Conventional models of the time-dependent current response to an impulse of injected carriers in an avalanche photodiode assume that carriers travel always at their saturated drift velocities. A Monte Carlo model is used to show that, while this assumption is reasonable for a 1.0 mum avalanche region in GaAs, it significantly underestimates the avalanche speed in a submicron device at high electric fields. The disparity is identified as due to an enhancement in the velocities of carriers to ionisation, defined as the path length to ionisation divided by the time to traverse it. Using the mean values of these velocities in the conventional model produces good agreement with the Monte Carlo results. Comparison with a local ionisation model also suggests that thin APDs will operate more quickly than expected.

The nonlocal enhancement in the velocities of charge carriers to ionization is shown to outweigh the opposing effects of dead space, increasing the avalanche speed of short avalanche photodiodes (APDs) over the predictions of a conventional local model which ignores both of these effects. The trends in the measured gain-bandwidth product of two short InAlAs APDs reported in the literature support this result. Relatively large speed benefits are predicted to result from further small reductions in the lengths of short multiplication regions.

The time response of APDs is conventionally modelled assuming that carriers travel always at their saturated drift velocity. The present study tests this assumption by comparing the distributions of carrier exit times in an avalanche process predicted from this conventional model and from a Monte Carlo model incorporating more realistic transport behaviour. While the two treatments give very similar results in a long (1.0 μm) structure, as the device width is reduced, the results from the conventional model increasingly diverge from those of the Monte Carlo model, with the latter predicting faster avalanche processes, so that in a 0.1 μm thick structure the speed predictions differ by more than a factor of 3. These results confirm that non-equilibrium transport plays an important part in the time response of sub-micron devices, where the conventional modelling approach is inappropriate.

Avalanche photodiodes (APDs) are particularly suited to detecting weak optical signals. However, in general, they suffer from a bandwidth limitation imposed by carrier feedback within the avalanche process. Although faster response times can be obtained by reducing the length of the avalanche region, dead space increasingly degrades the improvement relative to predictions from a purely local ionization model using the same velocities for the carriers. Conventionally these velocities are chosen to be the carriers' saturated drift velocities, vs. However, our recent Monte Carlo (MC) modelling showed that an enhancement in the mean velocities of carriers to ionization in short (<0.3 μm) APDs produces a much faster avalanche speed than a model with similar spatial ionization using saturated drift velocities. This velocity enhancement promises to compensate for the dead space degradation although the extent is not clear. For example, if the velocity enhancement overcompensates, APD bandwidth will be greater than expected from a local ionization model using vs. Since the latter (conventional) model is particularly popular for APD bandwidth a study of its accuracy in a non-equilibrium regime is desirable. The results obtained suggest that APDs with short avalanche regions can be expected to operate more quickly than conventional model predictions, particularly so in very short devices.

The time dependent current response to an impulse of injected carriers is calculated for an avalanche photodiode using Monte Carlo simulation. For low electric fields and long avalanche regions the results agree with the conventional model, which assumes that carriers travel always with their saturated drift velocities. However, while diffusion remains unimportant, for high fields and short avalanche regions, the conventional model underestimates the device speed. Monte Carlo simulations show that the mean downstream average velocity of ionizing carriers is significantly enhanced at high electric fields and agreement is restored if we allow for this effect in the conventional model.

The probability-distribution function (PDF) for impact-ionisation path length is a crucial quantity for understanding and modelling the low-noise behaviour of avalanche photodiodes with short multiplication regions. In these devices the high electric fields needed to produce avalanche narrow the PDE reducing the randomness in ionisation position and hence the noise in the multiplication. A simple method is presented for calculating PDFs using the 'lucky-drift' model. The results are compared with those predicted by corresponding Monte Carlo calculations employing a parabolic energy band deformation-potential optical-phonon scattering and hard-threshold impact ionisation. The overall behaviour expected for the PDF is reproduced by the simple model. However the unphysical, catastrophic assumption made for energy-relaxing collisions in lucky drift results in an unphysical delta function in the PDF which carries a significant weight at high electric fields.

The maximum useful gain of an avalanche photodiode is limited by the excess noise introduced by the stochastic nature of avalanche multiplication. Low avalanche excess noise can only be achieved in bulk materials with disparate electron and hole ionisation coefficients (α and β). The avalanche excess noise of bulk AlxGa1−xAs (x≤0.6) is relatively large as a result of α/β ratios that are close to unity. On the other hand, there is no information on the excess noise characteristics of bulk AlxGa1−xAs with x>0.6. A series of bulk Al0.8Ga0.2As p-i-n and n-i-p diodes were grown and characterised to investigate avalanche behaviour. Measurements indicate that bulk Al0.8Ga0.2As exhibit very low avalanche excess noise as a result of the significantly larger α/β ratio. This silicon-like characteristic is in stark contrast to that of almost all other III–V semiconductors, including InP. The results suggest that low-noise GaAs-based APDs can be realised using Al0.8Ga0.2As as the multiplication medium.

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 characteristics of Al0.8Ga0.2As have been investigated in a series of p-i-n and n-i-p diodes with i-region widths, w, varying from 1 mum to 0.025 mum. The electron ionization coefficient, alpha, is found to be consistently higher than the hole ionization coefficient, beta, over the entire range of electric fields investigated. By contrast with AlxGa1-xAs (x less than or equal to 0.6) a significant difference between the electron and hole initiated multiplication characteristics of very thin Al0.8Ga0.2As diodes (w = 0.025 mum) was observed. Dead space effects in the diodes with w less than or equal to 0.1 mum were found to reduce the multiplication at low bias below the values predicted from bulk ionization coefficients. Effective alpha and beta that are independent of w have been deduced from measurements and are able to reproduce accurately the multiplication characteristics of diodes with w greater than or equal to 0.1 mum and breakdown voltages of all diodes with good accuracy. By performing a simple correction for the dead space, the multiplication characteristics of even thinner diodes were also predicted with reasonable accuracy.

Avalanche multiplication and excess noise were measured on a series of Al/sub 0.6/Ga/sub 0.4/As p/sup +/in/sup +/ and n/sup +/ip/sup +/ diodes, with avalanche region thickness, w ranging from 0.026 /spl mu/m to 0.85 /spl mu/m. The results show that the ionization coefficient for electrons is slightly higher than for holes in thick, bulk material. At fixed multiplication values the excess noise factor was found to decrease with decreasing w, irrespective of injected carrier type. Owing to the wide Al/sub 0.6/Ga/sub 0.4/As bandgap extremely thin devices can sustain very high electric fields, giving rise to very low excess noise factors, of around F/spl sim/3.3 at a multiplication factor of M/spl sim/15.5 in the structure with w=0.026 /spl mu/m. This is the lowest reported excess noise at this value of multiplication for devices grown on GaAs substrates. Recursion equation modeling, using both a hard threshold dead space model and one which incorporates the detailed history of the ionizing carriers, is used to model the nonlocal nature of impact ionization giving rise to the reduction in excess noise with decreasing w. Although the hard threshold dead space model could reproduce qualitatively the experimental results, better agreement was obtained from the history-dependent model.

The impact ionization probability functions, P(x), are effectively histograms of the positions carriers ionize along the field direction, x, which determine the avalanche multiplication properties of a semiconductor device. In this work, we use a Monte Carlo model to investigate the form of these as multidimensional functions; in not just x, but also of the elapsed time, t, and the distance traveled perpendicular to the electric field direction, y. Despite most previous temporal calculations of the avalanche process assuming that all carriers travel at the drift velocity, vd, it is shown that electrons which ionize at the shortest distances travel several times faster than vd. There is also a significant spread in possible velocities with which ionizing carriers travel along the x direction due to diffusion. Diffusive spreading of the ionization probability in both x and y is also described.

The avalanche multiplication noise characteristics of AlxGa1-x,As (x=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 mum down to 0.05 mum. For x=0-0.6, the ratio of the electron to hole ionization coefficients, 1/k, decreases from 3 (for x=0) to 1 (for x=0.6), leading to higher noise in a local prediction as x increases. Measurements for x=0-0.6 in nominally 1 mum 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=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=0-0.6) diodes, thinner Al0.8Ga0.2As structures exhibit excess noise factor that is significantly reduced by the nonlocal deadspace effects.

A systematic study of the role of band edge discontinuities on ionization rates in periodic AlxGa1−xAs/GaAs structures has been performed by measuring the electron and hole multiplication characteristics in a series of submicron AlxGa1−xAs/GaAs multilayer p–i–n and n–i–p structures. These structures comprise alternating 500Å AlxGa1−xAs and GaAs layers in the intrinsic multiplication regions, with a total thickness of up to 0.5 μm. The results show little dependence on initiating carrier type for multiplication region widths above 0.3 μm, nor on whether they originate in GaAs or AlxGa1−xAs. Only alloy-like behavior is observed at all values of multiplication up to the breakdown voltage in contrast to earlier work on single heterojunction structures where a large difference was seen at low values of multiplication between carriers starting in GaAs and AlxGa1−xAs. The microscopic aspects of hot carrier transport in these devices were studied numerically using a simple Monte Carlo model. Simulations suggest that the energy gained from the conduction band edge discontinuity from AlxGa1−xAs to GaAs is offset by the increased energy loss via the higher phonon scattering rate in the preceding AlxGa1−xAs layer. We conclude that AlxGa1−xAs/GaAs multilayer structures offer no electron ionization enhancement.

Electron and hole multiplication characteristics, M-e and M-h, have been measured in AlinfinityGa1-infinityAs (x = 0-0.60) homojunction p(+)-i-n(+) diodes with i-region thicknesses, w, from I mu m to 0.025 mu m and analyzed using a Monte Carlo model (MC). The effect of the composition on both the macroscopic multiplication characteristics and microscopic behavior is therefore shown for the first time. Increasing the alloy fraction causes the multiplication curves to be shifted to higher voltages such that the multiplication curves at any given thickness are practically parallel for different x. The M-e/M-h ratio also decreases as a: increases, varying from similar to 2 to similar to 1 as x increases from 0 to 0.60 in a w = 1 mu m p(+)-i-n(+), The Monte-Carlo model is also used to extract ionization coefficients and dead-space distances from the measured results which cover electric field ranges from similar to 250 kV/cm-1200 kV/cm in each composition. These parameters can be used to calculate the nonlocal multiplication process by solving recurrence equations. Limitations to the applicability of field-dependent ionization coefficients are shown to arise however when the electric-field profile becomes highly nonuniform.

Electron and hole multiplication characteristics, and have been measured in Al Ga As -0.60) ho- mojunction p -i-n diodes with i-region thicknesses, from 1 m to 0.025 m and analyzed using a Monte Carlo model (MC). The effect of the composition on both the macroscopic multiplica- tion characteristics and microscopic behavior is therefore shown for the first time. Increasing the alloy fraction causes the multipli- cation curves to be shifted to higher voltages such that the mul- tiplication curves at any given thickness are practically parallel for different The ratio also decreases as increases, varying from 2t o 1a s increases from 0 to 0.60 in a =1 m p -i-n The Monte-Carlo model is also used to extract ionization coefficients and dead-space distances from the measured results which cover electric field ranges from 250 kV/cm-1200 kV/cm in each composition. These parameters can be used to calculate the nonlocal multiplication process by solving recurrence equations. Limitations to the applicability of field-dependent ionization coef- ficients are shown to arise however when the electric-field profile becomes highly nonuniform.

Electron and hole multiplication characteristics, M/sub e/ and M/sub h/, have been measured in Al/sub x/Ga/sub 1-x/As (x=0-0.60) homojunction p/sup +/-i-n/sup +/ diodes with i-region thicknesses, w, from 1 /spl mu/m to 0.025 /spl mu/m and analyzed using a Monte Carlo model (MC). The effect of the composition on both the macroscopic multiplication characteristics and microscopic behavior is therefore shown for the first time. Increasing the alloy fraction causes the multiplication curves to be shifted to higher voltages such that the multiplication curves at any given thickness are practically parallel for different x. The M/sub e//M/sub h/ ratio also decreases as x increases, varying from /spl sim/2 to /spl sim/1 as x increases from 0 to 0.60 in a w=1 /spl mu/m p/sup +/-i-n/sup +/. The Monte-Carlo model is also used to extract ionization coefficients and dead-space distances from the measured results which cover electric field ranges from /spl sim/250 kV/cm-1200 kV/cm in each composition. These parameters can be used to calculate the nonlocal multiplication process by solving recurrence equations. Limitations to the applicability of field-dependent ionization coefficients are shown to arise however when the electric-field profile becomes highly nonuniform.