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.     

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.     

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     

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     

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     

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     

Performance of thin separate absorption, charge, and multiplicationavalanche photodiodes

Previously, it has been demonstrated that resonant-cavity-enhanced separate-absorption-and-multiplication (SAM) avalanche photodiodes (APDs) can achieve high bandwidths and high gain-bandwidth products while maintaining good quantum efficiency. In this paper, we describe a GaAs-based resonant-cavity-enhanced SAM APD that utilizes a thin charge layer for improved control of the electric field profile. These devices have shown RC-limited bandwidths above 30 GHz at low gains and gain-bandwidth products as high as 290 GHz. In order to gain insight into the performance of these APDs, homojunction APDs with thin multiplication regions were studied. It was found that the gain and noise have a dependence on the width of the multiplication region that is not predicted by conventional models. Calculations using width-dependent ionization coefficients provide good fits to the measured results. These calculations indicate that the gain-bandwidth product depends strongly on the charge layer doping and on the multiplication layer thickness and, further, that even higher gain-bandwidth products can be achieved with optimized structures     

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.     

Frequency response of avalanche photodetectors with separateabsorption and multiplication layers

We present analytical expressions for the frequency response of avalanche photodetectors (APDs) with separate absorption and multiplication regions (SAM). The effect of the electric field profile in the multiplication layer on frequency response is considered for the first time. Previous theories have assumed that the multiplication layer is very thin and the peak electric field, which corresponds to the effective multiplication plane, is positioned away from the absorption layer. This is a poor assumption for many devices, and in particular for silicon hetero-interface photodetectors (SHIPs). We present a theoretical model in which the thickness of the multiplication layer is arbitrary and the peak electric field may be positioned arbitrarily in relation to the absorption layer. We also consider the effects of parasitics, transit-time, and avalanche buildup time. Both front and back illumination from either multiplication layer or absorption layer are considered. The calculated results are compared with experimental results for existing SHIP's and performance predictions are also made for optimized SHIP structures. SHIP APDs with gain-bandwidth product in excess of 500 GHz are possible     

Low-dark-current low-voltage 1.3?1.6 ?m avalanche photodiode with high-low electric field profile and separate absorption and multiplication regions by molecular beam epitaxy

The operation of the recently disclosed heterojunction avalanche photodiode with high-low electric field profile and separate absorption and multiplication regions (HI-LO SAM APD) is demonstrated. This new structure which features a doping spike in the wide gap layer offers several advantages over conventional SAM APDs (lower dark current and excess noise factor, greater gain stability). Low dark currents (?1 nA), low voltage operation (?26 V) and gains as high as 50 at 1.60 ?m are demonstrated in an Al0.48In0.52As/Ga0 47In0 53As prototype grown by molecular beam epitaxy.     

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     

A simplified approach to time-domain modeling of avalanchephotodiodes

A simplified algorithm for calculating time response of avalanche photodiodes (APDs) is presented. The algorithm considers the time course of avalanche processes for the general case of position-dependent double-carrier multiplications including the dead space effect. The algorithm is based on a discrete time setting ideally suited for computer modeling and can be applied to any APD structure. It gives a fast and accurate estimation of the time and frequency response of APDs. As an example, the present method is applied to InP-InGaAs separate absorption, grading, charge, and multiplication (SAGCM) APDs. The variation of multiplication pain with bias voltage and 3-dB electrical bandwidth at different multiplication gain obtained using the new algorithm show good agreement with experimental results. The algorithm can be used to study temperature dependence of APD characteristics and can be easily extended to calculate the excess noise factor     

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     

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.     

InP/InGaAs buried-structure avalanche photodiodes

Planar InP/InGaAs avalanche photodiodes with a new guardring structure have been designed and fabricated. The diodes had a buried n-InP layer and an n?-InP multiplication region under p-n junctions. A successful guardring effect was obtained. The diode exhibited a uniform multiplication over the active region, a maximum multiplication factor of 30, low dark currents of around 20 nA at 90% of breakdown voltage and a flat frequency response up to 1 GHz. Multiplication noise was measured up to a multiplication factor of 17.     

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     

Excess Avalanche Noise in In0.52Al0.48As

Avalanche multiplication and excess noise arising from both electron and hole injection have been measured on a series of In_0.52Al_0.48As p⁺-i-n⁺ and n ⁺-i-p⁺ diodes with nominal avalanche region widths between 0.1 and 2.5 mum. With pure electron injection, low excess noise was measured at values corresponding to effective k=beta/alpha between 0.15 and 0.25 for all widths. Enabled ionization coefficients were deduced using a non-local ionization model utilizing recurrence equation techniques covering an electric field range from approximately 200 kV/cm to 1 MV/cm     

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     

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.