Linear-mode single-photon APD detectors - Voxtel …

1 Linear-mode single - photon APD detectors Andrew S. Huntington*, Madison A. Compton, and George M. Williams Voxtel , Inc., 12725 SW Millikan Way, Suite 230, Beaverton, OR USA 97005 ABSTRACT In the past, it has been necessary to operate avalanche photodiodes (APDs) in Geiger mode to perform photon counting. The gain and noise performance of available Linear-mode APDs was too poor to detect the photocurrent pulse from a single photon using existing amplifier technology. We review the performance thresholds required to achieve Linear-mode photon counting, and present measurements from two APD designs that meet the gain and noise requirements. The first design is a previously-reported vertical-junction, electron-avalanche HgCdTe device fabricated from m-cutoff liquid phase epitaxy (LPE)-grown material. These HgCdTe APDs have an excess noise factor of approximately F~1 at a gain of M=150 when measured at 196 K.

2 The second design is a novel InAlAs/InGaAs structure grown by molecular beam epitaxy (MBE) entirely from alloys lattice-matched to InP. The maximum gain found for this new design was as high as M=2000 at 235 K, but the principle of its operation limits the best noise performance of the prototype to gains below M=20, for which it has an excess noise factor of F~ at room temperature (corresponding to k~ when fit to McIntyre s model). This design can be scaled to deliver the same noise performance at higher gains. Keywords: APD, SPAD, photon counting, HgCdTe, InAlAs, InGaAs, InP, excess noise factor, Linear-mode , impact-ionization engineering 1. Linear-mode photon COUNTING A basic Linear-mode APD receiver consists of the APD detector element and a transimpedance amplifier (TIA). The APD converts incident photons to primary photocarriers, and amplifies the resulting primary photocurrent through internal avalanche gain.

3 The TIA converts the APD s current signal into a voltage signal; if a capacitive feedback TIA is used (CTIA), then the voltage will be proportional to the total multiplied charge delivered by the APD. Linear-mode photon counting using such a receiver can be construed in two ways. The most direct comparison to Geiger-mode single - photon -sensitive APDs (SPADs) is a receiver configured as a binary threshold detector: a count is registered when the voltage exceeds a programmed threshold. Like a Geiger-mode SPAD, a thresholded Linear-mode photon -counter will discard signal amplitude information. Such a thresholded receiver can be considered single - photon -sensitive if it has a reasonably high probability of registering a count in response to a single photon signal. Alternatively, it is common to express receiver sensitivity by some measure of a noise-equivalent input.

4 Noise-equivalent power (NEP in W/Hz1/2) is the incident optical power for which a receiver s signal current will be equal to its noise current, expressed as a spectral density in the frequency domain for convenient integration over the receiver s noise bandwidth. Working in the time domain, noise-equivalent photons (NEPh) is the number of photons incident during an integration period for which the receiver s signal will be equal to its noise, expressed in electrons. (Some workers use noise-equivalent input or NEI for this measure, but we prefer NEPh because of potential ambiguity in the detector community between noise-equivalent input and noise-equivalent irradiance.) Accordingly, a Linear-mode receiver with an NEPh=1 can be said to be single - photon -sensitive, as it will measure the photon number of a signal pulse to within a standard deviation of 1 photon .

5 This definition of single - photon sensitivity is both more restrictive and more challenging than the first. We now review the APD performance thresholds required to achieve single - photon sensitivity by either definition. In subsequent sections, we present measurements from two APD technologies which may soon support Linear-mode photon counting. * Thresholded Linear-mode photon Counting Calculation of photon detection efficiency (PDE) for a thresholded Linear-mode APD receiver is based upon the pulse height distribution (PHD) of the APD. Most APDs, including the InAlAs/InGaAs design reported on in this paper, obey McIntyre s PHD. The discrete statistical distribution of multiplied outputs (n) as a function of average gain (M), ionization coefficient ratio (k), and primary photocarrier inputs (a) was found by McIntyre and Conradi to be: 1,2 ()ankknaMcIntyreMMkMMkakknannknanaPHD + + ++ + =)1()1(1111)!

6 (11),(1, (1) where 01)exp()(ttdtzz is the Euler gamma function. McIntyre himself pointed out that he derived (1), and a related commonly-used expression for excess noise factor, =21)1(1)(MMkMMF, (2) for APDs with thick homogenous multiplication layers which can be accurately described by uniform, carrier-history-independent impact ionization ,4 Both the HgCdTe and impact-ionization-engineered (I2E) InAlAs/InGaAs APDs discussed in this paper are measured to have excess noise characteristics that are inconsistent with (2), so it may be wondered whether (1) accurately describes the PHD of this class of APD. In particular, several groups have published data from HgCdTe APDs in which the avalanche gain process did not add any significant amount of excess noise at higher gain,5,6,7 meaning that the measured excess noise factor saturated at F(M)~1 and did not increase with gain.)

7 If k is limited to physically plausible non-negative values, then the least noisy APD described by k=0 in (2) should have F(M)~2 at high gain. Likewise, Lenox et al. have shown through a study of thin-multiplication-layer InAlAs/InGaAs APDs that when noise data is fit to (2), the extracted value for k depends upon multiplication layer Other thin-multiplication-layer APDs of this general variety have been measured with noise levels for which the fit k value changes with gain, and is in fact negative at low The noise performance of thin-multiplication-layer APDs is well explained by carrier-history-dependent impact ionization models including forms published by McIntyre3,4 and Saleh et ,11 We designed the ultra-low-noise InAlAs/InGaAs APD described in this paper using a Monte Carlo implementation of the dead space multiplication theory (DSMT) of Saleh et Our Monte Carlo simulation matches experimental noise data well (Fig.)

8 1), and the simulated PHD has the form of McIntyre s PHD (Fig. 2), supporting the use of (1) to calculate PDE for I2E APDs fabricated from InAlAs/InGaAs. We have not constructed a similar Monte Carlo model for HgCdTe APDs, but speculate that (1) may be used as a limiting case, with k=0. Ma et al. published a Monte Carlo analysis of a APD which demonstrated how the observed F(M)~1 noise performance can arise from the combination of very low k and a large difference in ionization threshold energy for electrons versus holes,13 but did not include a plot of the simulated PHD in their paper. The probability that a given number of primary photocarriers result in an amplified signal less than the receiver s threshold (nth) is found by summing the discrete PHD between a and nth. This is the chance that the pulse of primary current won t be detected.

9 Since the PHD is normalized, the probability that a primary carriers will be detected by a thresholded Linear-mode APD receiver is just one minus this quantity: [9]k = 0k = = Noise FactorMultiplication GainMonte Carlo DSMT Simulation of Heterojunction I2E APDFig. 1. Comparison of excess noise factor measured by Wang et al. for a heterojunction I2E APD9 to our Monte Carlo simulation of the structure. = =thnanLnaPHDaP),(1)(. (3) In the trivial case where a > nth, detection also occurs. For single photon counting, a=1, and the front-end quantum efficiency of the APD ( ) is used to scale the probability of detecting a single primary carrier to the probability of detecting a single photon . InGaAs APDs typically have unity-gain values of around 60% at 1550 nm and over 80% at 1064 nm. A majority of HgCdTe APD work is done in alloy compositions most suitable for operation in the mid-wave infrared (MWIR); the devices described in this paper had a peak quantum efficiency of about 60% at m.

10 It remains to estimate an appropriate threshold level for the receiver. High-bandwidth monolithic heterojunction bipolar transistor (HBT) TIA chips have been brought to market with noise power spectral density as low as 3 pA/Hz1/2, with preamp input impedance below 250 up to 4 Across a 4 GHz bandwidth, this is under 50 V RMS of amplifier noise. Amplifier voltage noise is scaled to charge noise by the input node capacitance. Small-diameter (~25 m) InGaAs APDs manufactured for high-speed telecommunications applications have about pF of capacitance, including their packaging. The junction capacitance of a 25- m InGaAs APD without packaging is on the order of just 20 fF, and bump-bonding an APD die directly to a TIA would incur an additional 15 fF of parasitic HgCdTe APDs often have wider junctions, so even large-area detectors such as the 200- m-square devices reported by Reine et al.