This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Page 1 of 9 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EE 105 Prof. Salahuddin Fall 2009 Homework Assignment #1 Solution Due at the beginning of class on Friday, 9/8/09 Problem 1 [10 points]: Intrinsic Semiconductor Material a) The first transistors were fabricated using germanium (Ge) as the semiconductor material. Ge has a much smaller bandgap energy ( E g,Ge = 0.66 eV) than silicon ( E g,Si = 1.12 eV). Would you expect the intrinsic carrier concentration in a Ge sample to be larger or smaller than that in a Si sample maintained at the same temperature? Explain your answer qualitatively, i.e. without resorting to any equations. b) A semiconductor sample is said to be intrinsic if its electron and hole concentrations ( n and p ) under thermal equilibrium conditions ( i.e. with no electric field, magnetic field, or radiation applied) are each equal to  or approximately equal to  the intrinsic carrier concentration ( n i ). This is because its electrical conductivity is (approximately) equal to that of an undoped semiconductor sample. A doped semiconductor sample can become intrinsic if it is heated to a sufficiently high temperature, such that the concentrations of carriers due to thermal generation is much (>10) greater than that due to dopant ionization. Estimate the temperature at which this occurs for a Si sample doped with phosphorus at a concentration of 10 15 cm3 , by finding the temperature at which n i is 10 greater than the dopant concentration. (Use the formula for n i given in Lecture 1, Slide 7. You may assume that the bandgap energy has no temperature dependence.) Solution : a) The lower melting point of Ge indicates that the covalent bonds are weaker in Ge. Therefore, it is easier to free an electron from a covalent bond in Ge, to generate an electronhole pair. Thus, at a given temperature, the intrinsic carrier concentration in a Ge sample is larger than that in a Si sample. b) Referring to Lecture 1, the intrinsic carrier concentration n i is given by = kT E T n g i 2 exp 10 2 . 5 5 . 1 15 [electrons/cm 3 ], where T is the temperature in K , E g is the bandgap energy in eV, and k is Boltzmanns constant in eV/K. Given E g,Si = 1.12 eV at T = 300 K, k = 8.62 105 eV/K, & D = 10 15 cm3 , assuming that the bandgap energy has no temperature dependence, we want to find the temperature at which n i = 10 & D = 10 16 cm3 . Substituting the parameter values into the equation for n i , = T T 5 5 . 1 15 16 10 62 . 8 2 12 . 1 exp 10 2 . 5 10 , from which T 708 K = 435 o C Page 2 of 9 Problem 2 [10 points]: Doping and Carrier Concentrations Consider a Si sample maintained under thermal equilibrium conditions at T = 300K, doped with boron at a concentration of 210 16 cm3 ....
View Full
Document
 Fall '07
 KingLiu

Click to edit the document details