Understanding the Average Electron–Hole Pair-Creation Energy in Silicon and Germanium Based on Full-Band Monte Carlo Simulations

The thermalization process of sub-10-eV charge carriers is examined with treating carrier transport with full-band Monte Carlo simulations. The average energy loss (3.69 eV in Si and 2.62 eV in Ge) required to create a thermalized electron-hole pair, obtained from the simulations, is very close to the experimentally measured radiation-ionization energies of Si and Ge irradiated with high-energy particles. These results suggest that only interactions that occur after the radiation-generated charge carriers decay to energies of ~10 eV or less determine the fundamental property of the radiation-ionization energies. In addition to an energy loss equal to the band gap energy via impact ionization, acoustic-phonon emission, which has been omitted in prior work, contributes 30% of the remaining carrier energy loss, while optical-phonon emission contributes the other 70%.

I. Introduction

The key basic mechanisms associated with single-event effects [1] in electronics are: 1) energy transfer via transport of the particle through the target material; 2) conversion of the energy deposited by the particle to free charge; 3) collection of that charge by sensitive regions within the semiconductor; and 4) the circuit response to the current produced by the collected charge. Of these four basic mechanisms, the second one is the least understood and is historically determined by experimental techniques. Understanding the radiation–ionization energy required to generate an electron–hole pair (EHP) is essential for determining the amount of free charge liberated by the ionizing particles (the same physical phenomena are also important for understanding the avalanche breakdown in p-n junctions [2] and photoemission efficiency [3]). The term ionization is used throughout this paper to refer to the creation of nonequilibrium free charge carriers in a semiconductor.