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MSE 2620 HW4 Solutions

MSE 2620 HW4 Solutions - MSE 2620 Spring `09 Homework#4...

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MSE 2620, Spring ‘09 Homework #4 Instructions: Due Tuesday, April 21st, 2009. Turn in one solution per group and be sure to include the group letter, the names of the group members, and if any group members did not participate enough to deserve full credit along with the reasons why. 1. Schottky and Ohmic a. Describe the difference between a Schottky and Ohmic contact. In a Schottky contact there is a potential energy barrier to overcome in order for carriers to transfer from the metal to the semiconductor. In an ohmic contact there is no barrier for the carriers in the metal to move to the semiconductor. b. If a metal makes a Schottky to n-type Si, would it more likely be an Ohmic or Schottky contact to p-type Si. Justify your answer. It would more likely make an ohmic contact to p-type Si. (I will update with the exact reason). c. Consider a Schottky junction diode between Au and n-Si doped with 10 16 donors cm -3 . The cross-sectional area is 1mm 2 . Given the work function of Au is 5.1 eV, what is the theoretical barrier height Φ B from the metal to the semiconductor? χ - Φ = Φ m B = 5.1 – 4.01eV (table 5.1) = 1.09 eV d. Given that the experimental barrier height Φ B is about 0.8 eV, i) what is the reverse saturation current and ii) the current when there is a forward bias of 0.3 V across the diode? Φ - = kT T B J B exp 2 0 and 3 2 0 / 4 h k em B e π = , where k is the Boltzmann constant, e is the elementary charge, m e is the electron mass, and h is Planck’s constant. Assume T = 300K 3 2 0 / 4 h k em B e π = = 1.2 x 10 6 A m -2 K -2 I 0 = Φ - = kT AT B JA B exp 2 0 =(1.2x10 6 )(1e -6 )(300) 2 - eV eV 026 . 0 8 . 0 exp I 0 = 4.68 nA
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I f = - 1 exp 0 kT V I f = - 1 026 . 0 3 . 0 exp 0 eV eV I = 480 μA 2. pn junctions a. Draw a band diagram for a pn junction for i) no bias ii) Forward Biased iii) reverse biased. The following should be clearly labeled on your diagrams: conduction and valence bands, Fermi level, built in potential and applied bias. Figure 6.11 Kasap. b. Consider a long Si diode made of an abrupt p + n junction which has 10 16 donors cm -3 on the n-side and 10 18 acceptors cm -3 on the p-side. The diode is kept at 27˚C. Calculate the built-in voltage.
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