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Resistivity - Technische Universität Ilmenau · Semiconductor Devices 1 Energy-band diagram Page 2...
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Semiconductor Devices 1 www.tu-ilmenau.de Page 1 Conductivity Resistivity Conductivity insulator semiconductor conductor
Transcript of Resistivity - Technische Universität Ilmenau · Semiconductor Devices 1 Energy-band diagram Page 2...
Semiconductor Devices 1
www.tu-ilmenau.dePage 1
Conductivity
Resistivity
Conductivity
insulator semiconductor conductor
Semiconductor Devices 1
Energy-band diagram
www.tu-ilmenau.dePage 2
Semiconductor Si Ge GaAs GaP GaN
Gap EG(eV) 1,12 0,66 1,42 2,26 3,39
ca. 8eV
Insulator Semiconductor Metal
EG
EG
EF
EF
VB
VB
VB
CBCB
CB
Semiconductor Devices 1
Conductivity
www.tu-ilmenau.dePage 3
in semiconductors electrons and holes:
Current density: pJ
nJ
Electron: en n n n
v µ E J n v
Hole: ep p p p
v µ E J p v
e e en p n p n p
J J J n v p v n µ p µ E E Current density:
en p
n µ p µ Conductivity:
E+ -
-+
pv
nv
Semiconductor Devices 1
Donors and Acceptors
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ED
EC
EC
EV
EV
EA
Donors
Acceptors
Semiconductor Devices 1
Ionization energies
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Semiconductor Devices 1
Carrier concentration at thermal equilibrium
www.tu-ilmenau.dePage 6
Charge neutrality:
Mass-action law:
0 0A DN n N p
2
0 0 in p n
2
2
0
1 1
2 4D A D A i
n N N N N n
Electrons:
2
2
0
1 1
2 4A D A D i
p N N N N n
Holes:
Semiconductor Devices 1
Wigner-Seitz-Cell
www.tu-ilmenau.dePage 7
Semiconductor Devices 1
Energy-band structure
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2 2
2
( ) ( , ) ( ) ( , )2
V r r k E k r km r
Operator potential total
kinetic energy energy energie
Schrödinger
equation:
( , ) - W a v e fu n c tio nr k
( , ) ( )i r k
n kr k e u r Bloch function:
Semiconductor Devices 1
Energy-band structure
www.tu-ilmenau.dePage 9
Shapes of constant-energy surfaces
electrons in Si
6 ellipsoids along the
<100> - axes
Semiconductor Devices 1
Energy-band structure
www.tu-ilmenau.dePage 10
EG
EC
EV
Electrons
Holes
Semiconductor Devices 1
www.tu-ilmenau.dePage 11
Effective mass
2
2
0 0 02
( ) 1 ( )( ) ( ) ( ) ( )
2
E k E kE k E k k k k k
k k
2
2 2
0 0 0 02
( )0 m a x im u m , m in im u m
1 ( )( ) ( ) ( ) ( ) ( )
2
E k
k
E kE k E k k k E k k k
k
2 2 2
*
*( )
2 2
kE k m m
m m Free electron:
Semiconductor Devices 1
www.tu-ilmenau.dePage 12
Effective mass and mobility
2
* 2 2
1 1 ( )
i j
E k
m k
Effective mass ( in general tensorial):
E
k
heavy
light
holes
Holes in Si
Semiconductor Devices 1
Energy bandgaps as a function of temperature
www.tu-ilmenau.dePage 13
Semiconductor Devices 1
www.tu-ilmenau.dePage 14
Density of states
* *
02 2
2( ) ( )
m mD E E E
Silicon
Electrons (ellipsoids)
2 2
* * 2 1 / 3
*
0
*
0
2( ) ( )
( )
- lo n g itu d in a l / 0 .9 8
- t ra n s v e rs a l / 0 .1 9
d e d e
n C C
d e l t
l
t
m mD E M E E
m m m
l m m
t m m
2 2
* 3 / 2 * 3 / 2 2 / 3
*
0
*
0
2( ) ( )
( )
/ 0 .1 6
/ 0 .4 9
d h d h
p V
d h lh h h
lh
h h
m mD E E E
m m m
m m
m m
Holes
Semiconductor Devices 1
Density of states
www.tu-ilmenau.dePage 15
Effective density of states:
conduction band valence band
3 / 2
2
2 k2
d e
C C
m TN M
h
3 / 2
2
2 k2
d h
V
m TN
h
Density of states:
Electrons Holes
1 / 2
2 1( )
k k
C
n C
E ED E N
T T
1 / 2
2 1( )
k k
V
p V
E ED E N
T T
Semiconductor Devices 1
Carrier concentration at thermal equilibrium
www.tu-ilmenau.dePage 16
Electrons:
1 / 2
2 1
k k1 e x p / kC
C
C
FE
E E d En N
T TE E T
Holes:
1 / 2
2 1
k k1 e x p / k
VE
V
V
F
E E d Ep N
T TE E T
Semiconductor Devices 1
Carrier concentration at thermal equilibrium
www.tu-ilmenau.dePage 17
Electrons:
1 / 2
1 / 2
0
2 2( )
1 e x p
n
C n C n
n n
n N d N F yy
Holes:
1 / 2
1 / 2
0
2 2( )
1 e x p
p
V p V p
p p
p N d N F yy
Fermi-Dirac-integral:
1 / 2
1 / 2
0
( )1 e x p
F y dy
Semiconductor Devices 1
Fermi-Dirac integral
www.tu-ilmenau.dePage 18
y
F1
/2(
)
3 / 22
3y
e x p2
y
Semiconductor Devices 1
Maxwell-Boltzmann statistics
www.tu-ilmenau.dePage 19
Electrons Holes
( , ) e x p ( , ) e x pk k
F F
n p
E E E Ef E T f E T
T T
e x p e x pk k
F C V F
C V
E E E En N p N
T T
Occupancy
Electrons Holes
Carrier concentration
Semiconductor Devices 1
Intrinsic carrier density
www.tu-ilmenau.dePage 20
e x p2 k
G
i C V
En N N
T
Semiconductor Devices 1
Fermi level for the intrinsic semiconductor
www.tu-ilmenau.dePage 21
e x p e x pk k
F C V F
C V
E E E EN N
T T
2 / 3
1 3( ) k ln
2 4
d h
i C V
d e C
mE E E T
m M
n p
1 1( ) k ln
2 2
V
F i C V
C
NE E E E T
N
Charge neutrality:
Semiconductor Devices 1
Fermi level for the n-type semiconductor
www.tu-ilmenau.dePage 22
e x pk
e x pk
1 e x pk
F C
C
V F D
V
F D
d
E EN
T
E E NN
E ETg
T
Dn p N
Charge neutrality:
Semiconductor Devices 1
D(E) f(E) n und p
www.tu-ilmenau.dePage 23
Intinsic SC
n-type SC
p-type SC
Semiconductor Devices 1
Temperature dependency
www.tu-ilmenau.dePage 24
n i ( T
2)
n i ( T
1)
E i
ED
EC
EV
NC
NV
N+
D
Tf
Ti
n i ( T
2)
n i ( T
1)
E i
ED
EC
EV
NC
NV
N+
D
n i ( T
1)
E i
ED
EC
EV
NC
NV
N+
D
p n
Ti – intrinsic temperature
Tf – freeze out temperature
neglected:
EG, NC, NV= f (T)
EF
EF
Semiconductor Devices 1
www.tu-ilmenau.dePage 25
Majority carrier density Conductivity
n-HL
µ influence
intrinsic
saturationfreeze-out
Tca. 100K
Semiconductor Devices 1
Temperature dependency of EF
www.tu-ilmenau.dePage 26
Freeze-out range and saturation range:
Approximation freeze-out range : EC-ED ≫kT
1 1k ln e x p
4 1 6 2 k
C DD
F D
C
E ENE E T
N T
1 1
+ k ln2 2 2
D
F D C
C
NE E E T
N
Majority carrier denity (insert EF):
e x p2 2 k
C D D CN N E E
nT
n-type: e x p
2 2 k
V A V AN N E E
pT
p-type:
Semiconductor Devices 1
Temperature dependency of EF
www.tu-ilmenau.dePage 27
Approximation saturation range : EC-ED <<kT
+ k lnD
F C
C
NE E T
N
Majority carrier denity:
2
2
2 2
D D
i
N Nn n
n-type:
2
2
2 2
A A
i
N Np n
p-type:
Semiconductor Devices 1
Temperature dependency of EF
www.tu-ilmenau.dePage 28
EF
T
EC
ED
Ei
freeze-out range
saturation range
intrinsic range
EF
T
Ei
EV
EAfreeze-out range
saturation range
intrinsic
range
n – type semiconductor p – type semiconductor
Semiconductor Devices 1
Built-in potential
www.tu-ilmenau.dePage 29
p – type n - type
j
jb
jF=0
j
jb
jF=0
jF=0
e x p e x p
ln
F i b
A i i
T T
A
b T
i
p N n nV
N
V
Vn
j j j
j
e x p e x p
ln
i F b
D i i
T T
D
b T
i
n N n
NV
V
n
nV
j
j j j
Semiconductor Devices 1
www.tu-ilmenau.dePage 30
Mobility
Mobility (low electric fields) vd<<vth:
e
e ff
µm
e
D
e ff
v E µ Em
Scattering on ionized impurities:
3 / 2 1
I Iµ T N
Interaction with acoustic phonon of
the lattice4
3 / 2
2 * 5 / 2 3 / 2
8 e
3 ( k )
l
L
d s
Cµ T
E m T
1 1 1
I Lµ µ µ
lattice
impuri-
ties
Matthiesen rule
Semiconductor Devices 1
Mobility
www.tu-ilmenau.dePage 31
Si
GaAs
Semiconductor Devices 1
www.tu-ilmenau.dePage 32
Mobility
0
1 /d
s
µ Ev µ E
E E
Mobility (high electric fields) :d th
v v
0
1 /
1 ( / )d
s
µ Ev
E E
vd
E
vs
ES
Semiconductor Devices 1
www.tu-ilmenau.dePage 33
Mobility
Semiconductor Devices 1
Drift mobility of GaAs
www.tu-ilmenau.dePage 34
E: low medium high
n: in the lower valley in both valleys in the upper valey
vd: high decrease const.
electric field
Semiconductor Devices 1
Current densities
www.tu-ilmenau.dePage 35
e ( )D r if tn p
J E n µ p µ E Drift:
e ( ) + e ( g ra d g ra d )n p n p
J n µ p µ E D n D p
Diffusion:
Nernst-Townsend-Einstein-relation:pn
T
n p
DDV
µ µ
e ( g ra d g ra d )D iffn p
J D n D p
Current-density equations:
Semiconductor Devices 1
Current densities and quasi Fermi levels
www.tu-ilmenau.dePage 36
e ( g ra d g ra d )
g ra d g ra d
n F n p F p
n F n p F p
J n µ p µ
n µ E p µ E
j j
drift current hole diffiusion
in n – type SC
Semiconductor Devices 1
Generation and Recombination
www.tu-ilmenau.dePage 37
2e x p
k
F n F p
r r i
E ER c n p c n
T
Band-to-band
E
Ec
Ev
-
+
Recombination
c o n s t . fo r T = c o n s t .th v c C V
G g N N
Generation
20
th r iU R G G c n
net transition rate in equilibrium:
net transition rate:2 2
( ) e x p 1k
F n F p
r i r i
E EU c n p n c n
T
n
p
Semiconductor Devices 1
Generation and Recombination
www.tu-ilmenau.dePage 38
indirect process
1st process
electron
capture emission
hole
capture emission
1(1 )
n t n t
n t t t
d ne n c n p
d t
c N f n f n
2nd process
1st process 2nd process
1(1 )
p t p t
p t t t
d pe p c p n
d t
c N f p f p
Semiconductor Devices 1
Shockley-Read-Hall (indirect mechanism)
www.tu-ilmenau.dePage 39
1
1 1( ) ( )
n p
t
n p
c n c pf
c n n c p p
Occupation probability of the traps:
2
1 1( ) ( )
i
p n
n p nU
n n p p
Net transition rate:
1 1
p n
p t n tc N c N
Lifetime of minority carriers:
Semiconductor Devices 1
SRH lifetime
www.tu-ilmenau.dePage 40
0 1 0 1
0 0 0 0
p n
n n n p p pn
U n p n n p p
0 1 0 1
0 0 0 0
p n
n n p p
n p n p
Low-injection:
Semiconductor Devices 1
Low-injection lifetime
www.tu-ilmenau.dePage 41
1 1
0 0
0 0 0 0
21 1 c o s h
k
i t in E En p
n p n p T
Assumption:
0p n
Semiconductor Devices 1
Auger-Recombination
www.tu-ilmenau.dePage 42
E
Ec
Ev
-
+
-E
Ec
Ev
- -
Et
band-to-band
2( ) ( )
A u A u
n n iU c n c p n p n
2
1 1( ) ( )
u n d a b h . v o n ,
i
A u A u
p n
A u A u
p n
n p nU
n n p p
n p
recombination through trap
Semiconductor Devices 1
Bandgap Narrowing
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donor
degenerated CB
non-degenerated CB
bandgap narrowing
donor level
density of states
Semiconductor Devices 1
Bandgap Narrowing
www.tu-ilmenau.dePage 44
1 71 8 .7 ln [ m e V ]
7 1 0G
NE
empirical equation
2 2e x p e x p
k k
G G G
ie ff C V i
E E En N N n
T T
Semiconductor Devices 1
Surface recombination
www.tu-ilmenau.dePage 45
2
, ,
1 1
1 1( ) ( )
i
p n p n th s t
p n
n p nU s v N
n n p ps s
Net transition rate:
Semiconductor Devices 1
Photogeneration
www.tu-ilmenau.dePage 46
E
Ec
Ev
-
+
h
G
ch h E
1 2 4 0[ n m ]
(e V )G G
h c
E E
0( ) (1 ) e - R e f le c t io n c o e ff ic ie n t
- A b s o rp tio n c o e ff ic ie n t
xx R R
Photon flux:
Semiconductor Devices 1
Photogeneration
www.tu-ilmenau.dePage 47
0
d( ) (1 ) e
d
xG x R
x
Generation rate:
Semiconductor Devices 1
Avalanche generation
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A V A n n p pG n v p v
Generation rate:
multiplication
of e- and h from impact
Ionization due to e- (n)
p=0
1( )
eA V A n n p p
G J J
Semiconductor Devices 1
Basic Equations
www.tu-ilmenau.dePage 49
Poisson equation:
Continuity equations:
0
d iv g ra d w ith e (p - n + N - N )D A
j
1 1d iv d iv
e ep p n n
p nJ U J U
t t
Current-density equations:
e e g ra d e g ra d
e e g ra d e g ra d
p p p p F p
n n n n F n
J p µ E D p p µ
J n µ E D n n µ
j
j
Semiconductor Devices 1
Excess majority carriers
www.tu-ilmenau.dePage 50
Debye length
0 0
0e
n T
D
n
D UL
n
LD
n(0)
n
x
neutral
x >> LD
space charge
x << LD
Dielectric relaxation time
2
0 0
0e
D
R
n n n
L
n µ D
( ) (0 ) e D
x
Ln x n
Semiconductor Devices 1
Excess minority carriers
www.tu-ilmenau.dePage 51
Diffusion length
b z w . p p p n n n
L D L D
Ln
np(0)
np
x
Semiconductor Devices 1
Space-Charge Limited Current (SCLC)
www.tu-ilmenau.dePage 52
2
0 3
9
8n n
VJ µ
d
Mott-Gurney law
20
0
e8
9
nV d
1 linear region, caused by ni
2 quadratic regime without traps
3 quadratic regime with traps
4 trap filling
5 linear
6 saturation
Semiconductor Devices 1
Metal-Semiconductor Contacts
www.tu-ilmenau.dePage 53
EF
Ohmic Contact: n-type SC
before contact
metal SC
after contact
metal SC
M
Evac
EC
Ev
S
Evac
EC
EFEi
Ev
M S
M < S
Ohmic Contact: p-type SC M > S
E
Semiconductor Devices 1
Metal-Semiconductor Contacts
www.tu-ilmenau.dePage 54
EF
Schottky contact: n-type SC
Evac
EC
EFEi
Ev
M S
M > S
M
Evac
EC
Ev
S
c
VBn
eVD
B n MV c Barrier: e
D M SV built-in (diffusion) potential:
E
before contact
metal SC
after contact
metal SC
Semiconductor Devices 1
Metal-Semiconductor Contacts
www.tu-ilmenau.dePage 55
EF
Schottky contact: p-type SC
M
M < S
Evac
EC
EFEi
Ev
M S
eVDEvac
EC
Ev
Sc
VBp
B p G MV E c Barrier: e
D M SV
E
before contact
metal SC
after contact
metal SC
built-in potential:
Semiconductor Devices 1
Metal-Semiconductor Contacts
www.tu-ilmenau.dePage 56
Real Ohmic contact:
metal n-type SC
n+-doped n-doped
degenerated non-degenerated
VBn
Tunneling
current EC
EF
Ev
p-Si
p++ -SiAl
example for p-type SC
Semiconductor Devices 1
Metal-Semiconductor Contacts
www.tu-ilmenau.dePage 57
V=0
V>0 (FD)
V<0 (RD)
n p
Semiconductor Devices 1
Schottky-barrier lowering (image-force lowering)
www.tu-ilmenau.dePage 58
2
0
e( ) e
1 6V x E x
x
0
e
1 6m
x
E
0
e
( ) e4
m m
E
V V x
Energy
Semiconductor Devices 1
Schottky-barrier lowering (image-force lowering)
www.tu-ilmenau.dePage 59
0
1 / 43
2 3 3
0
e
4
e
8
m
s
D D
s
E
N V V
j
Semiconductor Devices 1
Current transport processes
www.tu-ilmenau.dePage 60
1 – thermionic emission
2 – Tunneling
3 – Recombination
4 – Diffusion of e- to the metal)
5 – Diffusion of h form metal,
(minority-carriers)
V > 0 (forward biased)
Semiconductor Devices 1
Current transport processes
www.tu-ilmenau.dePage 61
EF
M
Evak
EC
Ev
VBn
eVD
--
V = 0
EF
M
Evak
EC
Ev
VBn
e(VD-V)
-
-EFn
EFp
V > 0 (FD)
EF
M
Evak
EC
Ev
VBn
- -
EFn
EFp
e(VD-V)
V < 0 (RD)Barrier for injection of electrons:
• metal to SC: independent on applied V
• SC to metal: dependent on applied V
Semiconductor Devices 1
Thermionic Emission
www.tu-ilmenau.dePage 62
Total current density (n-type SC):n S M M S
J J J
1 ) :S M
J
3 / 2
m in 3
4 ( 2 )e ( ) u n d e x p
h k
n F
D C
m E EE V V d n E E
T
m in
eS M x
E
J v d n
2
* 2 *
3
4 e ke x p e x p m it
k h
B n n
S M
T
V mVJ A T A
T V
Semiconductor Devices 1
Thermionic Emission
www.tu-ilmenau.dePage 63
Total current density (n-type SC):
2 ) :M S
J
fü r 0M S S M
J J V
* 2e x p e x p 1 e x p 1
k
B n
n S T
T T
V V VJ A T J
T V V
* 2e x p
k
B n
M S
VJ A T
T
Semiconductor Devices 1
Diffusion Theory
www.tu-ilmenau.dePage 64
Total current density (n-type SC):
( ) e x pk
F n F n C F n
n n n C
d E E E d EJ n x µ µ N
d x T d x
2
0
e 2 e ( )e x p e x p 1 e x p 1
k k
C n B nD D
n S D
s T T
N D VN V V V VJ J
T T V V
w ith in te g ra t io n o v e r s p a c e c h a rg e re g io nn
n
T
Dµ
V
Semiconductor Devices 1
Tunneling Current Density (Fowler-Nordheim)
www.tu-ilmenau.dePage 65
23 / 2 1 / 2*
2 4 ( 2 )ee x p m it
k 3 e h
B n n
F E
B n
V mA EJ
V E
Au-Si-barrier
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 66
-xp xn
-
AN N
D
E+-
Example: abrupt p-n junction 1D-Poisson equation
2
2
0
d
d x
j
Space charge
eD A
p n N N
x
log n,p
pp
pn
nn
np
ni
0
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 67
Emax for x=0:
A p D nN x N x
Depletion width:
02
e
s A D D
S
A D
N N V Vd
N N
m a x
0 0
e eA D
p n
s s
N NE x x
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 68
E
x
eVD
EC
EV
EiEF
-xp xn
p-type SC n-type SC
2ln ln ln
pn A D
D T T T
p n i
pn N NV V V V
n p n Built-in potential:
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 69
V > 0 (FD) V < 0 (RD)
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 70
Minority-carrier concentration at the boundary:
0 0
0
4( ) 1 e x p 1
2
p p
R p p
p T
p n Vn n x
p V
0 0
0
4( ) 1 e x p 1
2
n n
R n n
n T
n p Vp p x
n V
Low injection:
0
e x pR p
T
Vn n
V
0
e x pR n
T
Vp p
V
High injection:
e x p2
R R i
T
Vn p n
V
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 71
V > 0 (forward bias) V < 0 (reverse bias)
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 72
Minority-carrier concentration (holes in n-type semiconductor):
Long neutral region:
Short neutral region:
e x p e x p s in h
( )
e x p e x p s in h
n n n
p p p
n R R
n n n
p p p
w x w x w x
L L Lp x p p
w w w
L L L
0
( ) e x p e x p 1 e x pn R n
p T p
x V xp x p p
L V L
( ) 1n R
n
xp x p
w
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 73
Current densities of minority carriers :
in the n-side:
Total current density:
0
( ) e c o th e x p 1n n
p n p
p p T
p w VJ x D
L L V
0
( ) e c o th e x p 1p p
n p n
n n T
n w VJ x D
L L V
in the p-side:
0 0
e ec o th c o th e x p 1 e x p 1
p n n p pn
S
p p n n T T
D p D n ww V VJ J
L L L L V V
( ) ( )n p p n
J J x J x
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 74
IV characteristics
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 75
Generation/Recombination in the depletion layer
SRH with n1=p1=ni und p=n=:
2 2
1 1( ) ( ) ( 2 )
i i
p n i
n p n n p nU
n n p p n p n
Current density for generation/recombination:
/ , /
e ( )e x p 1 e x p 1
2 e x p 12
i s
r e c g en S re c g en
T T
T
n d V V VJ J
V VV
V
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 76
High-injection
J low J medium J high
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 77
IV
characteristics
of a practical
diode
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 78
IV characteristics for tunneling
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 79
Junction Breakdown
transition form
avalanche to
tunneling
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 80
Small-signal Behaviour
0 0e
e x p 1 1p n n p
p n
T T p n
D p D nA VY j j
V V L L
Admittance:
0 0
0
ee x p
p n n p
d
T T p n
D p D nA VG
V V L L
0 0
0
ee x p
2 2
p n n p
d
T T
L p L nA VC
V V
LF for p,n <<1:
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 81
0 0e
e x p2 2
p n n pp n
d
T T p n
D p D nA VG
V V L L
HF for p,n >>1:
Small-signal Behaviour
0 0e
e x p2 2
p n n pp n
d
T T p n
D p D nA VC
V V L L
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 82
Small-signal Behaviour
RBn RBprd
Cj
Cd
Equivalent circuit
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 83
Design and applications
VD=f(ni,ND,NA)
VBr=f(ND,NA)
IS=f(ni,ND,NA)
S
T
VI= I e x p -1
m V
I
U
metal metalplasticpackage
reverse current
limiting on current
thermal resistance
Semiconductor Devices 1
p-n Junctions
www.tu-ilmenau.dePage 84
Design and applications
Point contact diode:
for high power
1 holder
2 wafer
3 collector
4 package
5 insulator
6 conector cable
Junction diode:
Small junction diode
soldering n-type SC glas
wire end p-type SC
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 85
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 86
Lattice mismatch
isolated relaxed layer (mismatch) strained layer
Lattice mismatch:
e s
e
a a
a
Critical thickness:
2
2 2
e e
c
e s
a at
a a
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 87
before contact after contact
12C S S
E c c
Discontinuity in the band edges:
2 2 1 1 2 1
V S G S G C G GE E E E E Ec c
CB:
VB:
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 88
Built-in potential:2 1
eD S S
V c c
1 2 1 2
1 2 1 1 2 2
2
2
e
S S D A D
S
D A S D S A
N N V V
d
N N N N
Depletion-layer width:
1 1 2 2
1 1 2 2
2 2e e
e x p 1p i n i
p D n A T
D n D n VJ
L N L N V
Current density:
1
2
e x pk
Dn G
p A
NJ E
J N T
Ratio of the diffusion currents:
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 89
before contact EGn>EGp after contact
Semiconductor Devices 1
Heterojunctions
www.tu-ilmenau.dePage 90
Large lattice mismatch
before contact after contact
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 91
Integrated Transistor
Integraed Transistor
for high frequency
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 92
Current components for the
normal operating conditions Emitter injection efficiency
n c
T
n e
I
I
Base transport factor
C
n c
IM
I
Multiplication factor
Common-base current gain:C
N T
E
IA M
I
n e n e
E n e re p e
I I
I I I I
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 93
Current densities
( 0 ) ( )E n p E
J J J x
( ) ( )C n B p C
J J w J x
Minority-carrier concentration in the base:
0
s in h s in h
( ) e x p 1 e x p 1
s in h s in h
B
n B n B C BE B
B B
B BT T
n B n B
w x x
L L VVn x n
w wV V
L L
xC
wB
WB0
Doping profiles
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 94
Basic current-voltage relationship:
0 0 0
e e ec o th c o th e x p 1 e x p 1
s in h
p E E n B B n B B C BE B E B
E
Bp E p E n B n B T Tn B
n B
D p D n D n Vw w VI A
wL L L L V VL
L
0 0 0
e e ee x p 1 c o th c o th e x p 1
s in h
n B B p C C n B BC C BE B B
C
B T p C p C n B n B Tn B
n B
D n D p D nw VV wI A
w V L L L L VL
L
e x p 1 e x p 1C BE B
C N E S C S
T T
VVI A I I
V V
e x p 1 e x p 1C BE B
E E S I C S
T T
VVI I A I
V V
B E CI I I
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 95
In practical cases:
• shallow emitter
• Narrow base
• Long collector
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 96
-VBE(V)
VCB=5V
VCB=5V
VCB=1V
VCB=1V
I C,
I B(A
)
Gummel plotIC
IB
Output characteristics
VCE(V)
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 97
Common-base current gain:
0
0
1
c o s h 1
N E S
N
E S p E E BB
n B n B B E
A IA
I D p ww
L D n w
Emitter injection efficiency
: 0
0
1 1
11
n E
p E E B p E B A BE
n B E D En B B E
I
D p w D w NI
D w ND n w
Base transport factor:
21
12
c o s h
B
T
B n B n B
n B
w
w D
L
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 98
Common-emitter current gain:1
1 / 1
C C
N
B E C N
I IB
I I I A
0
0
n B B E n B E D E
N
p E E B p E B A B
D n w D w NB
D p w D w N 1 :
T
Doping profile:
( )( )
( )
T A B
A B
V d N xE x
N x d x
Built-in filed in the base:
( )e ( ) e 0
p p p
d p xJ p µ E x D
d x
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 99
Current gain
Gummel plot
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 100
Kirk effect
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 101
Output characteristics
0(1 )
C N E C s N I N E C BI A I I A A A I I
0/ (1 )
C N B C B O N N B C EI B I I A B I I
Common-base:
Common-emitter:
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 102
Common-base
configuration:0
0
1 1 1fo r 1
c o s h c o s h1
C
B BE p E E B
n B n Bn B B E
i
w wi D p w
L LD n w
2
2
1 1fo r
c o s h 1 1 12
B n B
B B
n n
n B n B
w Lw w
j jL L
Re
Im=0
ideal
real 2
1
12
B
n B
wj
D
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 103
Common-emitter
configuration:
2
2
1 1 1
11 c o s h 1 1
2
C
B BBn n
n B n B
i
w wij j
L L
0
1n
j
frequency (Hz)
cu
rre
nt
ga
in
2
2 1a n d
n B
B n
D
w
Limiting frequencies:
2
2n B
T
B
D
w
3dB:
Cutoff frequency:
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 104
Small-signal equivalent circuits
Low frequencies
Higher frequencies
Semiconductor Devices 1
Bipolar Transistor
www.tu-ilmenau.dePage 105
Cutoff frequency:
1
01
22
T
T F JE B JC
Cµ
Vf C C
Ir c c
F E B C
2 2
2 2
sC BE B
F
p E N n B s
ww w
D B D v
Maximum oscillation frequency:
m a x
8
T
B JB C
ff
R C
Semiconductor Devices 1
Heterojunction Bipolar Transistor (HBT)
www.tu-ilmenau.dePage 106
Current gain:
0
0
n B E B
N
p E B E
D w nB
D w p
2
0
e x pk
G B
C B V B
iB
B
A B A B
EN N
n Tn
N N
2
0
e x pk
G E
C E V E
iE
E
D E D E
EN N
n Tp
N N
e x pk
n B E D E G E G B
N
p E B A B
D w N E EB
D w N T
Semiconductor Devices 1
Heterojunction Bipolar Transistor (HBT)
www.tu-ilmenau.dePage 107
AlGaAs/GaAs
Semiconductor Devices 1
Heterojunction Bipolar Transistor (HBT)
www.tu-ilmenau.dePage 108
AlGaAs/GaAs
Semiconductor Devices 1
Heterojunction Bipolar Transistor (HBT)
www.tu-ilmenau.dePage 109
SiGe-HBT fT comparison
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 110
Schematic structure IV characteristics
and doping profile
x=0 x=d
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 111
FB RB FB
Mode of operation
C
C
VAC
VAC
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 112
Mode of operation
FB FB FB
RB FB RB FB
C
C
VAC
VAC
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 113
Current VAK>0:
Two-transistor
approximation:
C
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 114
Current VAK>0 and IG>0:
1 1 0 1 1C N A C B A BI A I I I I
1 1 0 11
B N A C BI A I I
2 2 0 2 2 0 2C N K C B N A G C BI A I I A I I I
Transistor 1:
Transistor 2:
1 2B CI I
2 0 1 0 2
2 11
N G C B C B
A
N N
A I I II
A A
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 115
1 21 0
N NA A
Str
om
ve
rstä
rku
ng
DC
AC
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 116
Comparison of VBr and VBf:
1 0 1 1
1 s in c e
1
N C B Nn
B r
C B b r
M I M A I I M A I
V
V
1 /
11
n
B r C B b r NV V A
VBr:
1 1 0 1
2 2 0 2
w ith
p n p C N A C B
n C N K C B
I M I I I I A I I
I I A I I
VBf:
1 2fo r 0 : = a n d
G A K N NI I I I I M I A A
1 /
1 21
n
B f C B b r N NV V A A
11
NM A
Semiconductor Devices 1
Thyristor
www.tu-ilmenau.dePage 117
Semiconductor Devices 1
DIAC (diode ac switch)
www.tu-ilmenau.dePage 118
A
K
Schematic structure IV characteristics
J1
J2
J3
J4
on
on
off
off
Semiconductor Devices 1
TRIAC (triode ac switch)
www.tu-ilmenau.dePage 119
Schematic structure IV characteristics
Semiconductor Devices 1
Microwave Devices
www.tu-ilmenau.dePage 120
Device Principle
Schottky diode Majority-carrier current
Tunnel diode Tunneling
Backward diode Tunneling
Impatt diode Avalanche and transit time
Resonant Tunneling diode Quantum-effect
Semiconductor Devices 1
Tunnel Diode
www.tu-ilmenau.dePage 121
EF
EV
EC
n+ p+depletion
region
Band diagram IV characteristics
e x p 1 e x pP S
P P T
V V VI I I
V V V
tunneling current difusion current (p-n junction)
Semiconductor Devices 1
Tunnel Diode
www.tu-ilmenau.dePage 122
V=0 V=VP VP<V<VV V>VV V<0
Semiconductor Devices 1
Backward Diode
www.tu-ilmenau.dePage 123
Tunnel diode Backward diode
rd< 0
Semiconductor Devices 1
IMPATT (impact ionization avalanche transit-time) Diode
www.tu-ilmenau.dePage 124
Read hi-lo lo-hi-lo
IMPATT
Semiconductor Devices 1
IMPATT Diode
www.tu-ilmenau.dePage 125
Semiconductor Devices 1
Resonant-Tunneling Diode
www.tu-ilmenau.dePage 126
Semiconductor Devices 1
Resonant-Tunneling Diode
www.tu-ilmenau.dePage 127
Semiconductor Devices 1
Resonant-Tunneling Diode
www.tu-ilmenau.dePage 128
rd< 0rd< 0
Semiconductor Devices 1
Photonic Devices
www.tu-ilmenau.dePage 129
before
after
Absorption spontaneous stimulated
emission emission
E2
E1
h h
E2
E1
hhh
2 1
1 2 1
a b s
d n d nB n W
d t d t
2
2 1 2
sp o n
d nA n
d t
2
2 1 2
s t im
d nB n W
d t
Semiconductor Devices 1
Photonic Devices
www.tu-ilmenau.dePage 130
Semiconductor Devices 1
LED (light-emitting diode)
www.tu-ilmenau.dePage 131
Semiconductor Devices 1
LED
www.tu-ilmenau.dePage 132
Energy gap Enegy-band structure
Semiconductor Devices 1
LED
www.tu-ilmenau.dePage 133
Semiconductor Devices 1
LED
www.tu-ilmenau.dePage 134
p-n junction
double heterojunction
Semiconductor Devices 1
OLED (organic light-emitting diode)
www.tu-ilmenau.dePage 135
Semiconductor Devices 1
LASER (light amplification by stimulated emssion of radiation)
www.tu-ilmenau.dePage 136
Semiconductor Devices 1
LASER
www.tu-ilmenau.dePage 137
Semiconductor Devices 1
Photoconductor
www.tu-ilmenau.dePage 138
Semiconductor Devices 1
Photodiode
www.tu-ilmenau.dePage 139
p-i-n diode p-n diode
Schottky diodes
Semiconductor Devices 1
Solar Cell
www.tu-ilmenau.dePage 140
p-Si
n-Si
Antireflection coating Metal contact
Solar spectrum
Semiconductor Devices 1
Solar Cell
www.tu-ilmenau.dePage 141
h
RLIL e x p 1
S
T
VI
V
RL
I
d( ) ( )
dG G
p h
L
E h E
I S E d E d hh
e x p 1S L
T
VI I I
V
Idealized equivalent circuit
Semiconductor Devices 1
Solar Cell
www.tu-ilmenau.dePage 142
ln 1 lnL L
o c T T
S S
I IV V V
I I
V
I
Isc
Voc
IPh
Im
Vm
RLopt
MPP
/ 1ln ln 1
1 /
L S m
m T o c T
m T T
I I VV V V V
V V V
MPP (maximum power point)
e x p 1m m T
m s L
T T m
V V VI I I
V V V
Fill factor m m
sc o c
I VF F
I V
Conversion efficiencym m sc sc
in in
I V I V F F
P P
Open-circuit voltage
