chapter03sm

# chapter03sm - Solutions Chapter 3 3.1 Calculate the speed...

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Solutions Chapter 3 3.1. Calculate the speed of an electron in Si with kinetic energy 0.013 eV. Draw an  equilibrium energy band diagram for silicon and indicate where this electron will  be. Compare your calculated thermal speed to the typical drift velocities cited in the  text of 10 cm/s. How does it compare to typical saturation velocities? The electron speed is ( 29 ( 29 19 5 * -31 5 7 2 0.013 1.6 10 / 2 1.3 10 / 0.26 9.1 10 100 1.3 10 / 1.3 10 / K ce eV J eV E v m s m kg cm m s cm s m - ״ = = = ° = Even with this very small kinetic energy, the electron’s instantaneous speed is still about 1000 times faster than the drift velocity. It is comparable to the drift saturation velocity for silicon of 1 × 10 7 cm/s. E C E V E g =1.12eV E K =0.013eV 3.2. Calculate the resistivity for a uniformly doped silicon sample with 10 17  donors  per cubic centimeter. Anderson & Anderson 1 2/15/04 Solutions Chapter 3

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From Equation (3.14), σ = q μ n n + q μ p p The material is n-type, and not degenerately doped, so n 0 =10 17 and ( 29 2 10 3 2 3 3 0 17 3 0 1.08 10 1.2 10 10 i cm n p cm n cm - - - = = = The mobilities are μ n =6.3 × 10 2 for majority carriers (electrons) at N D =10 17 and μ p =4.6 × 10 2 for minority holes. ( 29 ( 29 ( 29 ( 29 ( 29 19 17 19 3 1 1.6 10 630 10 1.6 10 460 1.2 10 10 n p q n q p cm σ μ μ - - - = + + = Ω - The resistivity ρ is 1 0.1 - cm ρ σ = = . Note that the contribution of holes to the conduction is negligible. 3.3. A lightly doped Si sample ( N D  = 10 14  cm -3 ) is heated from 300 K to 400 K. Is its  resistivity expected to increase or decrease? Explain your answer. Repeat for Si with  N D   = 10 18  cm -3 . For the lightly doped sample, as the temperature is increased the intrinsic concentration increases. It is still true that D i N n ? , though, and to reasonable approximation n 0 is constant. For this doping level, however, lattice (phonon) scattering predominates and mobility decreases with increasing temperature (Figure 3.8). Thus, the conductivity decreases or the resistivity increases Anderson & Anderson 2 2/15/04 Solutions Chapter 3
For the heavily doped sample, impurity scattering predominates. As the temperature is raised, the carriers’ thermal energy is increased so the effect of the impurity scattering is reduced, and the mobility should increase. Therefore the resistivity will decrease. 3.4. Germanium is an interesting semiconductor because it has a small band gap  ( E g =0.67eV). (In fact, for a while it was not considered to be a semiconductor but  was classified as a metal. Now it is a semiconductor again.) As a result, it has a  higher intrinsic concentration  n i  than either silicon or GaAs.  Do you expect the  conductivity of intrinsic germanium to be less than or greater than that of intrinsic  silicon? How about compared to GaAs? Why?

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