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Barrett, Junior Augustus (2014)
Languages: English
Types: Doctoral thesis
Subjects:
The work in this thesis is focussed on obtaining fast, e cient solutions to\ud the Schroedinger-Poisson model of electron states in microelectronic devices.\ud The self-consistent solution of the coupled system of Schroedinger-Poisson\ud equations poses many challenges. In particular, the three-dimensional solution\ud is computationally intensive resulting in long simulation time, prohibitive\ud memory requirements and considerable computer resources such as\ud parallel processing and multi-core machines.\ud Consequently, an approximate analytical solution for the coupled system\ud of Schroedinger-Poisson equations is investigated. Details of the analytical\ud techniques for the approximate solution are developed and the original\ud approach is outlined. By introducing the hyperbolic secant and tangent\ud functions with complex arguments, the coupled system of equations is transformed\ud into one for which an approximate solution is much simpler to obtain.\ud The method solves Schroedinger's equation rst by approximating the electrostatic\ud potential in Poisson's equation and subsequently uses this solution\ud to solve Poisson's equation. The complete iterative solution for the coupled\ud system is obtained through implementation into Matlab.\ud The semi-analytical method is robust and is applicable to one, two and\ud three dimensional device architectures. It has been validated against alternative\ud methods and experimental results reported in the literature and it\ud shows improved simulation times for the class of coupled partial di erential\ud equations and devices for which it was developed.
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    • Appendix B MOSFET characteristics 167 B.1 Operating regions of the n-channel MOSFET . . . . . . . . . . 167 B.2 Saturation region . . . . . . . . . . . . . . . . . . . . . . . . . 168 Appendix C The Wronskian 171 C.1 De nition of the Wronskian . . . . . . . . . . . . . . . . . . . 173 Appendix D The Evans Function 174 D.1 De nition of Evans function in one-dimension . . . . . . . . . 176 A.1 Metal, oxide and semiconductor energy band diagrams are separatedly shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A.2 Energy-band diagram of an ideal MOS at V = 0 for a p-type semiconductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.3 Energy-band diagram of an ideal MOS at V 6= 0 for a p-type semiconductor. The accumulation case. . . . . . . . . . . . . . . 165 A.4 Energy-band diagram of an ideal MOS at V 6= 0 for a p-type semiconductor. The depletion case. . . . . . . . . . . . . . . . . 166 A.5 Energy-band diagram of an ideal MOS at V 6= 0 for a p-type semiconductor. The inversion case. . . . . . . . . . . . . . . . . . 166 2 d
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