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hw3_solutions - ECE 440 Homework III Solutions Spring 2006...

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ECE 440 Homework III Solutions Spring 2006 Due: Friday, February 03, 2006 1. (a) It was mentioned in Section 3.2 that the covalent bonding model gives false impression of the localization of carriers. As an illustration, calculate the radius of the electron orbit around the donor in Fig. 3-12c, assuming a ground state hydrogen-like orbit in Si. Compare with the Si lattice constant. Use m n * = 0.26 m o for Si. Equation 2-10 in the Streetman text describes the relationship between an atomic radius and the effective mass of the element under the Bohr Model: Comparing to the Silicon lattice constant (a=5.43 angstrom), the atomic radius is approximately 4.4x as large. This should make sense because the tightly packed shells surrounding the core of the atom repulses the outer most electron to the point at which it is very loosely bounded. This is called charge screening. (b) Repeat part (a) for the radius of an electron orbiting around the donor in GaAs, assuming m n * = 0.067 m o for GaAs. Compare the radius with the GaAs lattice constant.
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Comparing to the Gallium Arsenide lattice constant (a=5.65angstrom), the atomic radius is
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