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FEKT VUT v Brně ESO / L1 / J.Boušek 1
Intrinsic semiconductor
FEKT VUT v Brně ESO / L1 / J.Boušek 2
Doped semiconductor N-type
FEKT VUT v Brně ESO / L1 / J.Boušek 3
Doped semiconductor P-type
ESO / L2 / J.Boušek 4
E
+
-v
vd
d
+
-
Electric current in semiconductors
Drift of charged carriers
ESO / L2 / J.Boušek 5
+
+
E
IA
Ip,drift = qpvd A Jp,drift = qpvd
vd = μpE
Jp,drift = qμppE Jn,drift = qμnnE
Electric current in semiconductors
ESO / L2 / J.Boušek 6
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.
ESO / L2 / J.Boušek 7
10 10 1010
elektrony
díry
14 15 16 17 18 19
1000
100
10
10 10
N nebo N [cm ]D A-3
pohyblivost [cm / Vs]2
Dependence on dopant concentration
ESO / L2 / J.Boušek 8
+
+
+
+
+
+
+
+
++
-
-
-
-
-
-
-
-
--
x x
difúze difúze
J Jp,dif n,dif
Diffusion
ESO / L2 / J.Boušek 9
cDz
c
y
c
x
cDJ grad.,,
dx
dnqDJ ndifn ,
dx
dnqDJ ndifn ,
Diffusion
1. Fick-Law:
ESO / L2 / J.Boušek 10
Jx = qEx(pp + nn) + q(Dn dn
dx- Dp
dp
dx)
D/ = kT/q
Dn
n =
Dp
p = kT
q = UT
Einstein equation
Diffusion + Drift
ESO / L2 / J.Boušek 11
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 recombination
electrones… n holes…. p
Generation and recombination
ESO / L2 / J.Boušek 12
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
Lifetime of the carriers
ESO / L2 / J.Boušek 13
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.
Thermal equilibrium
ESO / L2 / J.Boušek 14
Depletion region
PN-Junction in equilibrium state
ESO / L2 / J.Boušek 15
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
PN-Junction in equilibrium state
Concentration of dopants: ND = 1019 m-3 NA = 1020 m-3
Ionized dopants create space charge !!!!!!!!!
ESO / L2 / J.Boušek 16
Space charge in depletion area
Electrical field
Potential
ESO / L2 / J.Boušek 17
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 !!!!
Actual potential value given by the shape of electrical field
Potential difference between P and N : Diffusion voltage.
PN-Junction in equilibrium state
ESO / L2 / J.Boušek 18
Band-diagram of PN-Junction
ESO / L2 / J.Boušek 19
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.
ESO / L2 / J.Boušek 20
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 !!
ESO / L2 / J.Boušek 21
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 !!!!
PN junction in REVERSE polarisation
