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IFE T&CS
Semiconductor Devices
lectures 30 hours
lab. exercises 30 hours
Prof. Zbigniew Lisik
room: 116
e-mail: [email protected]
Department of Semiconductor and
Optoelectronics Devices
Fundamentals of Semiconductor Physics
Chapter 1
T
T
T
Metal Semiconductor Isolator
very low medium very large
Fundamentals of Semiconductor Physics
Chapter 1
What are semiconductors ?
1. They are crystals
2. They can be:
● atom crystals like: Si, Ge, C-diamond
● compound crystals like: GaAs, InSb, SiC, GaN
3. When they are pure, their resistivity is in
a middle range
Fundamentals of Semiconductor Physics
Chapter 1
Basic semiconductors:
Si - silicon
Ge - germanium
GaAs - gallium arsenide
SiC - silicon carbide
GaN - gallium nitride
Fundamentals of Semiconductor Physics
Chapter 1
Structure of crystal – energy band model
● - electron
●●
+
W W3
W2
W1●
●
●●
+
●●
+
R
W W3
W2
W1●●
●●
single atom
atoms in
crystal
Pauli restriction – elektrons must be recognisable
R
Fundamentals of Semiconductor Physics
Chapter 1
Structure of silicon crystal – so called
diamond structure
Crystal bond between 2 atoms
The bond arises when 2 atoms are so
close that two of their valance
electrons become common, which
results in quantum nature attraction
atom A atom B
electrons
Fundamentals of Semiconductor Physics
Chapter 1
Structure of silicon crystal – so called
diamond structure
Crystal bond between 2 atoms
The bond arises when 2 atoms are so
close that two of their valance
electrons become common, which
results in quantum nature attraction
two atoms molecula
two electron bond
Fundamentals of Semiconductor Physics
Chapter 1
Structure of silicon crystal – so called
diamond structure
Si
3D 2D
Si Si
Fundamentals of Semiconductor Physics
Chapter 1
Structure of silicon crystal –
2D representation
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
T = 0 K If the temperature of crystal T = 0K
all the valance electrons take part
in the atom bonds
W2
W1
W3
●●
●●
Conduction Band
Valence Band
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
The crystal temperature can,
however, increase and then T> 0K.
If the sufficient energy is delivered
to the valance electron, it can leave
its position in the interatom bond
and can become a free electron.
T = 0 K If the crystal temperature T = 0K
all the valance electrons take
part in the atom bonds
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
The valance electron taking
sufficient energy leaves its
position in the bond and
becomes free electron.
T > 0 K
Such a free electron can move in
the crystal without any restriction
and is called conduct electron in
contrast to the electrons in bonds
called valance electrons
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
T > 0 K The valance electron taking
sufficient energy leaves its
position in the bond and
becomes free electron.
The empty place in the bond
structure is called hole and can
also move through the crystal as
the result of valance electrons
hopping from one bond to another.
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSi
T > 0 K Conduct electrons are not connected
with any bonds and can freely move
inside the crystal. Since they are
negative charge –q their movement can
create an electric current
Holes are not connected with any
particular bond and can freely move
inside the crystal. Since the hole
means the lack of an electron, it is
connected with the local excess of
positive charge +q. This charge moves
together with the hole creating an
electric current.
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
The presented process is called
electron-hole pair generation
and has its energy band model:
Wg = Wc - Wv
T > 0 K
SiSiSiSi
SiSiSiSi
SiSiSiSi
SiSiSiSiWC
WV
Conduction Band
Valence Band
Fundamentals of Semiconductor Physics
Chapter 1
2D Structure of silicon crystal
The presented process is called
electron-hole pair generation
and has its energy band model:
WC
WV
Wg = Wc - WvValance band
Conduction band
Band gap
WC
WV
Electrons – fermions
fulfilling the Pauli restriction
Fundamentals of Semiconductor Physics
Chapter 1
Dopands in Silicon T = 0K
SiSiSiSi
SiSiGaSi
SiAsSiSi
SiSiSiSi acceptors
As donors
GaIII Mendeleiew group
Ga, B, Al
V Mendeleiew group
As, Sb, P
Fundamentals of Semiconductor Physics
Chapter 1
SiSiSiSi
SiSiGa-Si
SiAs+SiSi
SiSiSiSi
Dopands in Silicon T > 0K
Ga
As
acceptor
donor
Ionization energy of
dopands is very low
Wi << Wg
Fundamentals of Semiconductor Physics
Chapter 1
SiSiSiSi
SiSiGa-Si
SiAs+SiSi
SiSiSiSi
Dopands in Silicon T > 0K
WC
WV
WA
WD
Ionization energy of
dopands is very low
Wi << Wg
Energy band model:
Fundamentals of Semiconductor Physics
Chapter 1
Carrier concentration in doped semiconductor
Types of semiconductors
Na > Nd pp0 > np0 p-type
Na < Nd pn0 < nn0 n-type
Na = Nd p0 = n0 = ni i-type
Charge balance:nd + Na + nT = pT + Nd + pa
n0 + Na = p0 + Nd
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium carrier concentration
Thermodynamic equilibrium state
n0 , p0
The state of the system being in constant temperature
without any energy exchange with surroundings - so
called adiabatic conditions.
The equilibrium densities
of electrons and holes, n0
and p0, result from the
balance of generation and
annihilation processes:
gdT=rdT and gT=rT
WC
WV
WA
WD
rTgT
gdT rdT
Type n
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
● It is used to describe physical phenomena that are created
by huge number of elements – e.g. properties of gases that
can be considered as the set of molecules.
● The phenomenon is described by the parameters that
represent the behaviour of the set of elements being
related to the average value of particular element feature
Temperature – average kinetic energy of molecules
Pressure – average momentum of molecules
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
● The set of elements is characterised by the probability
function that determines the probability that the
considered parametr of an element has particular
magnitude.
● In the classical approach,
the probability function has
a bell-like shape with the maximum
value corresponded to the average
value of parameter (energy in
the figure) .
f(W)
Wav W
Boltzman distribution
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
● If we want to know how many particles (e.g. electrons)
have their energy in the range <W1,W2>, it is enough to
calculate the integral:
dW f(W) N(W) n 2
1
W
W
where:
N(W) – state density function (in classical approach,
total number of particles N(W) = N)
f(W) – probability that the state of energy W is
occupied
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
Classical approach – Bolzmann distribution
kT
W exp f(W)
Quantum approach – Fermi-Dirac distribution
1 kT
W-Wexp
1 f(W)
F
WF – Fermi energy (Fermi lavel)
f(W)
Wśr W
f(W)
WF W
0.5
1
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
Classical approximation – (W – WF) > 2kT
Quantum approach – Fermi-Dirac distribution
1 kT
W-Wexp
1 f(W)
F
WF – Fermi energy (Fermi lavel)
kT
W-Wexp f(W) F
Fundamentals of Semiconductor Physics
Chapter 1
Statistical physics
Classical approximation – (W – WF) > 2kT
If this approach can be used to estimate the electron and
hole density in semiconductor, such a semiconductor is
called non-degenerated
kT
W-Wexp f(W) F
Only such semiconductors will be considered in our lectures
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium carrier concentration
Classical aproximation for electrons
Conduction
band
Wc
Wc1
states occupied by
electrons
dW f(W) N(W) n C1
C
W
W
0
Concentration of electrons in
conduction band:
Under the assumption: WC1
kT
W-Wexp N n FC
C0
2/3
2
efeC
h
kTm2 N
NC – effective density of states
in the conduction band
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium carrier concentration
Classical aproximation for holes
Concentration of holes in
valance band:
dWf(W) - 1N(W) p V
V1
W
W
0
kT
W-Wexp N p VF
V0
states occupied by holes
Valance
band
Wv1
Wv
Under the assumption: WV1 -
NV – effective density of states
in the valance band
2/3
2
efhV
h
kTm2 N
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium in intrinsic semiconductor n0 = p0
kT
W-Wexp N
kT
W-Wexp N VFi
VFiC
C
efe
efhVC
C
VVC Fi
m
mln kT
4
3 WW
2
1
N
Nln kT
2
1 WW
2
1 W
From the equilibrium condition:
one can calculate WFi, the
Fermi energy for intrinsic
semiconductor :
WC
0.5 (WC – WV)
WFi
WV
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium in doped semiconductor
Transformation of electron equation:
n0 ≠ p0
kT
W-Wexp n
kT
W-Wexp
kT
W-Wexp N
kT
W-WW-Wexp N
kT
W-Wexp N n
FFii
FFiFiCC
FFiFiCC
FCC0
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium in doped semiconductor
Transformation of hole equation:
n0 ≠ p0
kT
W-Wexp n
kT
W-WW-Wexp N
kT
W-Wexp N p
FFii
VFiFiFV
VFV0
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium in doped semiconductor
Product of hole and electron
concentration:
n0 ≠ p0
kT
W-Wexp n
kT
W-Wexp n pn FFi
iFFi
i00
n pn 2
i00
At constant temperature n0p0 is constant
independently on the dopand concentration
Fundamentals of Semiconductor Physics
Chapter 1
Equilibrium in doped semiconductor
Transformation of hole and electron
product:
n0 ≠ p0
pn n 00
2
i
kT
W-Wexp N
kT
W-Wexp N pn VF
VFC
C00
kT
Wexp
300
T B
kT
Wexp NN
kT
W-Wexp NN
kT
W-Wexp N
kT
W-Wexp N n
g
3
2
g
VCVC
VC
VFV
FCC
2
i
ni = f(T)
Fundamentals of Semiconductor Physics
Chapter 1
Carrier concentration in doped semiconductor
T
ni
p0
n0
TiTs
ln n0
ln p0
Typ n
WC
WV
WD
n0 = nd + nT
p0 = pT
Ts – saturation temperature
Ti – intrinsic temperature
Fundamentals of Semiconductor Physics
Chapter 1
Carrier concentration in doped semiconductor
T
ni
p0
n0
TiTs
ln n0
ln p0
Type n
Ts – saturation temperature
Ti – intrinsic temperature
T
TiTs
ρ
Fundamentals of Semiconductor Physics
Chapter 1
Thermal limitation for semiconductor devices
T
ni
p0
n0
TiTs
ln n0
ln p0
Recommended area
If semiconductor devices are to keep their data sheet ratings,
the concentration of majority carriers cannot change
considerably. Condition 1: It is true when Tmin not lower than Ts.
For Si Tmin ≈ -50 °C
Ts[C]
Fundamentals of Semiconductor Physics
Chapter 1
Thermal limitation for semiconductor devices
T
ni
p0
n0
TiTs
ln n0
ln p0
Recommended area
If semiconductor devices are to keep their data sheet ratings,
the concentration of majority carriers cannot change
considerably. Condition 2: It is true when Tmax lower than Ti.
For Si Tmax < 400 °C
Fundamentals of Semiconductor Physics
Chapter 1
Thermal limitation for semiconductor devices
T
ni
p0
n0
TiTs
ln n0
ln p0
Recommended area
If semiconductor devices are to keep their data sheet ratings,
the concentration of majority carriers cannot change
considerably. Condition 2: It is true when Tmax lower than Ti.
Typical ranges defined for
silicon devices in catalogues:
Range [C]
Commercial 0 – 70
Industrial -25 – 85
Extended industrial -40 – 125
Military -55 – 125
Fundamentals of Semiconductor Physics
Chapter 1
Current filamentation – hot spot
T
TiTs
ρ
Safe area
If T inside <Ts,Ti>, the negative thermal feedback
occurs:
Current is pushed out from warmer
area and heat dissipation decreases
Silicon chip
Q
T
J
Ti
Fundamentals of Semiconductor Physics
Chapter 1
Current filamentation – hot spot
T
TiTs
ρ
Safe area
If T inside <Ts,Ti>, the negative thermal feedback
occurs:
Current is pushed out from warmer
area and heat dissipation decreases
Silicon chip
Q
T
J
Fundamentals of Semiconductor Physics
Chapter 1
Current filamentation – hot spot
T
TiTs
ρ
Safe area
If T outside <Ts,Ti>, the positive thermal feedback
occurs:
Current is squeezed in warmer area
and heat dissipation increases
Silicon chip
Q
T
J
Ti
Fundamentals of Semiconductor Physics
Chapter 1
Current filamentation – hot spot
T
TiTs
ρ
Safe area
If T outside <Ts,Ti>, the positive thermal feedback
occurs:
Current is squeezed into small area
and hot spot is generated
Silicon chip
Q
T
J
Fundamentals of Semiconductor Physics
Chapter 1
Nonequilibrium carrier concentration
Equilibrium concentrations
n0 , p0
n = n0 + Dn
p = p0 + Dp
Nonequillibrum concentrations
WC
WV
h
Dn
Dp
Δn, Δp – excess concentrationsDn = Dp
usually:
Fundamentals of Semiconductor Physics
Chapter 1
Nonequilibrium carrier concentration
Quasi-Fermi level
n = n0 + Dn
p = p0 + Dp
kT
WWexpN p
kT
WWexpN p
kT
WWexpN n
kT
WWexpN n
vFhv
vFv
Fecc
Fcc
D
D
kT
W-Wexp N n FC
C0
kT
W-Wexp N p VF
V0
Fundamentals of Semiconductor Physics
Chapter 1
Nonequilibrium carrier concentration
Quasi-Fermi level
kT
WWexpN p p p
kT
WWexpN n n n
vFhv0
Fecc0
D
D
WFe – quasi-Fermi level for electrons
WFh – quasi-Fermi level for holes
Wc
Wv
WF
WFe
WFh
n-type
Wc
Wv
WF
WFe
WFh
p-type
Phenomena in Semiconductors
Chapter 2
Recombination processes
WC
WV
gT rT
n0
p0
Equillibrum state:
gT – rate of electron-hole pairs
thermal generation
rT – rate of electron-hole pairs
thermal anihilation
gT = rT
Steady state
constant carrier concentrations
Phenomena in Semiconductors
Chapter 2
Recombination processes
WC
WV
h gT r
n0 + Δn
p0 + Δn
Non-equillibrum state:
gT – rate of electron-hole pairs
thermal generation
r – rate of electron-hole pairs
anihilation
gr + gT = r
gr
gr – rate of electron-hole pairs
radiative generation
Steady state
constant carrier concentrations
