A Monte Carlo study of the angular dependence of the depth distribution function of signal electrons in electron spectroscopies

The emission angle dependence of the depth distribution function of signal electrons in electron spectroscopies has been studied by means of a Monte Carlo simulation in which elastic scattering plays a significant role. Calculations were made for Si, InP, and In substrates at different emission angles (0°, and 40° to 80° off normal). The calculated depth distribution of signal electrons showed significant deviations from exponential attenuation at the more oblique emission angles. In consequence, the ‘‘attenuation length’’ of signal electrons loses its status of a material constant. A new empirical depth distribution function is proposed which consists of the sum of two exponential terms. This function describes the calculated Monte Carlo depth distribution as a function of the emission angle. The first term of this depth distribution function represents the contribution of those electrons which follow parallel straight‐line paths, whereas the second term accounts for a randomization of electron directions due to elastic scattering. Common to both terms is a parameter which we propose to call the attenuation parameter. A relationship is established between the attenuation parameter and the ‘‘effective attenuation length,’’ as proposed earlier [W. H. Gries and W. Werner, in Proceedings of the European Conference on Applied Surface and Interface Analysis, ECASIA, Antibes, France, 1989 (unpublished)]. The attenuation parameter is independent of the angle of emission, in contrast to the effective attenuation length. Evidence was found and is discussed, which indicates that the results apply equally to other materials. In special situations, the thickness dependence of the depth distribution function in the case of an overlayer situation is accounted for by using the new depth distribution function.