Injection of charge nanostructures into insulators

Abstract

The electron beam induced selfconsistent charge transport in insulators is described by means of an electron-hole flight–drift model FDM and an iterative computer simulation. Ballistic secondary electrons and holes, their attenuation and drift, as well as their recombination, trapping, and detrapping are included. Thermal and field-enhanced detrapping are described by the Poole–Frenkel effect.

As a main result the time dependent secondary electron emission rate $\sigma \left(t\right)$ and the spatial distributions of currents $j(x,t)$, charges $\sigma (x,t)$, field $F(x,t)$, and potential $V(x,t)$ are obtained. The spatial charge distributions with depth show a quadropolar plus–minus–plus–minus structure in nanometer dimensions.

Introduction

In electron microscopy like scanning electron microscopy (SEM) or Auger electron spectroscopy (AES), electron energy loss spectroscopy (EELS) etc., the prediction of electrical charging is essentially to interpret the measurements, see e.g.  [1]. Moreover, charging of non-conductive samples has to be known in order to manage applications such as functional layers and in nanotechnology, [2].

A great number of experimental and theoretical investigations have been published on the charging of insulators due to electron bombardment and the related secondary electron emission (SEE). Only for short pulse irradiation, target charging is prevented and the real charging-free secondary electron emission yield $\sigma \left(E_0\right)$ as a function of the primary electron energy $E_0$ can be measured as well as has been determined theoretically for various insulators [3], [4]. However, the charging behaviour under permanent electron irradiation is not yet fully understood and the stationary final state is still very complex to describe. Indeed, the total yield approach ($\sigma \stackrel{>}{<}1$) is often used to predict the sign ($\pm$) of charging in the case of stationary electron irradiation, but experimental results are not fully consistent with these predictions [1], [5].

It is of importance to determine the types of theory that have been led to enlighten this phenomenon. One of the first attempts was the planar (1-dimensional) selfconsistent charging simulation of our co-author (HJF) already in 1979, [6], later improved on in Refs. [7], [8], [9], [10]. These authors use field-dependent attenuation lengths $\lambda \left(F\right)$ for the ballistic transport of electrons and holes which had been found experimentally by means of electron beam induced current (EBIC) measurements.

The present paper will extend the model of ballistic electron and hole transport to drift processes, recombination and charge trapping processes, as has already been shown in Ref. [10]. Thus, spatial charge profiles in nanoscale dimensions are built up in insulating samples. The results will be presented in particular for silica SiO₂ similar to what has been shown earlier for alumina Al₂O₃ [8], [9], [10], but can be easily adapted to any insulator using the relevant material data available in the literature.