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     

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.     

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     

Performance degradation of APD-optical receivers due to darkcurrent generated within the multiplication region

General expressions for the effective gain and effective excess noise factor associated with dark current generated within the high-field region of an avalanche photodiode (APD) are given. The influence of this background current on the performance of a uniformly multiplying APD receiver is evaluated and compared with that due to a dark current component generated outside the multiplication region (diffusion current). The results indicate clearly that the former dark current component has less effect on receiver performance than the latter, especially when hole and electron ionization rates are very different     

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.     

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     

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     

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     

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     

Avalanche noise characteristics of single Al/sub x/Ga/sub 1-x/As(0.3

Groves  C. Chia  C.K. Tozer  R.C. David  J.P.R. Rees  G.J. 《Quantum Electronics, IEEE Journal of》2005,41(1):70-75

On the time dependency of the avalanche process in semiconductors

An equation is derived for the time dependent current in the avalanche region of a uniform diode, for the case of one charged carrier of either electron or hole is injected, for unequal ionization rates and drift velocities of electrons and holes. The appearing time-constant differs from earlier results, derived on the basis of the well known intrinsic response time. The noise characteristics of the current are established for a Poissonian injection of an electron or hole. The factor which describes the influence of the statistics of the multiplication for low frequencies, is also found to differ from previous published results. At high current multiplication factors the present study is in agreement with previous work.     

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     

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。     

Excess gate current analysis of junction gate FET's by two- dimensional computer simulation

Gate current in a JFET under high drain bias is much higher than expected from the classical theory for reverse-biased p-n junctions. This excess gate current is caused by minority carriers generated by low-level impact ionization in the conducting channel, while the so-called breakdown voltage is determined by high-level avalanche multiplication near the gate edge at the surface. A simple one-dimensional model for the excess gate current is proposed. This model is based on the results of two-dimensional numerical analysis, which neglects the minority carrier motion. The excess gate current and avalanche breakdown voltage are calculated from one-dimensional ionization integrals, which are obtained numerically by utilizing the solution of two-dimensional analysis. The reverberant effect of the generated carriers on the potential distribution is assumed to be negligible. The results of the calculation are in good agreement with experimental results, without any adjustable parameters. Moreover, various impurity doping profiles are analyzed for the purpose of minimizing excess gate current. The present model requires a reasonably short computation time and is useful for designing JFET devices.     

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     

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.     

New InGaAs/InP avalanche photodiode structure for the 1-1.6 µm wavelength region

Low dark current and low multiplication noise properties for an In0.53Ga0.47As/InP avalanche photodiode are described. The diode is prepared with an In0.53Ga0.47As light absorption layer and an InP avalanche multiplication region. The lowest dark current density of5.2 times 10^{-4}A/cm²is obtained at 90 percent of a breakdown voltage. Multiplication noise power is proportional to the 2.7th power of the current multiplication factor. Impact ionization coefficient by holes is larger by 2-3 times than that by electrons in     

Excess noise design of InP/GaInAsP/GaInAs avalanche photodiodes

An InP/GaInAsP/GaInAs avalanche photodiode (APD) with separate absorption and multiplication (SAM) regions has been designed taking into account the excess noise generated in GaInAsP and GaInAs. The multiplication factor dependence of the excess noise factorFhas been calculated using realistic electron and hole ionization rates in InP, GaInAsP, and GaInAs, assuming that the avalanche multiplication occurs not only in InP but in GaInAsP and GaInAs. The calculatedFvalues have been compared to the experimental ones measured on a planar-type InP/GaInAsP/GaInAs APD for illumination at a wavelength of 1.3 μm. It has been found the the calculated excess noise agrees very well with the experimental measurements. The limited ranges of device parameters in which the conditions of minimal excess noise, tunneling current, and charge pile-up are satisfied have been obtained. We conclude that the excess noise generated in GaInAsP and GaInAs should be considered in a practical device design.     

Low-frequency noise in Schottky barrier diodes

The low-frequency excess noise in Schottky barrier diodes has been investigated. In the ideal case where the saturation current is completely determined by thermionic emission of electrons, no 1/? noise will be produced in the barrier. The presence of trap states in the depletion region can lead to generation-recombination noise. At sufficient high forward currents 1/? noise can be generated in the series resistance of the Schottky diode. Deviations from the ideal diode, for example as a result of edge effects, produce 1/? noise and increase at the same time the ideality factor. It is empirically found that the 1/? noise level decreases very rapidly if the ideality factor tends to unity.     

Comparison of available detectors for digital optical fiber systems for the 1.2-1.55 µm wavelength range

Receiver sensitivity is estimated at 1.3 and 1.5 μm for commercial Ge APD's for bit rates between 8 and 1200 MBd, for a variety of APD diameters and operating temperatures. Although both holes and electrons are injected into the depletion region at these wavelengths, the measured photocurrent excess multiplication noise is found empirically to be well described by the simple expression for unilateral carrier injection into the depletion region, while the measured noise on the bulk leakage current can be characterized by the photocurrent parameters for wavelengthssim1.8 mum. Measurements at BTRL on a 140 Mbit/s system receiver using an Optitron GA-1 Ge APD at temperatures in the range20-60degC agree within 1 dB with the theoretical model using these data. The performance of Ge APD-based receivers is strongly influenced by noise on the leakage current and is therefore susceptible to temperature fluctuations. The ionization rates for holes and electrons are comparable in Ge, resulting in a high excess noise factor and a strong dependence of multiplication factor on bias voltage. Thus, APD's for long-wavelength digital optical receivers operating below ∼1 GBd require a bulk leakage current densityll 10^{-4}A/cm²and markedly different ionization rates for holes and electrons, in order to match the otherwise superior performance of the present-day high-impedance p-i-n/FET hybrid.