HgCdTe MWIR Back-Illuminated Electron-Initiated Avalanche Photodiode Arrays

Transcription

1 HgCdTe MWIR Back-Illuminated Electron-Initiated Avalanche Photodiode Arrays M. B. Reine, J. W. Marciniec, K. K. Wong, T. Parodos, J. D. Mullarkey, P. A. Lamarre, S. P. Tobin and K. A. Gustavsen BAE Systems Lexington, Massachusetts G. M. Williams Voxtel Inc. Beaverton, Oregon Presented at: Conference 6294, Infrared and Photoelectronic Imagers and Detector Devices II Conference 6297, Infrared Spaceborne Remote Sensing 2006 SPIE Optics and Photonics Meeting August 2006 San Diego, California To be published in: Proc. SPIE 6294 (2006) and Proc. SPIE 6297 (2006) BAE Systems retains all proprietary rights other than copyright, including patent rights. BAE Systems retains the right to make and distribute copies of this paper for internal purposes. BAE Systems retains the right to post a preprint or reprint of this paper on an internal or external server controlled exclusively by BAE Systems, provided such posting is noncommercial in nature and the paper is made available to users without a fee or charge, and provided the following statement appears on the first page or screen of the paper as posted on the server: Copyright 2006 Society of Photo-Optical Instrumentation Engineers. This paper will be published in Proceedings of SPIE, Volumes 6294 & 6297 (2006) and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Dr. Marion B. Reine Principal Engineering Fellow BAE Systems 2 Forbes Road Lexington, Massachusetts (-3638 FAX) marion.reine@baesystems.com -1-

2 HgCdTe MWIR Back-Illuminated Electron-Initiated Avalanche Photodiode Arrays M. B. Reine,* J. W. Marciniec, K. K. Wong, T. Parodos, J. D. Mullarkey, P. A. Lamarre, S. P. Tobin and K. A. Gustavsen BAE Systems Lexington, Massachusetts G. M. Williams Voxtel Inc. Beaverton, Oregon ABSTRACT This paper reports performance data for back-illuminated planar n-on-p HgCdTe electron-initiated avalanche photodiode (e-apd) 4 4 arrays with large-area unit cells ( µm²). The arrays were fabricated from p-type HgCdTe films grown by LPE on CdZnTe substrates. The arrays were bump-mounted to fanout boards and were characterized in the back-illuminated mode. Gain increases exponentially with reverse bias voltage, and gain versus bias curves are quite uniform from element to element. The maximum gain measured is 648 at V for a cutoff wavelength of 4.06 µm at 160 K. For the same reverse bias voltage, the gain at 160 K for elements with two different cutoff wavelengths (3.54 and 4.06 µm at 160 K) increases exponentially with increasing cutoff wavelength, in agreement with Beck s empirical model for gain versus voltage in HgCdTe e-apds. Spot scan data show that both the V=0 response and the gain at V=-5.0 V are quite uniform spatially over the large junction area. To the best of our knowledge, these are the first spot scan data for avalanche gain ever reported for HgCdTe e-apds. Capacitance versus voltage data are consistent with an ideal abrupt junction having a donor concentration equal to the indium counterdoping concentration in the as-grown LPE film. Calculations predict that bandwidths of 500 MHz should be readily achievable in this vertical collection geometry, and that bandwidths as high as 3 GHz may be possible with careful placement of the junction relative to the compositionally interdiffused region between the HgCdTe LPE film and the CdZnTe substrate. Keywords: HgCdTe, photodiode, avalanche photodiode, APD, infrared detector 1. INTRODUCTION The semiconductor alloy Hg 1-x Cd x Te has an energy band structure and other material properties that make it highly applicable to avalanche photodiodes (APDs) over a broad range of useful wavelengths. These advantages of HgCdTe for APDs were elucidated through the theoretical analyses of Leveque et al. 1 They describe two regimes in which the ratio k=α h /α e of the hole ionization coefficient α h to the electron ionization coefficient α e is either much greater than unity or much less than unity. For cutoff wavelengths shorter than approximately 1.9 µm (x=0.56 at 300 K), they predict that α h >>α e because of resonant enhancement of the hole ionization coefficient when the energy gap is near or equal to the spin-orbit splitting energy 0 (=0.938 ev from Ref. 2). This regime, with k=α h /α e >>1, is favorable for low-noise APDs with hole-initiated avalanche. de Lyon et al. 2 exploited this resonant enhancement regime with back-illuminated sixlayer HgCdTe hole-initiated SAM-APD 25-element arrays with µm² unit cells, grown in situ by MBE on CdZnTe, with a cutoff wavelength of 1.6 µm at 300 K, and with gains of at V reverse bias. For cutoff wavelengths longer than approximately 1.9 µm, Leveque et al. 1 predict that the hole ionization coefficient is non-resonant and decreases with increasing cutoff wavelength, while the electron ionization coefficient increases rapidly because of the decreasing electron effective mass, so that the ratio k=α h /α e is quite small, also a condition favorable for low-noise APDs, but now with electron-initiated avalanche. *marion.reine@baesystems.com -2-

3 Initially, there were isolated reports of experimental verification of the predicted small values of k=α h /α e in HgCdTe with cutoff wavelengths longer than 1.9 µm. Nguyen Duy et al. 3 reported k=α h /α e =0.1 for a 2.5 µm front-illuminated planar implanted n-on-p photodiode at 300 K, with a gain of 30 at -30 V bias. By fitting M(V) and I NOISE (V) of p- absorber lateral-collection loophole diodes with a cutoff wavelength of 11 µm at 77 K, Elliott et al. 4 deduced that the reverse bias I(V) curves (for reverse bias beyond -1.4 V) are limited by avalanche (impact ionization) mainly due to one carrier (electron); the largest gain reported is 5.9 at -1.4 V. It was, however, the paper by Beck et al. 5 in 2001 that first reported the clear and compelling advantages of the electroninitiated avalanche process, based on data on MWIR HgCdTe lateral-collection p-around-n photodiodes with p-type absorber regions: avalanche gain increases exponentially with reverse bias voltage, is quite uniform from element to element, and is essentially noiseless (i.e., F(M) 1.0). Soon thereafter, a theory by Kinch et al. 6 of the physics of electron-initiated avalanche in HgCdTe related the large inequity between α e and α h to key features of the band structure of HgCdTe (electron effective mass much smaller than the heavy hole effective mass, no subsidiary minima in the conduction band, and light holes not important). The key features of this theory were substantiated by Monte Carlo simulations by the University of Texas group. 7 Since the seminal papers of Beck et al. 5 and Kinch et al., 6 there have been reports of HgCdTe electron-initiated APDs in other configurations and architectures. Baker et al. 8 report a 1.55 µm range-gated FPA for 3D imaging with a lateral-collection loophole HgCdTe e-apd array having µm² unit cells, cutoff wavelengths of µm and gains over 100 at -7 V, operating at 90 K. Back-illuminated ion implanted planar n + -n - -p e-apd 1 64 arrays grown by MBE on CdZnTe were reported by Vaidyanathan et al. 9 with a gain of 1000 at V for a 4.2 µm cutoff at 78 K, and a gain >100 at -3.5 V for a 10.3 µm cutoff at 78 K. Hall et al. 10 report gain at 78 K of 100 at -12 V for a back-illuminated MWIR n-p-p structure grown by MOVPE on GaAs with an x=0.36 gain layer. More recent results on HgCdTe e-apds in the front-illuminated lateral-collection p-around-n architecture are in Refs In this paper we report new data for back-illuminated MWIR HgCdTe electron-initiated APDs in a 4 4 array configuration with large-area unit cells ( µm²). These are the largest-area HgCdTe e-apd elements yet reported. The large area allowed us to measure spot-scan profiles and to demonstrate, for the first time, that electroninitiated avalanche gain is spatially uniform within the detector active area. 2. OBJECTIVE AND PERFORMANCE GOALS The objective of the work reported herein is to design, develop and demonstrate the feasibility of a back-illuminated vertical-geometry n-on-p HgCdTe electron-initiated avalanche photodiode (e-apd) array suitable for use in an earthbased receiver for free-space infrared communication from planetary 14, 15 satellites. The performance goals for this array are: Active Area: 1 mm 1 mm, divided into a 4 4 array Unit cell size: µm² Operating temperature: 80 K Operating wavelength: µm Bandwidth: 500 MHz Quantum efficiency: >90% Gain: > 500 Dark current/gain: < 1 pa Cutoff wavelength: µm The 4 4 detector array is designed to be flip-chip bump-mounted onto a fanout board that will allow chips with 16 preamplifiers to be mounted adjacent to the 4 4 array. The optical area of mm² is segmented into 16 elements to reduce the junction capacitance seen by each preamplifier. -3-

4 3. HgCdTe e-apd DESIGN The device cross section for our back-illuminated planar n-on-p HgCdTe e-apd is shown in Figure 1. It is fabricated on a single HgCdTe film grown on an IR-transparent CdZnTe substrate. 250 µm Unit Cell CdTe Passivation Indium Bump N-Contact Metal P-Contact N + HgCdTe Layer N - HgCdTe W(V) P-HgCdTe CdZnTe Substrate Antireflection Coating IR Radiation Fig. 1. Cross-section of the back-illuminated planar n-on-p HgCdTe electron-initiated avalanche photodiode. Radiation is incident on the CdZnTe surface, which may have a thin-film antireflection coating or interference filter. Radiation is absorbed within the p-type region, creating electron-hole pairs that diffuse and drift toward the depletion region. The p-side is much more heavily doped than the n-side, so nearly the entire width W of the depletion region lies within the n-region. When the photogenerated minority carrier (electron) reaches the edge of the depletion region, it is accelerated by the strong electric field. It gains energy rapidly and begins the avalanche multiplication process. As reverse bias voltage is applied, the depletion region expands further into the n-region, toward the surface. The field increases, resulting in higher avalanche gain. This architecture has a number of advantages. It is a planar structure. It has high fill factor and high quantum efficiency, with spatially uniform response over its active area. It can be bump-mounted onto a fanout board or onto a Readout Integrated Circuit (ROIC) chip for high-gain multiplexed Focal Plane Arrays. The vertical geometry allows high bandwidth because photocarriers have only a short distance to traverse to the depletion region, and the traversal time can be shortened by acceleration in the effective electric field set up by the favorable compositional grading in the LPE film. 4. ARRAY FABRICATION 4 4 arrays and Test Chips with variable-area diagnostic diodes were fabricated in single-layer p-type HgCdTe films grown by horizontal-slider Liquid Phase Epitaxy (LPE) from Te-solution onto 4 6 cm² near-lattice-matched CdZnTe substrates. (Ref. 16 is a recent review of LPE HgCdTe technology at BAE Systems.) The acceptor is the doubly-ionized Hg vacancy. The Hg vacancy concentration in the p-layer is cm -3. Indium counterdoping at a concentration of cm -3 was introduced during film growth to establish the donor concentration in the n-region. No antireflection coating was used on these first devices, so there is a 21% reflection loss at the CdZnTe entrance surface. Excellent uniformity of HgCdTe alloy composition was achieved in the two films grown for this effort. Such uniformity is typical for LPE HgCdTe technology. Table 1 shows the statistics for predicted cutoff wavelength at T=80 K, as determined from 28 IR transmission spectra taken across the 4 6 cm² film areas. Values for σ/µ of 0.11% and 0.10% illustrate the high degree of compositional uniformity of HgCdTe alloy composition. -4-

5 Table 1. Excellent uniformity of HgCdTe alloy composition is shown by data for projected cutoff wavelength at T=80 K, as determined from 28 IR transmission spectra taken across each 4 6 cm² LPE film. Film PN163 PN177 Average cutoff at 80 K (µm) Std. Dev. (µm) Std.Dev./Average (σ/µ) Max-Min (µm) (Max-Min)/Average Micrographs of a 4 4 e-apd array are shown in Fig. 2. Each µm² unit cell contains a µm² junction area that is nearly fully covered by the n-side metal contact. There is an indium bump in the center of each junction. The p-side ground grid seen in Fig. 2 was incorporated in some of the 4 4 arrays. Fig. 2. Micrographs of a 4 4 e-apd array with µm² pixels. The µm² n-type junction areas are fully covered by n- side contact metals. Indium bumps on the p-side metal contact surround the 4 4 array. 5. ARRAY PERFORMANCE DATA Fig. 3 shows data for the R 0 A product, for the R D A products at reverse bias voltages of -10, -20 and -40 mv, and for the external quantum efficiency (QE) at peak wavelength for a 4 4 e-apd array at 160 K. There is good uniformity of these parameters across the 16 elements. The average value of external QE of about 60% would increase by a factor of 1.27 to 76% if a perfect antireflection coating were to be used. The quantum efficiency is independent of bias voltage over the range from 0 to -40 mv. The cutoff wavelength of this array at 160 K is 4.06 µm, and the wavelength of peak responsivity (in A/W) is 3.88 µm. The series resistances are all near 350 ohm, as determined from the forward-bias I(V) curve at +160 mv. The dark I(V) characteristics at 160 K near zero bias voltage are limited by diffusion current. This is seen clearly in the dark I(V) data shown in Fig. 4 for a µm² element in a 4 4 e-apd array at 160 K. The curve is a plot of the classic Shockley equation for diffusion current, I(V)=(kT/eR 0 ) [exp(ev/kt)-1], where the only variable is the zero-bias resistance R 0 which, for the curve plotted in Fig. 4, we set equal to the value actually measured for this element, ohm. The fit is excellent for over four orders of magnitude at forward bias and out to about -100 mv reverse bias. For larger reverse bias, another dark current mechanism is evident, increasing slowly with increasing reverse bias. (More is said about this additional dark current mechanism in connection with Fig. 8.) -5-

6 1E R D A(-40 mv) R 0 A and R D A (ohm-cm²) 1E+4 1E+3 QE R SERIES (+160 mv)=350 ohm R D A(-20 mv) R D A(-10 mv) R 0 A n-on-p HgCdTe e-apd Test Chip 163-A1 T=160 K λ CO (160 K)=4.06 µm A=250x250 µm² 10 1 QE at Peak Wavelength 1E Element Number Fig. 3. Profiles of R 0 A, R D A and external quantum efficiency (QE) for a 16-element 4 4 e-apd array at T=160 K. Dark Current [I(V)-I 0 ], abs value (A) 1E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 Data for El 54 Calculated with measured Ro Voxtel n-on-p Test Chip 163-A1 T=160 K Area=250x250 µm² Element 54 R 0 =5.06e6 ohm R 0 A=3.16e3 ohm-cm² R SERIES (+160 mv)=379 ohm 1E Bias Voltage (mv) Fig. 4. I(V) data at 160 K for a µm² element in a 4 4 e-apd array. The diffusion current seen in the I(V) data of Fig. 4 is most probably from the p-side rather than the n-side. The n-side carrier concentration is low, around cm -3, and lifetime is probably limited by the Auger-1 recombination process. However, the acceptor in the p-region is the Hg vacancy, which is known to be associated with a strong donor-like recombination center. We estimate the thermal generation rate for n-type HgCdTe to be two orders of magnitude smaller than the thermal generation rate for p-type, for the doping concentrations in these e-apd devices. So we expect approximately two orders of magnitude less diffusion current from the n-side than from the p-side. That the diffusion current is from the p-side is supported by the very good agreement, shown in Fig. 5, between R 0 A data for e-apds at 160 K and the theoretical R 0 A values calculated for p-side diffusion current. The blue data points in Fig. 5 are for µm² e-apd elements from films with cutoff wavelengths of 3.54 and 4.06 µm. The red data points are for 350 µm dia. e-apd elements from films with cutoff wavelengths of 3.92 and 3.94 µm. The curves are the theoretical R 0 A product, calculated for one-dimensional diffusion current from the p-side with the usual equations: 17-6-

7 2 2 2 e e e n i = jsat = g thd = 0A kt kt kt p 0τSR 1 R where e is the electron charge, k is Boltzmann s constant, T is the temperature, j SAT is the saturation current density, g th is the thermal generation rate per unit volume in the p-region, n i is the intrinsic carrier concentration for HgCdTe, p 0 is the thermal equilibrium hole concentration in the p-region, and τ SR is the Shockley-Read lifetime in the p-region. Kinch has given the following expression (Eq. 8 in Ref. 18) for the Shockley-Read lifetime in p-type HgCdTe with Hg vacancy acceptors, which agrees with a broad range of experimental data: τ SR = 9 s n 0 + N ) / C exp( (E C E t kt) cm p 0 1 N HgV where n 0 is the thermal equilibrium electron concentration in the p-region, N C is the effective density of states at the bottom of the conduction band, E C -E t is the position of the recombination center below the bottom of the conduction band (Kinch quotes 30 mev), and N HgV is the concentration of Hg vacancies. For the curves in Fig. 5 we set d=6 µm and N HgV = cm -3. The data for the shortest cutoff wavelength, 3.54 µm, fall below the calculations somewhat, presumably due to g-r current that is exposed as diffusion current becomes smaller at shorter cutoff wavelengths. However, the agreement between our data with cutoffs near 4.0 µm and the predictions is excellent, supporting the conclusion that the experimentally observed diffusion current is from the p-side. 1E+5 250x250 µm² e-apds 1E+4 R 0 A (ohm-cm²) 1E µm dia. e-apds 120 K 1E K 160 K 200 K 1E Cutoff Wavelength (µm) Fig. 5. Blue: R 0 A data at 160 K for µm² e-apd elements from films with cutoff wavelengths of 3.54 and 4.06 µm. Red: R 0 A data at 160 K for 350 µm dia. e-apd elements from films with cutoff wavelengths of 3.92 and 3.94 µm. Curves are the calculated R 0 A for one-dimensional diffusion current from a p-type HgCdTe absorber layer with Hg vacancy acceptors. Fig. 6 shows data for dark current, dark current plus dc photocurrent, and gain for an element in a 4 4 e-apd array at 160 K. Dark current and dark current plus dc photocurrent were measured in successive scans with an HP 4155A Parameter Analyzer. The dc photocurrent was generated by radiation from an unfiltered 1000 K blackbody. Both the dark current and the dark current plus photocurrent increase exponentially with increasing reverse bias voltage. The gain curve plotted on the right-hand axis in Fig. 6 was determined by subtracting the value for dark current from the value for dark current plus photocurrent at each bias voltage. The resulting gain curve M(V) is normalized to unity at V=0: I M(V) = I PHOTO PHOTO (V) = (V = 0) I I ILLUMINATED ILLUMINATED (V) I (V = 0) I DARK DARK (V) (V = 0) -7-

8 The resulting gain curve M(V) is an exponentially increasing function of reverse bias voltage. Current (abs. value) (A) 1E-4 1E-5 1E-6 1E-7 Dark Current + Photocurrent Dark Current n-on-p HgCdTe e-apd 163-A1, El 54 λ CO =4.06 µm T=160 K Area=250x250 µm² 1E+5 1E+4 1E+3 1E+2 Gain 1E-8 Gain Max gain=648 at V 1E+1 1E-9 1E Bias Voltage (V) Fig. 6. Dark current, dark current plus photocurrent, and gain for an element in a 4 4 e-apd array at 160 K. The gain versus bias voltage curves are quite uniform among elements in the same array. This uniformity is illustrated by the M(V) data in Fig. 7 for four elements in each of two 4 4 e-apd arrays in films with different cutoff wavelengths. Fig. 7 shows that there is good agreement between our M(V) data at 160 K for these two films and the empirical model of Beck 6 (dashed curves) for avalanche gain M(V) in HgCdTe e-apds: M(V) = 1+ 2 [2(V V th ) / Vth ], Vth = 6.8 E G where the values for the energy band gap E G that appear in the equation for the threshold voltage V th were calculated from the measured cutoff wavelengths λ CO with the usual relationship E G =hc/λ CO. Beck s model has only one adjustable parameter, the constant of proportionality between the energy gap E G and the threshold voltage V th. Beck uses a value of 6.8 to fit their M(V) data at T=77 K for their front-illuminated p-around-n HgCdTe e-apds with cutoff wavelengths ranging between 2.6 µm and 10.8 µm. The plots of Beck s model in Fig. 7 (dashed curves) are done with this same value of 6.8. There is good agreement between this model and the data for e-apds from our two films with different cutoff wavelengths. This good agreement may be somewhat fortuitous because the empirical model is based on M(V) data for p-around-n diodes with a cylindrical depletion region at 77 K, and our M(V) data are for a different depletion region geometry, mostly one-dimensional for our large-area diodes, and for a higher temperature, 160 K. Our spot scan data taken at 80 K (Fig. 9) suggest a 50% increase in gain from 160 K to 80 K. Nevertheless, the Beck model accounts well for the exponential increase of gain with increasing cutoff wavelength at the same reverse bias voltage for the elements with two different cutoff wavelengths shown in Fig. 7. Data for dark current I DARK (V) and for gain-normalized dark current I DARK (V)/M(V) for four elements in a 4 4 e-apd array at 160 K with a cutoff wavelength of 4.06 µm are plotted versus reverse bias in Fig. 8. There is reasonably good uniformity among the four elements. The dark current is gain-multiplied, increasing exponentially with increasing reverse bias voltage, but the gain-normalized dark current curves are not entirely independent of bias voltage. Moreover, the gain-normalized dark current is significantly above the saturation current expected if the only current mechanism at reverse bias were diffusion current, as seen by comparing the gain-normalized dark current curves to the saturation current I SAT (shown in Fig. 8 by the horizontal dashed line) calculated from I SAT =kt/er 0 with R 0 set at the measured -8-

9 average value of ohm for these four elements. This suggests that another dark current mechanism, in addition to diffusion current, becomes important for reverse bias voltages beyond about -100 mv. One possible source of this additional dark current may be g-r centers within the depletion region, either at the surface or within the bulk, which would generate electron-hole pairs that would experience avalanche gain. More of these centers would be exposed as the depletion region expands with increasing reverse bias, thus resulting in the gradual increase in gain-normalized dark current seen in the data of Fig A1 λ CO =4.06 µm Els 49, 51, 54, 62 n-on-p e-apds Voxtel Test Chips, Lot 1 T=160 K Area=250x250 µm² 100 Gain A2 λ CO =3.54 µm Els 36, 38, 48, 88 1 Beck model : M(V) = 1+ 2 V th = 6.8 E [2(V Vth ) / Vth ] G Bias Voltage (V) Fig. 7. Data for gain versus bias voltage at 160 K for four elements from each of two 4 4 e-apd arrays from two films with different cutoff wavelengths. The dashed curves are calculated from Beck s phenomenological model 6 for avalanche gain in HgCdTe e-apds. I DARK and I DARK /M (abs. value) (A) 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 I DARK I DARK /M Voxtel n-on-p Test Chip 163-A1 T=160 K Elements 49, 51, 54, 62 Area=250x250 µm² I SAT =kt/er 0 T=160 K R 0 A=2860 ohm-cm² R 0 =4.6e6 ohm 1E Bias Voltage (V) Fig. 8. Dark current and dark current divided by gain for four elements in a 4 4 HgCdTe e-apd array at 160 K. The cutoff wavelength is 4.06 µm. The average gain-normalized dark current density is 39 µa/cm² at V. The average gain-normalized dark current at 160 K and V for the four elements in Fig. 8 is 24 na, which corresponds to a gain-normalized dark current density of 39 µa/cm². Lowering the temperature below 160 K should reduce these values considerably. -9-

10 The spatial uniformity of unity-gain response and of avalanche gain were determined by spot scan measurements taken on several elements in a 4 4 e-apd array at 80 K. Incident radiation from a chopped 1000 K blackbody was focused to a near-diffraction-limited spot with reflective optics. A short-wave-pass filter with a 2.5 µm cutoff wavelength was used to achieve a small spot size. A mechanical step-scanner moved the spot across the diode active area in 2.0 µm steps. Spatial profile data are shown in Fig. 9 for one element at 79 K, measured sequentially for V=0 and V=-5.0 V. The profile for V=0 is uniform over the active area, as expected for a photodiode. The effect of applying a reverse bias voltage of -5.0 V is to raise the overall level of the profile due to avalanche gain, but there is no change is overall shape of the profile. The mask dimensions (200 µm wide on 250 µm centers) for the junctions of the 4 4 array elements in the scan direction are shown at the top of Fig. 9, and the spot scan profiles match these dimensions quite well. The response drops when the center of the spot just reaches an edge, and then decreases exponentially due to lateral collection by diffusion. The spatially-dependent avalanche gain, defined as the ratio of the profile at -5.0 V to the profile for V=0, is plotted in Fig. 9 on the right-hand axis. The avalanche gain is spatially uniform, no matter whether collection is vertical (within the junction area) or lateral (outside the junction area). There is a small but consistent increase in the FWHM at -5.0 V compared to the V=0 case by about 2.0 µm, responsible for the small features in the gain profile at the edges of the junction seen in Fig. 9. The average value of the gain is 11.2, somewhat higher than the average value of 7.5 at V=-5.0 V and T=160 K for the four elements in this array shown in Fig. 7. This higher value at 79 K is partly due to the smaller band gap at 79 K versus 160 K, and may be partly due to the different source wavelengths used in the two measurements, but may also be partly due to the temperature dependence of the avalanche mechanism itself. To the best of our knowledge, this is the first report of the spatial behavior of avalanche gain for HgCdTe e-apds. Spot scan data were reported 19 for a front-illuminated p-around-n HgCdTe photodiode at 297 K with a cutoff wavelength of 2.42 µm, but the reverse bias voltage was only 2 V, where the diode has essentially unity gain, 11,12 so there was no information reported about the spatial behavior of avalanche gain. 1E Relative Response 1E-8 1E-9 V=-5 V V=0 163-A1, El 64 T=79 K With filter 0V µm -5V µm Ratio (Gain) 1E-10 Average gain= E Distance (µm) Fig. 9. Spot scan profiles for a µm² unit cell in a 4 4 e-apd array at 79 K, with a cutoff wavelength of 4.24 µm, for V=0 and V=-5.0 V. The ratio of the -5.0 V data to the V=0 data is defined as the gain and is plotted on the right-hand axis. The gain is spatially uniform, with an average value of 11.2 at -5.0 V. Junction capacitance C(V) was measured versus reverse bias voltage on several elements in a 4 4 e-apd array at 80 K. Data for capacitance versus voltage are shown in the graph on the left in Fig. 10. The depletion width W(V), calculated from the measured capacitance data, is plotted versus voltage in the graph on the right in Fig. 10. The capacitance data in Fig. 10 are corrected for stray capacitance. At higher bias voltages, the capacitance data follows the V -1/2 voltage -10-

11 dependence expected for an ideal abrupt p-n junction, all the way out to the maximum reverse bias voltage of 10 V. Analysis of the C(V) data on the basis of a one-sided abrupt junction model gives an average value for the donor concentration in the n-region of cm -3. This value is in excellent agreement with the values of cm -3 and cm -3 from Hall data taken on two annealed piece of this film, and also with the value of cm -3 obtained from the SIMS profile for indium from another piece of this film. The vertical collection geometry of the back-illuminated n-on-p e-apd allows wide bandwidths to be achieved in relatively large-area devices while maintaining uniform spatial response. Estimates of the bandwidths that should be achievable with this geometry are plotted in Fig. 11 for two collection mechanisms, diffusion and drift. The bandwidth is given by 2.4/(2πt) where t is the transit time for a collection distance d. 19 For minority carrier (electron) diffusion, t=d²/d e where D e =(kt/e)µ e and µ e is the electron mobility. For drift, t=d/(µ e E) where E is the effective electric field due to the grown-in composition grading in the LPE film. For our LPE films with cutoffs of 4.0 µm, E is about 20 V/cm, as determined from SIMS profiles. At 80 K, the electron mobility is cm²/v-s, as measured by Hall effect on an unprocessed piece of Film 163 that was annealed to remove Hg vacancies. These bandwidth estimates are plotted in Fig. 11 versus collection distance d. A bandwidth of 500 MHz should be achievable with a collection distance as large as 7 µm, thanks to drift-assisted collection. Wider bandwidths should be possible, with 3 GHz being reached with a 2 µm collection distance. Capacitance (pf) Voxtel 163-A1, El 54 T=80 K Junction area = 200x200 µm² Corrected for stray capacitance N D (avg)=4.5e14 cm -3 El. 54 slope=-1/2 Depletion Width (µm) 10.0 Voxtel 163-A1, El. 54 T=80 K Junction area = 200x200 µm² Corrected for stray capacitance N D (avg)=4.5e14 cm -3 El. 54 slope=1/ Bias Voltage (V) Bias Voltage (V) Fig. 10. Junction capacitance (left) and depletion width (right) versus reverse bias voltage for an element in a 4 4 array at 80 K. 10 Bandwidths Due to Diffusion & Drift (GHz) 1 Diffusion P-type HgCdTe T=80 K x=0.34 λ CO =4.0 µm µ e =4.3e4 cm²/v-s Drift, 20 V/cm Collection Distance (µm) Fig. 11. Estimated bandwidths for a back-illuminated MWIR n-on-p HgCdTe e-apd for collection by diffusion and by drift. -11-

12 6. SUMMARY AND CONCLUSIONS This paper presents new data showing the feasibility of back-illuminated planar n-on-p HgCdTe electron-initiated avalanche photodiodes (e-apds) for high-gain large-area detector arrays. Our 4 4 arrays with µm² unit cells were fabricated in single-layer p-type HgCdTe films grown by LPE on CdZnTe substrates. These are the largest area HgCdTe e-apd elements yet reported. The 4 4 arrays were bump-mounted to fanout boards, although this same backilluminated architecture is equally compatible with bump-hybridization to a silicon ROIC to realize Focal Plane Arrays that feature the high gain and high speed of HgCdTe e-apds. These 4 4 e-apd arrays, characterized in the backilluminated mode, exhibit gain that exponentially increases with increasing reverse bias voltage, which is a characteristic of the electron-initiated avalanche process in HgCdTe. 5 The maximum gain measured is 648 at V for a device in a 4 4 array with a cutoff wavelength of 4.06 µm at 160 K. Gain versus bias voltage curves are quite uniform from element to element, another characteristic of electron-initiated avalanche in HgCdTe. 5 For the same reverse bias voltage, the gain at 160 K for elements in 4 4 arrays with two different cutoff wavelengths (3.54 and 4.06 µm at 160 K) increases exponentially with cutoff wavelength, in agreement with Beck s empirical model 6 for avalanche gain in HgCdTe e- APDs. Spot scan data at 79 K show that both the V=0 response and the gain at V=-5.0 V are quite uniform and wellbehaved over the junction area. To the best of our knowledge, these are the first spot scan data for avalanche gain ever reported for HgCdTe e-apds. Capacitance versus voltage data are consistent with an ideal abrupt junction having an n- region donor concentration equal to the indium counterdoping concentration in the as-grown LPE film. These are, to the best of our knowledge, the first C(V) data ever reported for HgCdTe e-apds. Calculations predict that bandwidths of 500 MHz should be readily achievable in this vertical collection geometry, and that bandwidths as high as 3 GHz may be possible with careful placement of the junction relative to the compositionally interdiffused region between the HgCdTe LPE film and the CdZnTe substrate. ACKNOWLEDGEMENTS This work is being done at the BAE Systems facility in Lexington, Massachusetts, and is funded by Voxtel, Inc. of Beaverton, Oregon under NASA Contract CA28C from the Jet Propulsion Laboratory, Pasadena, California. We acknowledge the collaboration and support of our colleagues at BAE Systems, including Gary R. Woodward, Peter W. Norton, Dr. Paul LoVecchio, John A. Maynard, Dr. Robert T. Carlson, and Dr. Steven R. Jost. We thank Jeff Beck and Dr. Michael Kinch for providing preprints of some of their publications, and Dr. Pradip Mitra for helpful comments on this paper. REFERENCES 1. G. Leveque, M. Nasser, D. Bertho, B. Orsal and R. Alabedra, Ionization energies in Cd x Hg 1-x Te avalanche photodiodes, Semicond. Sci. Technol. 8, 1317 (1993). 2. T.J. de Lyon, B. Baumgratz, G. Chapman, E. Gordon, A.T. Hunter, M. Jack, J.E. Jensen, W. Johnson, B. Johs, K. Kosai, W. Larsen, G.L. Olson, M. Sen and B. Walker, Epitaxial Growth of HgCdTe 1.55 µ Avalanche Photodiodes by Molecular-Beam Epitaxy, Proc. SPIE 3629, (1999). 3. T. Nguyen Duy, A. Durand and J.L. Lyot, "Bulk Crystal Growth of Hg 1-x Cd x Te for Avalanche Photodiode Applications," Mat. Res. Soc. Symp. Proc. 90, 81 (1987). 4. C.T. Elliott, N.T. Gordon, R.S. Hall and G. Crimes, "Reverse breakdown in long wavelength lateral collection Cd x Hg 1-x Te diodes," J. Vac, Sci. Technol. A8, (1990). 5. J.D. Beck, C-F Wan, M.A. Kinch and J.E. Robinson, "MWIR HgCdTe avalanche photodiodes," Proc. SPIE 4454, pp (2001). 6. M.A. Kinch, J.D. Beck, C-F Wan, F. Ma and J. Campbell, "HgCdTe Electron Avalanche Photodiodes," J. Electronic Mat. 33, (2004). -12-

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