Escape of implanted oxygen from molybdenum at different temperatures

It has been established that implantation of oxygen ions in single-crystalline molybdenum after the required thermal activation of the sample at sample temperatures above 650°C increases the vacuum work function by 0.4-0.7 eV [1], which with a cesium coating corresponds to an increase of the thermionic emissivity by several times. During the mandatory thermal activation, however, as well as at the working temperature oxygen diffuses* from the surface layer to the surface and evaporates, thus lowering the oxygen concentration at the surface. As a result, the increase in the vacuum work function due to the implanted oxygen decreases. The vacuum work function was measured on a thermionic-emission microscope by the total-current method [2], and the oxygen concentration at the surface and in the surface layer was measured with an Auger microanalyzer. In order to study the characteristics of the escape of implanted oxygen from the sample (i.e., determination of the diffusion characteristics of oxygen migration) we shall employ the results of multistep annealing of a Mo (111) sample with implanted oxygen at 700°C in the chamber of an Auger analyzer with the amount of oxygen remaining in the surface layer determined after each step. Two samples were investigated: The first sample was heated only with multistep annealing at 700°C and the second sample was first subjected to preliminary stepped annealing [3], and then rnultistep annealing at the same temperature. Knowing the characteristics of escape of implanted oxygen from molybdenum at 700°C and having sufficient experimental data on the escape of implanted oxygen at 600, 700, 1100, and 1600°C, we shall attempt to estimate the lifetime of such systems analytically. We employ the solution of Fick's diffusion equation for a point source, and we describe the initial distribution of the implanted oxygen as a superposition of point sources. In our case, in studying the escape of implanted oxygen from a molybdenum sample we shall consider a surface layer h in which the oxygen is concentrated in the form of a collection of k thin layers of thickness h k and concentration C k, where C k = Qk/hk. We obtain the total amount of implanted oxygen Q in the surface layer by summing the content of implanted oxygen Qk. When the sample is heated, the oxygen must evaporate from the surface in the measure determined by oxygen diffusion to the surface. It is assumed that over the entire experiment the oxygen concentration on the surfaces of the sample is maintained constant and equal to zero (C)x= / = 0 [41. For each layer xk(x0 k hk/2 < x k < xok + hk/2) we can find up to the time t the distribution over the thickness C(x ~, t) and the fraction ~xk(t) that has emerged from a given layer of the sample through the lateral surfaces, including also in the case of an asymmetric arrangement of the layer (in our experiments l /h' 104), where h' is the half-thickness of the layer with ion-implanted oxygen and ! is the thickness of the sample. Integrating over all layers we obtain the desired results for the total distribution and the total yield. Hence, having determined from the experimental values the coefficient, the rate, and the activation energy of diffusion, we can model the diffusion process over time. The problem for each layer can be formulated mathematically as follows. We are required to find the solution of the diffusion equation