Impact-ionization and noise characteristics of thin III-V avalanchephotodiodes

It is, by now, well known that McIntyre's localized carrier-multiplication theory cannot explain the suppression of excess noise factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and noise characteristics of thin InP, In_0.52 Al_0.48As, GaAs, and Al_0.2Ga_0.8As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-noise-factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess noise factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths     

History-Dependent Impact Ionization Theory Applied to HgCdTe e-APDs

The variation of the gain and the excess noise factor in HgCdTe avalanche photodiodes (APDs) with different junction geometries are compared with published theoretical and numerical work. It is shown that, although some features of the gain curves are reproduced, such as the constant exponential increase in the gain, the theoretical work fails to predict the observed variation of the gain as a function of multiplication layer width. In contrast, a new analytical gain model based on local impact ionization coefficients and a first direct comparison of the prediction of history-dependent impact ionization theory are shown to give a good general fit to the experimental gain data. A generic model of the gain in HgCdTe APDs has been obtained by fitting the analytical local model to gain curves of APDs with various geometries and cut-off wavelengths. The study of different hypotheses on the electric field dependence of the dead-space length and the saturation value of the impact ionization coefficient has shown that a variable dead-space effect has a direct impact on the excess noise of APDs, which is why exact excess noise measurements are necessary to achieve a pertinent estimation of the nonlocal impact ionization function.     

Gain-bandwidth characteristics of thin avalanche photodiodes

The frequency-response characteristics of avalanche photodiodes (APDs) with thin multiplication layers are investigated by means of a recurrence technique that incorporates the history dependence of ionization coefficients. In addition, to characterize the autocorrelation function of the impulse response, new recurrence equations are derived and solved using a parallel computer. The mean frequency response and the gain-bandwidth product are computed and a simple model for the dependence of the gain-bandwidth product on the multiplication-layer width is set forth for GaAs, InP, Al_0.2Ga_0.8As, and In_0.52Al_0.48 As APDs. It is shown that the dead-space effect leads to a reduction (up to 30%) in the bandwidth from that predicted by the conventional multiplication theory. Notably, calculation of the power-spectral density of the photocurrent reveals that the presence of dead space also results in a reduction in the fluctuations in the frequency response. This result is the spectral generalization of the reduction in the excess noise factor in thin APDs and reveals an added advantage of using thin APDs in ultrafast receivers     

Effect of dead space on gain and noise in Si and GaAs avalanchephotodiodes

The effect of dead space on the mean gain, the excess noise factor, and the avalanche breakdown voltage for Si and GaAs avalanche photodiodes (APDs) with nonuniform carrier ionization coefficients are examined. The dead space, which is a function of the electric field and position within the multiplication region of the APD, is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing impact ionization. Recurrence relations in the form of coupled linear integral equations are derived to characterize the underlying avalanche multiplication process. Numerical solutions to the integral equations are obtained and the mean gain and the excess noise factor are computed     

Optimal excess noise reduction in thin heterojunction Al/sub 0.6/Ga/sub 0.4/As-GaAs avalanche photodiodes

It has been recently found that the initial-energy effect, which is associated with the finite initial energy of carriers entering the multiplication region of an avalanche photodiode (APD), can be tailored to reduce the excess noise well beyond the previously known limits for thin APDs. However, the control of the initial energy of injected carriers can be difficult in practice for an APD with a single multiplication layer. In this paper, the dead-space multiplication recurrence theory is used to show that the low noise characteristics associated with the initial-energy effect can be achieved by utilizing a two-layer multiplication region. As an example, a high bandgap Al/sub 0.6/Ga/sub 0.4/As material, termed the energy-buildup layer, is used to elevate the energy of injected carriers without incurring significant multiplication events, while a second GaAs layer with a lower bandgap energy is used as the primary carrier multiplication layer. Computations show that devices can be optimally designed through judicious choice of the charge-layer width to produce excess noise factor levels that are comparable to those corresponding to homojunction APDs benefiting from a maximal initial-energy effect. A structure is presented to achieve precisely that.     

Avalanche Noise Characteristics in Submicron InP Diodes

We report excess noise factors measured on a series of InP diodes with varying avalanche region thickness, covering a wide electric field range from 180 to 850 kV/cm. The increased significance of dead space in diodes with thin avalanche region thickness decreases the excess noise. An excess noise factor of F = 3.5 at multiplication factor M = 10 was measured, the lowest value reported so far for InP. The electric field dependence of impact ionization coefficients and threshold energies in InP have been determined using a non-local model to take into account the dead space effects. This work suggests that further optimization of InP separate absorption multiplication avalanche photodiodes (SAM APDs) could result in a noise performance comparable to InAlAs SAM APDs.     

Effect of stochastic dead space on noise in avalanche photodiodes

A stochastic dead-space model for impact ionization is developed and used to study the effect of the soft nature of the ionization capability of carriers on the excess noise factor of avalanche photodiodes. The proposed model is based on the rationale that the gradual, or soft, transition in the probability density function (PDF) for the distance from birth to impact ionization can be viewed as that resulting from uncertainty in the dead space itself. The resulting soft PDF, which is parameterized by a tunable softness parameter, is used to establish the limitations of the existing hard-threshold ionization models in ultrathin multiplication layers. Calculations show that for a fixed operational gain and fixed average dead space, the excess noise factor tends to increase as a result of the softness in the PDF in very thin multiplication layers (viz, <70 nm), or equivalently, under high applied electric fields (viz., >800 kV/cm). A method is proposed for extracting the softness parameter from noise versus multiplication measurements.     

Excess noise analysis of separate absorption multiplication regionsuperlattice avalanche photodiodes

The operation of a separate absorption multiplication region avalanche photodiode (SAM-APD) introduces noise as results of randomness in the number and in the position at which dark carrier pairs are generated, randomness in the photon arrival number, randomness in the carrier multiplication, and the number and the position of the photogenerated carriers in the bulk of the diode. The dark current results in a smaller mean multiplication gain in excess noise factor versus mean multiplication plot due to the partial multiplication process of these generated carriers compared to the usual values associated with carriers injected at one edge of the diode. Previous analyses of mean multiplication and excess noise factor for an arbitrary superposition of injected carriers are extended to allow the presence of dark carriers in the multiplication region under the model, which admits variation (with position) of the band-gap, dark generated rate, and ionization coefficients with each stage for the superlattice APD, and the presence of impact ionization in the absorption region. The calculations reveal the presence of impact ionization carriers in the absorption region which results in a larger excess noise factor than the usual values associated with carriers injected at one edge of the device, and fits well with experimental results     

Avalanche multiplication noise characteristics in thin GaAs p+-i-n+ diodes

Avalanche noise measurements have been performed on a range of homojunction GaAs p⁺-i-n⁺ and n⁺-i-p ⁺ diodes with “i” region widths, ω from 2.61 to 0.05 μm. The results show that for ω⩽1 μm the dependence of excess noise factor F on multiplication does not follow the well-established continuous noise theory of McIntyre [1966]. Instead, a decreasing noise factor is observed as ω decreases for a constant multiplication. This reduction in F occurs for both electron and hole initiated multiplication in the thinner ω structures even though the ionization coefficient ratio is close to unity. The dead-space, the minimum distance a carrier must travel to gain the ionization threshold energy, becomes increasingly important in these thinner structures and largely accounts for the reduction in noise     

Effect of doping concentration on avalanche multiplication and excess noise factor in submicron APD

A realistic full-band Monte Carlo (FBMC) model is applied to study the effect of doping concentration on multiplication gain and excess noise factor for electron- and hole-initiated multiplication in thin InP p⁺–i–n⁺ diodes with a range of multiplication lengths of w = 0.1 and 0.24 μm. This model predicts a reduction in excess noise factor for both electron- and hole-initiated multiplication as the doping concentration increases. Besides dead-space effect and feedback impact ionization, the electric field profile controlled by the doping concentration significantly contributes to the fall of excess noise in submicron InP p⁺–i–n⁺ diodes.     

Boundary effects on multiplication noise in thin heterostructure avalanche photodiodes: theory and experiment [Al/sub 0.6/Ga/sub 0.4/As/GaAs]

The history-dependent recurrence theory for multiplication noise in avalanche photodiodes (APDs), developed by Hayat et al., is generalized to include inter-layer boundary effects in heterostructure APDs with multilayer multiplication regions. These boundary effects include the initial energy of injected carriers as well as bandgap-transition effects within a multilayer multiplication region. It is shown that the excess noise factor can be significantly reduced if the avalanche process is initiated with an energetic carrier, in which case the initial energy serves to reduce the initial dead space associated with the injected carrier. An excess noise factor reduction up to 40% below the traditional thin-APD limit is predicted for GaAs, depending on the operational gain and the multiplication-region's width. The generalized model also thoroughly characterizes the behavior of dead space as a function of position across layers. This simultaneously captures the effect of the nonuniform electric field as well as the anticipatory nature of inter-layer bandgap-boundary effects.     

An analytical approach to study the effect of carrier velocities onthe gain and breakdown voltage of avalanche photodiodes

A simplified model for calculating gain and breakdown voltage of avalanche photodiodes (APDs) having constant ionization coefficients in their multiplication layer is presented. Good agreement is seen between the calculated results and the experimental data for published InP-InGaAs separate absorption, grading, charge, and multiplication (SAGCM) APDs. The model denotes that the gain and the breakdown voltage have a dependence on the carrier velocity ratio that is not predicted by conventional models. Hence, by comparing the calculated and measured static characteristics of the APD, one can estimate the velocity of minority carriers in the multiplication region of the device     

Impact ionization characteristics of III-V semiconductors for awide range of multiplication region thicknesses

Recently, an impact ionization model, which takes the nonlocal nature of the impact ionization process into account, has been described. This model incorporates history-dependent ionization coefficients. Excellent fits to experimental gain and noise measurements for GaAs were achieved using an effective field approach and simple analytical expressions for the ionization probabilities. In the paper, we briefly review the history-dependent model and apply it to Al_0.2 Ga_0.8As, In_0.52Al_0.48As and InP avalanche photodiodes. For the study, the gain and noise characteristics of a series of homojunction avalanche photodiodes with different multiplication thicknesses were measured and fit with the history-dependent model. A “size-effect” in thin (<0.5 μm) multiplication regions, which is not adequately characterized by the local-field avalanche theory, was observed for each of these materials. The history-dependent model, on the other hand, achieved close agreement with the experimental results     

Performance of thin separate absorption, charge, and multiplicationavalanche photodiodes

Previously, it has been demonstrated that resonant-cavity-enhanced separate-absorption-and-multiplication (SAM) avalanche photodiodes (APDs) can achieve high bandwidths and high gain-bandwidth products while maintaining good quantum efficiency. In this paper, we describe a GaAs-based resonant-cavity-enhanced SAM APD that utilizes a thin charge layer for improved control of the electric field profile. These devices have shown RC-limited bandwidths above 30 GHz at low gains and gain-bandwidth products as high as 290 GHz. In order to gain insight into the performance of these APDs, homojunction APDs with thin multiplication regions were studied. It was found that the gain and noise have a dependence on the width of the multiplication region that is not predicted by conventional models. Calculations using width-dependent ionization coefficients provide good fits to the measured results. These calculations indicate that the gain-bandwidth product depends strongly on the charge layer doping and on the multiplication layer thickness and, further, that even higher gain-bandwidth products can be achieved with optimized structures     

Effect of dead space on the excess noise factor and time responseof avalanche photodiodes

The effect of dead space on the statistics of the gain process in continuous-multiplication avalanche photodiodes (APDs) is determined using the theory of age-dependent branching processes. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to cause an impact ionization. Analytical expressions are derived for the mean gain, the excess noise factor, and the mean and standard deviation of the impulse response function, for the dead-space-modified avalanche photodiode (DAPD), under conditions of single carrier multiplication. The results differ considerably from the well-known formulas derived by R.J. McIntyre and S.D. Personick in the absence of dead space. Relatively simple asymptotic expressions for the mean gain and excess noise factor are obtained for devices with long multiplication regions. In terms of the signal-to-noise ratio (SNR) of an optical receiver in the presence of circuit noise, it is established that there is a salutory effect of using a properly designed DAPD in place of a conventional APD. The relative merits of using DAPD versus a multilayer (superlattice) avalanche photodiode (SAPD) are examined in the context of receiver SNR; the best choice turns out to depend on which device parameters are used for the comparison     

Design considerations for high performance avalanche photodiodemultiplication layers

We have studied the effect of the thickness of the multiplication region on the noise performance characteristics of avalanche photodiodes (APD's). Our simulation results are based on a full band Monte Carlo model with anisotropic threshold energies for impact ionization. Simulation results suggest that the well known McIntyre expression for the excess noise factor is not directly applicable for devices with a very thin multiplication region. Since the number of ionization events is drastically reduced when the multiplication layer is very thin, the “ionization coefficient” is not a good physical parameter to characterize the process. Instead “effective quantum yield,” which is a measure of the total electron-hole pair generation in the device, is a more appropriate parameter to consider. We also show that for the device structure considered here, modeling the excess noise factor using a “discrete Bernoulli trial” model as opposed to the conventional “continuum theory” produces closer agreement to experimental measurements. Our results reinforce the understanding that impact ionization is a strong function of carrier energy and the use of simplified field-dependent models to characterize this high energy process fails to accurately model this phenomenon     

Low multiplication noise thin Al0.6Ga0.4Asavalanche photodiodes

Avalanche multiplication and excess noise were measured on a series of Al_0.6Ga_0.4As p⁺in⁺ and n⁺ip⁺ diodes, with avalanche region thickness, w ranging from 0.026 μm to 0.85 μm. 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_0.6Ga_0.4As bandgap extremely thin devices can sustain very high electric fields, giving rise to very low excess noise factors, of around F~3.3 at a multiplication factor of M~15.5 in the structure with w=0.026 μm. 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     

多级倍增超晶格InGaAs雪崩光电二级管的增益-噪声特性

重点研究了多级倍增超晶格InGaAs雪崩光电二级管(APD)的增益和过剩噪声,建立了新的载流子增益-过剩噪声模型。在常规弛豫空间理论基础上分析了其工作原理,考虑了预加热电场和能带阶跃带来的初始能量效应、电子进入高场倍增区时异质结边界附近的弛豫空间长度修正以及声子散射对碰撞离化系数的影响,提出了用于指导该类APD的增益-过剩噪声计算的修正弛豫空间理论。结果表明:在相同条件下,相比于常规的单层倍增SAGCM结构,多级倍增超晶格InGaAs APD同时具有更高增益和更低噪声,且修正的弛豫空间理论可被推广到更多级倍增的超晶格InGaAs APD结构,在保证低噪声前提下,通过增加倍增级数可提高增益。     

GaN基雪崩光电二极管及其研究进展

越来越多的民用与军事对高灵敏度紫外探测的需求促进了GaN基雪崩光电二极管（APD）的快速发展。雪崩光电二极管工作在高反偏电压状态,器件内部载流子在高场下发生碰撞离化,从而使探测信号产生增益。首先对GaN基雪崩光电二极管的研究进展进行了回顾,然后重点报道了器件的增益最大可达3105,介绍了本征层厚度与器件暗电流的关系,简单介绍了正在组建的基于相敏探测的交流增益测试系统,并研究了过剩噪声与调制频率之间的关系,发现在低频波段（30~2kHz）,过剩噪声呈现1/f噪声特性。最后,对盖革模式的雪崩光电二极管的研究进展及应用前景进行了简单介绍。