Excitons in small hydrogenated Si clusters

Abstract

The excitonic states of four small hydrogenated Si clusters (SiH 4 ,Si 2 H 6 ,Si 5 H 12 , and Si 10 H 16 ͒ are studied using the diffusion quantum Monte Carlo approach. The importance of using accurate guiding wave functions is stressed and we show that the quantum chemical singles-only configuration interaction method and the time-dependent density functional theory within the adiabatic local-density approximation can provide suitable zeroth-order approximations in these systems.Hydrogenated silicon clusters are of significant interest because they may be used to model the absorption and emission of visible light in quantum dots 1 and porous silicon. 2 The optical properties of these systems are strongly influenced by exciton formation, and the accurate prediction of their excitonic gap energies is one of the most challenging theoretical problems in these materials.Excitation energies in hydrogenated silicon clusters have been studied using many theoretical methods, including tight-binding and density-functional methods, and manybody perturbation theory. In this paper we present a study of the excitonic states of small Si n H m clusters using the diffusion quantum Monte Carlo ͑DMC͒ technique. [3][4][5] The small clusters that we study (SiH 4 ,Si 2 H 6 ,Si 5 H 12 , and Si 10 H 16 ͒ are at the molecular limit of semiconductor nanostructures. Small clusters have the advantage that a significant amount of experimental and theoretical data exists with which we can compare our results. Any method capable of giving an accurate description of excitonic behavior in semiconductor clusters at the microscopic level should be able to describe excitons in these clusters, which are therefore important systems for the benchmarking of theoretical methods.DMC is a stochastic method for evolving the imaginarytime Schrödinger equation. The fermionic symmetry is maintained using the fixed-node approximation 6 in which the nodal surface of the wave function is constrained to equal that of a guiding wave function. DMC presents an attractive approach for studying electronic systems because it can achieve very high accuracy and the computational cost scales as N 3 , where N is the number of electrons, which is much more favorable than other correlated wave-function methods.Accurate DMC calculations of ground-state energies have already been demonstrated and in principle such accuracy can also be attained for excited states. The DMC method gives the lowest energy consistent with the nodal surface of the guiding wave function 7,8 and it is therefore crucial that the guiding wave functions give a reasonable description of the excited states of the system. We use guiding wave functions of the Slater-Jastrow type where the Slater part, consisting of a sum of determinants, is multiplied by a nodeless Jastrow correlation factorwhere exp(J) is the Jastrow factor and D i ↑ and D i ↓ are Slater determinants of one-particle up-and down-spin orbitals. The Jastrow factor does not alter the nodal surface of the guiding wave function, which is therefo...

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