# Chapter 3: Metal-Semicond. Junctions     ## Problems Consider a gold-GaAs Schottky diode with a capacitance of 1 pF at -1 V. What is the doping density of the GaAs? Also calculate the depletion layer width at zero bias and the field at the surface of the semiconductor at -10 V bias voltage. The area of the diode is 10-5 cm2. Using the work functions listed in table 3.2.1, predict which metal-semiconductor junctions are expected to be ohmic contacts. Use the ideal interface model. Design a platinum-silicon diode with a capacitance of 1 pF and a maximum electric field less than 104 V/cm at -10 V bias. Provide a possible doping density and area. Make sure the diode has an area between 10-5 and 10-7 cm2. Is it possible to satisfy all requirements if the doping density equals 1017 cm-3? A platinum-silicon diode (area = 10-4 cm-2, Nd = 1017 cm-3) is part of an LC tuning circuit containing a 100 nH inductance. The applied voltage must be less than 5 V. What is the tuning range of the circuit? The resonant frequency equals , where L is the inductance and C is the diode capacitance. Consider two Schottky diodes with built-in potential fi = 0.6 V. The diodes are connected in series and reversed biased. The diodes are identical except that the area of one is four times larger than that of the other one. Calculate the voltage at the middle node, Vout, as a function of the applied voltage, Vin. Assume there is no dc current going through either diode so that the charge at the middle node is independent of the applied voltage. A metal-semiconductor junction consists of platinum and gallium arsenide with Nd = 1017 cm-3. The applied voltage equals -3 V. Calculate the electric field in the semiconductor at the metal-semiconductor interface. Use fi = 0.8 V. An aluminum-silicon Schottky diode has a breakdown voltage of 5 V. The silicon is p-type with a doping Na = 1018 cm-3. Calculate the breakdown field and the depletion layer width. (FM = 4.0 V) A metal-semiconductor junction, biased at an unknown voltage, has a doping density of 1017 cm-3 and a capacitance of 1 pF. The semiconductor is p-type germanium, the built-in potential of the junction is 0.5 V and the diode area is 10-4 cm2. Calculate the depletion layer width and the applied voltage. A metal-semiconductor junction, biased at an unknown voltage, has a maximum electric field of -105 V/cm and a capacitance of 1 pF. The semiconductor is n-type gallium arsenide, the built-in potential of the junction is 0.7 V and the diode area is 10-4 cm2. Calculate the doping density and the applied voltage. Silicon carbide contains three cigar-shaped conduction band minima. The constant energy surfaces of these are ellipsoids which are given by: and Derive an expression for the effective mass used in the Richardson constant for a flow of carriers in the z-direction. Derive an expression for the Richardson velocity in the z-direction. (Advanced problem, requires understanding of section 3.4.4.2)
 Boulder, October 2007