where P[k(t)]dt is the probability that an electron in the state k suffers a collision during the time dt. Because of the complexity of the integral at the exponent, it is impractical to generate stochastic free flights with the distribution of the equation above. In order to overcome this difficulty, people use a fictitious “self-scattering” scheme. By doing this, the total scattering rate, including this self-scattering, is constant and equal to, say, Γ Γ . By random selection, if self-scattering is selected, k′ after the collision is the same as k and the carrier continues its flight without perturbation. Introducing a constant P ( k ) = τ τ 0 − − 1 , the above equation reduces to