Mid-Term Exam with Solution

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  • Topic: MOSFET, Diode, P-n junction
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Final Exam

December 14, 2002
7. The slight slope of the collector current with increased collector voltage in the common-emitter characteristics of a BJT is called the ________early_____________ effect which is a result of ______________base width modulation_____________________.

Short Questions (1 point for each blank)

8. The total capacitance of an ideal MOS structure includes the capacitance of ____SiO2_______ and the capacitance of _____depletion_region____________. 1. The Hall effect measurements yield the following information about a piece of semiconductor : ____type of the material___________ , ______doping concentration_____________ , _________mobility________________________. 9. For a realistic MOS structure, the threshold voltage (VT) should include two terms in addition to those in the ideal model, representing _____work function difference________and ________________interface charge________________. 2. Reverse biasing of a p-n junction is to connect a positive voltage to the ______n_______-side of the junction. Under reverse bias, the energy band separation (electrastatic potential barrier) across the junction is _____larger_____ than at equilibrium. The electric field is _____increased_____ and the transition region width is______increased______ with increasing magnitude of reserve bias. 3. In a forward-biased n+p-junction, the forward current is due to injection of ___electrons_____ from _______n______ to ________p______, resulting in a large diffusion / drift (circle one) current which flows from ____p______ to ______n______. 4. The reserve breakdown of a p+n-junction increases as the concentration of donors / acceptors (circle one) ________decreases_________. 5. The reserve breakdown of a heavily doped junction (p+n+) is due to the ______zener_______effect, which is a result of______tunneling__________________. 6. The zero bias junction capacitance of a n+p junction is high if the concentration of donors / acceptors (circle one) is ____increased_______. For a diode with a constant doping concentration, the junction capacitance ____decreases_______ with increasing reverse bias. 13. The high electric field occurs at ______drain___________region of a p-channel MOSFET. 12. Boron ions (B+ ) are introduced to an enhancement-mode n-channel MOSFET will cause the threshold voltage to increase / decrease (circle one). 11. To make the threshold voltage of a p-channel MOS more negative, positive / negative (circle one) voltage should be applied to the substrate. 10. A gate voltage must be applied to eliminate the channel in depletion / enhancement (circle one) -mode MOSFET.

Long Questions (20 points each) (answer on exam sheet) 1. An ideal p-n junction diode is connected as shown. 1 A of reverse current flows in the diode for V = − 80V. 1 mA of forward current flows for V = 0.75V. W p at V = 0 n

(d) Sketch the energy band diagrams for the diode at forward bias and reverse bias. They must be distinguishable from the diode at equilibrium.

Forward bias

W is smaller than before ECp q(Vo − Vf ) Vf ECn EFn Ein

50 Ω + V −

Eip EFp EVp

EVn (a) Find the breakdown voltage of the diode. Vbr = V − IR = − 80 − (−1) 50 = − 30 V (b) Find the current for V = −15V. W is wider than before The current is the reverse saturation current. ECp Reverse Bias

Io = e

qVD − 1 kT

= e

0.75 − (1m ) ( 50 ) 0.0259

= 1.83 ×10 −1

− 15

Eip EFp EVp q(Vo + Vr ) ECn EFn Ein EVn


(c) Sketch the I-V characteristics of the diode including the breakdown region. Show all the given and calculated values on the graph.

Diode current

− 30 V

1 mA 0 0.7 V Voltage across the diode

2. Consider a forward-biased emitter-base junction in an n+pn BJT n+ emitter p base

(c) Obtain the expression of emitter injection efficiency from your answer to part (b). Simplify as far as possible.

Lp , Dp , N D

Ln , Dn , N A

 ∆p  − e I p ( x n ) = qAD p  L  p   In

xn Lp...
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