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Title: Macroscopic modeling of quantum effects in semiconductor devices
Authors: Narayanan, Venkatasubramanian
Keywords: semiconductors
carrier transport
quantum effects
quantum transport
macroscopic modeling
Issue Date: 4-May-2006
Abstract: This dissertation explores the use of macroscopic quantum hydrodynamic (QHD) models as tools for investigating the transport of charge carriers in semiconductor devices in the regime where quantum effects are important. Chapter 1 provides a panoramic view of the field of carrier transport modeling in semiconductors. The essential differences between classical and quantum transport is brought out and a brief outline is given of the derivation of successively less detailed models from the fundamental starting points of the Boltzmann transport equation (BTE) for classical transport and the quantum distribution function (Wigner function, density matrix) based methods for quantum transport. A mention is made of the various quantum hydrodynamic models without going into the details of their derivation and applicability. Chapter 2 brings into focus the area of quantum hydrodynamic modeling of carrier transport. A detailed derivation using the method of moments is presented for each of the popular quantum hydrodynamic models currently being explored in the literature, namely the density-gradient method and the smooth quantum potential model. A summary is made of their limitations and these limitations are then shown as arising out of particular assumptions made in their derivations that could hamper their applicable regimes. Chapter 3 presents an analysis of the boundary layers near interfaces obtained in density-gradient theory. An integral equation for the density near such interfaces is obtained and this is used to analytically compare the DG solution with the solutions from one-electron quantum mechanics in non-degenerate conditions. Confinement in simple potential wells is then discussed using the macroscopic equations. Chapter 4 discusses the derivation of macroscopic equations to describe quantum mechanical tunneling through large barrier potentials. Using the approximate solutions of the Schr?dinger equation it is analytically shown that the density profile inside the barrier satisfies a second order differential equation, very similar to the Schr?dinger equation for a carrier at a suitably chosen average energy. Use of this is made to derive a consistent macroscopic treatment of tunneling transport in the insulating barrier. Chapter 5, the final chapter, summarizes the major contributions of this dissertation and concludes it with several suggestions for future research directions that can stem from this work.
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