Avalanche multiplication and excess noise have been measured on a series of Al Ga1 As–GaAs and GaAs–Al Ga1 As ( = 0 3 0 45, and 0 6) single heterojunction p-i-n diodes. In some devices excess noise is lower than in equivalent homojunction devices with avalanche regions composed of either of the constituent materials, the heterojunction with = 0 3 showing the greatest improvement. Excess noise deteriorates with higher values of because of the associated increase in hole ionization in the Al Ga1 As layer. It also depends critically upon the carrier injection conditions and Monte Carlo simulations show that this dependence results from the variation in the degree of noisy feedback processes on the position of the injected carriers.

Single-photon avalanche diodes (SPADs) are primary devices in photon counting systems used in quantum cryptography, time resolved spectroscopy and photon counting optical communication. SPADs convert each photo-generated electron hole pair to a measurable current via an avalanche of impact ionizations. In this paper, a stochastically self-regulating avalanche model for passively quenched SPADs is presented. The model predicts, in qualitative agreement with experiments, three important phenomena that traditional models are unable to predict. These are: (1) an oscillatory behavior of the persistent avalanche current; (2) an exponential (memoryless) decay of the probability density function of the stochastic quenching time of the persistent avalanche current; and (3) a fast collapse of the avalanche current, under strong feedback conditions, preventing the development of a persistent avalanche current. The model specifically captures the effect of the load's feedback on the stochastic avalanche multiplication, an effect believed to be key in breaking today's counting rate barrier in the 1.55-μm detection window.

Infrared single-photon avalanche photodiodes (SPADs) are used in a number of sensing applications such as satellite laser ranging, deep-space laser communication, time-resolved photon counting, quantum key distribution and quantum cryptography. A passively quenched SPAD circuit consists of a DC source connected to the SPAD, to provide the reverse bias, and a series load resistor. Upon a photon-generated electron-hole pair triggering an avalanche breakdown, current through the diode and the load resistor rises quickly reaching a steady state value, after which it can collapse (quench) at a stochastic time. In this paper we review three recent analytical and Monte-Carlo based models for the quenching time. In the first model, the applied bias after the trigger of an avalanche is assumed to be constant at the breakdown bias while the avalanche current is allowed to be stochastic. In the second model, the dynamic negative feedback, which is due to the dynamic voltage drop across the load resistor, is taken into account, albeit without considering the stochastic fluctuations in the avalanche pulse. In the third model, Monte-Carlo simulation is used to generate impact ionizations with the inclusion of the effects of negative feedback. The latter model is based on simulating the impact ionizations inside the multiplication region according to a dynamic bias voltage that is a function of the avalanche current it indices. In particular, it uses the time evolution of the bias across the diode to set the coefficients for impact ionization. As such, this latter model includes both the negative feedback and the stochastic nature of the avalanche current.

Recently, considerable attention has been placed upon exploiting the negative-feedback effect in accelerating the quenching time of the avalanche current in passively quenched single-photon avalanche-diode (SPAD) circuits. Reducing the quenching time results in a reduction in the total charge generated in the SPAD, thereby reducing the number of trapped carries; this, in turn, can lead to improved after-pulsing characteristics. A passively quenched SPAD circuit consists of a DC source connected to the SPAD, to provide the reverse bias, and a series load resistor. Upon a photon-generated electron-hole pair triggering an avalanche breakdown, current through the diode and the load resistor rises quickly reaching a steady state value, after which it can collapse (quench) at a stochastic time. In this paper we review recent analytical and Monte-Carlo based models for the quenching time. In addition, results on the statistics of the quenching time and the avalanche pulse duration of SPADs with arbitrary time-variant field across the multiplication region are presented. The calculations of the statistics of the avalanche pulse duration use the dead-space multiplication theory (DSMT) to determine the probability of the avalanche pulse to quench by time t after the instant s at which the electron-hole pair that triggers the avalanche was created. In the analytical and Monte-Carlo based models for the quenching time, the dynamic negative feedback, which is due to the dynamic voltage drop across the load resistor, is taken into account. In addition, in the Monte-Carlo simulations the stochastic nature of the avalanche current is also considered.

Impact ionization and avalanche multiplication are conventionally described in terms of ionization coefficients which depend only upon the local electric field. Such a description takes no account of the effect of ionization dead space, within which the population distribution, and hence the ionization coefficient of carriers injected cool approach equilibrium with the high electric field, inhibiting ionization and reducing multiplication. This effect, which increases in importance as device dimensions are reduced, clearly benefits such high field devices as transistors by suppressing parasitic avalanche multiplication. It also improves the performance of avalanche photodiodes (APDs) by reducing the spatial randomness of impact ionization, so that the resulting excess multiplication noise is also reduced. It reduces temperature sensitivity and may also further enhance APD speed. This paper reviews these effects and some theoretical models used to describe them. In memory of Peter Robson, who inspired and encouraged scientists and engineers, young and old.

Single-photon avalanche diodes (SPADs) convert a single photo-excitation event, resulting from the absorption of a photon, into a measurable self-sustaining current in the external circuit consisting of a DC-bias source and a series load resistor. This avalanche current is produced with a certain probability that depends upon the bias voltage and the SPADpsilas structure. The mechanism for generating the self-sustaining avalanche current is the cascade of impact ionizations in the multiplication region of the SPAD, which occurs at or beyond the condition of avalanche breakdown. The breakdown condition corresponds to the smallest electric field (or bias) at which the multiplication factor of an avalanche photodiode becomes infinite, on average; equivalently, it is the smallest electric field at which the breakdown probability is nonzero. In practice, a SPAD is biased slightly above the breakdown voltage to maximize the probability that avalanche breakdown occurs without introducing too many dark carriers (that may result from band-to-band tunneling, for example) that can result in false counts.

The breakdown probability in a single-photon avalanche diode is calculated using a technique formulated by McIntyre that allows for dead space in impact ionization. Breakdown probability increases faster with overbias ratio when the dead space of impact ionizing carriers occupies a larger fraction of the avalanche region width and when the enabled ionization coefficients are more dissimilar. As the avalanche region width, and hence the operating electric field, changes, these effects may compete and partially cancel.

The effects of avalanche region width, ionization coefficient ratio, and dead space on the breakdown time and timing jitter of a single-photon avalanche diode are investigated. Using a random ionization path length model, the breakdown time and the timing jitter are shown to decrease with breakdown probability, but increase with avalanche region width, decreasing ionization coefficient ratio, and ionization dead space. The model is used to compare the dependence of avalanche timing performance in Si and InP on avalanche region width.

We report the first epitaxially grown, double transit region Gunn diode oscillator. The prototype device was operated at its second harmonic of 77 GHz, giving an RF output power of 64 mW as compared with 54 mW from the corresponding single transit region device. Measurements of threshold and breakdown voltage and of RF power support the interpretation of coherent nucleation of Gunn domains in the two transit regions and the satisfactory operation of the device.

Characterization of Geiger-mode avalanche photodiodes operated in gated mode requires fast rising-edge, well-defined over-bias pulses, and effective avalanche quenching. There has not been a suitable circuit that meets both criteria, thus, making systematic characterization and accurate comparison of these devices difficult. We present a capacitive quenching circuit (CQC) that satisfies both criteria and, thus, offers advantages over existing options such as a gated passive quenching circuit (G-PQC) and gated-mode operation without avalanche quenching. Test results using a commercial Si Geiger-mode avalanche photodiode, together with an experimental comparison between the CQC and the standard G-PQC circuit, are reported. The advantages of the CQC over the G-PQC circuit are demonstrated through comparisons of experimental over-bias pulses, distribution of avalanche current pulses, and dark count rate data. By each metric, the CQC is shown to yield results that are superior to those obtained using a standard G-PQC circuit.

A systematic study of avalanche multiplication on a series of In 0.52Al0.48As p+-i-n+ and n +-i-p+ diodes with nominal intrinsic region thicknesses ranging from 0.1 to 2.5 mum has been used to deduce effective ionization coefficients between 220 and 980 kVmiddotcm-1. The electron and hole ionization coefficient ratio varies from 32.6 to 1.2 with increasing field. Tunneling begins to dominate the bulk current prior to avalanche breakdown in the 0.1-mum-thick structure, imposing an upper limit to the operating field. While the local model can accurately predict the breakdown in the diodes, multiplication is overestimated at low fields. The effects of ionization dead space, which becomes more significant as the intrinsic region thickness reduces, can be corrected for by using a simple correction technique

We report a versatile system for measuring excess noise and multiplication in avalanche photodiodes, using a transimpedance amplifier front-end and based on phase-sensitive detection, which permits accurate measurement in the presence of a high dark current. The system, which we have used successfully on a wide variety of materials and device structures, can measure reliably the excess noise factor of devices with a capacitance of up to ∼50 pF.

Photomultiplication, initiated by both pure electron and pure hole injection, has been measured in submicrometer Si p + -i-n + and n + -i-p + diodes with intrinsic region thicknesses w between 0.1 and 0.8 mum, at temperatures between 15 and 420 K. A local analysis is used to extract the values of effective ionization coefficients. Values of bulk ionization coefficients, alpha and beta, are then deduced and parameterized in an extended form of Chynoweth's expression to cover their dependence on both electric field and temperature. Multiplication at various temperatures can be recovered from these bulk coefficients by using a simple dead space correction. beta falls faster with temperature than alpha so that the ionization coefficient ratio, k=beta/alpha, decreases with temperature. Decreasing w reduces this temperature sensitivity, which is weaker than in GaAs, possibly because of the softer ionization threshold in Si

We argue that a piece of paper, of thickness T and width W, can be folded a maximum number N = 0.962 ln(fW/T) times, where f is a factor of order unity, determined by mechanical constraints. N typically takes a value of around six.

The effects of impact ionization in the InGaAs absorption layer on the multiplication, excess noise and breakdown voltage are modeled for avalanche photodiodes (APDs), both with InP and with InAlAs multiplication regions. The calculations allow for dead space effects and for the low field electron ionization observed in InGaAs. The results confirm that impact ionization in the InGaAs absorption layer increases the excess noise in InP APDs and that the effect imposes tight constraints on the doping of the charge control layer if avalanche noise is to be minimized. However, the excess noise of InAlAs APDs is predicted to be reduced by impact ionization in the InGaAs layer. Furthermore the breakdown voltage of InAlAs APDs is less sensitive to ionization in the InGaAs layer and these results increase tolerance to doping variations in the field control layer.

Avalanche multiplication and excess noise have been measured on a series of AlxGa1-xAs-GaAs and GaAs-AlxGa1-xAs (x = 0.3, 0.45, and 0.6) single heterojunction p(+)-i-n(+) diodes. In some devices excess noise is lower than in equivalent homojunction devices with avalanche regions composed of either of the constituent materials, the heterojunction with x = 0.3 showing the greatest improvement. Excess noise deteriorates with higher values of x because of the associated increase in hole ionization in the AlxGa1-xAs layer. It also depends critically upon the carrier injection conditions and Monte Carlo simulations show that this dependence results from the variation in the degree of noisy feedback processes on the position of the injected carriers.

— Avalanche multiplication and excess noisehave been measured on a series of Al Ga 1 As–GaAs andGaAs–Al Ga 1 As ( =03 0 45 , and 0 6 ) single hetero-junction p + -i-n + diodes. In some devices excess noise is lowerthan in equivalent homojunction devices with avalanche regionscomposed of either of the constituent materials, the heterojunctionwith =0 3 showing the greatest improvement. Excess noisedeteriorates with higher values of because of the associatedincrease in hole ionization in the Al Ga 1 As layer. It alsodepends critically upon the carrier injection conditions and MonteCarlo simulations show that this dependence results from thevariation in the degree of noisy feedback processes on the positionof the injected carriers. Index Terms— Avalanche photodiodes (APDs), heterojunctions,impact ionization, noise. I. I NTRODUCTION A VALANCHE photodiodes (APDs) are key componentsof optical datacommunications systems because of theirhigh sensitivity which results from their internal avalanche gain.However,thisinternalgainisprovidedviathestochasticprocessof impact ionization and therefore contributes its own excessnoise.It is well known that excess avalanche noise can be reducedbelow the level predicted by the local model of McIntyre [1] byreducing the avalanche region width . This is because the deadspace, the distance travelled by carriers before their ionizationcoefficient reaches equilibrium with the electric field, becomesa larger fraction of their mean ionization path lengths. The as-sociated reduced uncertainty in ionization position reduces thefluctuations in multiplication and hence in excess noise.The use of heterojunctions in avalanche regions as a meansof reducing excess noise was first proposed by Chin

The mean avalanche current impulse response in an avalanche photodiode exhibits an initial transient and then grows or decays, above or below breakdown, at exponential rates which depend only on the probability distributions of the electron and hole ionization events. The process continues while the electric field profile remains unchanged by the applied bias or the evolving space charge. Below breakdown the distribution in the avalanche duration also exhibits an initial transient and then decays exponentially at the same rate as the mean current. Below breakdown the standard deviation in current decays exponentially at one half of the rate of the mean current, while above breakdown it grows exponentially at the same rate as the mean. Consequently the jitter in a Geiger mode avalanche photodiode becomes independent of time after the initial transients have decayed away. This behavior is quite general and independent of the electric field profile or of the presence of heterojunctions in the multiplication region. Using simple models for carrier transport we find the predicted enhancement in the velocity to ionization of those carriers which ionise shortly after their ballistic dead space significantly speeds up the avalanche dynamics in short devices.