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# Hw3 - 3 Calculate the approximate band gap of Si from Eq...

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ECE 340 Homework III Fall 2005 Due: Monday, September 12, 2005 1. In practice we assume that the intrinsic Fermi level, E i , coincides with the center of the band gap. In reality it is not true. Derive an expression relating the intrinsic level E i to the center of the band gap. Find the displacement of E i from the center of the band gap for both silicon and germanium at room temperature. The effective mass values are m n * = 0.55 m o for Ge and 1.1 m o for Si; m p * = 0.37 m o for Ge and 0.56m o for Si where m o is the free electron mass. 2. Math exercise: plot the function f(x)=exp(3x) from x=0.01 to 2.0 in two graphs. One is on a linear scale and the other on semi-logarithmic scale.
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Unformatted text preview: 3. Calculate the approximate band gap of Si from Eq. 3-23 and the plot of n i vs. 1/T (Fig. 3-17). Why is it moderately different from the measured 1.1 eV at room temperature? 4. The hole concentration in a silicon material is 4x10 5 /cm 3 at room temperature under equilibrium conditions. (a) What is the electron concentration? (b) Where is E F positioned relative to E i ? (c) Draw the energy band diagram for the material. Repeat for parts (a), (b) and (c) for the same sample if the temperature is 400 K. Refer to Fig. 3-17 to obtain the intrinsic carrier concentration at 400 K. Also, the band gap energy is reduced to 1.08 eV at 400 K....
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