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Problem Sheet 4 Solutions.pdf

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ENG 2002
Hany E.Z.Farag

ENG2002 Solutions to Chapter 8 problems on Semiconductors 10 3 1. In general, assume 10 free electrons / cm in Si at 300K. The thermal energy at 300K is 25 meV. But this is an average. Thus some small portion of electrons have energies greater than 1.1eV which allows them to break free of their bonds and leave the valence band for the conduction band. 2. There are 4 valence electrons in one Si atom. There are 10 Si atoms in cm . Thus 3 22 10 4x10 valence electrons. At room temperature, there are about 10 free electrons 3 10 22 in cm . So, 10 (free) electrons/4x10 (total valence) electrons = 1/4,000,000,000,000. 3. Doping adds electrons or holes, increasing the number of majority charge carriers. We assume that 100% of dopants contribute either an electron or a hole at room temperature. 4. n-type: Group V (phosphorous P, arsenic As, tin Sb) p-type: Group III (boron B, gallium Ga, indium In) 5. Number of atoms of pure Si/cm = 10 3 22 3 20 Number of dopant atoms in heavily doped Si/cm = 10
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