A ballistic transport model for electronic excitation following particle impact

We present a ballistic model for the transport of electronic excitation energy induced by keV particle bombardment onto a solid surface. Starting from a free electron gas model, the Boltzmann transport equation (BTE) is employed to follow the evolution of the temporal and spatial distribution function f(r→,k→,t) describing the occupation probability of an electronic state k→ at position r→ and time t. Three different initializations of the distribution function are considered: i) a thermal distribution function with a locally and temporally elevated electron temperature, ii) a peak excitation at a specific energy above the Fermi level with a quasi-isotropic distribution in k-space and iii) an anisotropic peak excitation with k-vectors oriented in a specific transport direction. While the first initialization resembles a distribution function which may, for instance, result from electronic friction of moving atoms within an ion induced collision cascade, the peak excitation can in principle result from an autoionization process after excitation in close binary collisions. By numerically solving the BTE, we study the electronic energy exchange along a one dimensional transport direction to obtain a time and space resolved excitation energy distribution function, which is then analyzed in view of general transport characteristics of the chosen model system.