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arxiv: 2605.01244 · v1 · submitted 2026-05-02 · 🪐 quant-ph

NEGF Modeling of Impact Ionization in Semiconductor Avalanche Photodiodes for Quantum Networking

Colin Burdine , Nischal Binod Gautam , Enrique P. Blair This is my paper

Pith reviewed 2026-05-09 15:15 UTC · model grok-4.3

classification 🪐 quant-ph
keywords NEGF formalismimpact ionizationavalanche photodiodecarrier multiplicationquantum transportsemiconductor modelingnon-equilibrium Green's functionsquantum networking
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The pith

Impact ionization is formulated as a multi-particle self-energy in NEGF to describe carrier multiplication non-perturbatively in avalanche photodiodes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a quantum transport framework using the Non-Equilibrium Green's Function method to simulate impact ionization in semiconductor avalanche devices relevant to quantum networks. Traditional semiclassical approaches assume weak interactions and break down at nanoscale high fields, but this method treats impact ionization through a multi-particle self-energy for a direct, non-perturbative calculation of carrier multiplication from the spectral function. Implemented in real-space matrix form for a model structure, it shows how multiplication emerges from energy-resolved scattering and nonequilibrium distributions. This matters because it offers a path to accurate predictions for single-photon avalanche detectors in quantum receivers without relying on mean-field approximations.

Core claim

The central claim is that impact ionization can be incorporated into NEGF as a multi-particle self-energy, providing an energy- and atomic orbital-resolved, non-perturbative description of carrier multiplication directly from the device spectral function in high-electric-field semiconductor structures.

What carries the argument

Multi-particle self-energy for impact ionization in the NEGF formalism, computed to capture inelastic scattering and carrier multiplication beyond semiclassical limits.

Load-bearing premise

That the chosen model semiconductor structure and its real-space matrix representation sufficiently represent the essential physics of real avalanche junctions without further experimental checks.

What would settle it

Measuring the actual onset field or multiplication factor in a nanoscale silicon junction and comparing it to the model's prediction for carrier multiplication from the spectral function; mismatch would disprove the formulation's accuracy.

Figures

Figures reproduced from arXiv: 2605.01244 by Colin Burdine, Enrique P. Blair, Nischal Binod Gautam.

Figure 1
Figure 1. Figure 1: The simplified block diagram of a representative view at source ↗
Figure 2
Figure 2. Figure 2: The quantum transport model of the generic silicon p–n junction device enables the modeling of incoherent NEGF view at source ↗
Figure 3
Figure 3. Figure 3: Physically, an ionization event requires: (i) an energetic view at source ↗
Figure 4
Figure 4. Figure 4: (a) The blue curves in the silicon band structure view at source ↗
Figure 6
Figure 6. Figure 6: (a): Unit cell band structure of a 2D slab of intrinsic view at source ↗
Figure 8
Figure 8. Figure 8: (a) The local density of states (LDOS) shows the view at source ↗
Figure 7
Figure 7. Figure 7: (a): Effective built-in potential of the nm-scale device view at source ↗
read the original abstract

We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes. Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents an atomistic NEGF-based quantum transport framework for modeling impact ionization in semiconductor avalanche photodiodes relevant to quantum networking. It formulates impact ionization as a multi-particle self-energy to obtain a non-perturbative, energy- and atomic-orbital-resolved description of carrier multiplication extracted directly from the device spectral function. The approach is implemented in a matrix-based real-space representation and is demonstrated on a model semiconductor structure under high electric fields, where the emergence of carrier multiplication is shown along with its dependence on energy-resolved transport and nonequilibrium charge distributions. The work positions this as a baseline for self-consistent calculations of avalanche processes beyond semiclassical methods.

Significance. If the central formulation and demonstration hold with supporting quantitative evidence, the work could provide a valuable microscopic, orbital-resolved tool for predicting avalanche behavior in nanoscale high-field devices, offering potential improvements over local ionization coefficient or Monte Carlo approaches for applications in silicon single-photon avalanche detectors and quantum-network receivers.

major comments (2)
  1. [Abstract / Results] Abstract and results section: The central claim that the multi-particle self-energy formulation yields a non-perturbative, orbital-resolved carrier-multiplication description 'directly from the device spectral function' is load-bearing, yet the manuscript reports no quantitative values for multiplication gain, energy-resolved ionization rates, spectral-function features, or any comparison to experimental data, semiclassical ionization coefficients, or Monte Carlo benchmarks. Without these, it is not possible to verify whether the real-space matrix representation captures the inelastic processes or whether hidden approximations remain.
  2. [Model and Methods] Methods / model description: The weakest assumption—that the chosen model semiconductor structure under high fields plus the matrix-based real-space representation captures the essential physics of real avalanche junctions—is stated without validation or sensitivity analysis; this directly affects whether the demonstrated emergence of carrier multiplication generalizes beyond the specific model.
minor comments (2)
  1. [Theory] Notation for the multi-particle self-energy should be introduced with an explicit equation number and contrasted with standard single-particle NEGF self-energies to clarify the non-perturbative aspect.
  2. [Figures] Figure captions (if present) should explicitly label axes, units, and what 'emergence of carrier multiplication' is quantified by, rather than relying on qualitative statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address each major comment point by point below, providing clarifications and indicating revisions made to strengthen the work.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results section: The central claim that the multi-particle self-energy formulation yields a non-perturbative, orbital-resolved carrier-multiplication description 'directly from the device spectral function' is load-bearing, yet the manuscript reports no quantitative values for multiplication gain, energy-resolved ionization rates, spectral-function features, or any comparison to experimental data, semiclassical ionization coefficients, or Monte Carlo benchmarks. Without these, it is not possible to verify whether the real-space matrix representation captures the inelastic processes or whether hidden approximations remain.

    Authors: We agree that quantitative support is needed to fully substantiate the central claim. The manuscript prioritizes establishing the NEGF multi-particle self-energy formulation and showing the qualitative emergence of carrier multiplication via the spectral function in a controlled model. In the revised version, we have added explicit calculations of the energy-resolved multiplication factor extracted from the nonequilibrium spectral function, along with ionization rates resolved by orbital and energy. We also include a direct comparison of these rates to semiclassical local ionization coefficients for the same structure. These additions allow verification of the inelastic processes captured by the real-space representation. Broader experimental and Monte Carlo benchmarks remain planned for subsequent work on realistic device geometries. revision: yes

  2. Referee: [Model and Methods] Methods / model description: The weakest assumption—that the chosen model semiconductor structure under high fields plus the matrix-based real-space representation captures the essential physics of real avalanche junctions—is stated without validation or sensitivity analysis; this directly affects whether the demonstrated emergence of carrier multiplication generalizes beyond the specific model.

    Authors: We acknowledge that the model is a simplified representation chosen to isolate the quantum transport mechanisms of impact ionization. In the revised manuscript, we have expanded the methods section with a detailed justification for the structure and parameters, including the rationale for the high-field regime. We have also performed and reported a sensitivity analysis by varying electric field strength and key band-structure parameters, confirming that carrier multiplication emerges consistently. This supports the robustness of the observed physics and clarifies that the framework is intended as a baseline for extension to full avalanche junctions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; formulation is an independent modeling choice.

full rationale

The paper introduces impact ionization as a multi-particle self-energy inside the NEGF framework as a deliberate modeling extension, then extracts carrier multiplication from the resulting spectral function on a model structure. This is presented as an ansatz-based approach rather than a derivation whose output is forced by redefinition of inputs or by a self-citation chain. No equations are exhibited that reduce a claimed prediction to a fitted parameter, no uniqueness theorem is invoked from prior self-work, and the central non-perturbative claim follows directly from the chosen self-energy construction without tautological collapse. The derivation chain remains self-contained against the NEGF Dyson equation and spectral-function definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the NEGF formalism to strongly non-equilibrium high-field junctions and the validity of treating impact ionization via a multi-particle self-energy; no explicit free parameters or invented entities are detailed in the abstract.

axioms (1)
  • domain assumption NEGF formalism applies to nanoscale high-field junctions with strongly inelastic scattering
    Invoked to justify the non-perturbative description beyond semiclassical approximations

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Reference graph

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