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ECE 875: Electronic Devices

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ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv_at_msu.edu Lecture 08, 27 Jan 14 Example ... – PowerPoint PPT presentation

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Title: ECE 875: Electronic Devices


1
ECE 875Electronic Devices
  • Prof. Virginia Ayres
  • Electrical Computer Engineering
  • Michigan State University
  • ayresv_at_msu.edu

2
Lecture 08, 27 Jan 14
Chp. 01 Concentrations Degenerate Nondegenerate
Effect of temperature Contributed by traps

3
ExampleConcentration of conduction band
electrons for a nondegenerate semiconductor n
hot approximation of Eqn (16)
3D Eqn (14)
Three different variables (NEVER ignore this)
4
AnswerConcentration of conduction band
electrons for a nondegenerate semiconductor n
MC
NC The effective density of states at the
conduction band edge.
5
AnswerConcentration of conduction band
electrons for a nondegenerate semiconductor n
Nondegenerate EC is above EF
Sze eqn (21)
Use Appendix G at 300K for NC and n ND when
fully ionised
6
Lecture 07 Would get a similar result for holes
This part is called NV the effective density of
states at the valence band edge. Typically
valence bands are symmetric about G MV 1
7
Similar result for holesConcentration of
valence band holes for a nondegenerate
semiconductor p
Nondegenerate EC is above EF
Sze eqn (23)
Use Appendix G at 300K for NV and p NA when
fully ionised
8
HW03 Pr 1.10
Shown kinetic energies of e- in minimum energy
parabolas KE ? E gt EC.
Therefore generic definition of KE as KE E -
EC
9
HW03 Pr 1.10
Define Average Kinetic Energy
Single band assumption
10
HW03 Pr 1.10
hot approximation of Eqn (16)
3D Eqn (14)
Average Kinetic Energy
Single band assumption
11
HW03 Pr 1.10
hot approximation of Eqn (16)
3D Eqn (14)
Average Kinetic Energy
Equation 14
Single band definition
12
Considerations
13
Therefore Single band assumption means
14
Therefore Use a Single band assumption in HW03
Pr 1.10
hot approximation of Eqn (16)
3D Eqn (14)
Start Average Kinetic Energy
Finish Average Kinetic Energy
15
Reference http//en.wikipedia.org/wiki/Gamma_func
tionIntegration_problems Some commonly used
gamma functions
n is always a positive whole number
16
Because nondegenerate used the Hot limit
E
C
E
F
E
i
E
V
-
F(E)
17
Consider as the Hot limit approaches the Cold
limitwithin the degenerate limit
E
C
E
F
E
i
E
V
Use
18
Will find useful universal graph from n
Dotted nondegenerate
Solid within the degenerate limit
y-axis Fermi-Dirac integral good for any
semiconductor
x-axis how much energy do e-s need (EF EC)
versus how much energy can they get kT
19
Concentration of conduction band electrons for a
semiconductor within the degenerate limit n
3D Eqn (14)
Three different variables (NEVER ignore this)
20
Part of strategy pull all semiconductor-specific
info into NC. To get NC
21
Next put the integrand into one single variable
22
Next put the integrand into one single variable
Therefore have
And have
23
Next put the integrand into one single variable
Change dE
Remember to also change the limits to hbottom and
htop
24
Now have
Next write Factor in terms of NC
25
Write Factor in terms of NC
Compare
26
Write Factor in terms of NC
27
F1/2(hF)
No closed form solution but correctly set up for
numerical integration
28
Note
  • hF (EF - EC)/kT is semiconductor-specific
  • F1/2(hF) is semiconductor-specific
  • But a plot of F1/2(hF) versus hF is universal
  • Could just as easily write this as F1/2(x) versus
    x

29
Recall on Slide 5 for a nondegenerate
semiconductor n
hot approximation of Eqn (16)
3D Eqn (14)
F1/2(hF)
30
Useful universal graph
Dotted nondegenerate
Solid within the degenerate limit
y-axis Fermi-Dirac integral good for any
semiconductor
x-axis how much energy do e-s need (EF EC)
versus how much energy can they get kT
31
(No Transcript)
32
Why useful one reason
Around -1.0 Starts to diverge
-0.35 ECE 874 definition of within the
degenerate limit
Shows where hot limit becomes the within the
degenerate limit
EC
EF
Ei
EV
33
Why useful another reason
F(hF)1/2 integral is universal can read
numerical solution value off this graph for any
semiconductor Example p.18 Sze What is the
concentration n for any semiconductor when EF
coincides with EC?
34
Why useful another reason
Answer Degenerate EF EC gt hF 0 Read off the
F1/2(hF) integral value at hF 0 0.6
Appendix G
35
ExampleWhat is the concentration of conduction
band electrons for degenerately doped GaAs at
room temperature 300K when EF EC 0.9 kT?
EF
0.9 kT
EC
Ei
EV
36
Answer
37
For degenerately doped semiconductors (Sze
degenerate semiconductors) the relative Fermi
level is given by the following approximate
expressions
38
Compare Sze eqns (21) and (23) for
nondegenerate
Compare with degenerate
39
Lecture 08, 27 Jan 14
Chp. 01 Concentrations Degenerate Nondegenerate
Effect of temperature Contributed by traps

40
Nondegenerate will show this is the Temperature
dependence of intrinsic concentrations ni pi
ECE 474
41
Intrinsic n pIntrinsic EF Ei Egap/2
Correct definition of intrinsic
Set concentration of e- and holes equal For
nondegenerate

42
Solve for EF
EF for n p is given the special name Ei
43
Substitute EF Ei into expression for n and p.
n and p when EF Ei are given name intrinsic
ni and pi
ni pi
pi
ni
44
Substitute EF Ei into expression for n and p.
n and p when EF Ei are given name intrinsic
ni and pi
ni pi
pi
ni
Units of 4.9 x 1015 ? cm-3 K-3/2
45
Plot ni versus T
ni
Note temperature is not very low
1018
106
46
Dotted line is same relationship for ni as in the
previous picture.However this is doped Si
lt liquid N2
1017
When temperature T high, most electrons in
concentration ni come from Si bonds not from
dopants
1013
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