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     

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     

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     

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     

Signal-to-noise ratio for lightwave systems using avalanchephotodiodes

An expression for the signal-to-noise ratio (SNR) at the output of an avalanche photodiode (APD) receiver is derived that includes the effects of photoinjected carriers, dark-generated carriers, and the receiver circuitry. It is found that the dark current alters both the magnitude of the SNR and the value of the mean multiplication where the SNR achieves its maximum value. The formula differs from the expression that is conventionally used (S.M. Sze, 1981) in that it makes use of different excess noise factors for photo-generated and dark-generated carriers     

A simplified non-Gaussian approach to digital optical receiverdesign with avalanche photodiodes: theory

A simplified theory of avalanche photodiode receiver sensitivity is presented in which the non-Gaussian nature of the avalanche multiplication process is taken into account. The theory predicts more accurately than a Gaussian theory the optimum avalanche gain and decision threshold and gives simple results for the influence of background photocurrent or dark current on receiver sensitivity, optimum gain, and threshold. For purposes of comparison, a parallel derivation using the Gaussian approximation for both the avalanche and receiver noises is given where simple expressions for the optimum avalanche gain and threshold settings are derived     

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.     

Effects of Ionization Velocity and Dead Space on Avalanche Photodiode Bit Error Rate

A model is presented for the bit error rate (BER) contributed by the receiver in an optical telecommunications system that includes the effects of ionizing carrier velocity and dead space in the avalanche photodiode (APD) and of additive circuit noise. The probability distribution functions of bit charge used to calculate BER are not, as is commonly assumed, Gaussian, confirming the need to directly compute the receiver statistics. Integrating the current over the central section of the bit period can minimize intersymbol interference. The assumption that carriers travel to ionization with infinite velocity underestimates BER in InP APDs with short avalanche region widths, and overestimates BER when . Models assuming constant carrier velocity or allowing for velocity enhancement predict distinctly different BER over a wide range of avalanche width and multiplication because of the manner in which the current evolves during the bit period.     

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     

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     

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     

Delta-doped avalanche photodiodes for high bit-rate lightwavereceivers

The authors estimate the GB (grain bandwidth) product limits and the noise performance of a new SAGM-APD (separate avalanche, grating, and multiplication avalanche photodiode) structure: the δ-doped SAGM-APD. It is shown that GB products in excess of 140 GHz for a 0.2-μm-thick multiplication layer and possibly larger GB products for smaller widths can be obtained. While recent calculations have predicted increased GB products for this δ-doped SAGM-APD structure, the authors explicitly prove using conventional theory that this is possible only with a concomitant increase in the multiplication noise. It is further demonstrated that it is essential to optimize the width of the multiplication layer for a given bit-rate to achieve minimum multiplication noise consistent with a GB product high enough to accommodate the requisite frequency response at the optimum gain. It is shown that the δ-doped SAGM-APD structure is a very good candidate for high bit-rate receiver applications     

Theoretical investigation of quantum-dot avalanche photodiodes for mid-infrared applications

A novel midinfrared sensor, called the quantum-dot avalanche photodiode (QDAP), is proposed which is expected to have improved signal-to-noise ratio (SNR) in the presence of Johnson noise over its quantum-dot (QD) counterpart. In the QDAP, an intersubband QD detector is coupled with a thin, low-noise GaAs avalanche layer through a tunnel barrier. The avalanche layer provides the necessary photocurrent gain required to overcome Johnson noise and nearly achieve the dark-current-limited SNR of the QD detector. In the proposed three-terminal device, the applied biases of the QD-detector and the avalanche-photodiode sections of the QDAP are controlled separately. This feature permits the control of the QDs responsivity and dark current independently of the operating avalanche gain, thereby allowing the optimization of the avalanche multiplication factor to maximize the photocurrent's SNR. Notably, a heterojunction potential-barrier layer can also be utilized to further improve the SNR. For example, when the standard deviation of the Johnson noise is four times greater than the dark current, calculations show that the SNR enhancement offered by an avalanche multiplication factor of 5 results in relaxing the cooling requirement from 20 to 80 K.     

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.     

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     

Receiver Design for Optical PPM Systems

An optimum receiver structure for optical PPM systemics is considered and from this a simple sub-optimum receiver is proposed which offers significant SNR improvement relative to existing design approaches and yet requires few circuit changes. Receivers incorporating either p-i-n or avalanche photodiodes and FET or BJT preamplifiers are analyzed. The optimization technique relies on matching the frequency response of the receiver to that of the incident optical pulse and setting the avalanche gain and threshold detector at optimum levels. For a FET preamplifier the SNR improvement is 10.8 dB with a p-i-n photodiode and 4.7 dB with an avalanche photodiode. For a BJT preamplifier the SNR improvement is 3.1 dB and 2.3 dB with the p-i-n and avalanche diodes, respectively.     

Counting distributions and error probabilities for optical receivers incorporating superlattice avalanche photodiodes

Exact gain distributions and electron counting distributions are presented for superlattice avalanche photodiodes that operate by single-carrier transport perpendicular to the superlattice planes. The characteristic shapes of these distributions are compared with those of the single-carrier conventional avalanche photodiode and the photomultiplier tube. The electron counting distributions, which assume Poisson photocarrier injection, are used to calculate the error performance of a simple optical communication system. This performance is compared with that achievable by a single-carrier conventional APD receiver of identical quantum efficiency and gain. For simplicity of calculation, the system consists of a transmitter emitting light pulses containing a Poisson number of photons and a maximum-likelihood integrate-and-dump receiver. It makes use of binary on-off keying and is subject to noise events arising from multiplied background radiation and/or multiplied dark noise. The performance of the superlattice photodiode receiver turns out to be always superior to that of the single-carrier conventional photodiode receiver, for all values of the gain. The advantage can attain several orders of magnitude (even though the excess noise factors for the two devices lie within a factor of two). The superlattice receiver with high impact-ionization probability is shown to behave like an ideal photon counter with the same quantum efficiency, even if the device has many stages. The deleterious effects of receiver thermal noise on probability of error are examined.