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 02421
G. M. Williams Voxtel Inc. Beaverton, Oregon 97005
Presented at: Conference 6294, Infrared and Photoelectronic Imagers and Detector Devices II Conference 6297, Infrared Spaceborne Remote Sensing 2006
SPIE Optics and Photonics Meeting 13-17 August 2006 San Diego, California
To be published in: Proc. SPIE 6294 (2006) and Proc. SPIE 6297 (2006)
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Dr. Marion B. Reine Principal Engineering Fellow BAE Systems 2 Forbes Road Lexington, Massachusetts 02421 781-863-3043 (-3638 FAX)
-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 02421
G. M. Williams Voxtel Inc. Beaverton, Oregon 97005
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 (250×250 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 -11.7 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 Hg1-xCdxTe 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=αh/αe of the hole ionization coefficient αh to the electron ionization coefficient αe 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
αh>>αe 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=αh/αe>>1, is favorable for low-noise APDs with hole-initiated avalanche. de Lyon et al.2 exploited this resonant enhancement regime with back-illuminated six- layer HgCdTe hole-initiated SAM-APD 25-element arrays with 50×50 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 30-40 at 85-90 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=αh/αe is quite small, also a condition favorable for low-noise APDs, but now with electron-initiated avalanche. ______*[email protected]
-2- Initially, there were isolated reports of experimental verification of the predicted small values of k=αh/αe in HgCdTe 3 with cutoff wavelengths longer than 1.9 µm. Nguyen Duy et al. reported k=αh/αe=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 INOISE(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 electron- initiated 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 αe and αh 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 320×256 FPA for 3D imaging with a lateral-collection “loophole” HgCdTe e-APD array having 24×24 µm² unit cells, cutoff wavelengths of 4.2-4.6 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 -10.5 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. 11-13.
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 (250×250 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 electron- initiated 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 earth- based receiver for free-space infrared communication from planetary satellites.14, 15
The performance goals for this array are:
Active Area: 1 mm × 1 mm, divided into a 4×4 array Unit cell size: 250×250 µm² Operating temperature: 80 K Operating wavelength: 1.5-2.2 µm Bandwidth: 500 MHz Quantum efficiency: >90% Gain: > 500 Dark current/gain: < 1 pA Cutoff wavelength: 2.7-4.0 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 1.0×1.0 mm² is segmented into 16 elements to reduce the junction capacitance seen by each preamplifier.
-3- 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 2×1016 cm-3. Indium counterdoping at a concentration of 4.5×1014 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- 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) 4.136 3.549 Std. Dev. (µm) 0.0045 0.0036 Std.Dev./Average (σ/µ) 0.0011 0.0010 Max-Min (µm) 0.0172 0.0132 (Max-Min)/Average 0.0042 0.0037
Micrographs of a 4×4 e-APD array are shown in Fig. 2. Each 250×250 µm² unit cell contains a 200×200 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 250×250 µm² pixels. The 200×200 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 R0A product, for the RDA 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 250×250 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/eR0)×[exp(eV/kT)-1], where the only variable is the zero-bias resistance R0 which, for the curve plotted in Fig. 4, we set equal to the value actually measured for this element, 5.06×106 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- 1E+5 100
RDA(-40 mV)
1E+4 RDA(-20 mV) 10
RDA(-10 mV) A (ohm-cm²) D R0A
1E+3 1 A and R
0 QE QE at QEPeak at Wavelength R n-on-p HgCdTe e-APD Test Chip 163-A1 T=160 K
λCO(160 K)=4.06 µm RSERIES(+160 mV)=350 ohm A=250x250 µm²
1E+2 0.1 80 85 90 95 100 105 Element Number Fig. 3. Profiles of R0A, RDA and external quantum efficiency (QE) for a 16-element 4×4 e-APD array at T=160 K.
1E-3 Data for El 54 Calculated with measured Ro 1E-4 Voxtel n-on-p Test Chip 163-A1 T=160 K 1E-5 Area=250x250 µm² Element 54
R0=5.06e6 ohm 1E-6 R0A=3.16e3 ohm-cm² ], abs], value (A)
0 RSERIES(+160 mV)=379 ohm
1E-7
1E-8
Dark Current [I(V)-I 1E-9
1E-10 -500 -400 -300 -200 -100 0 100 200 Bias Voltage (mV) Fig. 4. I(V) data at 160 K for a 250×250 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 5×1014 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 R0A data for e-APDs at 160 K and the theoretical R0A values calculated for p-side diffusion current. The blue data points in Fig. 5 are for 250×250 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 17 R0A product, calculated for one-dimensional diffusion current from the p-side with the usual equations:
-6- 1 e e 2 e 2 n 2 = j = g d = i R A kT SAT kT th kT p τ 0 0 SR where e is the electron charge, k is Boltzmann’s constant, T is the temperature, jSAT is the saturation current density, gth is the thermal generation rate per unit volume in the p-region, ni is the intrinsic carrier concentration for HgCdTe, p0 is the thermal equilibrium hole concentration in the p-region, and τSR 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:
9 ⎛ s ⎞⎡n 0 + N C exp(−(E C − E t ) / kT)⎤ 1 τSR = 5×10 ⎜ ⎟⎢ ⎥ cm3 p N ⎝ ⎠⎣ 0 ⎦ HgV where n0 is the thermal equilibrium electron concentration in the p-region, NC is the effective density of states at the bottom of the conduction band, EC-Et is the position of the recombination center below the bottom of the conduction band (Kinch quotes 30 meV), and NHgV is the concentration of Hg vacancies. For the curves in Fig. 5 we set d=6 µm and 16 -3 NHgV=2×10 cm . 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
350 µm dia. e-APDs 1E+3 120 K A (ohm-cm²) A 0 R
1E+2
260 K 160 K 200 K 1E+1 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Cutoff Wavelength (µm)
Fig. 5. Blue: R0A data at 160 K for 250×250 µm² e-APD elements from films with cutoff wavelengths of 3.54 and 4.06 µm. Red: R0A 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 R0A 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 (V) I (V) − I (V) M(V) = PHOTO = ILLUMINATED DARK I (V = 0) I (V = 0) − I (V = 0) PHOTO ILLUMINATED DARK
-7- The resulting gain curve M(V) is an exponentially increasing function of reverse bias voltage.
1E-4 1E+5 n-on-p HgCdTe e-APD Dark Current + Photocurrent 163-A1, El 54 λCO=4.06 µm 1E-5 1E+4 T=160 K Area=250x250 µm²
1E-6 1E+3
Dark Current Gain 1E-7 1E+2 Current (A) value) (abs. Gain 1E-8 1E+1 Max gain=648 at -11.7 V
1E-9 1E+0 -12-11-10-9-8-7-6-5-4-3-2-10 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 Beck6 (dashed curves) for avalanche gain M(V) in HgCdTe e-APDs:
M(V) = 1+ 2[2(V−Vth ) / Vth ] , V = 6.8× E th G where the values for the energy band gap EG that appear in the equation for the threshold voltage Vth were calculated from the measured cutoff wavelengths λCO with the usual relationship EG=hc/λCO. Beck’s model has only one adjustable parameter, the constant of proportionality between the energy gap EG and the threshold voltage Vth. 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 IDARK(V) and for gain-normalized dark current IDARK(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 ISAT (shown in Fig. 8 by the horizontal dashed line) calculated from ISAT=kT/eR0 with R0 set at the measured
-8- average value of 4.6×106 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. 8.
1000 n-on-p e-APDs 163-A1 Voxtel Test Chips, Lot 1 λ =4.06 µm CO T=160 K Els 49, 51, 54, 62 Area=250x250 µm²
100
177-A2 Gain λCO=3.54 µm Els 36, 38, 48, 88 10
Beck model : M(V) = 1+ 2[2(V−Vth ) / Vth ]
Vth = 6.8× E G 1 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 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 model6 for avalanche gain in HgCdTe e-APDs.
1E-4 Voxtel n-on-p Test Chip 163-A1 T=160 K 1E-5 Elements 49, 51, 54, 62 Area=250x250 µm² IDARK I =kT/eR 1E-6 SAT 0 T=160 K
R0A=2860 ohm-cm² R0=4.6e6 ohm 1E-7
/M (abs. value) (A) value) (abs. /M IDARK/M DARK 1E-8 and I DARK
I 1E-9
1E-10 -12-11-10-9-8-7-6-5-4-3-2-10 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 -11.0 V.
The average gain-normalized dark current at 160 K and -11.0 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- 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 reported19 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-7 10000
163-A1, El 64 V=-5 V T=79 K 1E-8 With filter 1000 0V 208.68 µm -5V 210.84 µm
V=0 1E-9 100 Ratio (Gain) Relative Response Relative
1E-10 10 Average gain=11.2
1E-11 1 -250 -200 -150 -100 -50 0 50 100 150 200 250 Distance (µm) Fig. 9. Spot scan profiles for a 250×250 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- 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 4.5×1014 cm-3. This value is in excellent agreement with the values of 4.25×1014 cm-3 and 5.21×1014 cm-3 from Hall data taken on two annealed piece of this film, and also with the value of 4.82×1014 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/De where De=(kT/e)µe and µe is the electron mobility. For drift, t=d/(µeE) 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 4.3×104 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.
10.0 10.0 El. 54 Voxtel 163-A1, El. 54 slope=-1/2 T=80 K Junction area = 200x200 µm² Corrected for stray capacitance -3 ND(avg)=4.5e14 cm
1.0
Capacitance (pF) Voxtel 163-A1, El 54
T=80 K DepletionWidth(µm) Junction area = 200x200 µm² Corrected for stray capacitance El. 54 N (avg)=4.5e14 cm-3 D slope=1/2
0.1 1.0 0.1 1.0 10.0 0.1 1.0 10.0 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
P-type HgCdTe T=80 K x=0.34 Diffusion λCO=4.0 µm µe=4.3e4 cm²/V-s
1 Drift, 20 V/cm Bandwidths Due & Drift to Diffusion (GHz)
0.1 1 10 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- 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 250×250 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 back- illuminated 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 back- illuminated 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 -11.7 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 model6 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 well- behaved 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.
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