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     

Avalanche multiplication in InP/InGaAs double heterojunctionbipolar transistors with composite collectors

The experimental and theoretical studies of electron multiplication in InP/InGaAs double heterojunction bipolar transistors (DHBT's) with an InGaAs/InP composite collector are carried out. Both local electric field model and energy model are used to investigate the electron impact ionization in the composite collector. The analysis reveals that the nonlocal effect of the electron impact ionization in the composite collector is responsible for the suppression of the contribution of electron multiplication in the InGaAs layer. Experimental results for the fabricated devices were compared with the theoretical calculations, indicating that the conventional impact ionization models based on the local electric field significantly overestimate the electron multiplication for the composite collector. The energy model which takes into account the nonlocal effect is found to provide a more accurate prediction of electron multiplication for the DHBT's     

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     

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.     

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 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     

Measurements of InGaP electron ionization coefficient using InGaP-GaAs-InGaP double HBTs

Electron impact ionization coefficients (/spl alpha/) in In/sub 0.52/Ga/sub 0.48/P have been extracted based on the measurements of electron multiplication factor in npn InGaP-GaAs-InGaP double heterojunction bipolar transistors (HBTs). The electron ionization coefficient of InGaP determined in this brief extends the previously reported data in low electric field by two orders of magnitude down to 1 cm/sup -1/ with the electric field as low as 330 kV/cm.     

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 multiplication in GaInP/GaAs single heterojunctionbipolar transistors

The electron multiplication factors in GaInP/GaAs single heterojunction bipolar transistors (HBT's) have been measured as a function of base-collector bias for a range of GaAs collector doping densities. In the lowest doped (5×10¹⁴ cm^-3) thick collector the multiplication is determined by the local electric field. As the collector doping increases, the measured multiplication is found to be significantly reduced at low values of multiplication from that predicted by the electric field profile. However, good agreement is always found at high multiplication, close to breakdown. This reduction in multiplication at low electric fields is attributed to the dead space, the minimum distance over which carriers must travel before gaining the ionization threshold energy. A simple correction for the dead space is proposed, allowing the multiplication to be accurately predicted even in heavily doped structures     

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.     

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.     

Monte Carlo simulations of the bandwidth of InAlAs avalanche photodiodes

We present a Monte Carlo simulation of the bandwidth of an InAlAs avalanche photodiode with an undepleted absorber. The carrier velocities are simulated in the charge layer and the multiplication region. It is shown that the velocity overshoot effect is not as significant as simpler models have suggested. At high electric field intensity, the electron effective saturation velocity is only slightly higher when impact ionization is significant, compared with when impact ionization is absent. The simulated 3 dB bandwidth is consistent with experiments for gains up to 50.     

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     

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     

Calculation of the diffusion curvature related avalanche breakdown in high-voltage planar p-n junctions

Avalanche multiplication calculations are performed in high-voltage planar p-n junctions to determine breakdown voltage limitations imposed by curvature effects. The issue of choice of ionization coefficient for avalanche multiplication is discussed. From the calculations, a series of design curves and equations are generated which relate the breakdown voltage and peak electric field to those of an ideal junction of the same doping profile, the critical parameters being the substrate doping concentration, the diffusion profile, and the ratio of the radius of curvature to the substrate depletion width for the ideal one-dimensional case. With appropriate distance normalization, these curves and equations can be reduced to a single curve and a single equation. The agreement between theory and experiment is consistently good provided the correct ionization coefficients are used in the theory.     

Temperature dependence of the electron impact ionization in InGaP-GaAs-InGaP DHBTs

Temperature dependence of electron impact ionization in InGaP-GaAs-InGaP double heterojunction bipolar transistors (DHBTs) were comprehensively studied in the temperature range of 300 to 450 K. It has been found that, as the temperature increases, the electron multiplication in the InGaP collector is found to be weakly reduced, which results in a relatively small negative temperature dependence of junction breakdown. The temperature dependence of electron impact ionization at elevated temperatures for InGaP material is investigated based on the electron multiplications measured from the InGaP collector region. An empirical expression is obtained to predict the electron ionization coefficients at elevated temperature up to 450 K in the electric field range of 380 to 650 kV/cm. As compared to InP and GaP binaries, the ternary InGaP shows a lower electron ionization coefficient and much weaker temperature dependence. We found that, introducing additional scattering mechanism such as alloy scattering would provide a better interpretation on the low electron impact ionization and its weak temperature dependence observed in InGaP.     

Ionization coefficient measurement in GaAs by using multiplication noise characteristics

Multiplication noise measurements for p⁺n type (100) GaAs avalanche photodiodes with various n-layer dopings ranging from 6 × 10¹⁵ to 9 × 10¹⁶ cm^?3 confirmed that the ionization coefficient of electrons α is about two times larger than that of holes β in the electric field range from 2.4 × 10⁵ to 5.6 × 10⁵ V/cm. When pure electrons were injected into the avalanche region, the multiplication noise power was proportional to the 2.7th power of the multiplication factor and the ionization coefficient ratio $\text{k =}\text{β}\text{α}$ was constant, where k = 0.5 in the above electric field range. The result was consistent with the multiplication factor dependence on light wavelength. Using the constant ionization coefficient ratio k and the multiplication factor dependence on applied bias voltage, ionization coefficients α and β for electrons and holes were estimated.     

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.