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. 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