Question

a) Show that the real and imaginary part of the dielectric function έ-εϊ +1e, İn a metal in th f high frequencies ωτ>>1, with τ being the mean free collision time of electrons limit o (equal to the invers collision rate l/y) can be written as εί-|-up and ε,--wit itten as 6, -1 and P with the plasma frequency op-vn.etlm*co Assume that there is no polarizability arising electrons bound to the ion cores at these high frequencies. Sketch εί and ε2 as a function of frequency Show that the position of the plasma frequency can be determined by the "energy loss function"-Im(1/2) if the frequency dependence of ε +s2 is known, energy loss function for Aluminum (Al) with a',-15.2 eV/h . Sketch the

Answer 1

We assume no polarizability arising from electrons band to ion copres at the high frequencies therefore E = E_0 I E_B we can also write C - epsilon_0 + i epsilon_2 in a metal in co epsilon > > 1 we know that wave vector 1C k = w/c n where n = squareroot mu E/ mu_01 epsilon_0 as K = beta + I alpha/2 therefore for n being complex number n = m_r + I n_i n_r = squareroot squareroot epsilon_i^2 + epsoilon^2_r + epsilon_r/2 n = squareroot squarew root epsilon_i^2 6 epsilon_r^2/82 - epsilon_r/2 therefore we know that epsilon_r = 1 + 6 N alpha_e/ epsilon_0 therefore Relation time I alpha d/sigma Hence we wrute epsilon_1 = 1- w_1^2/w^2 epsilon_2 = w_1^2/w I where cop = squareroot n epsilon^2 (m epsilon_0 position of plasma frequency is determined by energy loss function - J_m (1/ epsilon) is frequency dependence of epsilon^bar = epsilon_1 + I epsilon_2