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     

Effect of dead space on gain and noise ofdouble-carrier-multiplication avalanche photodiodes

The effect of dead space on the statistics of the gain in a double-carrier-multiplication avalanche photodiode (APD) is determined using a recurrence method. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. Recurrence equations are derived for the first moment, the second moment, and the probability distribution function of two random variables that are related, in a deterministic way, to the random gain of the APD. These equations are solved numerically to produce the mean gain and the excess noise factor. The presence of dead space reduces both the mean gain and the excess noise factor of the device. This may have a beneficial effect on the performance of the detector when used in optical receivers with photon noise and circuit noise     

An analytical approximation for the excess noise factor ofavalanche photodiodes with dead space

Approximate analytical expressions are derived for the mean gain and the excess noise factor of avalanche photodiodes including the effect of dead space. The analysis is based on undertaking a characteristic-equation approach to obtain an approximate analytical solution to the existing system of recurrence equations which characterize the statistics of the random multiplication gain. The analytical expressions for the excess noise factor and the mean gain are shown to be in good agreement with the exact results obtained from numerical solutions of the recurrence equations for values of the dead space reaching up to 20% of the width of the multiplication region     

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     

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.     

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     

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     

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.     

Lucky drift estimation of excess noise factor for conventionalavalanche photodiodes including the dead space effect

A technique for estimating the excess noise factor in conventional avalanche photodiodes has been developed. It is based upon a computer simulation of carrier motion using the lucky drift concept. The importance of the impact ionization dead space is demonstrated, and an established theory is shown to overestimate the excess noise factor due to the neglect of the dead space phenomenon in conventional avalanche photodiodes     

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     

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     

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.     

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 impact ionization in the InGaAs absorber on excess noise of avalanche photodiodes

The effects of impact ionization in the InGaAs absorption layer on the multiplication, excess noise and breakdown voltage are modeled for avalanche photodiodes (APDs), both with InP and with InAlAs multiplication regions. The calculations allow for dead space effects and for the low field electron ionization observed in InGaAs. The results confirm that impact ionization in the InGaAs absorption layer increases the excess noise in InP APDs and that the effect imposes tight constraints on the doping of the charge control layer if avalanche noise is to be minimized. However, the excess noise of InAlAs APDs is predicted to be reduced by impact ionization in the InGaAs layer. Furthermore the breakdown voltage of InAlAs APDs is less sensitive to ionization in the InGaAs layer and these results increase tolerance to doping variations in the field control layer.     

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     

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     

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。     

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 avalanche speed [APDs]

The effects of dead space (the minimum distance travelled by a carrier before acquiring enough energy to impact ionize) on the current impulse response and bandwidth of an avalanche multiplication process are obtained from a numerical model that maintains a constant carrier velocity but allows for a random distribution of impact ionization path lengths. The results show that the main mechanism responsible for the increase in response time with dead space is the increase in the number of carrier groups, which qualitatively describes the length of multiplication chains. When the dead space is negligible, the bandwidth follows the behavior predicted by Emmons but decreases as dead space increases