# Experimental Validation of Impact Ionization Models for TCAD Simulation by a Novel Characterization Technique

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## Contents

### Introduction

Modeling and simulation of impact ionization in semiconductors is fundamental to the design and the robustness of electronic devices.

Among the available models, the most accepted are the Chynoweth’s law, the Van Overstraeten and De Man model, and the New Bologna Model, which provide analytical expressions for the impact ionization coefficients of electron and holes αe(E) and αh(E), respectively.

Experimentally, the impact ionization coefficients are mainly measured based on the charge multiplication factor inferred from the reverse current of PN-junctions reverse-biased at a voltage quite close to the breakdown. However, this approach is not very accurate, because, in real devices, the breakdown first occurs at small isolated spots or lines (e.g. because of three-dimensional effects), where the local current density may achieve very high levels without reaching the current threshold, which can be detected by the usual instrumentation.

Furthermore, all these models, mainly provide an averaged value of the multiplication factor. The probability distribution of the multiplication factor can only be obtained by Monte Carlo simulation, that nonetheless needs independent experimental data for calibration.

The scope of this work is to validate the main existing impact ionization models (in particular the New Bologna model), which are used in the major TCAD simulation tools.

### Short Description

The experimental approach for this work makes use of a single alpha particle emitted from an almost monoenergetic, collimated radioactive source to generate a very localized burst of electron-hole pairs in the close vicinity of the P+N––junction of a power diode, biased at a given reverse voltage. A dedicated high-gain amplifying chain is used to collect the charge pulse (with duration in the nanosecond range) that arises at the terminals of the device as the initial charge burst drifted along the depleted layer. The probability distribution of the collected charge is built by cumulating typically 20000 independent events. Then, the probability distribution of the multiplication factor is obtained by statistical processing the acquired data.

The multiplication factor extracted from previous experiment are compared with the multiplication factor predicted by Sentaurus-Device, as well as with dedicated Monte Carlo simulation tools.

### Tasks

The work includes experimental (60%) and simulation tasks (40%; SRIM, Sentaurus-device, dedicated Monte Carlo tool).

- • Get acquainted with the electronics for Multi-Channels Pulse Analysis
- • Get acquainted with the existing setup
- • Monte Carlo simulation of the range distribution of the alphas in the depletion region of the P+N––junction
- • Monte Carlo simulation the distribution of the energy released in the depletion region the P+N––junction
- • Carry-out measurements at low multiplication regime
- • Carry-out measurements at high multiplication regime
- • Statistical analysis of the acquired data
- • Extract the multiplication factors for electron by TCAD simulation with Sentaurus-Device
- • Extract the multiplication factors for electron by Monte Carlo simulation
- • Compare the TCAD simulations (by different impact ionization models) with the experimental data

### Prerequisites

- • EE students or in experimental physics

### Status: Available

- • Looking for 1-2 interested students in Electrical Engineering or Experimental Physics (semester project, Master's thesis).
- • Contact: Dr. Mauro Ciappa Marco Pocaterra
- • -> ETHZ IIS H.78

### Supervisors