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     

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     

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     

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.     

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.     

Avalanche multiplication characteristics ofAl0.8Ga0.2As diodes

The avalanche multiplication characteristics of Al_0.8Ga _0.2As have been investigated in a series of p-i-n and n-i-p diodes with i-region widths, w, varying from 1 μm to 0.025 μm. The electron ionization coefficient, α, is found to be consistently higher than the hole ionization coefficient, β, over the entire range of electric fields investigated. By contrast with Al_xGa _1-xAs (x⩽0.6) a significant difference between the electron and hole initiated multiplication characteristics of very thin Al_0.8Ga_0.2As diodes (w=0.025 μm) was observed. Dead space effects in the diodes with w⩽0.1 μm were found to reduce the multiplication at low bias below the values predicted from bulk ionization coefficients. Effective α and β that are independent of w have been deduced from measurements and are able to reproduce accurately the multiplication characteristics of diodes with w⩾0.1 μm and breakdown voltages of all diodes with good accuracy. By performing a simple correction for the dead space, the multiplication characteristics of even thinner diodes were also predicted with reasonable accuracy     

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     

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     

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.     

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     

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.     

Breakdown probabilities for thin heterostructure avalanche photodiodes

The recurrence theory for the breakdown probability in avalanche photodiodes (APDs) is generalized to heterostructure APDs that may have multiple multiplication layers. The generalization addresses layer-boundary effects such as the initial energy of injected carriers as well as the layer-dependent profile of the dead space in the multiplication region. Reducing the width of the multiplication layer serves to both downshift and sharpen the breakdown probability curve as a function of the applied reverse-bias voltage. In structures where the injected carriers have an initial energy that is comparable to the ionization threshold energy, the transition from linear mode to Geiger-mode is more abrupt than in structures in which such initial energy is negligible. The theory is applied to two recently fabricated Al/sub 0.6/Ga/sub 0.4/As-GaAs heterostructure APDs and to other homostructure thin GaAs APDs and the predictions of the breakdown-voltage thresholds are verified.     

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     

Temperature dependence of the ionization coefficients of AlxGa1-xAs

As Al_xGa_1-xAs alloys are increasingly used for microwave and millimeter wave power devices and circuits that work under high electric field intensities and junction temperatures; understanding the temperature dependence of impact ionization and related properties in this material system becomes more and more important. Measurements of the multiplication gain and noise of avalanche photodiodes (APDs) provide insight to the avalanche characteristics of semiconductors. Previously, we have reported the characteristics of GaAs and Al_0.2Ga_0.8As APD's at room temperature. In this paper, the gain and noise of a series of homojunction Al_xGa_1-xAs APD's were investigated over a wide temperature range from 29°C to 125°C, and the temperature dependence of their ionization coefficients was extracted     

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     

Optimal excess noise reduction in thin heterojunction Al/sub 0.6/Ga/sub 0.4/As-GaAs avalanche photodiodes

It has been recently found that the initial-energy effect, which is associated with the finite initial energy of carriers entering the multiplication region of an avalanche photodiode (APD), can be tailored to reduce the excess noise well beyond the previously known limits for thin APDs. However, the control of the initial energy of injected carriers can be difficult in practice for an APD with a single multiplication layer. In this paper, the dead-space multiplication recurrence theory is used to show that the low noise characteristics associated with the initial-energy effect can be achieved by utilizing a two-layer multiplication region. As an example, a high bandgap Al/sub 0.6/Ga/sub 0.4/As material, termed the energy-buildup layer, is used to elevate the energy of injected carriers without incurring significant multiplication events, while a second GaAs layer with a lower bandgap energy is used as the primary carrier multiplication layer. Computations show that devices can be optimally designed through judicious choice of the charge-layer width to produce excess noise factor levels that are comparable to those corresponding to homojunction APDs benefiting from a maximal initial-energy effect. A structure is presented to achieve precisely that.     

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 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