Relating the Experimental Ionization Coefficients in Semiconductors to the Nonlocal Ionization Coefficients

Abstract

The experimentally determined impact ionization coefficients, α (β ), include intrinsically the presence of a dead-space, where carriers cannot impact ionize as they do not have sufficient energy. These, therefore, cannot be used by nonlocal ionization models, which require the enabled ionization coefficients, α * (β * ), which describe the ionization probability after the dead-space. A relatively simple relationship is shown to exist between α (β ) and α * (β * ), which requires only the knowledge of the carrier threshold energies. This allows α (β ), conventionally limited to the local model framework, to be used to give a very good prediction of the avalanche multiplication and excess noise for a wide range of device widths down to 0.05 μm, where the dead-space effect is significant. Parameterized values of α (β ) and the carrier threshold energies are listed for a range of commonly used III-V semiconductors lattice matched to GaAs and InP substrates, as well as Si and SiC.

Impact Ionization Coefficients in (Al x Ga1-x )0.52In0.48P and Al x Ga1-x As Lattice-Matched to GaAs

“…For the structures used in this study the effect of the dead space on the multiplication is small, but its effect on excess noise is nonnegligible. To account for all of these effects, the multiplication and noise data were simulated using the random path length (RPL) model of Cheong et al [25]. This model uses an ionization probability density function to account for the dead space.…”

“…It also accounts for any variation in the electric field profile across the device, to accurately simulate multiplication and excess noise. The ionization threshold energies, E the and E thh , for AlInP and GaInP are known [25], and those for the intermediate compositions were interpolated from these. The threshold energy for each intermediate composition was approximated as 2.05 times the energy bandgap, using bandgap values reported by Cheong et al [14].…”

A Physics Based Unified Circuit Model for Single Photon and Analog Detector

“…Multiplication coefficient models can be expanded to incorporate non-local effects using Eq. 15 in [25]. Transit time (tr) is the time required for the carrier to cross the gain region and can be approximated from the length of the gain region and carrier velocity.…”

“…The dynamic switching of the detectors between above breakdown and below breakdown bias prefer a unified circuit model applicable to all bias voltage and showing the dynamics of carrier multiplication. All parameters in our circuit model are related to fundamental material and design parameters: impact ionization coefficients for electrons and holes based on the local-field model [25], [26], and the carrier transit time across the multiplication region. The electron/hole impact ionization coefficients for commonly used semiconductors can be found from many published sources (Table I), and the carrier transit time is related to the specific device structure and can be estimated from the thickness of the gain region.…”

Low-Noise 3-D Avalanche Photodiodes

“…In our computing, different evaluations of ionization coefficients α i (j), β i (j) (the j th fraction of i th Line) in strong or weak field drew on the model presented in Ref. [12]. It should be noted that the average value of excess noise factors is not the overall excess noise factor.…”