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.
A simple Monte Carlo model is used to simulate excess noise characteristics of a range of Al0.6Ga0.4As - GaAs single heterojunction APDs in which the heterojunction is located at varying positions within the avalanche region. Excess noise is shown to depend critically upon the length of Al0.6Ga0.4As layer. The present results suggest that to achieve the lowest noise the Al0.6Ga0.4As layer must be sufficiently long to allow primary electrons to heat up and able to ionize as soon as they cross into the GaAs, but not so long as to allow significant hole ionization in the Al0.6Ga0.4As layer, which leads to noisy feedback processes. The excess noise characteristics of a range of AlxGa1-xAs - GaAs (x = 0.3, 0.45 and 0.6) single heterojunction APDs are measured experimentally. The excess noise is shown to increase with x, which is explained in terms of an increase in the hole ionization coefficient leading to increased noisy feedback chains.
Conventional wisdom suggests that, for low avalanche noise, avalanche photodiodes should operate at low electric fields, where electron and hole ionisation coefficients can differ widely. However, the associated weak ionization requires long multiplication regions, which in turn demand high bias voltages and result in long carrier transit times, reducing device speed. Moreover, multiplication is particularly sensitive to temperature in this region. In this paper we discuss the effects of dead space on reducing noise in short devices and on the associated benefits in predicted response time and reduced temperature sensitivity. The paper is illustrated with work from the Sheffield group.
Realization of high-speed avalanche photodiodes (APDs) requires the use of thin avalanche regions to reduce carrier transit time. A systematic investigation on the effect of dead space on the current impulse response and bandwidth of short APDs was carried out using a random path length model assuming a constant carrier velocity. The results indicate that, although dead space suppresses large multiplication values in a short device to give low excess noise, the number of impact ionization a carrier can undergo in a single transit is reduced. Consequently, multiple carrier feedback processes are necessary to achieve a given multiplication value. This results in an increase in the response time and reduces the bandwidth of short APDs. Conventional local models that take no account of the dead space effect will tend to overestimate the operating speed of these devices.
Conventional models of the time response of avalanche photodiodes (APDs) assume that carriers travel uniformly at their saturated drift velocity, vsat. To test the validity of this drift velocity assumption (DVA) the model was used to compute the distribution of exit times of electrons generated in an avalanche pulse and the results were compared with those of Monte-Carlo (MC) simulations. The comparison demonstrates that, while the DVA is valid for thick (1um) avalanching regions, it does not take account of non-equilibrium effects which occur in thin avalanching regions, nor of the effects of diffusion. As a consequence, the DVA model may increasingly underestimate the speed of APDs as the width of the avalanche region is reduced.
The avalanche multiplication noise characteristics of AlxGa1-xAs (x equals 0-0.8) have been measured in a wide range of PIN and NIP diodes. The study includes determining the effect of the alloy fraction, x, as it varies from 0 to 0.8 while the effect of the avalanche width, w, is investigated by varying it from 1 micrometers down to 0.05 micrometers . For x equals 0-0.6, the ratio of the electron to hole ionization coefficients, 1/k, decreases from 3 (for x equals 0) to 1 (for x equals 0.6), leading to higher noise in a local prediction as x increases. Measurements for x equals 0-0.6 in nominally 1um thick diodes indicates that the excess noise factor can be approximately predicted by the local model. However, as the avalanche width reduces, a lower than expected noise factor was measured. This behaviour is associated with the effect of deadspace, whereby carriers have insufficient energy to initiate ionization for a significant region of the device. The presence of deadspace leads to a more deterministic process, which acts to reduce excess noise. For x equals 0.8 however, its 1/k value is surprisingly high in a bulk structure, leading to noise performance that is primarily determined by the 1/k value and is comparable to that of silicon. Similar to the results of thin AlxGa1-xAs (x equals 0-0.6) diodes, thinner Al0.8Ga0.2As structures exhibit excess noise factor that is significantly reduced by the nonlocal deadspace effects.
Avalanche photodiodes with thin, sub-micron avalanching regions are found to give avalanche noise lower than predicted by conventional noise theory. Measurements of the excess noise on a range of sub-micron GaAs, InP and Si homojunction p-i-n diodes show that the noise decreases as the avalanching width decreases, even though the electron and hole ionization coefficients remain very similar at high electric fields. Simple Monte Carlo modeling of the ionization process suggests that this reduction is due to the increasing importance of the `dead-space', the minimum distance over which carriers need to travel in order to gain the ionization threshold energy. As this dead-space becomes more significant and the subsequent ionization coefficient increases, the ionization process becomes more deterministic and hence the avalanche noise decreases. Modeling also predicts that reductions in avalanche noise can be obtained in p-n junctions where the electric-field varies rapidly and this has now been observed experimentally.
We have measured avalanche multiplication and noise in Si p- i-n diodes with avalanche widths, w, of 0.12 micrometers , 0.18 micrometers and 0.32 micrometers , both for pure electron and mixed carrier injection. Multiplication and excess noise measurements were also performed with hole injection on a n+-i-p+ diode with w equals 0.84 micrometers . Pure electron initiated avalanche noise results were found to be almost indistinguishable in all three layers. The excess noise factor increases dramatically with increasing w when the injection is mixed.
Integration of a laser and modulator is shown to be possible in the InGaAs/AlGaAs material system by growing on a B GaAs substrate and utilizing the piezoelectric effect. The absorption characteristics of the modulator section are initially red shifted due to the built-in piezoelectric field and can be easily blue shifted with applied reverse bias. Since even under lasing conditions there is found to be a significant residual piezoelectric field in the quantum well, the modulator can be biased to a shorter wavelength than the lasing emission. Utilizing these effects a simple two-section laser-modulator device in which the absorber section lies within the laser cavity has been fabricated. The result show that the threshold current of the laser- modulator structure is controlled by the reverse bias voltage and hence absorption in the modulator section.
A systematic study has been carried out to understand how avalanche multiplication is modified by heterojunction band- edge discontinuities in AlxGa1-xAs/GaAs PIN diodes. A series of AlxGa1-xAs/GaAs structures have been investigated with well and barrier thicknesses fixed at 500 angstrom while the periods range from one up to twenty-five. Whereas the band-edge discontinuity of these structures has previously been suggested as responsible for producing large ratios of electron to hole ionization coefficients, this investigation shows that a significant ratio is only present in the thinnest 0.1 μm single period devices and that this is due to 'dead-space' effects rather than that of the heterojunction. In fact the multiplication characteristics of all structures are shown to approach those of the average alloy of the device as the number of periods increase, which also strongly suggests that the role of the heterojunction is insignificant. Varying the Al composition had little or no effect on the ionization coefficient ratio. The measured multiplication behavior is interpreted using a simple Monte-Carlo model which shows that the effect of the band-edge discontinuity is negligible because it is offset by different rates of energy relaxation in GaAs and AlxGa1-xAs.