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. 312c, assuming a ground state hydrogenlike orbit in Si. Compare with the
Si lattice constant. Use m
n
*
= 0.26 m
o
for Si.
Equation 210 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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 Spring '11
 Leburton
 Atom, Electron, Atomic Radius, donor binding energy

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