MSE1110ENGRI1110PS1Solutions - MSE1110/ENGRI1110 Fall 2009...

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MSE1110/ENGRI1110 Fall 2009 Problem Set 1 Solutions 1a. Show (using diagrams) what the band structure of a typical metal, semiconductor and insulator looks like. Make sure to label what is filled, forbidden and empty. Explain what a band gap is and show if there is any difference in band gaps between the semiconductor and the insulator by drawing the bands to a qualitative scale. How does this “physicist’s model” explain the different electronic conductivities in the three types of materials? 1b. Place the following energy amounts in order from lowest to highest: a) Energy band gap in a typical insulator b) Energy difference between states in a band c) Energy band gap of pure silicon (a semiconductor) d) Typical amount of energy at room temperature 1a.
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A band gap is the amount of energy between two different energy bands. It is denoted as the “forbidden” bands in the above energy band diagrams. As can be seen above, the band gap in an insulator is much larger than in a semiconductor. The movement of electrons (or holes) dictates whether a material is electrically conductive. At room temperature, the typical amount of thermal energy available is roughly 0.026 eV. Note: the thermal energy at room temperature (E = k B T) can be found by multiplying the Boltzmann constant (k B = 8.617×10 5 electron volts per degree Kelvin) with the typical value for room temperature (T = 300 Kelvin). This is easily enough energy to move within the individual states in a band, so in a metal (as shown above), the electrons can move freely from the “filled” portion to the “allowed” portion of the same energy band resulting in a metal’s excellent electronic conductivity. For insulators and semiconductors, the empty “allowed” band is separated from the filled energy band by a band gap. In semiconductors, the band gap is generally less than 2 eV, whereas in an insulator, the band gap is typically much higher. Since conduction involves promoting the electrons across the band gap, the chance for conduction to happen diminishes as the gap gets bigger. That’s why there is a chance for some limited conductivity in
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MSE1110ENGRI1110PS1Solutions - MSE1110/ENGRI1110 Fall 2009...

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