一1.What is semiconductor? List two elemental semiconductor materials and two compound semiconductor materials2. What is called Crystal?3. What is Unit Cell ? What is Primitive Cell? What is the difference between them?4. The lattice constant of a face-centered-cubic structure is 4.75 Å. Determine the volume density of atoms.Answer：1. Semiconductors are a group of materials having conductivities between those of metal and insultoars, typically ρ=10-4~10-7 Ω m. Two common elemental semiconductor materials are Silicon and Germanium. Two common compound semiconductor materials are Gallium phosphide （GaP）and Gallium arsenide（GaAs）2.Single-crystal materials, ideally, have a high degree of order, or regular geometric periodicity, throughout the entire volume of the material.3. A unit cell is a small volume of the crystal that can be used to reproduce the entire crystal. A unit cell is not a unique entity. A primitive cell is the smallest unit cell that can be repeated to form the lattice.4 Density = 4 atoms / (4.75 x 10-8)3 =8.421 x 1023atoms per cm3二1. Sketch three lattice structures: (a) simple cubic, (b) body-centered cubic, and (c) face-centered cubic.2. For a simple cubic lattice, determine the Miller indices for the planes shown in Figure 1.Fig.13. The structure of the unit cell for a mineral called perovskite is shown below. Assuming the cubic lattice with a=6 °A, what are the volume densities of Ti, Ca, and O atoms?4. What is meant by a substitutional impurity in a crystal? What is meant by anintcrstilial impurity?2. left:(313) ; right:(121)3. solution: Density (Ca)= 881⨯atoms / a 3 = 4.63 x 1021 atoms per cm 3 Density (O)=216⨯ atoms / a 3 =1.39 x 1022 atoms per cm 3 Density (Ti)=1/a 3 = 4.63 x 1021 atoms per cm 3三 1. Ultraviolet light (紫外光) of wavelength 150nm falls on a chromium [/kr əʊmi:əm] (铬Cr) electrode(电极). Calculate the maximum kinetic energy and the corresponding velocity of the photoelectrons (the work function of chromium is4.37eV).2. Calculate the photon energies for the following types of electromagnetic radiation: (a) a 600kHz radio wave; (b) the 500nm (wavelength of) green light; (c) a 0.1 nm (wavelength of) X-rays.1、Solution: using the equation of the photoelectric effect, it is convenient to express the energy in electron volts. The photon energy isSolution:(a) for the radio wave, we can use the Planck-Einstein law directly(b) The light wave is specified by wavelength, we can use the law explained in wavelength:四 1 Determine the energy of a photon having wavelengths of (a) λ = 10,000Ǻ and (b) λ= 10Ǻ.2 (a) Find the momentum and energy of a particle with mass of 5 x10-31 kg and a de Broglie wavelength of 180Ǻ. (b) An electron has a kinetic energy of 20 meV . Determine the de Broglie wavelength.eV Hz s eV h E 93151048.21060010136.4--⨯=⨯⨯⋅⨯==ν1、(a) 1.99 x10-19J or 1.24eV. (b) 1.99 x10-16J or 1.24x103eV2、(a) p=3.68 x10-26kgm/s, E=1.35 x10-21J or 8.46 x10-3eV. (b) p=7.64 x10-26kgm/s , λ= 86.7Ǻ五E2.5 The width of the infinite potential well in Example 2.3 is doubled to 10Ǻ. Calculatethe first three energy levels in terms of electron volts for an electron.E2.6 The lowest energy of a particle in an infinite potential well with a width of 100 Ǻ is0.025 eV. What is the mass of the particle？1、Ans. 0.376eV, 1.50eV, 3.38eV2、Ans. 1.37X10-31kg六1. What is the Kronig-Penney model ?2. Discuss the concept of allowed and forbidden energy bands in a single crystal qualitatively with your classmate.3. Discuss the splitting of energy bands in silicon with your classmate.4. (a) If 2X1016boron atoms per cm3are added to silicon as a substitutional impurity, determine what percentage of the silicon atoms and displayed in the single crystal lattice. (b) repeat part (a) for 1015 boron atoms per cm3. （课本P45）5. If 2X1015 gold atoms per cm3 are added to silicon as a substitutional impurity and are distributed uniformly throughout the semiconductor, determine the distance between gold atoms in terms of the silicon lattice constant. (Assume the gold atoms are distributed in a rectangular or cubic array.) （课本P45）七3.1Consider Figure 3.4b. which shows the energy-band splitting of silicon. Ifthe equilibrium lattice spacing were to change by a small amount. discusshow you would expect the electrical properties of silicon to change.Determine at what point the material would behave like an insulator or likea metal.3.2Show that Equations (3.4) and (3.6) are derived from Schrodinger's waveequation. using the fom~o f solution given by Equation (3.3).3.3Show that Equations (3.9) and (3.10) are solutions of the differentialequations given by Equations (3.4) and (3.8). respectively.3.4 Show that Equations (3.12) (3.14), (3.16). and (3.18) rcsult from theboundary conditions in the Kronig-Penney model.这四道题在课本第98页. 八For the electron near the top of the allowed energy band (see Figure 3.16b), show that it behaves as if it has a negative mass.(Refer to textbook pp77-78)2. p99,3.13-3.153. p45, E2.10 (selective)九Answer the questions:1. What is effective mass?2. What is a direct bandgap semiconductor? What is an indirect bandgap semiconductor?3. What is the meaning of the density of states function?4. What was the mathematical model used in deriving the density of states function?5. In general, what is the relation between density of states and energy? Problems:P1003.20, 3.22十3.13 m*（A）<m*（B）3.15 A, B: velocity =-x : C, D: velocity = +x;B. C: positive mass; A, D: negative mass19.3 Å十一Answer the questions1. In general, what is the relation between density of states and energy?2. What is the meaning of the Fermi-Dirac probability function?3. What is the Fermi energy?Problem：1.3P85, Example 3.32. Consider the density of states for a free electron given by Equation (3.69). Calculate the density of states per unit volume with energies between 0 and 2eV.3. To determine the possible number of ways of realizing a particular distribution. Let gi = 10 and Ni =8.4. Calculate the temperature at which there is a 10-6 probability that an energy state 0.55 eV above the Fermi energy level is occupied by an electron.十二Questions:1. Assuming the Boltzmann approximation applies, write the equations for n0 and p0 in terms of the Fermi energy.2. What is the value of the intrinsic carrier concentration in silicon at T = 300 K?3. Under what condition would the intrinsic Fermi level be at the midgap energy? Problems:P148,4.1, 4.2, 4.8, 4.12十三Questions:1. What is intrinsic semiconductor? What is extrinsic semiconductor? Why the extrinsic semiconductor is more useful than the intrinsic semiconductor?2. What is ionization energy? Why the resistance of the extrinsic semiconductor is quite sensitive to doping?Problems:1. Calculate the ionization energy of the hydrogen atom using Bohr theory.(-13.6eV)2. Calculate the ionization energy of the donor electron in silicon using Bohr theory. (for silicon, =1.17, =0.26). (-25.8meV)十四 P147, review questions, 7,8,10,11P149, 4.19, 4.21r *0/m m。
