Modeling Electron Transport and Degradation Mechanisms in Semiconductor Submicron Devices.
Abstract
A new efficient physically-based model for describing carrier transport and hot-electron degradation mechanisms in semiconductor devices is presented. The model combines the Legendre polynomial method with the energy transport technique in order to solve the Boltzmann transport equation and ascertain the electron momentum distribution function. Information from the distribution function is then used to predict MOSFET reliability problems induced by hot-electron degradation. Values obtained for the distribution function, as well as for drift velocity and average energy, agree with Monte Carlo calculations while requiring less than 1over {100} the CPU time to evaluate. Initially, Legendre polynomials and the parabolic band approximation are used to obtain an approximate solution to the homogeneous Boltzmann equation for electrons in silicon: this derivation incorporates the effects of intervalley and acoustic phonon scattering. The solution provides an analytical expression for the space-independent distribution function. By incorporating the non-parabolic silicon band structure into the analysis, a distribution function is then obtained which reflects quantum mechanical restrictions on electron transport. The homogeneous Boltzmann equation is solved numerically, using Legendre polynomials and matrix methods, while also including the effects of non-parabolicity, phonon scattering, and impact ionization. The resulting distribution function is then used to calculate average electron energy and drift velocity. An expression for mobility is then determined which accounts for the non -parabolic band structure. An optical phonon mean-free -path is derived, and the theoretical value obtained agrees with experiment. Space-dependence is incorporated using energy transport techniques. First, a new self-consistent method, which utilizes Legendre polynomials, to derive the continuity, momentum balance, and energy balance equations is presented. Next, the energy balance equation is solved numerically in one dimension. By mapping the space-dependent average energy, obtained from the solution to the energy balance equation, into the homogeneous Boltzmann equation, a space-dependent distribution function is determined. The techniques developed are combined into a user -friendly device simulation program, RELY, which is used to predict MOSFET reliability problems. RELY uses information obtained by solving the Boltzmann equation, to calculate gate leakage current and oxide charge deposition. Agreement with experiment was obtained.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 1989
- Bibcode:
- 1989PhDT.......119G
- Keywords:
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- Engineering: Electronics and Electrical; Physics: Condensed Matter