MES104TC-2425-S2
Integrated Circuits Design and Fabrication
Assignment
Note: Coursework 2 is based on an assignment and contributes to 15% of the final marks, with a total of 100 marks allocated for this coursework.
Question 1 (50 marks)
1. A PN junction diode has a concentration of 1016 acceptor atoms cm-3 on thep-side and a concentration of 1017 donor atoms cm-3 on the n-side. What will be the built- in potential for the semiconductor materials Ge, Si, InP, and GaAs? (10 marks)
2. Consider a p+n junction, which has a heavily doped p-side relative to the n-side, that is, Na ≫ Nd. Since the amount of charge Q on both sides of the metallurgical junction must be the same (so that the junction is overall neutral)
Q = eNa Wp = eNd Wn
it is clear that the depletion region essentially extends into the n-side. When Nd ≪ Na, the depletion region width (W0) is
What is the depletion width for a pn junction Si diode that has been doped with 1018 acceptor atoms cm-3 on thep-side and 1016 donor atoms cm-3 on the n-side? (10 marks)
3. The capacitance (C) of a reverse-biased abrupt Sip+n junction has been measured as a function of the reverse bias voltage, Vr, as listed in the Table 1. The pn junction cross-sectional area is 500 μm × 500 μm. By plotting 1/C2 versus Vr, obtain the built-in potential, Vo, and the donor concentration, Nd, in the n-region. What is Na ? (10 marks)
Table 1. Capacitance at various values of reverse bias (Vr)
|
Vr (V)
|
1
|
2
|
3
|
5
|
10
|
15
|
20
|
|
C (pF)
|
38.3
|
30.7
|
26.4
|
21.3
|
15.6
|
12.9
|
11.3
|
4. Consider an idealized silicon npn bipolar transistor with the properties listed in the Table 2. Assume uniform doping in each region. The emitter and base widths are between metallurgical junctions (not neutral regions). The cross-sectional area is 100 μm × 100 μm. The transistor is biased to operate in the normal active mode. The base-emitter forward bias voltage is 0.6 V and the reverse bias base-collector voltage is 18 V. (20 marks)
Table 2. Properties of an npn BJT
|
Emitter width
|
Emitter
doping
|
Hole
lifetime in Emitter
|
Base
width
|
Base
doping
|
Electron
lifetime in Base
|
Collector doping
|
|
10 μm
|
2×1018 cm-3
|
10 ns
|
4 μm
|
1×1016 cm-3
|
400 ns
|
1 × 1016 cm-3
|
Calculate the depletion layer width extending from the collector into the base and also from the emitter into the base. What is the width of the neutral base region?
Question 2 (50 marks)
1. You are in charge of a CMOS fabrication line and you have a problem because the thresholds of your n-and p-channel MOSFETs, which are supposed to be +1 V and -1 V, respectively, are turning out to be +3 V and +1 V, instead. You suspect that the interface between the silicon and the 20 nm thick oxide is contaminated with ions.
(a) What type of device is each transistor, enhancement mode (no channel when vGS = 0) or depletion mode (strongly inverted when vGS = 0)? Explain your answers. (10 marks)
• n-channel MOSFET:
Because:
• p-channel MOSFET:
Because:
(b) If you are right about the ions being the problem, what sign must they have, positive or negative. Explain your answer. (10 marks)
2. These questions concern the low frequency linear equivalent circuits of MOSFETs.
(a) Consider the n-channel MOSFET circuit pictured to the right. The circuit is biased with VAC = 2 Volts. The MOSFET has following parameters: (15 marks)
• K = 2 mA/V2
• VT = 1V
• α = 1
• λ = 0.01 V-1
• η = 0.2
A small signal voltage, vac(t), is added to the 2 V bias so now vAC(t) = 2 V + vac(t). First find the bias and small signal values of vGS, vDS, and vBS, and then draw a single element small signal linear equivalent circuit for this connection and give an expression for this element in terms of gm and go .
VGS:
VBS:
VDS:
vgs:
vds:
vbs:
Linear equivalent circuit:
(b) Consider two MOSFETs, one an n-channel MOSFET and the other a p-channel MOSFET. They have identical dimensions, and both are biased in saturation at the same drain current, |ID |. Which of the devices, if either, would have the larger transconductance, gm? Choose one and explain your answers. (15 marks)
n-channel ________; p-channel_______; they are similar________
Because: