Excess noise in GaAs avalanche photodiodes with thin multiplicationregions

It is well known that the gain-bandwidth product of an avalanche photodiode can be increased by utilizing a thin multiplication region. Previously, measurements of the excess noise factor of InP-InGaAsP-InGaAs avalanche photodiodes with separate absorption and multiplication regions indicated that this approach could also be employed to reduce the multiplication noise. This paper presents a systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses. It is demonstrated that there is a definite “size effect” for multiplication regions less than approximately 0.5 μm. A good fit to the experimental data has been achieved using a discrete, nonlocalized model for the impact ionization process     

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     

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     

Low avalanche noise characteristics in thin InP p+-i-n+ diodes with electron initiated multiplication

We have performed electron initiated avalanche noise measurements on a range of homojunction InP p⁺-i-n⁺ diodes with “i” region widths, w ranging from 2.40 to 0.24 μm. In contrast to McIntyre's noise model a significant reduction in the excess noise factor is observed with decreasing w at a constant multiplication in spite of α, the electron ionization coefficient being less than β, the hole ionization coefficient. In the w=0.24 μm structure an effective β/α ratio of approximately 0.4 is deduced from the excess noise factor even when electrons initiate multiplication, suggesting that hole initiated multiplication is not always necessary for the lowest avalanche noise in InP-based avalanche photodiodes     

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 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     

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.     

A Monte Carlo investigation of multiplication noise in thin p+-i-n+ GaAs avalanche photodiodes

A Monte Carlo (MC) model has been used to estimate the excess noise factor in thin p⁺-i-n⁺ GaAs avalanche photodiodes (APD's). Multiplication initiated both by pure electron and hole injection is studied for different lengths of multiplication region and for a range of electric fields. In each ease a reduction in excess noise factor is observed as the multiplication length decreases, in good agreement with recent experimental measurements. This low noise behavior results from the higher operating electric field needed in short devices, which causes the probability distribution function for both electron and hole ionization path lengths to change from the conventionally assumed exponential shape and to exhibit a strong dead space effect. In turn this reduces the probability of higher order ionization events and narrows the probability distribution for multiplication. In addition, our simulations suggest that fur a given overall multiplication, electron initiated multiplication in short devices has inherently reduced noise, despite the higher feedback from hole ionization, compared to long devices     

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.     

A new look at impact ionization-Part II: Gain and noise in shortavalanche photodiodes

For Part I see R.J. McIntyre, ibid., vol.46, no.8, pp.1623-31 (1999). In Part I, a new theory for impact ionization that utilizes history-dependent ionization coefficients to account for the nonlocal nature of the ionization process has been described. In this paper, we will review this theory and extend it with the assumptions that are implicitly used in both the local-field theory in which the ionization coefficients are functions only of the local electric field and the new one. A systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses is also presented. It is demonstrated that there is a definite “size effect” for thin multiplication regions that is not well characterized by the local-field model. The new theory, on the other hand, provides very good fits to the measured gain and noise. The new ionization coefficient model has also been validated by Monte Carlo simulations     

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     

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 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.     

Dead space effect on the wavelength dependence of gain and noise inavalanche photodiodes

We extend the dead space model proposed by Hayat et al. in order to determine the wavelength-dependent multiplication mean gain 〈G(λ)〉 and excess noise factor F(λ) in the case of mixed electron and hole injection, as it is the case when photons are absorbed within the multiplication region. We compare the predictions of the model with measurements performed on a silicon ultraviolet-selective avalanche photodiode with submicron thick multiplication region. We show that the multiplication gain is constant in the visible and near-infrared part of the spectrum, and increases in the UV range by a factor of 1.8. Furthermore, the excess noise factor is minimal for UV radiation and increases rapidly for longer wavelengths. It appears that the extended dead space model is very adequate at predicting the gain and noise measurement results. In order to unambiguously determine the effect of the dead space, we compare the predictions of our model with those of McIntyre's local noise model. The latter qualitatively describes the wavelength dependence of the gain, but greatly overestimates the excess noise factor     

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     

Full-band Monte Carlo simulation of thin InP p-i-n diodes

A full-band Monte Carlo (FBMC) model is developed to simulate the avalanche characteristics of thin InP p⁺-i-n⁺ diode. The realistic energy band structure of InP used in this model is generated from the local empirical pseudopotential method. The electron and hole ionisation coefficients are fitted to the available measurement in the wide range of electric fields with a softer threshold than the Keldysh model. The multiplication gain and excess noise factor of electron-and hole-initiated multiplication in the thin InP p⁺-i-n⁺ diodes were simulated using FBMC model. Our FBMC results are compared to a simple random path length (RPL) model. The FBMC model predicted lower noise as compare to the results simulated from RPL model in thin InP p⁺-i-n⁺ diodes.     

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     

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