The Design And Simulation Of Subminiature Semiconductor Devices

We study transport theory that contains both non-equilibrium and quantum effects, suitable for simulation nano electron devices. Mature drift-diffusion based transport theory is no longer valid for studying and simulation of current nano electron device. There is an urgent need to develop general, accurate, computationally efficient transport theory which can conprehensively describe non-equilibrium and quantum effects. Compared with mature drift-diffusion model, higher order partial differential equations are added to the fluid mechanics model, which can describe the carrier temperature, thermo electron and partial nonequilibrium effect caused by the miniaturization of the device independently. Our research applies the moment expansion of the Boltzmann transport equation to the first three order to get three partial differential equations of particles of conservation, momentum conservation and energy conservation which are called the general equations of fluid mechanics. This model is suitable for arbitrary energy band. And the general fluid mechanics model (Thomas Model) is deduced in detail, we applies the moment expansion of the Wigner transport equation to get the quantum hydrodynamic model, which is fully considering quantum-mechanical effects and making up for the quantum scattering effect which is neglected by the semi classical Boltzmann equation. We simply the quantum energy transmission model and use the central finite difference method to discrete the equations in order to determine the relationship between electron density and temperature. Then We introduce the cumulant expansion method to check the validity of characteristic function when the distribution satisfies the shifted maxwellian. After showing the advantages over moment expansion, we perform Fourier transformation to the Boltzmann transport equation and obtain a set of partial differential equations for the cumulants, after factoring out a characteristic function from each term.The collisions of the BTE in the nano device are mainly composed of phonon (lattice) scattering, interfacial scattering and ionized impurity scattering. The quantum mechanical Fermi method is used to study the microscopic scattering of optical phonons, acoustic phonons, interfaces and ionized impurities, which is suitable for the carrier band structure model. We use the microscopic quantum scattering model instead of mobility and the relaxation time approximation and apply the cumulant expansion to the collision operator for the Boltzmann transport equation to get the first three cumulant collisions. Then, with the aid of perturbation quantum mechanics knowledge, in the case of optical phonon, collision term specific expression is deduced which get rid of the present inaccurate relaxation in non-equilibrium transport theory. Finally, we use the software Maple to verify the accuracy of characteristic funcion when the distribution function satifies gaussian distribution, the relationship between the moment expansion and cumulant expansion, and the partial differential equations after doing the Fourier transform to BTE and factoring out a characteristic from each term respectively.