# HW3_sol - ECE 440 Homework III Fall 2009 Due: Friday,...

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Unformatted text preview: ECE 440 Homework III Fall 2009 Due: Friday, September 18, 2009 Print your name and netid legibly. Show all work leading to your answer clearly and neatly. Staple multiple pages. 1. a) Construct a semi-logarithmic plot for the following experimental results as shown in the table. Position (cm) Carrier concentration (1/cm3) 1 1x10 15 1.1 2x10 15 1.2 2.5x10 15 1.3 4x10 15 1.4 5x10 15 1.5 6x10 15 1.6 7.5x10 15 1.7 8x10 15 1.8 9x10 15 1.9 12x10 15 2.0 2x10 16 Plot the results showing the carrier concentration as a function of position from x=1 cm to 2 cm. Repeat a) for a linear plot. Answer: 2. Nanohub: We will use the following applet for this problem: https://www.nanohub.org/resources/3963/ The applet explores the effects of doping and temperature on carrier concentration and the energy band diagram of Si. Please go to and play around with this simulator. (Note that the first slider under the carrier concentrations vary by orders of magnitude, while the second slider varies between 1 to 10). Please answer the following questions at room temperature (300K) using the applet unless otherwise stated: (a) In terms of E f E i when is the semiconductor intrinsic, p-type, n-type? What is compensation (verify using the applet)? Explain why E f changes with doping Answer: Intrinsic: =- F i E E p-type:- F i E E n-type:- i F E E The total number of electrons in the conduction band is given by the sum over all possible energy states that exist weighted by the Fermi-Dirac probability. In the text we have approximated it as : ( ) ( ) ( ) o FD c MB n g E f E d N f Ec = Where c N is the effective density of states in conduction band edge and has units of cm-3 . Therefore for a particular density of electrons in the conduction band, there is a specific value of Fermi Energy to satisfy the above condition. (b) Using the applet, vary the Temperature from 250 to 500 Kelvin (in steps of 25 Kelvin) to plot the following: (i) n i as a function of temperature. (both linear and semilog scale). (ii) ni vs. 1000/T (Reproduce figure 3-17) (iii) Eg vs. T (linear plot) What happens to n i as the temperature is increased above room temperature? as the temperature is increased above room temperature?...
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## This note was uploaded on 10/14/2009 for the course ECE 440 taught by Professor Lie during the Fall '09 term at University of Illinois at Urbana–Champaign.

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HW3_sol - ECE 440 Homework III Fall 2009 Due: Friday,...

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