An Improved Nonlocal History-Dependent Model for Gain and Noise in Avalanche Photodiodes Based on Energy Balance Equation

Abstract

We present a non-local history-dependent model for impact ionization gain and noise in avalanche photodiodes (APDs) especially suited for staircase APDs. The model uses a simple energy balance equation to define effective electric fields valid also in the presence of band discontinuities which are then used to express the ionization coefficients. The model parameters have been calibrated against literature data for gain and noise in GaAs and AlxGa1−xAs (x = 0.2, 0.6, 0.8) p-in diodes. Application to experimental data for gain and noise in heterojunction and staircase SAM-APDs is reported to demonstrate the ability of the model in describing complex APD structures. It is found that, in spite of conduction band discontinuities being much larger than valence band ones, hole impact ionization contributes a significant degradation of the noise metrics in GaAs/AlGaAs staircase APDs. These non-trivial insights demonstrate the usefulness of the model to steer device design and optimization.

A New Expression for the Gain-Noise Relation of Single-Carrier Avalanche Photodiodes With Arbitrary Staircase Multiplication Regions

“…5 using the EBHDM. When we have steps with an electric field in between, the F (M ) curve obtained using the EBHDM [9], lies between the results obtained using Eq. 1 and the ones obtained using the Local Model in Fig.…”

“…The main limitation of the proposed formula is that it is valid only when hole impact ionization is negligible. However, we would like to point out that the effects of hole II become relevant when the conduction band discontinuities do not provide electrons with sufficient energy to ionize, as for example in the AlGaAs/GaAs system [9]. When this happens, multiplication in the regions between the steps tends to have the same impact as the one at the steps.…”

“…5 must be coupled to an impact ionization model for each step in the ladder suited to compute the gains M i accurately. To this end we use the nonlocal history dependent model of [9]. This model follows the framework proposed in [8] to relate the ionization probability to gain and multiplication noise.…”

“…The accurate prediction of gain and excess noise factor is fundamental for device optimization. To reach this objective, many different approaches have been proposed in the literature, ranging from the Monte Carlo solution of the Boltzmann Transport equation with a detailed description of electronphonon and impact ionization scattering mechanisms [5], [6], to numerical local or nonlocal models that relate M and F to the spatial profiles of α and β [7], [8], [9], to simplified analytical formulas that can guide the design of APDs [2], [10].…”

“…A model accounting for hole II due to the electric field between the steps has been proposed in [10] based on the theory in [11] and assuming that all steps have the same amplitude. A large electric field between the steps is needed in AlGaAs/GaAs systems where the conduction band discontinuity is in the order of 0.5 eV and the energy gap is larger than 1 eV [9]. On the other hand, in InAsSb structures [4], steps as large as 0.6 eV can be fabricated, that are more than twice the corresponding energy gap (≈0.25 eV).…”