Abstract

Silicon nanostructures have recently been a subject of interest demonstrating optimistic optical properties like luminescence. The scientific community predicts quantum effects to be the predominant cause for such optical properties of silicon nanostructures, hence it becomes prudent to pursue the roots of such reduced dimensional devices. With this view as a motive, a simulation model for a 2D thin film quantum confined 2D pn junction in silicon is developed in this work. A thin film silicon layer is considered in the regime of strong confinement. A pn junction in such a film is considered so that the carriers are confined in thickness dimension while they are quantum mechanically transported along the device length. The transverse dimension in considered infinitely wide for plane wave approximation. For device simulation, after a careful study of various schemes to incorporate quantum effects (Van Dort model, Density Gradient Method, etc.) it was decided to use the more rigorous self-consistent Schrödinger-Poisson method. Keeping in mind the computational resource constraints, for problem formulation, decoupled 1D set of equations for carrier transport is deployed. For electrons, the well known single-band effective mass Hamiltonian is used while for holes, multi-band effective mass Hamiltonian with light and heavy holes is applied (though a full 6 band k.p Hamiltonian and spin orbit interaction is required to account for a full featured valence band, no effective work has been done to use such a formulation for a reduced dimensional device). Overall discretization is done using the finite element method with matrix representation of equations. The ohmic contacts in longitudinal direction are simulated with semi infinite open boundary contacts through self energy matrix, and broadening of energy states is incorporated. The simulation is done in Matlab as it gives the highest flexibility (in comparison to Silvaco, Femlab and C++ with the latter being unrealistically involved in numerical solution algorithm). For solution, instead of Wigner function or Green's function, a more direct wave-function perspective is taken. First the equilibrium condition was simulated, and then extension under externally applied voltage was carried out. As the results show, confinement of carrier in lateral dimension results in energy quantization, and consequently subbands. As the material is degenerately doped, the number of carrier is comparable to existing states and carriers exist in excited states also. The occupancy of only three subbands upholds the earlier assumption that only a few subband are occupied. And along with the retention of subband shapes along device length, validates decoupling of the dimensions. The depletion region width is found to be more than that predicted by 3D junction equations. This may be due to the fact that the thin film cannot fully screen the electric field. Current voltage characteristics also do not show any significant tunneling current