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     

Dead-space-based theory correctly predicts excess noise factor forthin GaAs and AlGaAs avalanche photodiodes

The conventional McIntyre carrier multiplication theory for avalanche photodiodes (APDs) does not adequately describe the experimental results obtained from APDs with thin multiplication-regions. Using published data for thin GaAs and Al_0.2Ga_0.8As APDs, collected from multiplication-regions of different widths, we show that incorporating dead-space in the model resolves the discrepancy. The ionization coefficients of enabled carriers that have traveled the dead space are determined as functions of the electric field, within the confines of a single exponential model for each device, independent of multiplication-region width. The model parameters are determined directly from experimental data. The use of these physically based ionization coefficients in the dead-space multiplication theory, developed earlier by Hayat et al. provide excess noise factor versus mean gain curves that accord very closely with those measured for each device, regardless of multiplication-region width. It is verified that the ratio of the dead-space to the multiplication-region width increases, for a fixed mean gain, as the width is reduced. This behavior, too, is in accord with the reduction of the excess noise factor predicted by the dead-space multiplication theory     

A simple model for avalanche multiplication including deadspaceeffects

A simple Monte Carlo model (SMC) using single effective parabolic valleys and accurately accounting for deadspace effects is presented for calculating the avalanche process. Very good agreement is achieved with a range of measured electron and hole multiplication results from GaAs p ⁺-i-N⁺'s with i-region thicknesses, ω, from 1 μm down to 0.025 μm and with the excess noise factors down to 0.05 μm. While the results are insensitive to the precise values of input parameter for structures with ω⩾0.2 μm, this is not the case in thinner structures where the deadspace represents a significant fraction of the device. For ω<0.2 μm, the energy dependence of the ionization rate becomes increasingly important. The SMC model is tested against a full-band Monte Carlo model (FBMC) by comparing the mean distance between ionization events and the probability density functions, which are effectively the histograms of distances between ionization events, for equivalent material parameters. The good agreement between these suggests that the SMC, with a relatively small number of fitting parameters and much faster calculation times than the FBMC, is a useful tool for device simulation and interpreting experimental results     

超晶格雪崩光电二极管的结构优化及性能研究

基于碰撞离化理论研究了异质材料超晶格结构对载流子离化率的作用,设计得到In0.53Ga0.47As/In0.52Al0.48As超晶格结构的雪崩光电二极管。通过分析不同结构参数对器件性能的影响,得到了低隧道电流、高倍增因子的超晶格结构雪崩层,根据电场分布方程模拟了器件二维电场分布对电荷层厚度及掺杂的依赖关系,并优化了吸收层的结构参数。对优化得到的器件结构进行仿真并实际制作了探测器件,进行光电特性测试,与同结构普通雪崩光电二极管相比,超晶格雪崩光电二极管具有更强的光电流响应,在12.5~20 V的雪崩倍增区,超晶格雪崩光电二极管在具备高倍增因子的同时具有较低的暗电流,提高了器件的信噪比。     

The frequency response of avalanching photodiodes

The Townsend equations for avalanche breakdown in back biased p-n junctions may be derived from the transport equations for semiconductors. Integral solutions of the time independent equations are well known. An integral solution of the time dependent equations is given for multiplication by one carrier only. An exact solution is given for multiplication by two carriers with equal ionization coefficients in a constant junction field. The Townsend equations are nonlinear because of space charge effects. It is shown, however, that the nonlinearity, which imposes an upper limit on the current multiplication possible, is not important until the total multiplied current approaches the space charge limited current for the junction. Assuming multiplication is due to one carrier, frequency response curves are calculated for constant and linear junction fields and for a generation rate, due to photon absorption, which is either uniform or given by a delta function at the junction boundary. The curves indicate a relatively slight dependence of the frequency response on multiplication. Frequency response curves are also given for multiplication by both carriers with equal ionization coefficients when the junction field is constant. In this case the frequency response decreases continuously as the multiplication is increased. For multiplication by two carriers with unequal ionization coefficients, the frequency response is independent of multiplication until the product of the multiplication and the ratio of the ionization coefficients approaches one. Thereafter the frequency response decreases with multiplication.     

雪崩光电探测器的击穿效应模型分析

基于CMOS工艺制备了空穴触发的Si基雪崩探测器(APD),基于不同工作温度下器件的击穿特性,建立空穴触发的雪崩器件的击穿效应模型。根据雪崩击穿模型和击穿电压测试结果,拟合曲线得到击穿电场与温度的关系参数(dE/dT),器件在250～320 K区间内,击穿电压与温度是正温度系数,器件发生雪崩击穿为主,dV/dT=23.3 mV/K,其值是由倍增区宽度以及载流子碰撞电离系数决定的。在50～140 K工作温度下,击穿电压是负温度系数,器件发生隧道击穿,dV/dT=-58.2 mV/K,其值主要受雪崩区电场的空间延伸和峰值电场两方面因素的影响。     

Mean gain of avalanche photodiodes in a dead space model

Based on a first order expansion of the recursive equations, we derive approximate analytical expressions for the mean gain of avalanche photodiodes accounting for dead space effects. The analytical solutions are similar to the popular formula first obtained in local approximation, provided that the ionization coefficients, α and β, are replaced with suitable effective ionization coefficients depending on dead space. The approximate solutions are in good agreement with the exact numerical solutions of the recursive equations for p-i-n devices as well as for photodiodes with nonconstant electric field profile. We also show that dead space causes non negligible differences between the values of the effective ionization coefficients entering in carrier continuity equations, the carrier ionization probability per unit length and the ionization coefficients derived by experimenters from 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     

Simplified particle simulation of millimeter-wave IMPATT devices

A simplified microscopic model for investigating energy relaxation effects in millimeter-wave IMPATT devices is presented. A statistical process is used to describe electron-hole multiplication by impact ionization from knowledge of the ionization coefficients. These coefficients are assumed to be functions of the individual energy of carriers (holes and electrons). A relaxation time formulation is used to calculate the energy of each carrier. Drift in the electric field and diffusion are modeled using the diffusive model proposed by Hockney. Simulations are carried out for silicon diodes. It is found that inclusion of the energy relaxation mechanisms modifies mainly the avalanche process for such material. The implications of these mechanisms on device performances are then discussed by calculating the large signal level dependence of the conversion efficiency and admittance for a typical double-drift structure at 100 GHz. The resulting calculations show good agreement with existing experimental data on these structures.     

A new look at impact ionization-Part I: A theory of gain, noise,breakdown probability, and frequency response

Impact ionization in thick multiplication regions is adequately described by models in which the ionization coefficients are functions only of the local electric field. In devices with thin multiplication lengths, nonlocal effects become significant, necessitating new models that account for the path that a carrier travels before gaining sufficient energy to impact ionize. This paper presents a new theory that incorporates history-dependent ionization coefficients, and it is shown that this model can be utilized to calculate the low-frequency properties of avalanche photodiodes (APD's) (gain, noise, and breakdown probability in the Geiger mode) and the frequency response. A conclusion of this work is that an ionization coefficient is not a fundamental material characteristic at a specific electric field and that any experimental determination of ionization coefficients is valid only for the particular structure on which the measurement was performed     

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     

碲镉汞雪崩光电二极管的发展

雪崩光电二极管(APD)工作在足够的反偏下,光生载流子到达耗尽区并诱发放大过程.碲镉汞(MCT)电子和重空穴有效质量之间的非对称性会产生不相等的电子电离系数和空穴电离系数,提供一个由单独一类载流子诱发的碰撞电离过程,从而形成具有包括接近无噪声增益在内的“理想”APD特征的电子雪崩光电二极管(EAPD).对于包括低光子数...     

A model for dark current and multiplication in HgCdTe avalanche photodiodes

In this paper we report the calculated results of the dark current and multiplication factor in MBE grown HgCdTe avalanche photodiodes with separate absorption and multiplication (SAM-APD). The device architecture used for this analysis comprises the following layers: p⁺ contact, p junction, n⁻ multiplication, n charge sheet, n⁻ absorber, and n⁺ contact. Various leakage current mechanisms are considered and the generation-recombination term is found to be the dominant one for this device structure. However, experimental reverse bias I-V characteristics reported earlier by T. de Lyon et al. shows a large deviation from ideality, which can not be explained in terms of bulk leakage current mechanism. To explain the large difference between experimental and theoretical data we consider that the dominant generation-recombination current is multiplied through impact ionization process. To validate this assumption, multiplication is calculated as a function of reverse bias. Electric field profile is obtained and the multiplication is computed using the ionization coefficients and avalanche gain equations. Breakdown voltage is found to be 85 V for room temperature operation in agreement with available data in the literature. The theoretical I-V curves considering multiplication are compared with the experimental ones and a close agreement is found which validate this model.     

Avalanche Multiplication in InAlAs

A systematic study of avalanche multiplication on a series of In _0.52Al_0.48As 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     

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     

Avalanche noise characteristics of thin GaAs structures withdistributed carrier generation [APDs]

It is known that both pure electron and pure hole injection into thin GaAs multiplication regions gives rise to avalanche multiplication with noise lower than predicted by the local noise model. In this paper, it is shown that the noise from multiplication initiated by carriers generated throughout a 0.1 μm avalanche region is also lower than predicted by the local model but higher than that obtained with pure injection of either carrier type. This behavior is due to the effects of nonlocal ionization brought about by the dead space; the minimum distance a carrier has to travel in the electric field to initiate an ionization event     

An avalanche photodiode with metal-insulator-semiconductor properties

A new design of the avalanche photodetector combining the avalanche photodiode and MIS structure properties was tested. The noise and high-frequency properties of the device were studied. The device exhibited a noise factor of less than 10 at a high multiplication factor (M>1000) even with hole injection. This is indicative of a drastic change in the effective ratio of the coefficients of impact ionization by electrons and holes in favor of the latter. Measurements of the photosensitivity distribution over a photodetector area for M=8000 showed a high uniformity.     

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     

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.     

InGaAs/InAlAs雪崩光电二极管仿真设计

设计了一种InGaAs/InALAs雪崩光电二极管(APD),并利用MEDICI软件进行了模拟仿真.器件采用背入射探测方式.雪崩增益区采用埋层设汁,省略了保护环等结构;并使用双层掺杂,有效降低了增益区电场的梯度变化.由于结构简单,因此仪需要利用分子束外延(MBE)生长精确控制每层结构即可.由于InAlAs材料的空穴与电子的离化率有较大的筹异,因此器件具有较低的噪声因子.