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| 所組別： | 電子工程學系甲組 | 科目： | 半導體元件 | 考試時間： | 4月29日第3節 |
| 1. | Answer the questions that follow making use of the unit cell for the Si crystal lattice given in Fig. [20%] | |
| (a) | If, as pictured, the origin of coordinates is located at the lower back corner of the unit cell, what are the Miller indices of the plane passing through the points ABC? | |
| (b) | What are the Miller indices of the direction vector running from the origin of coordinates to the point D? | |
| (c) | In terms of the lattice constant a, what is the distance between nearest neighbors in the Si lattice? | |
| (d) | In terms of the lattice constant a, what is the nearest spacing of any two {400} equivalent planes? | |
| (e) | Modifying the pictured Si unit cell, indicate how one would visualize a donor. | |
| 2. | (a) | What is the relation between the electron and hole concentrations in a nondegenerate semiconductor under equilibrium conditions? |
| (b) | Explain in your own words what is the Fermi level? | |
| (c) | Fig.2 shows the dependence of the intrinsic carrier concentration on inversetemperature for a semiconductor material. What is the energy gap of this semiconductor? [Boltzmann constant/q (kB/q)=8.61738x10-5eV/K] | |
| Hint: you may neglect the temperature dependence of the densities of states foran estimate of the energy gap based on Fig.2. [12%] |
| 3. | A light source is turned on at t=0 creating a uniform generation rate G=1014cm-3s-1 in a piece of an n-type semiconductor material doped at 1013cm-3. The hole life time is 5x10-6s. The intrinsic carrier density is 1010cm-3. Sketch the time dependence of the hole concentration and explain. [12%] |
| 4. | (a) | Show schematically the approximate temperature dependence of carrier mobility in a very pure semiconductor sample and also indicate what dominate the mobilities in the high-temperatureand low-temperature ranges, respectively. |
| (b) | For a given n-type semiconductor, present one measurement that can be performed to know the electron concentration and mobility. Describe your measurement by deriving the related equations for both the carrier concentration and the carrier mobility.[20%] |
| 5. | The current-voltage characteristic of a tunnel diode is shown in Fig.3. Give respective simplified energy band diagrams of this diode correspond to the points (a), (b), (c) and (d) in the same figure and explain how these characteristics can b achieved. [16%] |
| 6. | A pn junction has the doping profile sketched in Fig.4. Throughout this problem, assume the carrier concentrations may be neglected (n=0, p=0) in the 0 ≦ x ≦ xi region of the diode. [20%] | |
| (a) | What is the built-in voltage across the junction? | |
| (b) | Invoking the depletion approximation, make a sketch of the charge density inside the diode. Label significant ρ and x values. | |
| (c) | Obtain an analytical solution for the electric field, E(x), at all points inside the depletion region (-xp≦ x ≦ xn). Show all workandmake a sketch of the deduced E(x) versus x. | |
| (d) | In a standard pn step junction NAxp=NDxn. How are xn and xp related here? (e)Draw the energy band diagram for the diode under equilibrium conditions. Clearly identify the points x=0 and x=xi on your diagram. Also indicate how your diagram differs from that of a simple pn step junction where NA=ND=NB. | |
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