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Transcript of 1 Electrical Engineering 2 Microelectronics 2 Dr. Peter Ewen (Room G08, SMC; email - pjse) Lecture...
1
Electrical Engineering 2
Microelectronics 2
Dr. Peter Ewen
(Room G08, SMC; email - pjse)
Lecture 4
ELECTRICAL ENGINEERING 2
Microelectronics 2
Dr. P.J.S. Ewen
LECTURES: Mondays 12.10-13.00 Swann 7.20 Fridays 10.00-10.50 JCMB 5327
TUTORIALS: Mondays 11.10-12.00 Eng. CR 4(Monday Lab Group)
Tuesdays 11.10-12.00 Eng. CR 4(Friday Lab Group)
N.B. Tutorials run in weeks 3, 5, 7, 9, 11
3
Fig. 20
Si Si Si
+ve charge associated with vacancy the vacancy is mobile
Electric field-ve +ve
the vacancy acts like a mobile +ve charge
+-Semiconductor
Electron-hole pair
4
ni – intrinsic carrier concentration
(N.B. ni ≠ n + p)
At 300K: ni = 1.5x1016 m-3 for Sini = 2.5x1019 m-3 for Ge
INTRINSIC SEMICONDUCTORS Pure semiconductors are termed “intrinsic”:
n = p = nin – free electron concentration; p – hole concentration
Si Si Si
5
CARRIER LIFETIME - : 10-9 < < 10-6 s
C.B.
V.B.
GENERATION RECOMBINATION
Fig. 21
Eg
6
n-type
pentavalent
donoratoms
p-type
trivalent
acceptoratoms
Substitutional impurities – they can be incorporated into the semiconductor lattice without distorting it.
Typical doping concentrations:
1020 – 1026 m-3
EXTRINSICSEMICONDUCTORS
7
Fig. 22
Si As Si
Si
Si Donoratom
En
erg
y
~0.01 eV
n-type Si
C.B.
V.B.
Donor levels
8
Fig. 22
Si B Si
Si
Si Acceptor
atom
En
erg
y
~0.01 eV
p-type Si
C.B.
V.B.
Acceptor levels
9Fig. 23: Typical range of conductivities/resistivities
for metals insulators and semiconductors.
i
i
i
i
i
10
The effect of increasing temperature on resistance/resistivity.
MetalIntrinsic
semiconductorInsulator Extrinsic
semiconductor
As T R R R R or R or R constant
TCR +ve -ve -ve +ve, -ve or ~0
Fig. 24
dT
dR
RTCR
1def
Temperature Coefficient of Resistance
11
LECTURE 4
Influence of temperature on carrier concentrations in semiconductors
Majority and minority carriers
The Fermi-Dirac distribution function
12Temperature / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n,
n
/ m
-3Fig. 25: Free electron concentration vs. temperature for
intrinsic and extrinsic silicon
1021
2×1021
3×1021
ni
Intrinsic Si
100 200 300 400 500 600
n-type Si doped with ND = 1021 m-3
EXTRINSIC REGION
IONISATION REGION
INTRINSIC REGION
0
13
Si Si Si
Si
Si
Donoratom
Si As Si
Si
Si
Energy required to break a silicon bond is ~1.1ev
Intrinsic Si
Energy required to detach a donor electron is ~0.01ev
n-type Si
14
Same considerations apply to p-type Si (p = NA in saturation region)
Extrinsic material effectively becomes intrinsic above a certain transition temperature – bad news for devices!
Temperature, T / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n,
n
/ m
-3
1021
2×1021
3×1021
ni
100 200 300 400 500 600
H
ole
co
nce
ntr
atio
n,
p
/ m
-3
Ge Si GaAs
ni ni
15
8. Maximum working temperature for a semiconductor device
The maximum temperature, Tmax, at which a device can operate is fixed by the semiconductor material from which it is made. At Tmax, ni = ND for n-type material and ni = NA for p-type material.
If ni = C exp (-Eg / 2kT)
where Eg is the energy gap, T the temperature in degrees K, C is a constant and k is Boltzmann's constant, determine Tmax for a GaAs sample doped with 1020 donors m-3, given that for GaAs, Eg = 1.42 eV and C = 18.1x1023 m-3.
16
8. Maximum working temperature for a semiconductor device
For an n-type semiconductor, by definition the (approximate) maximum working temperature, Tmax, is the temperature at which
ni = ND.
Temperature, T / KTemperature, T / K
10102121
22××10102121
33××10102121
nnii
100 200 300 400 500 6100 200 300 400 500 60000
Fre
e el
ectr
on
co
nce
ntr
atio
n, n
/ m
Fre
e el
ectr
on
co
nce
ntr
atio
n, n
/ m
-- 33
MaximumMaximumWorkingWorking
temperaturetemperature
NNDD==
nnii=N=NDD
Temperature, T / KTemperature, T / K
10102121
22××10102121
33××10102121
nnii
100 200 300 400 500 6100 200 300 400 500 60000100 200 300 400 500 6100 200 300 400 500 60000
Fre
e el
ectr
on
co
nce
ntr
atio
n, n
/ m
Fre
e el
ectr
on
co
nce
ntr
atio
n, n
/ m
-- 33
MaximumMaximumWorkingWorking
temperaturetemperature
NNDD==
nnii=N=NDD
)2
exp(kT
ECn g
i
kT
E
C
n gi
2)ln(
17
]/ln[2
]/ln[2
:side hand-lefton Tget togRearrangin2
)ln(
i
g
i
g
gi
nCk
E
Cnk
ET
kT
E
C
n
)570(840]
10101.18
ln[1038.12
106.142.1
20
2323
19
max CKT
So for a GaAs sample doped with 1020 donors m-3:
(The 1.610-19 in the above converts eV to joules.)
]/ln[2 Hence max
D
g
NCk
ET
But at T = Tmax, ni = ND
18
Fig 19: Variation of the energy bands with Fig 19: Variation of the energy bands with interatomicinteratomicspacing for silicon (and also germanium and carbon).spacing for silicon (and also germanium and carbon).
Energy levels of the
isolated atom
Equilibrium spacingEquilibrium spacing INTERATOMIC SPACINGINTERATOMIC SPACING
ELECTRON ELECTRON ENERGYENERGY
As temperature increases,structure expands
Valence electrons
Fig 19: Variation of the energy bands with Fig 19: Variation of the energy bands with interatomicinteratomicspacing for silicon (and also germanium and carbon).spacing for silicon (and also germanium and carbon).
Energy levels of the
isolated atom
Equilibrium spacingEquilibrium spacing INTERATOMIC SPACINGINTERATOMIC SPACING
ELECTRON ELECTRON ENERGYENERGY
As temperature increases,structure expands
Valence electrons
This calculation ignores the change in Eg due to temperature:
Eg decreases from 1.42 to 1.2eV over this temperature range. However,
even if you correct for this, the maximum working temperature for GaAs is still greater than 450oC, much higher than for Si.
19
Majority and Minority Carriers
For intrinsic semiconductors:
n = p = ni
np = ni2
For extrinsic semiconductors:
nn >> pn for n-type pp >> np for p-type
For extrinsic semiconductors it also turns out that:
np = ni2
ni – the intrinsic carrier concentration
n – the free electron concentration
p – the hole concentration
*
Temperature, T / K
Car
rier
co
nce
ntr
atio
n
/ m
-3
1021
2×1021
3×1021
ni
100 200 300 400 500 600
*Provided semiconductor is in this temperature
range
20
So for extrinsic semiconductors:
nnpn = ni2 for n-type
nppp = ni2 for p-type
Temperature, T / K
Car
rier
co
nce
ntr
atio
n
/ m
-3
1021
2×1021
3×1021
ni
100 200 300 400 500 600
*Provided semiconductor is in this temperature
rangenn ≈ ND for n-type
pp ≈ NA for p-type
ND – donor concentrationNA – acceptor concentration
*
Thus for n-type: nn ≈ ND ; pn ≈ ni2 / ND
for p-type: pp ≈ NA ; np ≈ ni2 / NA
Electrons in n-type – majority carriers Holes in n-type – minority carriers Holes in p-type – majority carriers Electrons in p-type – minority carriers
21
9. Carrier concentrations (Bogart, 4th Edition, Ex. 2-18, p.41)
A silicon wafer is doped with 1.8x1020m-3
atoms of As. If ni = 1.6x1016m-3 determine the electron and hole concentrations, n and p.
(Assume the temperature is in the extrinsic region of operation.)
Temperature, T / K
Ele
ctro
n c
on
cen
trat
ion
/
m-3
4×1020
6×1020
ni
100 200 300 400 500 600
*Provided semiconductor is in this temperature
range
2×1020
22
320108.1 mNn D
31220
21622
1042.1108.1
)106.1(
mN
n
n
np
D
ii
9. Carrier concentrations
Arsenic is an n-type dopant hence:
nn--typetype
pentavalentpentavalent
donordonoratomsatoms
pp--typetype
trivalenttrivalent
acceptoracceptoratomsatoms
SubstitutionalSubstitutional impurities impurities ––they can be incorporated they can be incorporated into the semiconductor into the semiconductor lattice without distorting it.lattice without distorting it.
Typical doping Typical doping concentrations:concentrations:
10102020 –– 10102626 mm--33
EXTRINSICEXTRINSICSEMICONDUCTORSSEMICONDUCTORS
nn--typetype
pentavalentpentavalent
donordonoratomsatoms
nn--typetype
pentavalentpentavalent
donordonoratomsatoms
pp--typetype
trivalenttrivalent
acceptoracceptoratomsatoms
pp--typetype
trivalenttrivalent
acceptoracceptoratomsatoms
SubstitutionalSubstitutional impurities impurities ––they can be incorporated they can be incorporated into the semiconductor into the semiconductor lattice without distorting it.lattice without distorting it.
Typical doping Typical doping concentrations:concentrations:
10102020 –– 10102626 mm--33
EXTRINSICEXTRINSICSEMICONDUCTORSSEMICONDUCTORS
23
Which of the following statements is true:
Holes in an n-type semiconductor are…
A) Majority carriers that are thermally produced
B) Minority carriers that are produced by doping
C) Minority carriers that are thermally produced
D) Majority carriers that are produced by doping
24
En
erg
y
C.B.
V.B.
Donor levelsEg
Statisticalprocesses
E
N(E)
Total number of electrons at energy E
Probability that a state at energy E is occupied
Total number of states at energy E
The Fermi-Dirac Distribution Function
F(E) x n(E) =
25
kTEE FkT
EE F if)(exp
)(exp11)(
kT
EE FEF
F(E) is the Fermi-Dirac Distribution Function
EF – the Fermi Level
2
1)0(exp1
1)(
FEF
A state at the Fermi level, EF, has a 50-50 chance of being occupied
26
Fig. 26E
ner
gy,
E
C.B.
V.B.
E
EC
EF
EV
½EG
½EG
0 ½ 1 F(E)
F(E) for an INTRINSIC semiconductor
THE FERMI-DIRAC DISTRIBUTION
27
Fig. 27E
ner
gy,
E
C.B.
V.B.
E
EC
EF
EV
0 ½ 1 F(E)
F(E) for an n-type semiconductor
THE FERMI-DIRAC DISTRIBUTION
donor levels
For n-type semiconductors the Fermi level lies closer to the conduction band edge, Ec
28
Fig. 28E
ner
gy,
E
C.B.
V.B.
E
EC
EF
EV
0 ½ 1 F(E)
F(E) for a p-type semiconductor
THE FERMI-DIRAC DISTRIBUTION
acceptor levels
For p-type semiconductors the Fermi level lies closer to the valence band edge, Ev
29
Fig. 29E
ner
gy
C.B.
V.B.
Donor levels
EF
C.B.
V.B.
C.B.
V.B.EF
EF
Metal
Degenerate n-type Degenerate p-type
Degenerate Semiconductors
Acceptor levelsEG
EG
30
For a semiconductor sample at 0 K, what is the probability that a state at the top of the valence band is occupied by anelectron?
A. 0
B. 1
C. ½
D. Between 1 and ½
31
The Fermi level, EF, for a silicon sample lies 0.8eV above the valence band edge. If the energy gap for silicon is 1.1eV, is this sample
A. p-type
B. n-type
C. intrinsic
32
SUMMARYINFLUENCE OF TEMPERATURE ON CARRIER
CONCENTRATIONS
Temperature / KTemperature / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
-- 33
Fig. 25: Free electron concentration vs. temperature forFig. 25: Free electron concentration vs. temperature forintrinsic and extrinsic siliconintrinsic and extrinsic silicon
10102121
22××10102121
33××10102121
nnii
Intrinsic Intrinsic SiSi
100 200 300 400 500 6100 200 300 400 500 60000
nn--type type SiSi doped with Ndoped with NDD = 10= 102121 mm--33
EXTRINSIC REGIONEXTRINSIC REGION
IONISATIONIONISATIONREGIONREGION
INTRINSIC INTRINSIC REGIONREGION
00Temperature / KTemperature / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
-- 33
Fig. 25: Free electron concentration vs. temperature forFig. 25: Free electron concentration vs. temperature forintrinsic and extrinsic siliconintrinsic and extrinsic silicon
10102121
22××10102121
33××10102121
nnii
Intrinsic Intrinsic SiSi
100 200 300 400 500 6100 200 300 400 500 60000100 200 300 400 500 6100 200 300 400 500 60000
nn--type type SiSi doped with Ndoped with NDD = 10= 102121 mm--33
EXTRINSIC REGIONEXTRINSIC REGION
IONISATIONIONISATIONREGIONREGION
INTRINSIC INTRINSIC REGIONREGION
00
For intrinsic semiconductors the carrier concentrations increase steadily as T increases. In Si, ni is small below 400K but increases rapidly above this temperature.
33
For extrinsic semiconductors the concentration vs. T plot has three regions:
1. Ionisation region – the impurities are being ionised2. Extrinsic region – all the impurities are ionised; few electron hole pairs3. Intrinsic region – electron-hole pairs produced in large numbers – material effectively becomes intrinsic
There is a transition temperature below which devices must operate, otherwise pn junctions will be lost.
33
Temperature / KTemperature / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
-- 33
Fig. 25: Free electron concentration vs. temperature forFig. 25: Free electron concentration vs. temperature forintrinsic and extrinsic siliconintrinsic and extrinsic silicon
10102121
22××10102121
33××10102121
nnii
Intrinsic Intrinsic SiSi
100 200 300 400 500 6100 200 300 400 500 60000
nn--type type SiSi doped with Ndoped with NDD = 10= 102121 mm--33
EXTRINSIC REGIONEXTRINSIC REGION
IONISATIONIONISATIONREGIONREGION
INTRINSIC INTRINSIC REGIONREGION
00Temperature / KTemperature / K
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
(Fre
e) e
lect
ron
co
nce
ntr
atio
n, n
/ m
-- 33
Fig. 25: Free electron concentration vs. temperature forFig. 25: Free electron concentration vs. temperature forintrinsic and extrinsic siliconintrinsic and extrinsic silicon
10102121
22××10102121
33××10102121
nnii
Intrinsic Intrinsic SiSi
100 200 300 400 500 6100 200 300 400 500 60000100 200 300 400 500 6100 200 300 400 500 60000
nn--type type SiSi doped with Ndoped with NDD = 10= 102121 mm--33
EXTRINSIC REGIONEXTRINSIC REGION
IONISATIONIONISATIONREGIONREGION
INTRINSIC INTRINSIC REGIONREGION
00
34
MAJORITY AND MINORITY CARRIERS
Majority carriers - electrons in n-type and holes in p-type
Minority carriers - electrons in p-type and holes in n-type
np = ni2
In n-type: nn ≈ ND ; pn ≈ ni
2 / ND
In p-type: pp ≈ NA ; np ≈ ni2 / NA
35
THE FERMI-DIRAC DISTRIBUTION FUNCTIONThis is a statistical function giving the probability
that a state at energy E is occupied by an electron
EF is the FERMI LEVEL - the energy at which a state has a 50-50 chance of occupancy.
)(exp11)(
kT
EE FEF
36
Fig. 26Fig. 26
En
erg
y, E
En
erg
y, E
C.B.C.B.
V.B.V.B.
EE
EECC
EEFF
EEVV
½½EEGG
½½EEGG
0 0 ½½ 1 F(E) 1 F(E)
F(E) for anF(E) for an INTRINSICINTRINSIC semiconductorsemiconductor
THE FERMITHE FERMI--DIRAC DISTRIBUTIONDIRAC DISTRIBUTION
Fig. 26Fig. 26
En
erg
y, E
En
erg
y, E
C.B.C.B.
V.B.V.B.
EE
EECC
EEFF
EEVV
½½EEGG
½½EEGG
0 0 ½½ 1 F(E) 1 F(E)
F(E) for anF(E) for an INTRINSICINTRINSIC semiconductorsemiconductor
THE FERMITHE FERMI--DIRAC DISTRIBUTIONDIRAC DISTRIBUTION
The Fermi Level is approximately in the middle of the gap for an intrinsic semiconductor.
The position of the Fermi Level is a measure of how n-type or p-type the material is.
A degenerate semiconductor is one which is very heavily doped.