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Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity

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Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity ( nanomechanics-quantum-size-effects-contacts-and-triboelectri )

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44 Number of electrons in square cross-section % ******************************************************** % * The program calculates the number of electrons % * below Fermi level EF for standing electron waves on % * a square cross section d0 x d0 with energy % * E = E0*(n1^2 + n2^2) where n1,n2 = 1,2,3,... and E0 % * is given by E0 = hbar^2 Pi^2/(2 m d0^2). % ******************************************************** Nmax = 50; % Nmax > sqrt(EF/E0) N = 0; % The number of electrons E0 = 0.02348; % 4 x 4 nm cross section %E0 = 0.3757; % 1 x 1 nm cross section EF = 5.5; % Fermi energy for gold in eV % Sum over all energy levels that can contribute: for n1=1:Nmax for n2=1:Nmax % Calculate energy using n1 and n2: E = E0*(n1*n1+n2*n2); % Add electrons only if energy is below EF: if (E < EF) % Add one electron at this level: N = N + 1; end end end % Print the result: N Using d0 = 1 nm in the program we obtain N = 8 electrons below Fermi level and from d0 = 4 nm we obtain N = 172 electrons. This is to be compared with the more simple asymptotic formula used in Paper I: En = 􏰞2 4πn, (A.2) 2m S where S = d20. This one yields N = 11 and N = 183 electrons respectively.

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