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# Monte Carlo studies of ionized impurity scattering in silicon and silicon-germanium alloys

#### Abstract

An improved Monte Carlo model for ionized impurity scattering is developed and applied to transport problems in Si and the Si$\sb{1-x}$Ge$\sb x$ alloy system. The model includes scattering cross sections derived from phase-shift analysis, implementation of the Friedel Sum Rule, and a simple phenomological model for multiple-potential scattering. Using a single adjustable parameter, majority and minority electron mobilities are calculated for Si and fit to experimental data. Experimental results for Si of $\mu\sb n(N\sb A)/\mu\sb n(N\sb D) \approx$ 2 at 300 K are reproduced and a value of 3 $< \mu\sb n(N\sb A)/\mu\sb n(N\sb D) <$ 4 is predicted at 77K.^ Low-field mobilities are then calculated for both strained and unstrained Si$\sb{1-x}$Ge$\sb x$ over wide ranges of doping, Ge mole fraction, and electric field, at 300K and 77K. A significant improvement in mobility (up to 50%) is observed for transport perpendicular to the growth plane in strained Si$\sb{1-x}$Ge$\sb x$, especially at 77K. High field MC simulations show that some strained mobility enhancement remains even at an electric field of 100 kV/cm.^ The improved model is then used in both DDE and Monte Carlo simulations at 300K and 77K of two strained-layer n-p-n Si$\sb{1-x}$Ge$\sb x$ HBTs with basewidths of 1000 A and 650 A and maximum Ge contents of 15% and 10% respectively. We find that as a result of improved mobility in the base and collector and velocity overshoot in the high field region, $h\sb{fe}$ and $f\sb T$ are improved significantly for the strained 650 A basewidth HBT as compared to a similar unstrained structure, especially at 77K. ^

#### Subject Area

Engineering, Electronics and Electrical|Physics, Electricity and Magnetism|Physics, Condensed Matter

#### Recommended Citation

Leonard Edward Kay, "Monte Carlo studies of ionized impurity scattering in silicon and silicon-germanium alloys" (January 1, 1991). Doctoral Dissertations Available from Proquest. Paper AAI9120900.
http://scholarworks.umass.edu/dissertations/AAI9120900

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