HW3_solutions - Homework 3 1 Problem Calculate the value of...

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Unformatted text preview: Homework 3 1. Problem. Calculate the value of the Fermi level and sketch its position in a band diagram for the following cases: a. Ge, n-type, N D = 10 17 cm- 3 , T = 300 K. b. Si, p-type, N A = 2 × 10 18 cm- 3 , T = 450 K. c. GaAs, n-type, N D = 10 18 cm- 3 , N A = 5 × 10 17 cm- 3 , T = 300 K. Solution. a. From E F = E i + k B T ln N D n i , (1) since n i = 2 . 5 × 10 13 cm- 3 , we have E F- E i ≈ . 214 eV. b. In the case of p-type doping we have: E F = E i- k B T ln N A n i . (2) Since for Si n i = 1 . 45 × 10 10 cm- 3 at 300 K, at 450 K we will have n i (450 K ) = n i (300 K ) exp E g 2 k B 1 300- 1 450 ≈ 2 . 4 × 10 13 cm- 3 , (3) so that E F- E i ≈ - . 438 eV. c. Using Eq. (1) once more and n i = 2 × 10 6 cm- 3 for GaAs, we get E F- E i ≈ - . 678 eV. 2. Problem. We have seen that the phonon-limited mobility increases with decreasing temperature roughly as μ ph ∝ T- 3 / 2 . For Si we have μ ph = 1 , 500 cm 2 /Vs at 300 K. With this information calculate the drift ECE344 Fall 2009 1 velocity of electrons in Si at T = 77 K for a field of 10 2 V/cm....
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HW3_solutions - Homework 3 1 Problem Calculate the value of...

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