中興大學電機所博士班元件物理資格考題庫題目出處:1. Semiconductor Devices physics and technology, S.M. Sze2. An Introduction to Semiconductor Devices, Donald Neamen Part 1: Semiconductor Physics(1) If the lattice constant of silicon is 5.43, calculate (a) the distance from the center of one silicon atom to the center of its nearest neighbor, (b) the number density of silicon atoms(#/cm3), and (c) the mass density (grams/cm3) of silicon.(2) Consider the (100), (110), (111) plane in silicon. (a)Which plane has the highest surface density of atoms? What is that density? (b)Which plane has the smallest surface density of atoms? What is that density?(3) A one-dimensional infinite potential well with a width of 12 contains an electron. (a)Calculate the first two energy levels that the electron may occupy. (b)If an electron drops from the second energy level to the first, what is the wavelength of a photon that might be emitted?(4) Consider a three-dimensional infinite potential well. The potential function is given by V(x) = 0 for 0 x a, 0 y a, 0 z a, and V(x) = elsewhere. Start with Schrdingers wave equation, use the separation of variables technique, and show that the energy is quantized and is given by * MERGEFORMAT 2222()xyznxyzEnnmah(1.1)* MERGEFORMAT (1.2)Where nx = 1,2,3, ny = 1,2,3., nz = 1,2,3(5) (a) Estimate the tunneling probability of particle with an effective mass of 0.067m0 (an electron in gallium arsenide), where m0 is the mass of an electron, tunneling through a rectangular potential barrier of height V0 = 0.8 eV and width 15. The particle kinetic energy is 0.20 eV. (b) Repeat part (a) if the effective mass of the particle is 1.08m0 (an electron in silicon).(6) Show that the probability of an energy state being occupied by E above the Fermi energy is the same as the probability of a state being empty E below the Fermi level.(7) Assume the Fermi energy level is exactly in the center of the bandgap energy of a semiconductor at T = 300K. (a) Calculate the probability that energy state at E = EC + kT/2 is occupied by an electron for Si, Ge, and GaAs. (b) Calculate the probability that an energy state at E = EV - kT/2 is empty for Si, Ge, and GaAs.(8) (a) The carrier effective masses in a particular semiconductor are mn* = 1.15m0, and mp* = 0.38m0, Determine the position of the intrinsic Fermi level with respect to the midgap energy. (b)Repeat part (a) if mn* = 0.082 m0, mp* = 1.15m0(9) If the density of states function in the conduction band of a particular semiconductor is a constant equals to K, derive the expression for the thermal-equilibrium concentration of electrons in the conduction band, assuming Fermi-Dirac statistics and assuming the Boltzmann approximation is valid.(10) (a) Consider silicon at T = 300K. Determine p0 if EFi - EF = 0.35 eV. (b)Assuming that p0 from part (a) remains constant, determine the value of EFi - EF when T = 400K. (c)Find the value of n0 in both parts (a) and (b).(11) For the Boltzmann approximation to be valid for a semiconductor, the Fermi level must be at least 3 kT below the donor level in an n-type material and at least 3 kT above the acceptor level in a p-type material. If T = 300K, determine the maximum electron concentration in a n-type semiconductor and maximum hole concentration in p-type semiconductor for the Boltzmann approximation to be valid in (a)silicon and(b)gallium arsenide. (12) A sample of silicon at T = 150K is doped with boron at a concentration of 1.51015cm-3 and with arsenic at a concentration of 81014cm-3. (a) Is the material n or p type? (b) Determine the electron and hole concentrations. (c) Calculate the total ionized impurity concentration.(13) For a particular semiconductor, Eg = 1.50 eV, mp* = 10 mn*, T = 300K, and ni = 1105cm-3. (a) Determine the position of the intrinsic Fermi energy level with respect to the center of the bandgap. (b) Impurity atoms are added so that the Fermi energy level is 0.45 eV below the center of the bandgap. (i) Are acceptor or donor atoms added? (ii) What is the concentration of impurity atoms added?(14) Determine the carrier density gradient to produce a given diffusion current density. The hole concentration in silicon at T = 300K varies linearly from x = 0 to x = 0.01 cm. The hole diffusion current density is Jdif= 20 A/cm2, and the hole concentration at x = 0 is p = 4 1017 cm-3. Determine the hole concentration at x = 0.01 cm.(15) A silicon semiconductor at T = 300K is homogenously doped with Nd = 51015cm-3 and Na = 0. (a) Determine the thermal equilibrium concentration of free electrons and free holes. (b) Calculate the drift current density for an applied -field of 30 V/cm. (c) Repeat parts (a) and (b) for Nd = 0 and Na = 51016cm-3.(16) A silicon crystal having a cross-sectional area of 0.001 cm2 and a length of 100mA in the silicon. Calculate: (a) the required resistance R, (b) the required conductivity, (c)the density of donor atoms to be added to achieve this conductivity, and