每小題５分
1.	Silicon can crystallize in diamond structure with lattice constant (the edge of the conventional cubic cell) a=5.43.
	(1).	Please calculate the number of Si atoms per .
	(2).	Determine the surface number density (in unit of #/) of (100) and (111) planes.
	(3).	Use x-ray powder diffraction method with x-ray wavelength of 1.54 to characterize Si (100) single crystal wafer. Please draw the intensity of detected x-ray versus 2 for 0<2<90°, and write down the (hkl) index and 2 value of each peak.
2.	A Si semiconductor resistor, as shown in Figure 1, was doped with As atoms at a concentration of of , assuming the impurities are completely ionized at T=300K.
	(1).	If the applies voltage V in Figure 1 is 5V, please determine L so that it carries a current I of 5mA.
	(2).	If a magnetic field of 500 Gauss is applied in the direction shown in Figure 1, please calculate the induced voltage between A and B (i.e. VA-VB).
	(3).	If the Si was doped with As atoms for and B atoms for , will the current be larger, smaller or equal to 5 mA? Please explain you answer.
3.	Consider a Si semiconductor in thermal equilibrium (no current). Assume that the donor concentration varies exponentially as , where x is measured in mm and is limited to m.
	(1).	Sketch the band diagram including Ec, EV, EF and Efi along x.
	(2).	Calculate the electric field at 300 K as a function of x for m.
	(3).	Calculate the potential difference between x=0 and x=25 m.
4.	Consider an ideal Si p-n junction diode at 300K. In p-region, , in n-region .
	(1).	Sketch the thermal equilibrium energy band diagram of the p-n junction including the values of Fermi level with respect to the intrinsic Fermi level on each side of the junction.
	(2).	Sketch the electric field versus x (metallurgical junction position locates at x=0) in space charge region.
	(3).	Sketch the ideal electron and hole current, respectively, through the p-n junction under forward bias.
	(4).	Calculate the change in diode forward voltage that will cause a factor of 10 increase in current.
	(5).	Sketch and compare the I-V curves for (a) p-region and n-region are long , and (b) short, compared with minority carrier diffusion length.
5.	Consider a linearly graded Si p-n junction at 300K. The space charge density as function of x is shown in Figure 2, and can be expressed as , where
	(1).	Please sketch the electric field in space charge region versus x.
	(2).	If the built-in voltage is 0.7V, find the junction capacitance C when reverse biased at 3.5V.
	(3).	In some circuit application, we would like to have resonant frequency be a linear function of reverse bias, so we need . What do you have to do for the doping profile?
6.	Consider an n-channel MOSFET at 300K with an polysilicon gate and channel doping concentration of , gate oxide thickness , gate length L=1mm, equivalent fixed oxide charge located in the oxide directly adjacent to the oxide-semiconductor interface. (Eg=1.12eV, nI=, kT(300K)=0.0259eV, s(Si)=11.7, , ox(SiO2)=3.9, F/cm)
	(1).	Calculate the threshold voltage VT.
	(2).	Determine the type of impurity and ion implantation density (atoms/) required to achieve a VT=0.5V.
	(3).	If the gate length becomes 0.1 mm, will the answer in (b) be larger or smaller? Explain your answer. If you don't want to use ion implantation to adjust the VT, what do you have to change in the oxide thickness?

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