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     

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     

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.     

Avalanche multiplication properties of GaAs calculated from spatially transient ionisation coefficients

In this paper the high field phenomenon of avalanche multiplication in a GaAs p-i-n infrared detector is studied using a Monte-Carlo simulation. The Lucky-Drift model of impact ionization is used to give the characteristic lengths for transport through the device. The transport is then modelled by generating motion consistent with the probability functions derived from the mean free paths. This produces a spatially transient ionization coefficient for each carrier and allows the realistic statistical simulation of avalanche multiplication. Properties such as mean gain, multiplication noise and the transient response to a photonic pulse have been calculated and explained for a length of i-GaAs, with an emphasis on short active region phenomena. The effect on the ionization coefficients of a periodic field change has been investigated. It has been found that the effective carrier deadspace is approx. 1.35 times the absolute deadspace. The transient current calculations indicate the narrow bandwidth of this type of device. The presence of a periodic field change, caused by periodic δ-doping, was found to increase both electron and hole ionization coefficients by different proportions.     

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     

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 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     

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     

Impactron-a new solid state image intensifier

This paper describes the theory of operation and up to date achieved performance of a new image sensor concept that is using Impact Ionization to multiply photo-generated charge before sensing. It is shown that the charge multiplication based on a single carrier impact ionization is almost noiseless. This allows detected signal charge to be amplified directly in the charge domain and be always kept above the charge detector amplifier noise floor. Charge is repeatedly transferred in a CCD fashion through high field regions where the impact ionization occurs. Even though the impact ionization has a low probability and the high field regions are short the number of transfers is large and significant charge gains are obtained. The developed charge multiplication structure can be easily incorporated into pixels of any standard CCD image sensor and included in the image sensing area, the memory area, or any other vertical or horizontal CCD register with a minimum area penalty. This feature thus provides high flexibility in designing new sensors with various performance characteristics suitable for an extreme low light level imaging. The paper describes in detail the theory of charge multiplication and excess noise generation that is supported by the measured data obtained form the test image sensors. The measurement methods that are used to characterize the charge multiplication gain and noise are also described in detail     

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     

Wavelength dependence of multiplication noise in silicon avalanche photodiodes

Theoretical and experimental results on wavelength dependence of multiplication noise in silicon avalanche photodiodes are described. When the photodiode has a p-n⁺-junction and is illuminated from the n⁺-side, multiplication noise increases by decreasing optical wavelength. Effective ionization coefficient ratio keffis equal tokexp (2Kw_{a}) for a uniform junction electric field, wherekis the ratio of ionization coefficients of electrons α and holes β. The multiplication noise depends on the product of optical absorption coefficientKand the avalanche-region width wa. Calculations show that there exists an optimum wafor minimizing multiplication noise at a given wavelength. Theoretical results are shown to agree with results of experiments on diodes with a low-high-low impurity profile. Measured ionization coefficient ratiokvalues are 0.04 and 0.08 at 0.811- and 0.633-µm wavelength, respectively.     

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     

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 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     

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     

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.     

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     

Investigation of the transition from tunneling to impact ionization multiplication in silicon p-n junctions

White noise spectra of diodes breaking down between 1·5 and 5 V have been used to investigate the details of the transition from tunneling to avalanche breakdown in silicon p-n junctions. It is found that the transition and carrier multiplication in these junctions is dominated by the influence of the threshold energies for ionization. Because this influence is not explicitly taken into account in the existing theories of carrier multiplication and noise, they are not applicable to low breakdown voltage diodes. Consequently, a multiplication onset model and alternate schemes for calculating the DC multiplication and noise in low breakdown voltage diodes are developed.Analysis of the noise data indicates that the threshold energies for ionization depend slightly on junction widths and, for the diodes employed in this study, range between 1·66–1·9 eV for electrons and 1·79–2·04 eV for holes. The minimum distance between ionizing collisions is found to range from 190 to 240 A for electrons and 200 to 250 A for holes.Application of the threshold energies for ionization to the multiplication onset model permits evaluation of the doping densities on both sides of the step junctions. From it, it is determined that the solubility of aluminum in silicon is N_A = 9·5 ± 0·5 × 10¹⁸ cm^?3.     

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。     

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.