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Intrinsic semiconductor
Si
Si
Si
+
Si
Si
Si
Si
EC
Si
+
Si
Si
Si
Si
Si
Si
Si
Si
FEKT VUT v Brně
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E
V
1
Doped semiconductor N-type
FEKT VUT v Brně
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2
Si
Si
Doped semiconductor P-type
Si
Si
Si
Si
Si
Si
Si
EC
Si
1,12
eV
Si
B
Si
Si B
1,12
eV
Si Si
Si eV
0,045
+
Si
Si
Si
Si
Si
FEKT VUT v Brně
-
0,045 eV
+
Si
Si
EC
+
+
Si
Si
Si
Si
Si
EA
EV
EA
EV
Si
Si
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Electric current in semiconductors
Drift of charged carriers
E
vd
+
-
+
vd
-
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Electric current in semiconductors
Jp,drift = qμppE
Jn,drift = qμnnE
E
A
I
+
+
vd = μ pE
Ip,drift = qpvd A
Jp,drift = qpvd
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Carrier mobility : 
Dimension : m2V-1s-1. cm2V-1s-1.
- n > p
Si , T=300K :
n = 1300 cm2V-1s-1 pro ND = 1014 cm-3 N- typ p = 490 cm2V-1s-1 pro NA = 1014 cm-3.
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Dependence on dopant concentration
pohyblivost [cm2 / Vs]
1000
elektrony
100
díry
10
10 14
10 15
10 16
10 17
1018
1019
N D nebo NA [cm-3 ]
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Diffusion
J p,dif
difúze
J n,dif
+
-
difúze
+ +
+ + +
+ + + +
x
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-
-
-
-
x
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Diffusion
1. Fick-Law:
 c c c 
J   D , ,    D.gradc
 x y z 
J n,dif
dn
 qDn
dx
J n, dif
ESO / L2 / J.Boušek
dn
 qDn
dx
9
Diffusion + Drift
dn
dp
Jx = qEx(pp + nn) + q(Dn
- Dp )
dx
dx
Einstein equation
D/ = kT/q
Dp
kT
Dn
=
=
q
p
n
ESO / L2 / J.Boušek
= UT
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Generation and recombination
Generation = need energy = generation in pairs: (electron + hole)
- photo-generation
- thermal excitation of the crystal lattice
- high energy electron
Recombination = loss of energy = recombination in pairs: (el. + hole) :
- large number of complicated processes
- direct (interband)
- undirect (recombination centres, traps)
- surface
generation
lifetime
electrones… n
recombination
holes…. p
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Lifetime of the carriers
Doped semiconductor:
Type N n >> p
;
Type P p >> n
Usually : n , p ≈ 1 s
High quality silicon : n , p ≥ 1 ms
High density of traps / of recombination centres :
n , p ≈ 1 s ÷1 ns
- High speed devices: Intentionally ... Au (Al)
- Low quality production: Crystal distortions, Impurities
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Thermal equilibrium
p0 n0 = ni2
equilibrium state (index "0")
Distortion of thermal equilibrium: n = n0 + n ;
p = p0 + p
(n a p concentration of non-equilibrium carriers)
Injection : np > ni2
low (n << n0) - medium (n  n0) -
high (n >> n0)
Extraction : np < ni2.
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PN-Junction in equilibrium state
Depletion region
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PN-Junction in equilibrium state
Concentration of dopants:
ND = 1019 m-3
NA = 1020 m-3
Electrons in N: nn = ND = 1019 m-3
Electrons in P: np = ni2 / NA = 1032 m-6 / 1020 m-3 = 1012 m-3
Difference in concentration 107
electron diffusion to P !!!!!
In N only ionized donors (ND +) standing firmly in the lattice
Holes in P: pp = NA = 1020 m-3
Holes in N: pp = ni2 / ND = 1032 m-6 / 1019 m-3 = 1013 m-3
Difference in concentration 107
diffusion of holes to N !!!!!
In N only ionized donors (ND +) standing firmly in the lattice
Ionized dopants create space charge !!!!!!!!!
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Space charge in depletion area
Electrical field
Potential
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PN-Junction in equilibrium state
Density of the space charge given by dopants concentration
Junction area with lower dopants concentration ís wider
Consequence : Electrical field in depletion area
Emax- in metalurgical junction !!!!
Potential difference between P and N : Diffusion voltage.
Actual potential value given by the shape of electrical field
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Band-diagram of PN-Junction
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Band-diagram of PN-Junction
1) The position of EF in both areas P and N must correspond to
the type of semiconductor / type of conductivity.
(shift EF to EV in case of “P-type“ or to EC in case of “N-type“)
2) In Thermal equilibrium the value of Fermi level EF is constant.
To fulfuill both 1) + 2) :
a) mutual shift of Conductive and Valence bands (band-bending)
b) The shift corresponds to qUD .
qUD : energetic treshold - prevents diffusion of majority carriers.
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PN junction in FORWARD polarisation
Diffusion voltage - barrier against diffusion of majority carriers
Equilibrium state :
Only small diffusion current which is compensated with the drift
casused by potential difference in space charge area.
majority carriers - diffusion
minoritní carriers - drift
In forward polarisation : external voltage acts against the
potential in depletion area - the barrier / treshold is lower !!!
Forward current is made by DIFFUSSION of majority carriers !!
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PN junction in REVERSE polarisation
Polarity of external voltage is the same as the polarity of electrical
field in the space charge region:
!! Electrical field in the space charge region grows !!
Electrical field in space charge region enhance the drift of minority
carriers from quasineutral parts of the junction:
-The concentration of minority carriers in quasineutral parts of the
junction drops.
- When increasing the reverse voltage the reverse current does not
increase !!!!
Reverse current : DRIFT current of minority carriers !!!!
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