3. Calculate the maximum width of surface depletion region for a metal-SiO₂-Si capacitor having N_A=.(20%)

(a) Find the carrier concentrations. (10%)

(b) Find the Fermi level. (10%) (Note: Sketch the band diagram and mark Ec, Ev, EF and Ei； indicate clearly the location of the Fermi level with respect to intrinsic level.)

(a) Calculate the value of ND with an intrinsic region thickness of 20 Jum, and a permitted △E of 105 V/Im. △E is the change in electric field across the depletion region. (10%)

(b) An electric field of 3.5 x105  V/Im is needed to reach the saturation region. Find the bias voltage. (10%)

4. A solar cell under an illumination of 80 W/Im2 has a short circuit current of 40 mA and an open circuit output voltage of 0.55V. What are the short circuit current and open circuit voltages when the light intensity is halved? (20%)

5. Consider the p'n junction of a uniformly doped silicon n-channel JFET has doping concentrations of NA = and ND = at T = 300K. The metallurgical channel thickness is 0.8 μm. Determine the built-in potential barrier and the pinchoff voltage of the JFET. (20%)

(b) evaporation and sputtering (5%)

(a) positive photoresist and negative photoresist (5%)

5. For DRAM operation, assume that we need a minimum of 105 electrons for the MOS storage capacitor. The capacitor has an area of 0.6 μmx 0.6 um on the wafer, an oxide thickness of 7 nm, and is fully charged to 3 V. What is the required minimum depth of a rectangular-trench capacitor?

4. Answer the following questions about MOS capacitor. (a) Explain the flat-band voltage. (5%)( b) Consider a n+polysilicon-SiO2-Si capacitor with a p-type silicon substrate doped to NA = cm, a silicon dioxide insulator with a thickness of 300 . The metal-semiconductor work function diference is -0.98 V. The fixed charge within the SiO2-Si interface Q/q = 4✖The dielectric constant of SiO2 is 3.9. Calculate the flat-band voltage. (15%)

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