Displacement damage in silicon studied by the electronic force field method in the keV regime

Highlights

• Electronic effect has a high impact to low-energy irradiation event in Si with eFF-MD.

• Nonadiabatic coupling is important for the energy dissipation in the DD processes.

• Amorphous clusters only result from overlapping of displacement cascades.

Abstract

Displacement damage (DD) caused by neutron irradiation is one of the major causes of the degradation and failure of semiconductor devices in hazardous environments. Classical molecular dynamics (MD) has been the method of choice in computer simulation of DD. In this paper, it is found, contrary to common belief, that not including electronic effects is a serious flaw of classical MD even in the study of low-energy DD. The DD of bulk silicon in keV regime is investigated with the electron force field (eFF), which incorporates explicit electron movement in MD. The eFF results agree with those of the experiments, but differ significantly from those of classical MD.

Introduction

Semiconductor devices have become an inseparable part of modern life. Many semiconductor devices based on various types of materials have been developed, has a variety of applications, such as in transistors, rectifiers, photovoltaic cells, and so on. In hazardous environments, such as the outer space, particle accelerators or nuclear reactors, the irradiation of energetic particles over semiconductor devices could lead to device degradation or even failure. For all the semiconductor devices, the displacement damage (DD), where the atoms are knocked off their equilibrium positions by incident particles, is a major effect of irradiation [1], [2]. Understanding the mechanism of irradiation DD in materials is crucial for designing irradiation hardened devices. However, the microscopic detail of irradiation process can be difficult to reveal due to the limitation of experimental techniques. Two methods for the numerical simulation of the irradiation DD process are widely used in the past, which provide some insight into the mechanism of DD. The first one is the binary collision approximation (BCA), which is proved to be an efficient model for calculating the recoil atom range since 1960’s [3], [4], [5], [6], [7], [8]. The second one is the classical molecular dynamics (MD), which has been used to describe the dynamics of the irradiation cascade since 1980’s [9], [10], [11], [12], [13], [14]. Both the methods are unable to incorporate the electron effect, which is critical for the high energy ions irradiation and photons irradiation. This restricts their applications to low energy ions irradiation events, which is considered to have little relation with electrons.

Although a large amount of low energy ions irradiation simulations are available in literature, they rarely agree with each other [15]. Moreover, the existing simulation results do not agree well with experiments: classical MD simulations predict amorphous defect clustering with a single incident particle with the energy as low as 20 keV [15], [16], while experiments show the formation of amorphous defect cluster needs the overlap of two or more cascades [17], [18]. These discrepancies might attribute to the electron effect. The expensive ab-initio MD (AIMD) simulation has been shown to yield good agreement with experiment on threshold energy [19], suggesting the importance of the electronic effect in DD. However, AIMD has the limitation that simulations do not incorporate non-adiabatic effects such as thermal electron excitations, due to the use of Born-Oppenheimer approximation. The much higher computational cost of AIMD comparing with classical MD forbids its application to large systems, which limits its usefulness in the study of DD. Although the two-temperature model MD (TTM-MD) is an alternative method to include the non-adiabatic effects, the choice of electron related parameters is subtle. In recent years, the time-dependent density functional theory (TD-DFT) is employed to get an excellent description on the electron-phonon coupling and electron stopping power [20], [21]. Based on these parameters of electron, the TTM-MD has been successful on the DD simulation [22]. We are not aware of any first principle non-adiabatic molecular dynamics method that has been applied to the study of DD, as the cost would be prohibitively high.

In this paper, we investigate the irradiation DD process in silicon with the electron force field (eFF) method [23], [24], [25], which is a semi-classical approach to the Ehrenfest MD for incorporating the effect of electronic movement, but with much less computational cost. We find that, contrast to common belief, 1. Individual PKA cannot produce amorphous defect cluster but only a few Frenkel pairs, and formation of amorphous defect cluster requires more than one PKA; 2. The electron-phonon coupling effect is important in energy dissipation of the DD process, even for low energy PKAs in which the nuclear energy loss dominates over the electronic energy loss. Contrary to results of the classical MD, the eFF-MD results are qualitatively consistent with experiments.