Computational study of energy filtering effects in one-dimensional composite nano-structures

Possibilities to improve the Seebeck coefficient S versus electrical conductance G trade-off of diffusive composite nano-structures are explored using an electro-thermal simulation framework based on the non-equilibrium Green's function method for quantum electron transport and the lattice heat diffusion equation. We examine the role of the grain size d, potential barrier height Phi(B), grain doping, and the lattice thermal conductivity kappa(L) using a one-dimensional model structure. For a uniform kappa(L), simulation results show that the power factor of a composite structure may be improved over bulk with the optimum Phi(B) being about k(B)T, where k(B) and T are the Boltzmann constant and the temperature, respectively. An optimum Phi(B) occurs because the current flow near the Fermi level is not obstructed too much while S still improves due to barriers. The optimum grain size d(opt) is significantly longer than the momentum relaxation length lambda(rho) so that G is not seriously degraded due to the barriers, and d(opt) is comparable to or somewhat larger than the energy relaxation length lambda(E) so that the carrier energy is not fully relaxed within the grain and |S| remains high. Simulation results also show that if kappa(L) in the barrier region is smaller than in the grain, S and power factor are further improved. In such cases, the optimum Phi(B) and d(opt) increase, and the power factor may improve even for Phi(B) (d) significantly higher (longer) than k(B)T (lambda(E)). We find that the results from this quantum mechanical approach are readily understood using a simple, semi-classical model. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3678001]