Electron transport and quantum effects in semiconductor devices

This dissertation presents the research being conducted on the development of physical simulation models. First, a rigorous method to calculate the MOSFET gate leakage current is discussed. This method is based on the physical evaluation of the distribution function by the Spherical Harmonics Boltzmann Transport Equation (SH-BTE). The MOSFET tunneling current by WKB and thermionic current are studied extensively for different gate lengths, oxide thicknesses and bias conditions. The distribution of the gate leakage current along the gate and its dependence on energies are demonstrated. The physical phenomenon of barrier lowering by image charge is included in this model. A set of experimental data is fitted by this method and excellent agreement is obtained.; Second, a new approach for modeling quantum transport in nanoscale semiconductor devices is developed. Modeling is achieved by self-consistently solving the Poisson equation with the Wigner equation of quantum transport. The Wigner equation can be considered to be an extension of the semiclassical Boltzmann transport equation (BTE). Extending the spherical harmonic methodology to the Wigner equation allows for the reduction of dimensionality, as well as for a rigorous treatment of collisions. The solution of the Wigner transport equation provides the Wigner function throughout the device. The new approach has been applied to the simulation of a 2-D MOSFET, as well as a 1-D BJT. Results show corrections which are expected from quantum mechanical calculations, including reduction in electron concentrations in the vicinity of potential energy barriers. Calculated MOSFET current-voltage curves show a small reduction in the drain current when compared to the semiclassical results.; Third, the spherical harmonics are applied to realize the scattering matrix method of carrier transport modeling. Using the spherical harmonics has the advantage of reducing the matrix by approximately a factor of 10 less than the previous discrete basis approach. To realize the approach, new spherical harmonic functions are defined to overcome difficulties associated with orthogonality. The scattering matrix is calculated using Monte-Carlo techniques to populate the new basis functions. As an initial step towards demonstrating the accuracy of the new mathematical formulation, we calculate the electron energy distribution function in silicon for various homogeneous electric fields, and excellent agreement with both Monte Carlo and discrete basis simulations are obtained. Then, the average energy and average velocity are simulated for step fields by scattering matrix. Excellent agreement is also achieved when compared with the Monte-Carlo method.