/W = 1.75/0.05 µm) at
different positions in the aperture plane (X/Y/H = 12/8/1.8 µm). The origin is defined as
the center of the rectangular aperture plane.……………………………..………………61
Fig. 3.18
Simulated antenna (a) input resistance and (b) reactance at 28.3 GHz of a
dipole (L/W = 1.75/0.05 µm) at different positions in the aperture plane (X/Y/H =
12/8/1.8 µm). The origin is defined as the center of the rectangular aperture plane…….62
Fig. 3.19
Simulated input resistance and gain at 28.3 GHz of a dipole (L/W =
1.75/0.05 µm) at different vertical position in the cavity (X/Y/H = 12/8/1.8 µm). The
reference position is defined when the dipole is in the aperture plane…………………..63
Fig. 3.20
Input resistance of dipoles (L/W = 1.75/0.05 µm) using PEC and skin-
depth approximation on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).…………………..65
Fig. 3.21
(a) E- and (b) H-plane radiation pattern of dipoles using PEC and skin-
depth approximation on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm)…………………...66
Fig. 3.22
Simulated radiation efficiency and directivity of a dipole (L/W = 1.75/0.05
µm) on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The metal loss is calculated using
the skin-depth approximation.…………………………………………………………...67
Fig. 4.1
(a) Simulated boresight gain at 28.3 GHz for a dipole (L = 1.54 mm) on
PMMA-filled cavities with different aperture (X and Y) and fixed depth (H=1.905 mm).
(b) Simulated boresight gain at 28.3 GHz and resonant frequency of different dipole
length (fixed W=380 µm) on a PMMA-filled cavity (X/Y/H = 13/8.5/1.905 mm)……..70
Fig. 4.2
Illustration of a dipole with tapered-ground microstrip feed. Notice the
microstrip ground plane (in red) is tapered and becomes one dipole arm. It has a 180-
x
degree phase difference with respect to the microstrip signal line (in black) that forms the
other antenna arm.…………..………………..………………..………………..………..72
Fig. 4.3
(a) Illustration of a back-to-back structure of tapered-ground microstrip
feed. Front (b) and back (c) view of a fabricated back-to-back test structure…………...74
Fig.4.4
Measured and simulated scattering parameters of the back-to-back
structure balun…………..………………..………………..………………..……………75
Fig.4.5
(a) Front and back view of a fabricated dipole antenna and its feed (b) a
fabricated cavity-backed dipole antenna structure.…………..………………..…………77
Fig. 4.6
Typical oven temperature profile in PMMA curing.……………….……78
Fig. 4.7
Measured and simulated E- and H-plane pattern at 28.3 GHz for a dipole
(L=1.54 mm) backed by a cavity (X/Y/H=13/8.5/1.905 mm). The H-plane sidelobe is due
to the feed microstrip line….…………..………………..………………..…….………..80
Fig. 4.8
(a) Measured and simulated directivity at boresight and (b) measured
antenna efficiency for a dipole (L=1.54 mm) backed by a PMMA-filled cavity
(X/Y/H=13/8.5/1.905 mm).…………..………………..………………..……………….81
Fig. 4.9
Measured (a) E- and (b) H-plane pattern at 31 GHz for a dipole (L=1.54
mm) backed by a cavity (X/Y/H=13/8.5/1.905 mm). The multi-lobe radiation pattern is
due to high-order mode fields excited at the aperture plane.…………..……………….83
xi
Fig. 4.10
Measured and simulated (a) E-plane and (b) H-plane pattern at 28 GHz for
a dipole (L=1.54 mm) backed by a cavity (X/Y/H=13/8.5/3.175 mm). Multiple lobes in
both planes can be clearly seen, indicating the cavity depth is excessive.………………84
Fig. 4.11
Measured and simulated s-parameters of a dipole with length (a) L=1.54
mm and (b) L=2.0 mm backed by PMMA-filled cavity (X/Y/H=13/8.5/1.905 mm)……86
Fig. 4.12
Resonant frequency of dipoles with different lengths backed by the same
cavity (X/Y/H=13/8.5/1.905 mm)…………..……………………………………..…….87
Fig. 4.13
Measured and simulated boresight gain of a dipole (L/W = 2.0/0.38 mm)
backed by a PMMA-filled cavity (X/Y/H = 13/8.5/1.905 mm).…………..…………….87
Fig. 4.14
Boresight gain at 28.3 GHz of dipoles (L=1.54mm) with different mis-
alignment distance along the y-axis axis backed by the same cavity (X/Y/H=13/8.5/1.905
mm).…………..………………..………………..………………..………………..…….88
xii
ACKNOWLEDGEMENTS
The biggest bow goes to my advisor, Dr. Patrick Fay, whose work ethic, academic
vision, and self-motivation are the most valuable I learned from him. I am grateful for his
constant encouragement. I appreciate Dr. Wolfgang Porod, Dr. Gary Bernstein, and Dr.
Debdeep Jena for serving in my thesis committee. The multi-year research is not possible
without funding support from the State of Indiana and the Office of Naval Research.
I am indebted to my friends, Bo Yang, Xiang Li and Rajkumar Sankaralingam, in
every aspect of my stay at Notre Dame. People in the department including Michael
Thomas, Clint Manning, Keith Darr, and Mark Richmond were always ready to help.
After spending four fruitless months on surface preparation of samples, Dr. Lars-Erik
Wernersson (Lund University, Sweden) rescued me by suggesting wet etching for Si
surface preparation. I received lots of help from Dr. Greg Snider when using his 2-D
Poisson for capacitance calculations. Dr. Alan Seabaugh generously lent me his universal
test fixture. Fellow E.E. students also offered a hand when I needed. Thanks especially to
Jeffrey Bean for sharing his thoughts on the controlled oxidation process; Heng Yang and
Jie Su for helping with spin-on dielectrics fabrication; Vishwanath Joshi and Qing Liu for
discussing the Bosch process in deep reactive ion etching; Yong Tang for demonstrating
circuit board milling.
To finish a thesis is very demanding. I thank my family and friends, both here in
the States as well as those back at home, for their patience and support. Their
encouraging calls and e-mails are tremendous and have cheered me up along the way.
xiii
CHAPTER 1
INTRODUCTION
The enormous success of Si VLSI technologies has enabled on-chip applications
deep into the microwave and millimeter wave range [1]. High-permittivty Si substrates,
however, are known to significantly influence the performance of on-chip integrated
passive components and impede aggressive integration efforts [2]. To understand the
underlying problem and enable further improvement, an in-depth study of the interaction
between passive components and the substrate is necessary. We characterized coplanar
wavegudies (CPWs) with electrodes in direct contact with moderately doped Si substrates
at microwave frequencies, shown in Fig. 1.1. A new compact circuit model has been
developed that includes nonlinear junction conductance and capacitance due to the
Schottky barriers formed at the metal-semiconductor interfaces. The substrate doping
concentration is found to be important for controlling both the junction contact
capacitance and conductance, as well as the substrate coupling in the CPW structure.
At the other end of the frequency spectrum, infrared (IR) signal detection,
especially in the long wavelength (8-12 µm) atmospheric transmission window, has a
wide range of applications, including manufacturing process control, medical imaging,
surveillance, remote sensing, space radiometry, and night vision [3]. In contrast to
conventional thermal and photon-counting detectors, a detection scheme (see Fig.1.2)
based on an antenna-coupled rectifying diode appears promising for offering both room-
1
temperature operation and super-fast operational bandwidth for rapid events detection
[4]-[5]. This is in stark contrast to many competing devices, which require cryogenic
cooling or are relatively slow. As the most important part of this type of detector, an
integrated antenna on Silicon substrates is critical for the detector performance. We
examined the prospective performances of integrated dipole antennas on highpermittivity substrates, such as Si, and have demonstrated a design approach to address
the surface wave loss problem that limits the performance of conventional designs. Our
novel 3-D MEMS-inspired cavity-backed antennas achieve high power gain and show
promises for IC imaging applications in the infrared range. K-band scale models have
been fabricated, and validate the projected performance of the antenna structures. The
proposed antenna schemes are designed to be compatible with conventional IC
fabrication processes to allow direct insertion of these antenna structures in IC designs.
2
Fig. 1.1
Perspective view of Schottky-contact CPW lines on Silicon.
Fig. 1.2
Illustration of a typical antenna-coupled diode detector. The incident
radiation power is collected by an antenna (a dipole in the figure) and the induced voltage
at the antenna terminals will be rectified by the diode for detection.
3
1.1 Coplanar waveguides for integrated RF/microwave applications
With the development of SiGe technology and continued scaling of CMOS, the
feasibility of low-cost Si ICs with operating frequencies from the low GHz up to
millimeter wave frequencies has been successfully demonstrated [6]. Performance
projections based on standard lumped-element circuit theory are not accurate when the
physical size of the chip is comparable to the signal wavelength. To achieve the best
possible performance from an integrated system and to accurately evaluate the overall
system performance, careful design and modeling of on-chip interconnections over a
wide frequency range is critical. This is especially true for advanced system-on-a-chip
(SoC) implementations where both digital and analog modules are co-integrated, such as
transceivers [7].
An important type among various on-chip transmission lines, coplanar
waveguides (CPWs) are known to be superior to microstrip lines in a number of
applications due to their greater compatibility with planar active devices (no throughwafer vias are required), reduced sensitivity to the substrate thickness, and less radiation
loss [8]-[9]. Metal-oxide-semiconductor (MOS) CPWs on SiO2/Si substrates (see Fig.
1.3a), have been studied extensively in the literature. These structures are especially
common in SOI applications. MOS CPWs have been studied by various approaches
including finite element method [10], ABCD matrix partitioning [11], quasi-TEM
approximation [12], device-level simulation [13], and by analogy to MOS varactors [14].
Another type of CPWs, the direct-contact CPW (see Fig. 1.1), is also important
for applications ranging from mixed-signal circuits to advanced System-on-a-Chip (SoC).
4
Integrated circuits must often be fabricated on comparatively low-resistivity substrates
for compatibility with active device requirements. Such low-resistivity substrates result in
significant transmission line dispersion and nonlinearity due to the bias-dependent shunt
capacitance
and
conductance.
In
metal-semiconductor
structures,
“slow-wave”
propagation in the metal-semiconductor CPW is expected, just as is commonly observed
for MOS structures, since the depletion capacitance at the metal-semiconductor interface
is qualitatively similar to MOS capacitance [10]-[14]. The quasi-TEM equivalent circuit
[12] of conventional MOS CPW lines is shown in Fig. 1.3b, where the influence of the
oxide layer under the center and ground conductors is modeled by a single capacitor,
Coxide. However, in contrast to the negligible oxide conduction current in MOS CPWs, the
nonlinear Schottky barrier conductances in metal-semiconductor CPWs must be treated
more carefully.
Very limited results and analysis are available in the literature for CPWs on lowresistivity Si substrates with direct metal-semiconductor (MS) contacts. CPW lines on
lossy Silicon substrates with Schottky contact have been modeled by a conventional
RLCG transmission line model to match measured s-parameters [15]. Unfortunately, the
phenomenologically modeled shunt conductance and capacitance in [15] are frequencydependent and non-physical. Moreover, no theoretical or experimental validation of the
formation of Schottky barriers at metal-semiconductor interface was performed to explain
the measured results. Conductances and capacitances of the metal-semiconductor contact
were simulated in a study of trenched CPWs on p-type high-resistivity (10 kΩ-cm) Si
5
(HRS) [16]. However, doping type dependence and direct experimental verification of
the assumed Schottky barrier were not presented.
By treating the CPW as a distributed semiconductor device, we have developed a
nonlinear equivalent circuit model that includes frequency-independent shunt parameters
that accurately reflects the physical processes governing current transport within the
structure. In this new model, the shunt components in the transmission line equivalent
circuit are represented in a general form that allows for accurate quantification of biasdependent coplanar line performance by including depletion capacitance and conductance
[17]. The frequency-independent model parameters in particular allow time-domain
signal integrity evaluation for coplanar lines. To our knowledge, this is the first report
and experimental verification of a nonlinear quasi-TEM equivalent circuit for CPW
transmission lines on low-resistivity Si substrates suitable for either metal-semiconductor
Schottky or metal-oxide-semiconductor (MOS) contacts.
6
(a)
(b)
Fig. 1.3
(a) Perspective view of MOS-contact CPW line (b) Schottky- contact
CPW lines on Silicon. (b) An equivalent circuit of an incremental section of MOScontact CPW lines on Silicon substrates. Full transmission lines are composed of
concatenated identical sections of this form.
7
1.2 Cavity-backed high-gain antennas for infrared detection
For a number of IR applications, including plasma diagnosis, laser-matter
interaction experiments, space radiometry, and military operations, the ability to detect
rapid events without cryogenic cooling is critical [18]. In contrast to conventional thermal
and photon IR detectors (see Appendix A1 for a brief review), antenna-coupled diode
detectors offer the potential for both room-temperature operation and very large
bandwidth. Since IR radiation in essence is an electromagnetic wave propagation
phenomenon, instead of coupling IR radiation as photons directly into the sensing device,
an antenna-based detector collects the IR radiation energy as an electromagnetic wave
and delivers the induced signal at the antenna terminals to a detecting device.
Using an antenna to couple incident radiation to a diode decouples the power
collection and signal rectification process. By separating the “collection” and “detection”
processes and utilizing the potentially large effective area of a receiving antenna, more IR
radiation can be coupled by the antenna into a small detector load (see Appendix A2 and
A3). Compared with an absorptive IR detector of the same area, the noise equivalent
power (NEP) of an antenna-coupled diode detector is reduced by a factor of λG1/2/2bπ1/2,
where λ is the operation wavelength, G is the antenna directive gain, and b is the detector
dimension [19]. This yields a reduction in NEP by a factor of 40 when using half-wave
dipole (G=1.64) coupled 100×100 nm diode detectors at λ=10.6 µm. Using planar
antenna structures overcomes the problems suffered by whisker-like antennas when
integrated with diodes for detection and mixing, such as low packaging density,
fabrication irreproducibility, mechanical instability and inherent incompatibility with
8
standard Si IC fabrication processing [20]. There also have been efforts on the integration
of antennas with bolometers [21]-[22] or photodiodes [23]-[24] for infrared detection.
These efforts, however, do not address the fundamental speed or temperature limits posed
by their detection mechanism. One attractive device for the detection function is the
metal-oxide-metal (MOM) diode. The ultimate speed limit of MOM diodes has been
calculated to be as short as 10-16 sec., based on 1-D Gaussian wave packet transmission
through a rectangular potential barrier [25]. MOM diodes with direct diode mixing output
at 148 THz [26] further indicates infrared detection using MOM diodes will not be
limited by the tunneling process. It has been theoretically demonstrated that, compared
with thermionic emission current, the tunneling current dominates when the insulating
layer is less than 40 Å thick and the barrier height is greater than 1.25 eV [27]. The
barrier height of a plasma oxidized Al/Al2O3/Al junction ranges from 1.8 eV to 2.4 eV
with increasing oxide thickness from 30-50 Å [28]. MOM diodes, thus, appear to be good
candidates for ultra-fast detection at room temperature.
Because the antenna controls the coupling of incident power to the sensing diode,
high-performance integrated antennas are essential for a successful demonstration of
antenna-coupled diode detectors. Among all the design parameters, the antenna's
directive gain, a measure of the antenna's directional radiating or receiving capability, is
the most critical to achieve high detector performance (see Appendix A4 and A5 for
closed-form expressions of detector sensitivity, bandwidth, and signal-to-noise ratio).
Integrated planar antennas on high permittivity substrates (e.g. Silicon or GaAs)
are well documented for their poor radiation and receiving capability to the air-side.
9
When placed at the air/dielectric interface (see Fig. 1.4a), antennas radiate preferentially
towards the high-permittivity dielectric side [29]. It has been shown that the broadside
radiation power varies as εr3/2 on each side [29]-[30]. As seen in Fig. 1.4b, radiated power
to the dielectric side is more than 10 times greater than that to the air-side when the
relative permittivity of the dielectric is greater than 5. As a result, this effect is more
prominent for antennas on high-permittivity substrates, such as Si or GaAs in terms of
antenna efficiency and radiation pattern. Despite this trend, normal incidence from the air
side is usually preferred for imaging array applications due to practical considerations
such as packaging limitations.
In practice, microstrip dipoles (dipoles on a grounded thin substrate, see Fig. 1.5a)
are often regarded as being more promising than printed dipoles (dipoles on an
ungrounded substrate) due to their relatively higher gain and better field confinement,
since microstrip dipoles can not radiate through the ground plane. However, because of
its air/dielectric/metal sandwich structure and the wave propagation due to total internal
reflection (the so-called "surface waves"), a large portion of the microstrip dipole's power
is trapped inside the dielectric layer without contributing to the air-side radiation, thus
substantially lowering the antenna efficiency and limiting the maximum achievable
antenna gain [31]-[32]. The radiation resistance along with the radiation efficiency for a
microstrip dipole on a low-εr (εr=2.7) dielectric substrate with various thickness is plotted
in Fig. 1.5b. The radiation efficiency is seen to decrease with increasing substrate
thickness since more surface modes are allowed to propagate. Although higher efficiency
can be achieved by using extremely thin substrates, this also results in very low radiation
10
(a)
(b)
Fig. 1.4
(a) A dipole at the air-dielectric interface (b) Ratio of the radiated power
on the dielectric side (θ=180o) to the air-side (θ=0o) for a dipole. The theoretical analysis
uses results from [30].
11
(a)
(b)
Fig. 1.5
(a) Microstrip dipole radiation in a ray-tracking picture. (b) Computed
boresight gain and resonant resistance of a microstrip dipole (L/W=1.75/0.05 µm) on a
dielectric (εr=2.7) as a function of substrate thickness.
12
resistance (about 1 Ω for a 0.2 µm thick substrate in Fig. 1.5b) and consequently very
small radiated power from typical source impedances. To strike a balance between
optimal efficiency and maximum power, the substrate thickness should be such that the
second surface wave mode is just about to propagate, since the TM0 fundamental surface
wave mode always propagates [32].
Following the E- and H- plane notions marked in Fig. 1.4a, the radiation pattern
of a resonant dipole on a substrate (εr=2.7) with the optimal thickness (1.8 µm) is shown
in Fig. 1.6. The boresight gain (substrate normal direction) on the air-side is 4 dB with
80% efficiency. Strong lateral radiation (θ=90o, E-plane) due to the TM0 fundamental
mode is observed. Earlier research has shown that surface wave problems are more
severe on higher permittivity substrates [31]-[32]. A similar dipole on a Silicon (εr=11.9)
substrate shows about 1 dB boresight gain and 25 % efficiency [32].
Several approaches to improve the reception performance of the antenna for
normally-incident radiation have been demonstrated. One is to intentionally couple the
light from the dielectric side using “substrate lens” [33]. Successful implementations in
the millimeter wave and infrared range [34]-[35] have been reported in the literature.
Nonetheless, manufacturing of the parabolic dielectric lens is not trivial and is
incompatible with conventional IC fabrication processing.
Other approaches for better reception of air-side illumination are mainly based on
substrate micromachining: either to synthesize a low-permittivity substrate [36]-[39] or to
construct an electromagnetic bandgap (EBG) structure [40]. However, most of these
solutions are either not fully compatible with standard IC processing (e.g. backside
13
anisotropic etching) or consume significant amounts of precious chip area (several
wavelengths for typical EBG structures), thus impeding the integration of antennas with
established peripheral circuits, as in an antenna-coupled diode detector imaging array.
Alternatively, using a dead-end metallic waveguide section as an open cavity, as
illustrated in Fig. 1.7, to back the dipole is a simple yet effective approach to address the
surface wave problem. The cavity is filled with low-permittivity dielectric material to
provide mechanical support of the dipole antenna. By judiciously choosing cavity
geometries, one can design the antenna resonance to excite an aperture field distribution
that is dominated by TE10 waveguide mode fields, resulting in single-beam, high
boresight gain operation.
The proposed 3-dimensional high-gain receiving structure is electrically small and
comparatively simple. The optimal cavity aperture in our design is found to be
approximately 1.5 effective wavelengths square through numerical simulations. The
proposed design also avoids backside etching and specialized film deposition [41],
yielding a simple fabrication process that can be inexpensively implemented. Our
numerical simulations have revealed that a dipole’s directive gain at the boresight can be
improved by at least 6 dB compared to the best possible performance of a simple
microstrip dipole on a low-εr substrate (εr=2.7), and even greater improvement compared
with a dipole on Silicon (εr=11.9) substrates.
14
Fig. 1.6
Computed radiation pattern of a microstrip dipole (L/W=1.75/0.05 µm) on
a 1.8 µm thick dielectric (εr=2.7) substrate at 29.27 THz.
Fig. 1.7
Cross-sectional view of a cavity-backed dipole receiving structure. A lowpermittivity dielectric, Benzocyclobutene (BCB, εr=2.7), is assumed in this illustration.
15
1.3 Thesis outline
In this thesis, research on two Si-based passive devices is described: the modeling
of coplanar waveguides (CPWs) on moderately doped Silicon substrates at microwave
frequencies for high speed on-chip interconnects, and the design of cavity-backed highgain dipole antennas using IC-compatible fabrication process for infrared detection.
In Chapter 2, a physics-based nonlinear equivalent circuit model for CPWs
fabricated on Si substrates is developed and verified experimentally. Physics-based
numerical calculations, and both capacitance-voltage and current-voltage measurements
have been used to validate and simplify the proposed model. Good fidelity between the
model predictions and measured CPW performances is obtained. In Chapter 3, we present
a parametric study of cavity-backed dipole antennas for antenna-coupled diode infrared
detectors. Using a low-permittivity (εr=2.7) filling dielectric, the cavity and dipole design
parameters are optimized through 3-D electromagnetic simulations for the best
antenna/detector performance. In Chapter 4, the design and fabrication details of K-band
scale models of the proposed dipole/cavity antenna structures are described. The sparameter and radiation pattern measurements of several different dipole and cavity
geometries are discussed to further validate the projected performances of our infraredfrequency design. In Chapter 5, a summary of this work and directions for future research
are provided. In the appendices, we have evaluated the performance of antenna-coupled
diode infrared detectors and included closed-form expressions of detector sensitivity,
bandwidth, and signal-to-noise ratio.
16
CHAPTER 2
MODELING OF SILICON COPLANAR WAVEGUIDES
2.1 A physics-based generic circuit model
Figure 2.1 shows a schematic cross-section of a metal-semiconductor CPW on a
Si substrate and its quasi-TEM wide-band small-signal equivalent circuit, assuming evenmode propagation. In our analysis, the capacitance of free space above the substrate
between “signal” and “ground” electrodes is neglected, since most of the transverse
electric field energy is stored in the substrate due to the large dielectric constant of Si
(εr=11.9). Contributions from the “signal” and “ground” Schottky-contact electrodes are
modeled by two diodes, with junction conductance and capacitance in parallel. Our study
reveals that for CPW lines on moderately doped Si substrates, the nonlinear junction
conductance is comparable to the junction reactance due to the depletion capacitance up
to a few GHz and therefore should be included in the model to accurately reflect the
measured performance. The junction conductance and capacitance at each electrode are
introduced separately, in contrast to the common practice in modeling MOS CPWs (see
Fig. 1.3b) of using a single “equivalent” capacitance and ignoring junction conductance
[11]-[12]. The combination of Csub and Gsub accounts for substrate coupling [42]. It is
well known that Wheeler’s incremental inductance rule is not suitable for determining the
frequency-dependent series resistance (R) and inductance (L) of practical non-ideal metal
strips with thickness comparable to the skin depth [43]-[44]. Instead, a numerically
17
(a)
(b)
Fig. 2.1
(a) Cross-sectional schematic view of a CPW on Si substrate. The
semiconductor depletion region is shown schematically as a shaded region. (b) Wideband quasi-TEM equivalent circuit model for an incremental length of Si-based CPW.
The full model is composed by concatenating many identical sections of this form.
18
inexpensive closed-form approximation [43] is used to capture the dispersive
characteristics of R and L in the model. Figure 2.2 shows the computed series resistance
and inductance for a typical CPW line and illustrates the importance of modeling this
dependence. The frequency range in this study is from 100 MHz to 10 GHz. It is
observed that at 10 GHz R increases by approximately 28% while L decreases
approximately 18% with respect to their low-frequency (100 MHz) values.
In contrast to previous studies of CPWs on MOS and metal-semiconductor
substrates reported in the literature [10]-[14], this new model is amenable for use with Si
substrates over a wide range of doping concentrations and for structures with direct
metal-semiconductor contacts. The investigation of Si-based CPW lines fully accounts
for the influence of both conduction and displacement current at the metal-semiconductor
interface and the corresponding effects on transmission line performance. The nonlinear
Schottky barrier conductances in metal-semiconductor CPWs require a more general
formulation than conventional MOS CPW models, but the resulting model is suitable for
both MOS and metal-semiconductor structures. Our new model is based on treating the
CPW structure as a distributed semiconductor device, but does so in a computationally
efficient and compact manner. Different doping type (n- or p-type) is also found to be
significant to the model complexity. For CPW lines on p-type substrates, a simplified
model is found to be accurate enough for many cases to predict line performance.
19
Fig. 2.2
Computed series resistance and inductance of a CPW line (s=30 µm,
w=18 µm, g= 147 µm) composed of 40nm Ti/200nm Al. See Fig. 2.1a for an illustration
of CPW geometries.
20
2.2 Fabrication and measurement
CPW lines with several combinations of “signal” and “ground” conductor widths
on both n- and p-type Si substrates with several different doping concentrations were
fabricated. Tables 1 and 2 provide a summary of the substrates and CPW geometries that
were used (geometries are labeled in Fig. 2.1a). Prior to defining the electrodes with
photolithography, all samples were wet-etched in a hydrofluoric-nitric-acetic acid
solution (3 HF: 25 HNO3: 10 CH3COOH) for 5 minutes to remove surface contamination
[45] and to ensure a good metal-semiconductor contact. Ti/Al electrodes were deposited
by electron-beam evaporation and patterned by a conventional lift-off process. No
backside ground plane was used.
Current-voltage and capacitance-voltage characteristics of the CPW lines were
measured using an Agilent 4155C semiconductor parameter analyzer and a HP 4280A 1
MHz capacitance meter, respectively. The external dc bias voltage is defined with respect
to the outer “ground” electrodes, as shown in Fig. 2.1a, for devices on both n- and p-type
substrates. Two-port bias-dependent s-parameters of all CPW lines were also measured
on-wafer from 100 MHz to 10 GHz. The dc bias was supplied by an Agilent 4155C to the
device under test through the network analyzer’s built-in bias tees. A relatively low RF
power level of –35 dBm was used during s-parameter measurement to ensure no
nonlinear effects were present, while still maintaining an adequate signal amplitude for
accurate s-parameter measurement. The measured s-parameters of the CPW lines were
de-embedded from probe pad parasitics whose equivalent circuit parameters were
extracted from measurements of on-wafer “open”, “short” and “through” test structures
21
TABLE 1
SUBSTRATE SPECIFICATIONS
Substrate
Resistivity
(Ω-cm)
Type
I
20 - 40
N
II
III
1-2
10 - 18
P
IV
3 - 6.6
TABLE 2
LAYOUT GEOMETRIES OF CPW LINES
Line
s
(µm)
w
(µm)
g
(µm)
A
70
42
103
B
50
30
125
C
30
18
147
Note: s: center metal width, w: slot width, g: ground metal width. Geometries are labeled in Fig. 2.1a.
22
2.3 Results and discussion
2.3.1 Scattering parameters
The de-embedded s-parameters of CPW lines were used to extract bias-dependent
small-signal equivalent circuit parameters by nonlinear least squares curve-fitting over
the frequency range of 100 MHz to 10 GHz. The bias dependence of the circuit
parameters was found by fitting to measured s-parameters independently at each bias
point. Figure 2.3 shows the measured and modeled s-parameters for a typical CPW line
with geometry “C” on substrate II (see Tables I and II) with no applied dc bias. As seen
in the figure, the model matches the measurement well over the full frequency range. In
addition, the non-ideal propagation delay caused by junction depletion capacitances is
also accurately predicted by the model, as illustrated by the phase of S21. The attenuation
and slow-wave factor [46] of the CPW line under dc bias is plotted in Fig 2.4. Compared
to MOS [10]-[14] and direct-contact CPWs on high-resistivity substrates [16] with
similar line geometries, the attenuation is higher, mainly due to the lower substrate
resistivity. Typical extracted model parameters for CPW lines with geometry “C” on
different substrates are summarized in Table 3.
23
Fig. 2.3
Comparison between measured and modeled s-parameters of a typical line
with geometry “C” on substrate “II” with no applied dc bias.
24
(a)
(b)
Fig. 2.4
Comparison of (a) measured and modeled attenuation and (b) slow-wave
factor for line with geometry “C” on Si (n-type, ρ=1~2 Ω-cm).
25
TABLE 3
MODEL PARAMETERS FOR CPW LINES “C”
(a) n-type Si (ρ=1~2 Ω-cm)
Vbias
(V)
C1
C2
(pF/mm) (pF/mm)
G1
(µS/mm)
G2
(µS/mm)
Csub
Gsub
(fF/mm) (mS/mm)
-0.5
4.8
81.8
9.1
4131.5
26.0
75.5
0
8.4
81.8
2754.5
2754.5
27.4
74.7
+0.5
8.9
48.8
4131.7
98.3
27.1
72.7
(b) n-type Si (ρ=20~40 Ω-cm)
-0.5
1.5
28.0
G1
(µS/mm)
2.3
0
2.9
28.0
1747.6
+0.5
3.0
14.9
2621.2
Vbias
(V)
C1
C2
(pF/mm) (pF/mm)
26
G2
(µS/mm)
2283.9
Gsub
Csub
(fF/mm) (mS/mm)
22.9
6.3
1748.9
21.7
5.8
90.5
21.4
5.7
2.3.2 Waveguide geometry and substrate doping concentration
Quantitative validation of model parameters extracted from the measured sparameters was performed to illustrate their influence on the transmission line
performance. The equivalent shunt capacitance (Ceq) between “signal” and “ground”
electrodes is defined as:
Ceq =
G2 2C1 +G1 2C 2 +ω 2 (C1 +C 2 )C1C 2
(G1 +G2 )2 +ω 2 (C1 +C 2 )2
(1)
where ω is the angular frequency and C1, C2, G1, G2 are defined as shown in Fig. 2.1a.
Ceq for different line geometries on substrate “II” as a function of applied bias is shown in
Fig. 2.5. Also shown on Fig. 2.5 are the measured 1 MHz capacitance-voltage
characteristics of the CPW lines. All modeled capacitances match very well with the
measured 1 MHz capacitance values. It is worth noting that Ceq displays a markedly
different junction area dependence in positive and negative bias regime. For example,
line A has the smallest capacitance under positive bias, while it shows the largest
capacitance under negative bias. This effect arises because (for n-type substrates) the
“signal” electrode depletion capacitance dominates for negative bias, while the “ground”
electrode depletion capacitance dominates at positive bias. For all of the lines examined
here, line A has the largest “signal” electrode and the smallest “ground” electrodes, while
line C has the smallest “signal” and largest “ground” and line B is intermediate between
these extremes.
To verify the origin of this effect, the depletion capacitance of each CPW
structure was calculated by “2D Poisson” [47], a program that solves Poisson’s equation
27
in two dimensions based on the finite differences method, to numerically model the 2D
depletion region contour under each contact. The calculated capacitances from the 2D
simulations are plotted along with the results from device measurement and circuit
modeling in Fig. 2.5. Comparison between 2D numerical calculations and measurements
shows excellent agreement for all devices in both positive and negative regions. The
overestimation of Ceq around zero bias for the 2D numerical calculation arises from the
fact that the calculation only considers the dominant reverse-biased junction, a poor
approximation when the conductances of both reverse-biased and forward-biased
junctions are comparable, as occurs for bias voltages close to zero. Similar trends of the
nonlinear bias-dependence of Ceq have been observed for CPW lines on Si with substrate
doping concentrations ranging from 1.8×1014 cm-3 to 2.2×1015 cm-3, demonstrating the
doping concentration scalability. Figure 2.6 shows the measured and modeled equivalent
junction capacitances for lines with the same geometry ("A") with on two substrates with
different doping concentrations.
28
Fig. 2.5
Comparison among the measured and modeled equivalent junction
capacitances, Ceq, for lines of different geometries on substrate “II” as a function of bias
voltage.
Fig. 2.6
Comparison of the measured and modeled equivalent junction capacitance
for Line "A" on two substrates with different doping concentrations (see Table I).
29
2.3.3 Substrate doping type
CPWs on p-type substrates were also studied to examine the influence of substrate
doping type. Typical I-V characteristics of the line with geometry “C” on p-type substrate
IV are shown in Fig. 2.7, along with that for n-type substrate II. The junction current on
the p-type substrate is seen to be approximately three orders of magnitude smaller than
that for an n-type structure over the same bias voltage range. Assuming the measured
current, I, is limited by the reverse-biased junction due to current continuity in the backto-back contacts, the effective Schottky barrier height, φb = (kT/q)ln(SA*T2/I), was
extracted to be 0.49 eV and 0.61 eV for contacts on n- and p-type substrates, respectively,
where S is the junction area and A* is the effective Richardson constant (A*=112
A/cm2/K2 for n-type; A*=32 A/cm2/K2 for p-type [48]). These results are consistent with
reports in the literature for Schottky contacts on Si [49]-[50].
Compared with contacts on n-type substrates, the higher φb for p-type substrates
implies smaller junction conductances and thus a significantly smaller contribution to the
wide-band circuit model even at low frequencies. Since Eq. (1) can be reduced to Ceq =
C1C2 / (C1 + C2) if the junction conductances are negligible, a more compact circuit
model can be used for CPWs on p-type substrates, as shown in the inset of Fig. 2.7. The
Ceq obtained from circuit optimization, 2D numerical calculation, and 1 MHz C-V
measurement for CPWs on this substrate are plotted in Fig. 2.8. The voltage dependence
of lines A, B, and C are all well described by the circuit model, with only slight
discrepancies within the measurement uncertainty. This is consistent with trends
observed for trenched CPWs on p-type high-resistivity Silicon substrates [16].
30
Fig. 2.7
Measured current-voltage characteristics for typical lines with geometry
“C” on n-type (II) and p-type (IV) substrates. Inset: the simplified equivalent circuit
model for CPWs on p-type Si or MOS substrates with low junction conductances.
31
Fig. 2.8
Comparison among measured and modeled Ceq for different lines on ptype substrate “IV” as a function of bias voltage.
32
CHAPTER 3
DESIGN OF CAVITY-BACKED DIPOLE ANTENNAS
3.1 Dipole-cavity structure and design rules
The other Si-based passive device explored is a cavity-backed dipole antenna that
can be realized using MEMS-inspired fabrication techniques. The cavity-backed dipole
antenna consists of a feed antenna and a reflector, as illustrated in Fig. 3.1a. The cavity
sidewalls are not necessarily vertical, as shown in Fig. 3.1b for a cavity with invertedtruncated-square-pyramid (ITSP) shape. One possible fabrication sequence is as follows.
The reflector can be constructed by anisotropic etching for the desired sidewall profile
[51]. The inner surfaces of the cavity are then coated with metal to form a reflector. A
low-εr dielectric, e.g. benzocyclobutene (BCB, εr=2.7), is then applied to fill the cavity
and cured to provide the necessary mechanical support for the feed antenna. BCB has
been used extensively in a wide range of microwave and optical applications, such as
packaging, interconnect, and wafer bonding [52]-[55]. The receiving antenna and diode
are then patterned on top of the BCB using conventional processing steps.
Compared to a conventional microstrip dipole shown in Fig. 3.2, the metallic
cavity sidewalls in our design act as shorting planes to block all propagating surface
waves. By judiciously choosing cavity geometries, we have designed the antenna
resonance to excite an aperture field distribution that is dominated by TE10 waveguide
mode fields, resulting in single-beam, high boresight gain operation.
33
(a)
(b)
Fig. 3.1
(a) Illustration of a dipole antenna backed by a dielectric-filled cavity and
(b) a cross-sectional view of a cavity-backed dipole antenna with slanted cavity sidewall.
34
The proposed structure is electrically small and comparatively simple. The
optimal cavity aperture in our design is found to be approximately 1.5 effective
wavelengths square through numerical simulations. Our design avoids backside etching
and specialized film deposition [41], yielding a simple fabrication process that can be
easily implemented. The cavity design also lends itself to future imaging array
applications, as it reduces potential cross-talk and interference between antennas in
neighboring pixel cells due to surface waves.
Among all design parameters of the dipole/cavity structure, the dipole strip length
(L) and width (W), cavity aperture size (X and Y), depth (H), and filling dielectric
permittivity (εr) were found to be the most important design parameters for achieving
high boresight gain (i.e. surface normal direction) and single-lobe beam operation at the
desired frequency range. A large number of 3-dimensional electromagnetic simulations
have been performed using HFSS (Ansoft v.9.1) for different antenna and cavity design
parameters to map out the design space. From analysis of the observed trends, the
following design guidelines have been developed: 1) the cavity aperture size should be
chosen to favor an aperture field distribution dominated by the TE10 mode and the dipole
should be designed to efficiently couple to this mode; 2) the cavity depth should be
approximately a quarter of an effective wavelength at the desired dipole resonant
frequency; 3) a low-permittivity filling dielectric, as close to vacuum as possible, is
desired for broadband operation; 4) the resonant frequency of the dipole monotonically
increases with decreasing dipole length, while too short a dipole will suppress effective
resonance; and 5) increasing the dipole strip width results in a broader input impedance
35
bandwidth. A more detailed discussion of these effects is presented in the following
sections. Our research has also concluded that dipole parameters mainly determine the
antenna resonant frequency and input impedance, while cavity parameters are primarily
responsible for the far-field pattern and boresight gain.
Fig. 3.2
Illustration of a microstrip dipole antenna on Silicon substrate.
36
3.2 Parametric study of antenna design
3.2.1 Cavity parameters
3.2.1.1 Cavity aperture size
Cavity aperture size (X and Y) has been identified the most critical parameter to
establish an aperture field distribution that is predominantly the TE10 mode at the
operation frequency for a far-field pattern with high boresight gain and a single-lobe
beam. Figure 3.3 shows the simulated boresight gain at 28.3 THz of a dipole
(L/W=1.75/0.05 µm) on BCB-filled (εr=2.7) cavities with fixed cavity depth (H=1.8 µm)
but different aperture sizes (X and Y). An equal-gain contour in the x-y plane is also
shown in Fig. 3.3. It is seen that high boresight gain (~10 dB) is achieved when the
aperture is within the "optimal" neighborhood (close to X/Y=12/8 µm).
The simulated radiation pattern of an 'optimal' design (X/Y/H=12/8/1.8 µm) of
our proposed cavity-backed dipole antenna is plotted in Fig. 3.4a. The antenna is seen to
have 10 dB boresight gain, about 6 dB better than the best possible performance of a
microstrip dipole on a very low permittivity (εr=2.7) substrate [32]. In contrast to the
microstrip dipole pattern in Fig. 1.6, our design shows reduced lateral radiation due to the
suppression of the surface waves. The high-gain, single beam operation is obtained
mainly because of the excitation of a TE10 mode field is excited at the cavity aperture.
Except for regions close to the dipole antenna, a TE10 mode distribution is clearly seen in
the electric field plot at 28.3 THz in Fig. 3.4b.
37
Fig. 3.3
Simulated gain at 28.3 THz for a dipole (L = 1.75 µm) on BCB-filled
cavities with different aperture sizes (X and Y) and a fixed depth (H=1.8 µm). High gain
(~ 10dB) is achieved when X/Y = 12/8 µm.
38
(a)
(b)
Fig. 3.4
Simulated (a) radiation pattern and (b) electric field distribution of a
dipole (L/W = 1.75/0.05 µm) backed by a cavity (X/Y/H = 12/8/1.8 µm). The dipole is
centered at the coordinate origin and aligned to the y-axis.
39
Compared to the optimal aperture, neither smaller nor larger apertures are desirable. Too
small an aperture does not confine the beam effectively in the far-field. As can be seen in
Fig. 3.5, the pattern has decreased boresight gain and higher gain along surface with
decreasing Y-direction cavity aperture for a fixed X-direction cavity size of 12 µm. The
3-dB angle of the beam, illustrated in the inset of Fig. 3.5, becomes larger when the
aperture becomes smaller. Considering the far-field radiation is essentially controlled by
Fraunhofer diffraction due to a dipole illumination on the aperture opening, the trend of
the 3-dB beamwidth seen in Fig. 3.5 is expected, since the width of the major diffraction
lobe is inversely proportional to aperture size, according to diffraction theory.
Fig. 3.5
Simulated directive gain and E-plane beamwdith at 28.3 GHz of a dipole
(L/W = 1.75/0.05 µm) backed by cavities (X//H = 12/1.8 µm) with different lengths (Y).
The inset shows schematically the definition of the beamwidth.
40
On the other hand, too large an aperture allows the excitation of higher-order
modes in the cavity aperture and produces grating lobes in the far-field due to more
efficient excitation/coupling to higher-order aperture fields. As an extreme case, Figure
3.6a shows the simulated radiation pattern of a dipole backed by an oversized cavity
(X/Y=12/9.5 µm) at 28.3 THz. As shown in Fig. 3.6a, there is an E-plane null at
boresight while the lateral radiation is enhanced, since the higher-order TM12 mode fields
rather than the TE10 mode are excited most efficiently in the aperture plane. Fig. 3.6b
shows the aperture electric field for this case, confirming the high-order mode excitation.
The strong lateral radiation in the E-plane is further understood by examining both the
magnitude and phase distribution of the aperture electric fields shown in Fig. 3.7. It is
noticed in Fig. 3.7 that there are two regions with equal magnitude but 180-degree phase
difference for the y-component of the E-field. If one considers these two regions as two
radiating elements, the boresight null is seen to arise naturally from the destructive
interference between two anti-phase elements. Considering the center distance of these
two elements is approximately half the cavity dimension in the Y-direction (Y/2=4.9 µm)
and the free-space wavelength (λ0) of 28.3 THz is 10.6 µm, it is easy to understand the
lateral radiation peak is the result of constructive interference by two anti-phase radiation
elements separated by λ0/2.
41
(a)
(b)
Fig. 3.6
Simulated (a) radiation pattern and (b) aperture electric field distribution
of a dipole (L/W = 1.75/0.05 µm) backed by a cavity (X/Y/H = 12/9.5/1.8 µm). The
dipole is centered at the coordinate origin and aligned to the y-axis.
42
(a)
(b)
Fig. 3.7
Simulated (a) magnitude and (b) phase distribution of the aperture electric
field's y-component at 28.3 THz (λ0=10.6µm) for the antenna shown in Fig. 3.6. Notice
two regions with equal magnitude but 180-degree phase difference. The center distance
of these two regions is ~Y/2=4.9 µm, close to λ0/2.
43
3.2.1.2 Cavity depth
The presence of the metallic cavity bottom suggests that the far-field pattern can
be qualitatively understood as a 2-element radiator that consists the dipole and its image.
The maximum radiation resistance and high boresight gain is achieved when the depth is
approximately a quarter of the effective wavelength of resonance, enabling constructive
interference in the far-field by the dipole and its anti-phase image. Thus to achieve a
single-beam radiation pattern and maximum radiated power, the cavity depth must be
properly chosen.
Through simulations, we have shown that too small a depth gives rise to a low
radiation resistance. In the extreme case when the cavity bottom is infinitely close to the
dipole, the radiation resistance will be zero, i.e. no radiated power. This is similar to the
case of a dipole over an infinitely large ground plane [56]. As an example, Figure 3.8
shows the performance of a dipole antenna (L/W=1.75/0.05 µm) on BCB-filled cavities
with fixed aperture size (X and Y) and various depths (H). The radiation resistance and
boresight gain both become smaller when the depth approaches zero. Too large a depth is
also problematic. Large cavity depths result in sidelobes in the far-field pattern, and more
importantly a decreasing radiation resistance. This is seen in Fig. 3.9 for a dipole on three
different cavities with same X and Y but different H. Also notice in Fig. 3.8 is that the
radiation resistance also starts decreasing after peaking around 1.6 µm. The radiation
resistance declines because cavities with greater depth resonate at a frequency lower than
the dipole resonance, effectively reducing the benefit of using the cavity.
44
Fig. 3.8
Simulated resonant resistance and boresight gain of a dipole (L/W =
1.75/0.05 µm) backed by cavities (X/Y = 12/8 µm) as a function of cavity depth.
45
(a)
(b)
Fig. 3.9
(a) E- and (b) H-plane radiation pattern of a dipole (L/W = 1.75/0.05 µm)
backed by BCB-filled cavities (X/Y = 12/8 µm) with different depth (H). Notice a lower
boresight gain for smaller depth cavity and stronger sidelobes for larger depth cavity.
46
3.2.1.3 Cavity sidewall slant angle
There is another important parameter in cavity design, the cavity sidewall slant
angle. In Chapter 1, we have mentioned that the cavity sidewalls are not necessarily
vertical. Cavities of inverted-truncated-square-pyramid (ITSP) shape were explored. We
studied ITSP cavities and found similar improvements boresight gain and reduced surface
wave loss as in vertical-sidewall cavities.
However, dipoles backed by ITSP cavities exhibit more interesting properties
with different slant angles. We studied a dipole (L/W=1.75/0.05 µm) backed by cavities
of the same aperture size and cavity depth (X/Y/H = 12/8/1.8 µm) but different sidewall
slant angle (α). As seen in Figure 3.10a, higher-order mode fields are coupled less
strongly to the dipole (as manifested by fewer ripples in the simulated s-parameters) with
decreasing cavity sidewall slant angle. Because higher-order mode fields are more
evanescent and suppressed more effectively in cavities with smaller α, a larger
impedance bandwidth (e.g. 10-dB bandwidth in the s-parameter in Fig. 3.10a) is obtained
for the same sensing dipole. The resulting far-field pattern plot, shown in Fig. 3.10b, also
suggests this trend. The suppression of the both the fundamental TE10 and higher-order
waveguide modes also gives rise to a decreasing boresight gain and greater beamwidth,
since the equivalent cavity aperture is smaller and the beam is not confined as effectively
as in a vertical cavity.
47
(a)
(b)
Fig. 3.10
Simulated (a) s-parameters and (b) boresight gain and 3-dB E-plane
beamwidth of a dipole (L/W = 1.75/0.05 µm) backed by cavities (X/Y/H = 12/8/1.8 µm)
with different slant angle.
48
To further relate the sidewall slant angle to antenna-coupled diode detector
performance, we look at a case when an MOM detector diode is placed at the center feed
point of the dipole/cavity structures. As shown in Appendix A4, the antenna-coupled
diode detection is a two-step process: power coupling by the antenna followed by
nonlinear conversion and detection by the diode. Furthermore, an antenna's coupling
capability is best characterized by its effective area, as summarized in Appendix A3. The
effective area is given by the ratio of the captured power to the incident radiation power
density.
Assuming the antenna is loaded with a 50×50 nm square MOM diode junction
with a capacitance (Cd) of 0.1 fF (2 nm thick MOM diode oxide, εr=10), Fig. 3.11a shows
the simulated effective area of a dipole (L/W= 1.75/0.05 µm) backed by cavities with the
same dimensions (X/Y/H=12/8/1.8 µm) but different sidewall slant angle. The sidewall
slant angle clearly influences both peak effective area and signal bandwidth (see
Appendix A4 for bandwidth definition in antenna-coupled diode detectors). The sidewall
angle, therefore, allows for tuning of the sensitivity-bandwidth product in future
applications. To illustrate this point more clearly, peak effective area and relative
bandwidth are shown in Fig. 3.11b. It is seen that while using a vertical cavity can
increase the peak Ae nearly 2.5 times compared to using a 45o ITSP cavity, it is also
accompanied by 75% reduction of the detector's bandwidth.
49
(a)
(b)
Fig. 3.11
Simulated (a) antenna effective area and (b) peak effective and detector
bandwidth of a dipole (L/W = 1.75/0.05 µm) backed by cavities (X/Y/H = 12/8/1.8 µm)
with different slant angle.
50
3.2.1.4 Filling dielectric permittivity
All the studies summarized in previous sections are based on cavities filled with
BCB (εr=2.7). The choice of filling dielectric materials, however, is not limited to only
BCB. Any low-loss dielectric with good filling properties is a potential candidate. In the
cavity design, the most important selection criterion is the permittivity (εr) of the
dielectric. We now study its impact on antenna radiation pattern and radiation resistance.
As discussed in Chapter 1, for a dipole placed at air/dielectric interface, the ratio
of substrate side to air-side radiation becomes greater on higher permittivity dielectrics.
Dielectric-filled cavity-backed dipole antennas show similar behaviors. Table 4 lists a
number of dipole and cavity geometries for designs aiming at a resonance of 28.3 GHz. It
is seen in Fig. 3.12a that stronger substrate mode fields are excited with increasing
permittivity of the filling dielectric materials. The boresight gains at 28.3 THz, plotted in
Fig. 3.12b, are essentially the same for all these structures, while higher resonant
resistances are attained when using low-εr filling dielectrics. We found in our study that
1
the resonant resistance appears to have a (
εr + 1 −2
) dependence on εr (0.992 correlation),
2
1
ε +1 −
suggesting a good scaling potential in cavity/dipole design. The ( r ) 2 dependence is
2
well known in conventional microstrip transmission line and microstrip antenna designs.
Considering that cavity sidewalls can be treated as electric-wall boundaries at infinity for
microstrip lines and microstrip antenna, it is only reasonable for a cavity-backed dipole
1
ε +1 −
antenna to exhibit a similar ( r ) 2 dependence.
2
51
TABLE 4
DIPOLE AND CAVITY GEOMETRIES WITH DIFFERENT FILLING DIELECTRICS
εr
L (µm)
X (µm)
Y (µm)
H (µm)
1
2.50
15.0
10.0
2.55
1.5
2.20
13.5
9.25
2.20
2.25
1.85
12.5
8.50
1.90
2.7
1.75
12.0
8.00
1.80
3.3
1.63
11.2
7.45
1.67
3.6
1.59
10.85
7.25
1.62
Note: Dipole with is fixed at 50 nm. The antennas are designed to have resonance close to 28.3 THz with
single-beam and high boresight gain operation.
52
(a)
(b)
Fig. 3.12
Simulated (a) s-parameters and (b) boresight gain at 28.3 THz and
resonant resistance of different cavity and dipole geometries (see Table V). The resonant
1
resistance shows a (
εr + 1 −2
) dependence.
2
53
3.2.2 Dipole parameters
3.2.2.1 Dipole length
Among all the dipole design parameters, the most important is dipole length (L).
The dipole length primarily determines the dipole resonant frequency and input
impedance for fixed cavity geometries. We found in our numerical experiments that too
short a dipole does not have a resonance, consistent with previous studies [57]-[58]. Our
research also has concluded that boresight gain is essentially independent of dipole length
for a given cavity, a point illustrated in Fig. 3.13. It is seen that while the boresight gain
at 28.3 THz is essentially unchanged (~10 dB) for dipoles with different lengths, the
resonant frequency of the dipole decreases with increasing dipole length. The resonant
frequency appears inversely proportional to the dipole length in our numerical study. This
is not entirely surprising, since a thin dipole without backing cavity should scale as
approximately 1/L from simple theory.
The input impedance at a given frequency does change substantially for different
length dipoles, as shown in Fig. 3.14a. On the other hand, the resonant resistance –
defined as the resistance seen at the antenna's resonant frequency – only varies
moderately with dipole length as shown in Fig. 3.14b. In addition, the boresight gain at
resonance also changes along with dipole length monotonically, indicating less efficient
coupling to the cavity fields with increasing dipole length.
54
Fig. 3.13
Simulated boresight gain at 28.3 THz and resonant frequency of different
dipoles (fixed W=50 nm) backed by a BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The
resonant frequency from simulation shows a 1/L dependence, as expected.
55
(a)
(b)
Fig. 3.14
Simulated (a) input impedance (resistance R and reactance X) at 28.3 THz
and (b) resonant resistance and boresight gain of dipoles as a function of length (W=50
nm) backed by a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).
56
3.2.2.2 Dipole width
Similar to a simple dipole antenna [56], dipole width (W) has a direct impact on
the input impedance bandwidth of a cavity-backed dipole antenna. To quantify its
influence, we studied feed dipoles with same length (L=1.75 µm) but different widths.
The dipoles are backed by the same BCB-filled cavity (X/Y/H=12/8/1.8 µm). Figure 3.15
shows the simulated scattering parameters for three dipole widths. The input impedance
bandwidth (e.g. 10-dB bandwidth) increases along with an increase in dipole width.
To further illustrate the bandwidth increase, we plot the antenna effective area, Ae,
in Fig. 3.16a, assuming an MOM diode with 0.1 fF junction capacitance is fed to these
dipoles. The peak Ae is seen to remain virtually the same, while the operation bandwidth
displays a noticeable increase. The peak effective area and detector bandwidth are
summarized in Fig. 3.16b. When a 100 nm wide dipole is used instead of a 10 nm wide
dipole, the detector fractional bandwidth increases from 6.5% to 9.8% (an increase of
~50%), while its peak Ae only decreases by 1.5%.
57
Fig. 3.15
S-parameters of dipoles of different widths (L = 1.75 µm) backed by a
BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The impedance bandwidth increases for wider
dipoles.
58
(a)
(b)
Fig. 3.16
Simulated (a) antenna effective area and (b) peak effective area and
detector bandwidth of dipoles (L = 1.75 µm) backed by a cavity (X/Y/H = 12/8/1.8 µm)
as a function of dipole width.
59
3.2.2.3 Dipole position
The boresight gain is also sensitive to the dipole position in the cavity, namely the
position in the aperture plane as well as the vertical position within the cavity. We discuss
the position in the aperture plane first.
The antenna's boresight gain and input impedance are both sensitive to the
dipole's position in the aperture plane. Figure 3.17 plots the gain of a dipole at different
positions in the cavity aperture plane. The origin is defined as the center of the
rectangular aperture plane. It is seen that maximum boresight gain is achieved when the
dipole is centered at the cavity aperture plane, suggesting a maximum and most efficient
coupling between the symmetric dipole fields and the cavity modes. The input impedance
is also strongly dependent to the dipole position, as shown in Fig. 3.18, since the aperture
fields dictate the input impedance of the dipole. Previous studies have reported similar
observations [58].
The vertical dipole position is equally important for dipole/cavity design. It is
interesting to notice in Fig. 3.19 that the boresight gain does not change significantly
along with the vertical position of the dipole in the cavity, but the input impedance – the
reactance in particular – does. The dipole reactance is inductive when the diode is inside
the cavity (Z<0), because evanescent higher-order mode fields inside the cavity are
potentially more inductive. However, when the dipole is positioned above the aperture
plane (Z>0), it operates much like a dipole in vacuum. Since the resonant frequency of
the dipole (L=1.75) is 38 THz in vacuum, its input reactance is capacitive at 28.3 THz.
60
Fig. 3.17
Simulated boresight gain at 28.3 GHz of a dipole (L/W = 1.75/0.05 µm) at
different positions in the aperture plane (X/Y/H = 12/8/1.8 µm). The origin is defined as
the center of the rectangular aperture plane.
61
(a)
(b)
Fig. 3.18
Simulated antenna (a) input resistance and (b) reactance at 28.3 GHz of a
dipole (L/W = 1.75/0.05 µm) at different positions in the aperture plane (X/Y/H =
12/8/1.8 µm). The origin is defined as the center of the rectangular aperture plane.
62
Fig. 3.19
Simulated input resistance and gain at 28.3 GHz of a dipole (L/W =
1.75/0.05 µm) at different vertical position in the cavity (X/Y/H = 12/8/1.8 µm). The
reference position is defined when the dipole is in the aperture plane.
63
3.2.2.4 Metal loss
The metal loss should also be examined carefully in dipole/cavity design, because
the structure is aiming to operate at infrared frequencies. Metal loss is taken into account
in the numerical simulation using the skin-depth approximation. A detailed treatment of
this approximation is included in Appendix A6. We found a typical metallic structure
adds an extra 20 Ω into the antenna resistance and lowers the power gain by 1.2 dB in the
boresight.
Figure 3.20 shows a comparison of the simulated cavity-backed dipole antenna's
input resistance around resonance (28 THz) for perfect electric conductor (PEC) and
using the skin-depth approximation for Aluminum strip modeling. Dipole strips are
assumed to be 50 nm wide and 60 nm thick. The resistance is seen to increase by 20 Ω
throughout the frequency range with the inclusion of the metal loss in the simulation. The
added metal resistance lowers the antenna's power gain and efficiency. The boresight
gain in these two cases are found to have a 1.2 dB difference in the boresight direction, as
shown in Fig. 3.21. Accordingly, the radiation efficiency is lowered due to this metal loss.
We plot the radiation efficiency of this dipole/cavity structure along with it boresight
directivity in Fig. 3.22. It is noticed that even with metal loss, an 80% radiation efficiency
can be achieved around the resonant frequency of 28.3 THz.
64
Fig. 3.20
Input resistance of dipoles (L/W = 1.75/0.05 µm) using PEC and skindepth approximation on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).
65
(a)
(b)
Fig. 3.21
(a) E- and (b) H-plane radiation pattern of dipoles (L/W = 1.75/0.05 µm)
using PEC and skin-depth approximation on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).
66
Fig. 3.22
Simulated radiation efficiency and directivity of a dipole (L/W = 1.75/0.05
µm) on a BCB-filled cavity (X/Y/H = 12/8/1.8 µm). The metal loss is calculated using
the skin-depth approximation.
67
CHAPTER 4
ANTENNA EXPERIMENTAL VALIDATION
4.1 Scale model experiments
4.1.1 Scale model design
Antennas are known to display good scalability with frequency, and advanced
concepts can often be explored efficiently by evaluating a low-frequency prototype
before more complex high frequency designs with increased parasitics and complexity
are implemented. For example, a 1000× downscaling in frequency for 28.3 THz antennacoupled MOM diode infrared detectors means the scale model antenna operates at 28.3
GHz (K-band). Applying the appropriate geometric scaling results in cavity and dipole
dimensions on the scale of several millimeters vs. several micrometers for the infraredfrequency structure. A 1000× larger dipole/cavity structure also lends itself to wellestablished microwave/millimeter-wave antenna measurement technologies, and permits
more complete characterization of the radiation performance of the design.
The 1000-fold size increase in antenna and cavity dimensions also leads to some
important design considerations for the scale model prototypes. Because the cavity depth
increases to several millimeters in the scale model, it is well beyond the thickness of
typical Silicon substrates (0.6 mm). Hence, circuit board materials appear more suitable
for prototype construction. Accordingly, board milling process were used instead of
Silicon substrate micromachining. Secondly, filling dielectrics other than BCB (εr=2.7)
68
should be explored for process compatibility, since millimeter-scale BCB layers are
difficult to achieve in practice. Viable candidates include Polyimide (εr=2.6), Teflon
(εr=2.1), and poly methyl-methacrylate (PMMA, εr=2.25). We choose to use PMMA in
our experiments because of its low dielectric constant and similar processing to BCB.
Applying the design rules summarized in Chapter 3, we determined the "optimal"
cavity size for a dipole antenna operating at microwave frequencies. Figure 4.1a shows
the simulated boresight gain and its equal-gain contour of a dipole (L/W=1.54/0.38 mm)
on PMMA-filled cavities with different aperture size (X and Y) while fixing the cavity
depth (H). It is seen that at 28.3 GHz, high boresight gain (~10 dB) is achieved when the
aperture is within the "optimal" neighborhood (X/Y=13/8.5 mm). Similar to the findings
described in Chapter 3, smaller apertures result in a broader beam and lower boresight
gain, while larger apertures allow higher-order modes and grating lobes in the far-field.
The dipole resonant frequency decreases with increasing dipole length and the
boresight gain at a given frequency is mainly determined by the cavity size while
virtually independent of the dipole length as shown in Fig. 4.1b. We also notice the
resonant frequency does not appear to scale directly with the reciprocal of dipole length.
Further simulations indicate that the resonant frequency of thinner dipoles (W=0.05 mm)
does exhibit a good 1/L dependence. We conclude that a thin-wire condition (W<0.02λ0,
λ0: free-space resonant wavelength) must hold for the dipole resonant frequency to have
1/L dependence. However, using "fat" dipoles (W=0.38 mm) is sufficient to demonstrate
the antenna operation principles, while making the fabrication of the scale model easier.
69
(a)
(b)
Fig. 4.1
(a) Simulated boresight gain at 28.3 GHz for a dipole (L = 1.54 mm) on
PMMA-filled cavities with different aperture (X and Y) and fixed depth (H=1.905 mm).
(b) Simulated boresight gain at 28.3 GHz and resonant frequency of different dipole
length (fixed W=380 µm) on a PMMA-filled cavity (X/Y/H = 13/8.5/1.905 mm).
70
4.1.2 Antenna feed design
Direct verification of the proposed cavity-backed dipole antenna design requires a
comparison of simulated antenna impedance and radiation pattern against measured
performance. For a complete and accurate characterization, a dipole feed network must
be designed. Because dipoles are balanced structures with two arms, while typical test
equipment is single-ended, an intermediate stage to convert between balanced and
unbalanced signals using a balun between the dipole and signal source is necessary.
The geometry of the balanced dipole arms suggests they are essentially coplanar
striplines (CPS). On the other hand, the single-ended signal source can most easily be
introduced using either microstrip line or coplanar waveguide (CPW). For simplicity, we
limit our balun design to a microstrip-line-coupled source. There have been many reports
on microstrip-to-CPS hybrids in the literature [59]-[62]. In our study, we employed a
tapered-ground microstrip balun for its simplicity, compact size, and fabrication
compatibility [62].
A dipole and its balun implemented on a thin substrate are shown in Fig. 4.2. The
dipole arms have balanced inputs due to the 180-degree phase difference of the
microstrip "signal" and "ground" line. A thin (~0.01λ0, λ0: free-space wavelength at
resonance) microstrip layer is used to ensure its transparency for the dipole's far-field
radiation. The bottom ground plane of the microstrip line is tapered to make a proper
transition. In HFSS simulations, we found a steep transition results in poor impedance
match and higher radiation loss, while too gradual a transition can upset the cavity
aperture fields and the far-field radiation pattern.
71
Fig. 4.2
Illustration of a dipole with tapered-ground microstrip feed. Notice the
microstrip ground plane (in red) is tapered and becomes one dipole arm. It has a 180degree phase difference with respect to the microstrip signal line (in black) that forms the
other antenna arm.
72
To characterize the balun's performance, a back-to-back test structure with the
optimized geometries was designed and illustrated in Fig. 4.3a. Key parameters of this
test structure include: microstrip ground width (Wf=4 mm), total length (Ltotal=14.38 mm),
tapered length (Lf=5.5 mm), and microstrip ground length (Le=1 mm). The structure was
fabricated on a 127 µm thick RT/Duroid 5880 substrate (εr=2.2, tanδ=0.001) with ½ oz.
deposited copper. The microstrip line has 380 µm trace width and a 50 Ω characteristic
impedance on the Duroid substrate. The front and backside view of the structure after
fabrication are shown in Fig. 4.3b and c.
The structure was clip-mounted on a Wiltron universal test fixture (model 3680V).
Its two-port scattering parameters were measured using an Agilent 8722 vector network
analyzer calibrated by an offset short-open-load-thru standard. When measuring the backto-back structure, we experienced an unexpected open-cavity resonance, which was later
identified due to the fixture's two metallic sidewalls. This problem was solved by
covering both test port planes with absorptive silicone rubber sheets (BSR-1 from
Emerson & Cuming with 135 dB/cm attenuation at 25 GHz). A comparison of the
measured and simulated S11 and S21 of the back-to-back structure is shown in Fig. 4.4. It
is seen in Fig. 4.4 that the structure has very small insertion loss (~0.6 dB) and good
impedance match (-20 dB) over the frequency band of interest (20-30 GHz), and the
measured performance is quite similar to the simulation prediction.
73
(a)
(b)
(c)
Fig. 4.3
(a) Illustration of a back-to-back test structure of tapered-ground
microstrip feed. Front (b) and back (c) view of a fabricated back-to-back test structure.
74
Fig.4.4
Measured and simulated scattering parameters of the back-to-back
structure balun.
75
4.1.3 Prototype fabrication
Antenna scale models with different combinations of dipole length and cavity
geometry were fabricated. Fixed-width (W=380 µm) dipoles with feeds were patterned
by double-sided photolithography on a 127 µm thick RT/Duroid 5880 (εr=2.2,
tanδ=0.001) with ½ oz. deposited copper. The alignment tolerance of the double-sided
lithography is approximately 50 µm. APS-100 copper etchant was used to etch the
pattern with an etching rate of 8 nm/second. Figure 4.5a shows the front and back view of
a fabricated dipole with its feed.
Prototype cavities were constructed by through-board milling on RT/Duroid 6010
laminate. Another piece of Duroid, serving as the cavity bottom, was then attached to the
processed laminate using conductive epoxy. A 500 nm thick Aluminum coating was
sputtered to cover the cavity sidewalls. PMMA (Nano950 from Microchem) was applied
and the PMMA-filled cavity was cured in an oven at 95oC for 35 minutes. Upon
completion of the cavity, the dipole with its microstrip feed was glued to the cavity with
careful alignment to the center of the cavity aperture. A finished dipole-cavity structure is
shown in Fig. 4.5b.
In our experiments, we found multiple filling/curing cycles were necessary to
completely fill up the cavity with PMMA. After loading the dipole/cavity structure into
the oven for PMMA curing, it takes several minutes to rise to the set temperature. We
noticed this ramp rate affects the final PMMA quality. Our experiments indicate a lower
ramp rate typically yields better results. Figure 4.6 plots a recorded oven temperature
profile for a typical curing process.
76
(a)
(b)
Fig.4.5
(a) Front and back view of a fabricated dipole antenna and its feed (b) a
fabricated cavity-backed dipole antenna structure.
77
Fig. 4.6
Typical oven temperature profile in PMMA curing.
78
4.2 Results and discussion
4.2.1 Cavity geometry
A dipole (L/W=1.54/0.38 mm) backed by an "optimal" cavity (X/Y/H=13/8/1.905
mm) was fabricated. A comparison between the measured and simulated radiation
pattern, seen in Fig. 4.7, exhibits a good match to the HFSS simulation. A sidelobe in the
left half of the H-plane due to the microstrip feed line is also seen in the plot. The HFSS
simulation including the feed structure verifies this, as shown in the left half of Fig. 4.7b.
Due to the presence of the dipole, the antenna is expected to have a linear polarization.
As seen in Fig. 4.7, the measured cross-polarization performance of this structure is good,
about 25 dB lower than the co-polarization in the boresight (θ=0o).
The measured boresight directivity and efficiency of this design are shown in Fig.
4.8. The measured high boresight directivity (~10dB), seen in Fig. 4.8a, shows good
agreement with the HFSS simulation over the entire frequency range. Because of the use
of backing cavity, we expect the cavity-backed dipole antenna to have a high efficiency.
The radiation efficiency, measured by comparing the antenna's received power with a
standard gain horn, is plotted in Fig. 4.8b. The cavity-backed dipole including its balun
feed shows peak efficiency of 94% and greater than 70% over the whole frequency range.
The possible sources for the power loss include lossy PMMA, metallic sidewall, and
cross-polarization loss. The proposed cavity–backed dipole antenna demonstrates
favorable performance compared to the "optimal" performance of a perfect electric
conductor (PEC) microstrip dipole on a lossless substrate (εr=2.25), which has an 80%
predicted efficiency and 4 dB boresight gain [32].
79
(a)
(b)
Fig. 4.7
Measured and simulated E- and H-plane pattern at 28.3 GHz for a dipole
(L=1.54 mm) backed by a cavity (X/Y/H=13/8.5/1.905 mm). The H-plane sidelobe is due
to the feed microstrip line.
80
(a)
(b)
Fig. 4.8
(a) Measured and simulated directivity at boresight and (b) measured
antenna efficiency for a dipole (L=1.54 mm) backed by a PMMA-filled cavity
(X/Y/H=13/8.5/1.905 mm).
81
As summarized in Chapter 3, cavity geometries, especially cavity aperture size,
are critical to establish TE10-like cavity mode fields for high boresight gain and singlebeam operation at a given frequency. However, for an optimal cavity design, higher-order
mode fields can be excited at higher frequencies. Figure 4.9 illustrates this point by
showing the radiation pattern of a dipole (L/W=1.54/0.38 mm) backed by a cavity
(X/Y/H=13/8/1.905 mm) at 31 GHz. The cavity is optimized for the dipole at 28.3 GHz
for high-gain and single beam operation. The multi-lobe pattern shown in Fig. 4.9 arises
because high-order mode fields are excited at 31 GHz.
The impact on the radiation pattern due to cavity depth effects was also studied
experimentally. The presence of the metallic cavity bottom suggests the far-field pattern
can be qualitatively understood as a 2-element mini-array radiator, i.e. the dipole and its
image. To achieve a single-beam radiation pattern and maximum radiated power, the
cavity depth must be properly chosen. Fig. 4.10 shows the radiation pattern of a dipole
(L/W=1.54/0.38 mm) backed by a cavity (X/Y/H=13/8/3.175 mm) at 28 GHz. Compared
to the optimal cavity shown earlier, this antenna has the same dipole geometry and cavity
aperture size but larger cavity depth. As seen in Fig. 4.10, the measured pattern shows
qualitatively good match to HFSS simulations. In contrast to the optimal design, strong
sidelobes in both the E- and H-planes are clearly observed at a comparable frequency,
indicating that the cavity depth is excessive in this case.
82
(a)
(b)
Fig. 4.9
Measured (a) E- and (b) H-plane pattern at 31 GHz for a dipole (L=1.54
mm) backed by a cavity (X/Y/H=13/8.5/1.905 mm). The multi-lobe radiation pattern is
due to high-order mode fields excited at the aperture plane.
83
(a)
(b)
Fig. 4.10
Measured and simulated (a) E-plane and (b) H-plane pattern at 28 GHz for
a dipole (L=1.54 mm) backed by a cavity (X/Y/H=13/8.5/3.175 mm). Multiple lobes in
both planes can be clearly seen, indicating the cavity depth is excessive.
84
4.2.2 Dipole length
Figure 4.11 shows the measured and simulated s-parameters of dipoles with
different lengths on a cavity (X/Y/H=13/8.5/1.905 mm) filled by PMMA. For both dipole
lengths, the measured and simulated performances match quite well over the entire
frequency range. Resonant frequencies at 27.9 GHz and 22 GHz are observed. The
measured impedance bandwidth is relatively broader than simulation prediction, due to
device dimension deviations in fabrication. We notice the resonant frequency for dipoles
with different lengths, plotted in Fig. 4.12, decreases with increasing dipole length.
Compared to the optimal design (L=1.54mm), a dipole with longer length
resonates at a lower frequency and has lower resonant boresight gain. Figure 4.13 shows
the measured and modeled boresight gain of a dipole (L=2.0 mm) with the same cavity.
The gain is ~1dB lower than that seen Fig. 4.8a, suggesting less efficient dipole/cavity
mode coupling. This is consistent with our numerical simulation in Fig.3.14b.
4.2.3 Dipole position
We also studied the impact of dipole position by intentionally misaligning the
dipole along the y-axis direction in our optimal design. Figure 4.14 shows the boresight
gain at 28.3 GHz for three different dipole misalignment positions. The boresight gain is
clearly the maximum without misalignment and decreases with increasing misalignment.
This is understood since the highest gain is achieved with maximum coupling between
symmetric dipole and cavity fields. We notice the measured gain is lower than simulation
predictions due to imperfect PMMA film quality.
85
(a)
(b)
Fig. 4.11
Measured and simulated s-parameters of a dipole with length (a) L=1.54
mm and (b) L=2.0 mm backed by PMMA-filled cavity (X/Y/H=13/8.5/1.905 mm).
86
Fig. 4.12
Resonant frequency of dipoles with different lengths backed by the same
cavity (X/Y/H=13/8.5/1.905 mm).
Fig. 4.13
Measured and simulated boresight gain of a dipole (L/W = 2.0/0.38 mm)
backed by a PMMA-filled cavity (X/Y/H = 13/8.5/1.905 mm).
87
Fig. 4.14
Boresight gain at 28.3 GHz of dipoles (L=1.54mm) with different misalignment distance along the y-axis backed by the same cavity (X/Y/H=13/8.5/1.905
mm).
88
CHAPTER 5
SUMMARY
We have developed and experimentally verified a wide-band nonlinear equivalent
circuit model for quasi-TEM coplanar waveguide (CPW) transmission lines fabricated on
low and intermediate-resistivity Si substrates. The model includes nonlinear biasdependent junction conductances and capacitances, which enable the model to scale with
substrate doping concentration and transmission line geometry. We have performed
numerical calculation of the CPW capacitance, based on 2D solutions of Poisson’s
equation, as well as experimental investigations of the dependence of model parameters
on substrate doping type (both n- and p-type) and doping concentration. Measurements of
typical devices show excellent agreement between the model prediction and measured
transmission line s-parameters from 100 MHz to 10 GHz. Our analysis of junction
current transport indicates a full back-to-back metal-semiconductor junction contact
model is required for CPWs on n-type substrates, while the higher Schottky barrier height
of typical metal contacts to p-type Si permits a simplified one-sided junction model that
is suitable for devices on p-type substrates with Schottky contacts, as well as MOS CPW
structures.
We have also explored and demonstrated a simple yet effective scheme to
alleviate surface wave leakage for planar dipole antennas by placing a dielectric-filled
dead-end waveguide section under the dipole. The dielectric-filled cavity-backed dipole
is designed to be compatible with conventional IC fabrication processes for novel
89
antenna-coupled diode detectors in the infrared range. Through 3-D electromagnetic
simulations, our detailed parametric study of antenna design shows that boresight gain
higher than 10 dB can be achieved on a dielectric-filled (εr=2.7) cavity at 28.3 THz, when
the cavity geometries are chosen properly to excite TE10-like mode aperture fields.
Resonant resistances in optimized structures are close to 50 Ω. The dipole resonant
frequency and input impedance are found to be sensitive to the dipole length and its
position in the cavity.
Qualitatively good match of input impedance and radiation pattern has been
obtained in measurements of fabricated K-band scale models. Prototypes were measured
at 28.3 GHz and demonstrated 10 dB boresight directivity and greater than 70% radiation
efficiency. The possible sources of the power loss include lossy filling dielectric material
and lossy metallic cavity sidewalls. The prototype antennas also showed good linear
polarization with –25 dB cross-polarization level at the boresight direction, which is
limited by the dipole feed line and misalignment in processing.
Although the operation principle of cavity-backed dipole antennas has been
demonstrated, many aspects remain to be explored for applications of the structures for
antenna-coupled diode detectors in the infrared range. To implement the proposed design
on Silicon substrates in the infrared range, some important considerations include: 1)
recipe development of dry Si substrate micromachining; 2) cavity dielectrics deposition
and processing; and 3) antenna design in an imaging array. Although standard Bosch
ICP-RIE processes for deep reactive ion etching on Silicon are readily available,
additional effort to develop a recipe yielding slanted sidewall cavities is needed. The
90
dielectric filling and subsequent planarization also require special attention to ensure that
the dielectric fills the entire cavity. Antenna alignment is also critical for determining the
dipole input impedance. As expected, our proposed design has also shown a relatively
high radiation level (about 12 dB lower than the boresight) along the surface in the Eplane. Since the coupling from a neighboring cell is usually undesirable, this may require
additional design considerations for imaging array applications.
91
APPENDIX A1
INFRARED DETECTORS
In this appendix, we will briefly review conventional IR detectors and summarize
key aspects that limit their ability to act as good ultra-fast detectors at room temperature.
Based on the detection mechanisms employed, conventional IR detectors can be
broadly divided into two categories: thermal detectors and photon-counting detectors.
Based on thermal effects that result from a temperature rise due to incident IR radiation,
bolometers, thermopiles, and pyroelectric sensors rely on the temperature dependence of
material properties for converting the induced change in temperature to an electrical
output. Photon-counting IR detectors generate electrical signals due to the change of
electron energy distribution that results from the interaction with incoming IR radiation.
This is typically implemented using small bandgap materials such as InAs, InSb, or
HgCdTe, for which the bandgap energy is comparable to the photon energy to be
detected. Quantum-well infrared photodetectors (QWIPs) based on inter-subband optical
transitions [63]-[64] also have received more and more attention. SiGe/Si QWIPs due to
their potential for monolithic integration with Si readout devices by well-established
CMOS technologies. By tailoring the quantum well parameters, optical transitions from
the medium (λ=3~5 µm) to long wavelength (λ=8~12 µm) infrared range have been
demonstrated [65]. For a nonoptimized device, specific detectivity as high as D*=1×1010
cm-Hz1/2/W was obtained in experiment for 9.5 µm radiation at 77 K [66].
92
Key shortcomings of conventional IR detectors, especially for long wavelength
infrared (LWIR, λ= 8-12 µm) applications, are speed, fabrication compatibility and
operation temperature. Bolometers and thermopiles using exotic materials (VOx, Bi/Sb,
etc.) have high responsivities but are inherently slow, due to the need for the structure to
reach thermal equilibrium. Commercial products have response times in the milli-second
range, which is fundamentally limited by the material properties such as heat capacity
and thermal impedance [67]. Bolometers and thermopiles that are fully compatible with
IC processing, using conventional IC materials (Aluminum, poly-silicon, etc.) have been
demonstrated and show modest detectivities (D*~2×108 cm-Hz1/2/W) [68]-[69].
Response time of these detectors remains about 10 ms. The speed of pyroelectric
detectors, on the other hand, is limited only by the bandwidth of the associated electrical
circuit [67] and the lattice vibration frequency of the active element [70]. PbTiO3-based
pyrodetectors have been reported showing D*~3×108 cm-Hz1/2/W with 10 kHz
bandwidth at 297 K [65]. Pyroelectric IR detectors, however, usually require exotic
materials such as lithium tantalate, lead titanate, and barium strontium titanate, which
make IC compatible processing very difficult. Unlike thermal detectors, photodetectors
using small-bandgap materials require cryogenic cooling to achieve low-noise operation.
This is governed by their detection mechanism, either interband or inter-subband optical
transitions. For QWIPs, another important consideration is the difficulty in coupling of
light into the structure with the electric field polarized along the growth axis in n-type
QWIPs [71]-[73].
93
APPENDIX A2
DIODE NON-LINEARITY
To further understand the nonlinear diode detection process, a brief derivation is
summarized as follows [74]. Let us assume the IR radiation is an un-modulated ac signal
Vd=Vd0 cosωt (a similar argument holds for an amplitude modulated signal, see [75] for a
detailed derivation). The total output current of a diode with nonlinear current-voltage
characteristics, as sketched in Fig. A2.1, is the response to the sum of the diode dc bias
(V0) and ac signal (Vd). This output current can be expressed in a Taylor expansion form
around V0 :
I(V0+Vd) =I(V0)+dI/dV Vd + 1/2 d2I/dV2 Vd2 + … = I1+I2+I3+…
(A2.1)
When Vd is sufficiently small, terms beyond 2nd-order can be ignored in (A2.1).
I
I0
V
V0
Fig. A2.1
A generic nonlinear current-voltage curve of a diode.
94
Let Rd= dV/dI = 1/(dI/dV), three components of the output current are identified
in (A2.1): I1= I(V0), the dc bias; I2= Vd/Rd, the linear response; and I3=1/2 d2I/dV2 Vd2,
the nonlinear output. The time-averaged I3, <I3>, results in a small change in total dc
output current and is the dc output of interest for detection due to nonlinear rectification.
Define diode curvature, γ = (d2I/dV2)/(dI/dV), then <I3> can be rewritten as
<I3> = 1/2 d2I/dV2 <Vd2> = 1/4 d2I/dV2 |Vd|2= 1/4 γ|Vd|2 / Rd
(A2.2)
Diode current sensitivity, Si, is defined as the ratio of dc short-circuit output
current to received ac power.
Si = Idc / Prec = <I3> / Pac = 1/4 γ|Vd|2 / Rd/ (1/2|Vd|2 /Rd) = γ/2
(A2.3)
Similarly, diode voltage sensitivity, Sv, is defined as the ratio of dc open-circuit
output voltage to received ac power.
Vdc= <I3> Rd = 1/4 γ |Vd|2
(A2.4)
Sv =Vdc / Prec = 1/4 γ |Vd|2 / (1/2 |Vd|2 /Rd) = γRd/2
(A2.5)
From (A2.3) and (A2.5), we identify the sensitivity is proportional to the diode
curvature in both current and voltage measure.
95
APPENDIX A3
ANTENNA EFFECTIVE AREA
When an incident wave with power density, Pinc, impinges on an antenna, an ac
voltage is induced to drive a load with input impedance, Zin, at the antenna's feed, as
illustrated in Fig. A3.1. Thevenin's theorem states the load sees an equivalent voltage
source with an open-circuit voltage, Voc, and antenna impedance, Za. The power
delivered to the load, Prec, and the voltage across the load, Vin, are given by
Za=Ra+jXa
Pinc
Voc
Prec
+
Vin
-
Zin=Rin+jXin
Fig. A3.1
A generic illustration of an antenna (Za) with its load (Zin). The incident
power is in the form of an equivalent voltage source.
96
Prec= 1/2 |Vin|2 Re(1/Zin*)
(A3.1)
Vin= Voc Zin/(Za+Zin)
(A3.2)
Combining (A3.1) and (A3.2), we obtain
Prec= 1/2 |Voc|2 Re(Zin) /|Za+Zin|2
(A3.3)
Under polarization and impedance matching condition, the maximum effective
area (Aem) of an antenna is related to its directive power gain (Ga(θ,φ)) [56] by
Aem =Prec/Pinc = 1/4 λ2Ga(θ,φ)/π
(A3.4)
The unit of Aem is m2, since Prec and Pinc have the units of W and W/m2,
respectively. We notice the impedance matching condition (Zin=Za*) in (A3.4) and also
recall (A3.3), the maximum available ac power to the load is
Aem Pinc = |Voc|2 / (8 Re(Za) )
(A3.5)
If there is an impedance mismatch, i.e. Zin≠Za*, (A3.3) still holds. A general
expression for the coupled power and effective area for any load impedance can be
obtained by eliminating Voc in (A3.3) and (A3.5). Thus we obtain the following general
expressions for the power delivered to the load and antenna effective area:
Prec= Aem Pinc 4 Re(Zin) Re(Za) / |Za+Zin|2
(A3.6)
Ae = Prec/Pinc = Aem 4 Re(Zin) Re(Za) / |Za+Zin|2
(A3.7)
From (A3.7) and (A3.4), the antenna effective area is seen to be proportional to
the antenna directive gain and the antenna resistance. An improved matching to the load
also leads to a higher effective area.
97
APPENDIX A4
DETECTOR SENSITIVITY AND BANDWIDTH
Understanding diode non-linearity and antenna coupling (see Appendix A2 and
A3) enables us to analyze an antenna-coupled MOM diode detector. Figure A4.1 shows
an equivalent circuit of the detector. In addition to the diode junction capacitance and
resistance, the diode equivalent circuit model also includes a series resistance (r) due to
metal contact and/or spreading resistance [76].
Antenna
MOM Diode
Prec
Za=Ra+jXa
Pinc
Voc
<I3>
+ r
Vin
Cd Rd
-
+
Vd
-
Zin=Rin+jXin=r+Rd//(1/jωCd)
Fig. A4.1
Equivalent circuit of an antenna-coupled MOM diode detector. Pinc is the
incident radiation power density and Prec is the power delivered to the MOM diode. Vd is
the ac voltage responsible for the nonlinear detection within the MOM diode.
98
Similar to the diode current and voltage sensitivity defined in Appendix A2, the
detector current, Sid, and voltage, Svd, can be defined:
Sid = Idc / Pinc = (Idc/Prec) (Prec/Pinc) = Si Ae
(A4.1)
Svd = Vdc / Pinc = (Vdc/Prec) (Prec/Pinc) = Sv Ae
(A4.2)
The detector sensitivity is the product of two coupled figures of merit: antenna
effective area and diode sensitivity. The antenna effective area dictates the amount of
power coupled to the MOM diode, while the diode sensitivity is responsible for the
nonlinear rectification.
To derive detector sensitivity, the expression for diode sensitivity (Si and Sv) need
to be modified slightly to reflect the presence of the diode series resistance, as shown in
Fig. A4.1. By recalling (A2.2), the short-circuit output current and open-circuit output
voltage, shown in Fig. A4.2, due to the diode nonlinearity are given by [76]:
Idc= <I3> Rd/(r+Rd) = 1/4 γ |Vd|2 / (r+Rd)
(A4.3)
Vdc = Idc (r+Rd) = 1/4 γ |Vd|2
(A4.4)
We recognize the input power and impedance at the diode's RF terminals are:
Zin = r + Rd/(1+jωCdRd)
(A4.5)
Prec = 1/2 |Vin|2 Re(1/Zin*)
(A4.6)
The diode output is also related to its input terminals by
|Vd|2 =|Vin|2 /[(1+r/Rd)2+ω2Cd2r2]
(A4.7)
We can then obtain a simplified relationship of input power and diode output:
Prec = 1/2 |Vd|2[(1+r/Rd)/Rd+ω2Cd2r]
(A4.8)
99
Ishort = <I3>Rd/(r+Rd)
<I3>
r
Rd
Rload=0
(a)
r+Rd
+
Vdc=Ishort(r+Rd)
-
Rload=∞
(b)
Fig. A4.2
Equivalent circuit of an antenna-coupled MOM diode detector with (a)
short-circuit current output and (b) open-circuit voltage output. Notice the series
resistance in the diode equivalent circuit.
100
By plugging (A4.3), (A4.4), and (A4.8) to (A4.1) and (A4.2), we obtain
Si = Idc / Prec = 1/2 γ / [(1+r/Rd)2 + ω2Cd2r(r+Rd)]
(A4.9)
Sv =Vdc / Prec = 1/2 γ / [(1+r/Rd)/Rd+ω2Cd2r]
(A4.10)
Sid = 2γ Aem Re(Zin) Re(Za) / |Za+Zin|2 / [(1+r/Rd)2 + ω2Cd2r(r+Rd)]
(A4.11)
Svd = 2γ Aem Re(Zin) Re(Za) / |Za+Zin|2 / [(1+r/Rd)/Rd+ω2Cd2r]
(A4.12)
where γ = (d2I/dV2)/(dI/dV) and Aem = 1/4 λ2Ga(θ,φ)/π according to (A3.7)
(A4.11) and (A4.12) can be further approximated when the load is an MOM diode.
The junction capacitance (Cd) is estimated 0.1 fF for 2 nm oxide (εr=10) sandwiched by
two 50 nm square metal plates, while r is assumed to be 20Ω and Rd is at least several kΩ.
Furthermore, for 1-10 µm detection applications, ω2Cd2Rdr >> 1 usually holds. Thus
Re(Zin) = r + Rd / [ 1+ ω2Cd2Rd2] ≈ r
(A4.13)
Im(Zin) = -ωCdRd2/ [ 1+ ω2Cd2Rd2] ≈ -1/(ωCd)
(A4.14)
Using (A4.13) and (A4.14) and also considering r << Rd holds for typical r and Rd,
we have an approximate expression of (A3.7), (A4.9), (A4.10), (A4.11) and (A4.12)
Ae = 4Aem r Ra / [(Ra+r)2+(Xa-1/ωCd)2]
(A4.15)
Si = γ /(2ω2Cd2rRd)
(A4.16)
Sv =γ /(2ω2Cd2r)
(A4.17)
Sid ≈ 2γ Aem Ra / [(Ra+r)2+(Xa-1/ωCd)2] / ω2Cd2Rd
(A4.18)
Svd ≈ 2γ Aem Ra / [(Ra+r)2+(Xa-1/ωCd)2] / (ω2Cd2)
(A4.19)
101
As an example of antenna effective area, diode sensitivity, and detector sensitivity,
we studied a cavity-backed dipole-coupled MOM diode detector. The diode is placed at
the center of the dipole and assumed to have an equivalent circuit (shown in the inset of
Fig. A4.3a) with Cd= 0.1fF, r= 20Ω, Rd= 2kΩ, and zero-bias γ=0.1. The dipole (L/W =
1.75/0.05 µm) is backed a BCB (εr=2.7) cavity (X/Y/H = 12/8/1.8 µm). Figure A4.3a
shows the simulated antenna effective area (Ae) and the diode current sensitivity (Si)
using (A4.17) and (A4.15). It is noticed that the antenna effective area exhibits a peak
around 28.5 THz, while the diode sensitivity is a slowly changing function with respect to
frequency. This observation suggests the shape of the detector current sensitivity plot is
dominated by the antenna effective area, since Sid is the product of Ae and Si (see Eq.
A4.1). This is confirmed in the Sid plot, shown in Fig. A4.3b.
To find the detector's bandwidth, we define the detector's operation bandwidth as
its full-width-half-maximum (FWHM) of Sid as shown in Fig. A4.3b. Figure A4.4 plots
the extracted FWHM of several detectors with different circuit parameters. Also shown in
the figure is the FWHM extracted from their antenna effective area. As expected, the
difference between these two bandwidth measures is marginal, as the shape of Sid is
determined by Ae. We conclude both the FWHM of the antenna effective area and
detector sensitivity can be used to characterize the detector bandwidth.
102
(a)
(b)
Fig. A4.3
(a) Antenna effective area and diode sensitivity and (b) detector
sensitivity. The dipole (L/W = 1.75/0.05 µm) is backed a BCB-filled cavity (X/Y/H =
12/8/1.8 µm). The diode equivalent circuit (inset of A4.3a) has Cd= 0.1fF, r= 20Ω and
Rd= 2kΩ.
103
Fig. A4.4
(a) Full-width-half-maximum (FWHM) bandwidth of the antenna-coupled
diode detector. The dipole (L/W = 1.75/0.05 µm) is backed by a BCB-filled cavity
(X/Y/H = 12/8/1.8 µm). A diode capacitance of 0.1fF has been used in this calculation.
104
APPENDIX A5
DETECTOR SIGNAL-TO-NOISE RATIO
The signal-to-noise ratio (SNR) of an antenna-coupled diode detector is critical
for successful low-level infrared signal detection. Signal and noise analysis is also
necessary to decide the proper equipment setting, e.g. pre-amplifier gain and bandwidth,
in low-level measurements. In this appendix, we derive the SNR in measurements using a
current or voltage pre-amplifier.
Figure A5.1a illustrates the equivalent circuit of an antenna-coupled MOM diode
detector. In this circuit, the series resistance is small compared to junction resistance and
has been safely ignored. To gain a quantitative measure of the detector noise, we make
the following assumptions: 1) the antenna is a dipole (L/W=1.75/0.05 µm) backed by a
BCB-filled cavity (X/Y/Z = 12/8/1.8 µm); 2) the incident radiation power density is Pinc
=0.1 W/m2; 3) The antenna and diode are dominated by thermal noise. Based on these
assumptions and also recalling the current sensitivity expression for an antenna coupled
MOM diode detector (A4.18), the signal and noise current at the diode output are:
Id = PincSid= PincA0γ/Rd
(A5.1)
ins = (4kT/ Rd)1/2
(A5.2)
where γ = (d2I/dV2)/(dI/dV) and A0=Ga(θ,φ)Raλ2 / [Ra2+(Xa-1/ωCd)2] / (2πω2Cd2 )
The detector SNRi= Id /ins/∆f1/2 are plotted in Fig. A5.1b for three different
junction resistances.
105
(a)
(b)
Fig. A5.1
(a) Equivalent circuit of an MOM diode (Cd= 0.1fF, Rd= 2kΩ) with its
noise source and (b) detector SNR under 0.1W/m2 incident radiation. The dipole (L/W =
1.75/0.05 µm) is backed a BCB-filled cavity (X/Y/H = 12/8/1.8 µm).
106
When a transimpedance low-noise current pre-amplifier is connected to the
detector output, the added noise due to the pre-amp stage should be included when
calculating the SNR at the pre-amp output. Fig. A5.2a illustrates the equivalent circuit of
a detector with an SR-570 current pre-amp for signal and noise calculation. The pre-amp
noise is represented by an equivalent noise current and noise voltage at its input. As seen
in Fig. A5.2a, the signal voltage, noise voltage, and SNR at SR-570 output are:
Vso = IdRdRf /(Rd+rin) = PincA0γRf /(Rd+rin)
(A5.3)
vno = (4kTRd+ina2Rf2+vna2)1/2Rf /(Rd+rin)
(A5.4)
SNRo = PincA0γ / (4kTRd+ina2Rf2+vna2)1/2/∆f1/2
(A5.5)
where γ = (d2I/dV2)/(dI/dV) and A0=Ga(θ,φ)Raλ2 / [Ra2+(Xa-1/ωCd)2] / (2πω2Cd2 )
To simplify our calculation, we assume a measurement gain of 20nA/V and a
single-RC output filter in SR-570, which gives Rf= 50 MΩ, rin= 1 MΩ, and a noise
bandwidth of ∆f= 600 Hz. Furthermore, we estimate ina= 20 fA/Hz1/2 and vna= 5 nV/Hz1/2
for a typical pre-amp. SNRs at the current pre-amp output for three different diode
junction resistances are plotted in Fig. A5.2b. Compared to the detector SNR shown in
Fig. A5.1b, these output SNRs show similar shapes in all three cases. However, the
output SNR is significantly lowered for a small Rd (~kΩ) diode, because the pre-amp
current noise adds substantially to the total noise when Rd is small, according to (A5.5).
A closer look at (A5.5) reveals ways to improve the output SNR in antenna and
diode design: 1) using a high-gain antenna structure for higher Ga(θ,φ) or A0; 2)
increasing the diode nonlinearirty (γ); 3) designing antenna and diode carefully for better
impedance matching; 4) reducing the diode junction capacitance (Cd).
107
(a)
(b)
Fig. A5.2
(a) Equivalent circuit of an antenna-coupled MOM detector connected
with a transimpedance current pre-amplifier. (b) Signal-to-noise ratio at a transimpedance
current pre-amplifier output.
108
Similarly, we can derive the output SNR when the detector is connected to a
voltage pre-amplifier (e.g. SR-560). Figure A5.3a shows an equivalent circuit of an
MOM diode detector and a voltage pre-amplifier. The open-circuit voltage signal and
thermal noise are:
Vd = IdZd ≈ IdRd= PincA0γ
(A5.6)
vns = (4kTRd)1/2
(A5.7)
When the detector is connected to the voltage pre-amp, the signal voltage, noise
voltage, and SNR at SR-560 output are:
Vso = VdRd/(Zd+Zin) = PincA0γ /(Zd+Zin)
(A5.9)
vno = (4kTRd+vna2)1/2 Zin /(Zd+Zin)
(A5.10)
SNRo = Vso /vno/∆f1/2 = PincA0γ / (4kTRd+vno2)1/2/∆f1/2
(A5.11)
where γ = (d2I/dV2)/(dI/dV) and A0=Ga(θ,φ)Raλ2 / [Ra2+(Xa-1/ωCd)2] / (2πω2Cd2 )
Using the same diode as in the current pre-amplifier calculations and keeping our
assumptions on the incident power, amplifier noise, and noise bandwidth, we plot the
output SNR for different diode junction resistances in Fig. A5.3b. In contrast to the
current pre-amp output shown in Fig. A5.2b, the SNR at a voltage pre-amplifier output is
not noticeably deteriorated by the amplifier noise in all three diodes. This is
understandable because the amplifier noise is much smaller than the diode thermal noise,
according to (A5.11). We conclude voltage pre-amp should be preferred in measurements.
Similar to using current pre-amp, a higher SNR can be achieved by choosing a
high-gain antenna with improved impedance matching and an MOM diode with stronger
nonlinearity and smaller junction capacitance.
109
(a)
(b)
Fig. A5.3
(a) Equivalent circuit of an antenna-coupled MOM detector connected
with a low-noise voltage pre-amplifier. (b) Signal-to-noise ratio at a voltage pre-amplifier
output.
110
APPENDIX A6
METAL LOSS AT INFRARED
Modeling of metal conductivity in the infrared range is important in practice for
accurate antenna performance prediction. In most cavity/antenna structures presented in
this dissertation, metals are assumed to be perfect electric conductors (PEC). In some
cases, a simple skin-depth approximation is made to estimate possible metal loss due to
finite metal conductivity. In this appendix, we will argue that skin-depth approximation is
a simple yet effective method in impedance and loss calculation with slight
overestimation in antenna power gain (~0.5 dB).
Because of finite electron velocity and grain boundaries, conventional scaling
rules for antennas are known to break down in the infrared range and have limited
success in downscaling IR antennas to the microwave range [77]. On the other hand,
metal loss characterization is very hard to measure directly in infrared. A new approach
was recently demonstrated in near- and mid- infrared frequencies by treating metals as
generalized dielectric materials [78].
Considering the success of this dielectric
approximation method (see Fig. A6.1), a fair comparison in numerical simulations
between skin-depth approximation and actual antenna performance is made possible. In
this appendix, we evaluate whether the skin-depth approximation, which is implemented
in many commercial electromagnetic simulation packages, is sufficiently accurate for
calculating the metal loss in the infrared range.
111
Fig. A6.1
A comparison of measured and simulated power of a gold slot-ring
frequency selective surfaces (FSS) [78]. Excellent match between simulation and
measurement over the whole wavelength range is obtained.
Following the dielectric approximation method [78], we simulated the input
impedance and radiation pattern of a simple Al dipole (metal strip length=1.75µm,
width= 50nm, height= 60nm). Figure A6.2 shows the input impedance and power gain of
this dipole using two different methods to approximate its metal loss: the dielectric and
skin-depth approximation. Also shown in Fig. A6.2 is the performance of a PEC dipole.
Compared to a PEC dipole, the shape of the input impedance curve for both
approximations remains qualitatively the same, while the resonant frequency shifts down
by several THz in both cases. We see the metal loss is about 1 dB using the skin-depth
approximation. The skin-depth approximation also slightly overestimates the power gain
(~0.5 dB) compared with dielectric approximation. We thus conclude that skin-depth
approximation offers a fairly good estimation of metal loss and power gain in the infrared.
112
(a)
(b)
Fig. A6.2
A comparison of simulated (a) input impedance and (b) power gain of a
dipole in vacuum using different metal modeling methods: perfect electric conductor,
skin-depth approximation, and dielectric approximation.
113
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