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Table 1 and Table 2 contain the parameters
that you may need. |
| |
| B.4 Silicon,gallium arsenide,and
germanium properties(T=300°K) |
|
| Property |
Si |
GaAs |
Ge |
|
| Atoms(cm-3) |
5.0x1022 |
4.42x1022 |
4.42x1022 |
| Atomic weight |
28.09 |
144.63 |
72.60 |
| Crystal structure |
Diamond |
Zincblende |
Diamond |
| Density(g/cm-3) |
2.33 |
5.32 |
5.33 |
| Lattice constant(Å) |
5.43 |
5.65 |
5.65 |
| Melting point(°C) |
1415 |
1238 |
937 |
| Dielectric constant |
11.7 |
13.1 |
16.0 |
| Bandgap energy(eV) |
1.12 |
1.42 |
0.66 |
| Electron affinity,X,(volts) |
4.01 |
4.07 |
4.13 |
| Effective density of states in |
|
|
|
| conduction band,Nc,(cm-3) |
2.8x1019 |
4.7x1017 |
1.04x1019 |
| Effective density |
|
|
|
| of states in valence band,Nv,(cm-3) |
1.04x1019 |
7.0x1018 |
6.0x1018 |
| Intrinsic carrier concentration(cm-3)
|
1.5x1010 |
1.8x106 |
2.4x1013 |
| Mobility (cm2/V-s) |
|
|
|
| Electrons,µn |
1350 |
8500 |
3900 |
| Hole,µp |
480 |
400 |
1900 |
Effective mass, |
|
|
|
| Electrons |
 =0.98 |
0.067 |
1.64 |
| |
 =0.19 |
|
0.082 |
| Holes |
 =0.16 |
0.082 |
0.044 |
| |
 =0.49 |
0.45 |
0.28 |
| Effective mass(density of states) |
|
|
|
Electrons, |
1.08 |
0.067 |
0.55 |
Holes, |
|
|
|
| |
0.56 |
0.48 |
0.37w |
|
|
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|
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B.3 Physical constants |
| |
|
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| Avogadro's number |
NA=6.02x10+23 |
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atoms per gram |
| |
molecular weight |
| Boltzmann's constant |
k=1.38x10-23J/K |
| |
=8.62X10-5eV/K |
| Electronic charge |
|
| (magnitude) |
e=1.06x10-19C |
| Free electron rest mass |
m0=9.11x10-31kg |
| Permeability of free space |
µ0= x10-7H/m |
| Permittivity of free space |
 =8.85x10-14F/cm |
| |
=8.85x10-12F/m |
| Planck's constant |
h=6.625x10-34J-s |
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=4.135x10-15eV-s |
| |
 |
=h=1.054x10-34J-s |
|
| Proton rest mass |
M=1.67X10-27kg |
| Speed of light in vacuum |
c=2.998x1010cm/s |
| Thermal voltage(T=300°K) |
Vt= |
 |
=0.0259volt |
| |
kT=0.0259eV |
|
|
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|
| 1. |
Suppose you have a silicon wafer in hands,without
any further information. Please present and describe a measurement clearly
for: |
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(1) |
How to determine the orientation of the wafer(i.e. the direction
perpendicular to wafer surface).(5%) |
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(2) |
How to determine the doping type (p or n?) and concentration of the wafer.
Describe your measurement clearly with the related equations.(5%) |
| |
|
| 2. |
Consider an n-type Si with uniform carrier concentration of
1016/cm3, which
is connected to a voltage supply of V as the following figure. |
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(1) |
Please sketch the energy diagram (E vs. x) with Ec,
Ev, and Ef, and determine the Fermi-level positive
respect to intrinsic Fermi-level Efi, when V=0(at thermal equilivrium).(5%) |
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(2) |
Sketch the energy diagram(E vs. x) with Ec, Ev,
and Ef at V=V0
(>0).(5%) |
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|
 |
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|
| 3. |
Consider three p-n junction diodes with the same doping concentration
and junction areas, but made of Si,Ge and GaAs, respectively. Given the
Eg ( energy gap ) of each material from Table 1, compare the current density
for the three diodes at the same forward bias, and sketch the three I-V
characteristics on a single set of axes. (10%) |
| |
|
| 4. |
Compare the I-V characteristics of two ideal p+-n
step junction diodes which are identical except that Nd1=1015
cm-3 in diode 1, and Nd2=1016cm-3
in diode 2. Sketch both I-V characteristics of the two diodes for forward
and reverse biased on a single set of axes.(10%) |
| |
| 5. |
Consider an abrupt Si p-n junction diode at 300K, with Nd=1015cm-3
and Na=1018cm-3. |
| |
(1) |
Please sketch the energy diagram and calculate the Fermi level on each
side of junction with respect to intrinsic Fermi level at thermal equilibrium.(5%) |
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(2) |
Determine the build-in voltage at thermal equilibrium.(5%) |
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(3) |
If the junction area is 6x10-4cm2,
an inductance of 2.2 mH is placed in parallel with the p-n juntion, calculate
the resonant frequency of the circuit for reverse-bias voltage of VR=10V.(6%) |
| |
|
| 6. |
An ideal MOS capacitor at 300K with n+polysilicon
gate has SiO2 thickness of 500Å on
a p-type silicon substrate with an acceptor concentration of Na=1016
cm-3. The dielectric constant of SiO2
is 3.9. |
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(1) |
Please calculate the threshold voltage VT.(6%) |
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(2) |
Please sketch the capacitance versus Vg (C-V characteristics)
at high frequency of 1MHz from negative to positive voltage and determine
the maximum and minimu of the capacitance.(8%) |
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(3) |
If fixed oxide charge of Qss=5x1011cm-2
is entirely located at the oxide-semiconductor interface, calculate the
shift of threshold voltage, and sketch the high frequency C-V characteristics
in compared to that of(2).(6%) |
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(4) |
If fixed oxide charge of Qss=5x1011cm-2
is uniformly distributed through out the oxide, calculate the shift of threshold
voltage.(6%) |
| |
|
| 7. |
Consider an abrupt n-Al0.3Ga0.7As-
intrinsic GaAs heterojunction. The n-Al0.3Ga0.7As
is doped to 1018cm-3.
The Schottky barrier height is 0.85V and the heterojunction conduction band
edge discontinuity is  Ec=0.22eV.The
dielectric constant of Al0.3Ga0.7As
is 12.2. |
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(1) |
Determine the thickness of Al0.3Ga0.7As
layer so that the threshold voltage Voff=-0.4V.(6%) |
| |
(2) |
Sketch the energy band diagram from metal gate through Al0.3Ga0.7As
to GaAs at thermal equilibrium.(6%) |
| |
(3) |
Determine the two dimensional electron concentration for Vg=0
V.(6%) |
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