课程名称︰固态电子学 课程性质︰选修 课程教师︰吴育任 教授 开课学院：电机资讯 开课系所︰电机工程 考试日期（年月日）︰2014/04/16 考试时限（分钟）：180分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Open book, total 105 points but maximum one can get is 100 1. At T=300K and consider GaAs material, if the Nd = 10^17 (cm^-3) and the measured electron carrier density n = 10^-5 (cm^-3). What is the hole 0 concentration and acceptor doping density N ? (10 points) A 2. If the material's electron mobility is 1000 (cm^2/V-s) and the electron effective mass is 0.2m , (see textbook chapter 5.1.2). (10 points) 0 (1) What is the diffusion coefficient (Dn)? (2) What is the average electron velocity at Electric field = 100(V/cm)? 3. For GaAs, if the doping density Nd is 10^17 (cm^-3) and fully activated, what is the temperature required to have n = 2 x 10^17(cm-3)? (10 points) 0 (Be careful about temperature related constant) 4. As shown in Fig. 5.13, consider Si sample. The device is fabricated by following geometry: d = 5 x 10^-3 (cm). W = 5 x 10^-2 (cm) and L = 0.5cm. The electrical measurement are Ix = 1.0 (mA), Vx = 1.50 (V), Bz = 0.05 (tesla). The Hall voltage is V = 1.0 (mV). Please determine (15 points) H (a) The conductivity type (b) The majority carrier concentration (in cm^-3) (c) The mobility (cm^2/V-s) 5. For the 2 quantum well cases with 1 barrier in between, if the barrier is thin enough that the coupling between the quantum well is possible. Please roughly plot out the eigen wave function shape of the first 4 lowest eigen functions (10 points, no calculation needed!) 6. In Fig. 5.6, when temperature decreases, the carrier density decreases at the same time. But the conductivity decreases, then increases and decreases again, please explain the reasons for this behavior? (i.e. what is the major factor to affect this?) (10 points) 7. By considering two major factors limiting the mobility mentioned in the class. For a doped material, the total mobility at T=300K is 800 (cm^2/V-s) and for the same pure material without doping, the total mobility at 300K is 1200(cm^2/V-s). What is the total mobility for this material at T=100K? (both doped and undoped?) (15 points) 8. For a material, the E(k) relation can be expressed as, the unit of k is m^-1 and unit of E is joule which is in MKS unit E(k) = e [ 2.0(k /10^10) + 4.0(k /10^10)^2 - 0.5(k /10^10)^3 ] 0 x x x (a) What is the instant electron velocity at k = 10^9 (m^-1) and x k = 3 x 10^9 (m^-1) (5 points) x (b) What is the effective mass at the same k point (in unit of m ?) (5 points) x 0 (c) If the material is a "cubic symmetric system" lattice system ( like Si or GaAs), what is the velocity at the same "ky" point? (5 points) 9. For a semiconductor GaAs quantum well with infinite potential barrier assumption, if the bulk material bandgap is 1.42eV, and after quantum confined effect, the effective bandgap becomes 1.48eV. The electron effective mass is 0.067m , Heavy hole effective mass is 0.45m . light 0 0 hole effective mass is 0.087m , What is the quantum well width in nm? 0 (10 points) --

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