Some Concepts of Solid State Materials with Applications in Optoelectronic Devices
ContentsThe Semiconductors in Equilibrium
Nonequilibrium Condition
Generation-Recombination
Generation-Recombination rates
Photoluminescence & Electroluminescence
Photon Absorption
Photon Emission in Semiconductors
Basic TransitionsRadiative
NonradiativeSpontaneous EmissionStimulated Emission
Luminescence EfficiencyInternal Quantum EfficiencyExternal Quantum Efficiency
Photon AbsorptionFresnel Loss
Critical Angle Loss
Energy Band Structures of SemiconductorsPN junctionsHomojunctions, HeterojunctionsMaterialsIII-V semiconductors
Ternary SemiconductorsQuaternary Semiconductors
II-VI SemiconductorsIV-VI Semiconductors
Classification of Devices
• Combination of Electrics and Mechanics form Micro/Nano-Electro-Mechanical Systems (MEMS/NEMS)
• Combination of Optics, Electrics and Mechanics form Micro/Nano-Opto-Electro-Mechanical Systems (MOEMS/NOEMS)
Optical Electronics
Mechanical
MEMS
MOEMS
Schematic illustration of the the structure of a double heterojunction stripecontact laser diode
Oxide insulator
Stripe electrode
SubstrateElectrode
Active region where J > Jth.
(Emission region)
p-GaAs (Contacting layer)
n-GaAs (Substrate)
p-GaAs (Active layer)
Current
paths
L
W
Cleaved reflecting surfaceElliptical
laser
beam
p-AlxGa
1-xAs (Confining layer)
n-AlxGa
1-xAs (Confining layer)
12 3
Cleaved reflecting surface
Substrate
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Solid State Optoelectronic Devices
Optical Sources: Laser, LED
Switches
Photodiodes
Photodetectors
Solar Cells
Sensors
Type of Semiconductors
• Simple Semiconductors
• Compound Semiconductors
• Direct Band gap Semiconductors
• Indirect Band gap Semiconductors
Classification of Solid Structures
Amorphous: Atoms (molecules)
bond to form a very short-range
(few atoms) periodic structure.
Polycrystalline: made of pieces of
crystalline structures (called grain)
each oriented at different direction
(intermediate-range-ordered)
Crystals: Atoms (molecules) bond to
form a long-range periodic structure.
The constant bonds (coordination) ,
bond distance and angles between
bonds are the characteristics of a
crystal structure
Represents an atom or a
molecule
An IDEAL CRYSTAL is constructed by the infinite repetition of identical
structural units in space.
Crystals
Crystalline Structures
(b)
Z
X
y
Z
X
y
Z
X
y
Z
X
y
(110)(100)
(111) (200)
Some popular lattice planes
Some Properties of Some Important Semiconductors
Compound Eg Gap(eV) Transition λ(nm) BandgapDiamond 5.4 230 indirect
ZnS 3.75 331 direct
ZnO 3.3 376 indirect
TiO2 3 413 indirect
CdS 2.5 496 direct
CdSe 1.8 689 direct
CdTe 1.55 800 direct
GaAs 1.5 827 direct
InP 1.4 886 direct
Si 1.2 1033 indirect
AgCl 0.32 3875 indirect
PbS 0.3 4133 direct
AgI 0.28 4429 direct
PbTe 0.25 4960 indirect
Common Planes
• {100} Plane
• {110} Plane
• {111} Plane
a
a
a – Lattice Constant
For Silicon
a = 5.34 Ao
Two Interpenetrating Face-Centered Cubic Lattices
Silicon – Diamond Structure
100
101
000
001011
010
110
111
z
y
x
The unit cell of diamond (zinc blend) lattice structure. The
position of each lattice point is shown with respect to the 000
lattice point.
43
41
43
2
10
2
1
41
41
41
43
43
41
41
43
43
021
21
a
b
c
xy
z
a/2
a
a
222
4
2)4( n
qmE
o
o
n
hpe
-=
0/
2/3
0
100
11 arq
a
-
=
p
Energy States & Energy Bands
Pauli’s Exclusion Principle
1
s
2
s
2
p
1
s
2
s
2
p
1
s
2
s
2
p
1s
2s
2
p
1
s
The potential wells due to the interactions
between 2 atoms (in one molecule). Some
electrons are shared between the atoms. Due
to the interactions between electrons-
electrons, nucleons-nucleons, and electrons-
nucleons, the energy levels split, creating 1s,
2s, 2p,… doublets.
The potential experienced by an electron due to the coulomb
interactions around an atom. 1s, 2s, 2p,… are the energy
levels that the electron can occupy.
Larger molecules, larger splitting.
In Solid with n≈ 10e23 atoms, the sublevels are extremely close to each other.
They coalesce and form an energy band. 1s, 2s, 2p… energy bands.
Energy Band Structure of Semiconductors
EEh
mEg
EEh
mEg
v
p
v
cn
c
-=
-=
3
2/3*
3
2/3*
)2(4)(
)2(4)(
p
p
Density of State.
Electrons Distribution.
E EF
0
1/2
1.0
T = 0
T = T1
T = T2 > T1
The Fermi probability function versus energy for differential temperatures.
f F(E
)
-
=
kT
EEEf
F
F
exp1
1)(
Fermi-Dirac Distribution
dEEfEgn F
E
Ec
c
c
)()(0
=
Concept of positive charges in solids (holes)
Doped Semiconductors
+5
As
+4
Si+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
Eg
Ec
Ev
Ef
Ed
Conduction
electron
N - Type
Doped Semiconductors
+3
Al
+4
Si+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si+4
Si
Eg
Ec
Ev
Ef
Valence holeEa
P-type
The Semiconductors in Equilibrium
• The thermal equilibrium concentration of carriers is independent of time.
• The random generation-recombination of electrons-holes occur continuously due to the thermal excitation.
• In direct band-to-band generation-recombination, the electrons and holes are created-annihilated in pairs:
• Gn0 = Gp0 , Rn0 = Rp0
• -The carriers concentrations are independent of time therefore:
• Gn0 = Gp0 = Rn0 = Rp0
Nonequilibrium Conditions in Semiconductors
• When current exist in a semiconductor device, the semiconductor is operating under nonequilibrium conditions. In these conditions excess electrons in conduction band and excess holes in the valance band exist, due to the external excitation (thermal, electrical, optical…) in addition to thermal equilibrium concentrations.
n(t) = no + n(t), p(t) = po + p(t)
• The behavior of the excess carriers in semiconductors (diffusion, drift, recombination, …) which is the fundamental to the operation of semiconductors (electronic, optoelectronic, ..) is described by the ambipolar transport or Continuity equations.
Continuity Equations
t
nng
x
En
x
nE
x
nD
t
ppg
x
Ep
x
pE
x
pD
n
nnn
p
ppp
=-
=-
-
)(
)(
2
2
2
2
Nonequilibrium Conditions in Semiconductors
Generation-Recombination Rates
• The recombination rate is proportional to electron and hole concentrations.
is the thermal equilibrium generation rate.
dt
tnd
dt
tnndtptnn
dt
tdni
)())(()]()([
)( 02 =
=-=
)()( 0 tnntn = )()( 0 tpptp =
2
in
Generation-Recombination Rates
• Electron and holes are created and recombined in pairs, therefore,
• n(t) = p(t) and no and po are independent of time.
)]())[(()]())((([))((
0000
2 tnpntntpptnnndt
tndi
-=-=
Considering a p-type material under low-injection condition,
)())((
0 tnpdt
tnd
-= 00 )0()0()( n
t
tpenentn
-
-==
no = (po)-1 is the minority carrier electrons lifetime, constant for low-injections.
Generation-Recombination Rates
• The recombination rate ( a positive quantity) of excess minority carriers (electrons-holes) for p-type materials is:
0
'' )(
n
pn
tnRR
==
Similarly, the recombination rate of excess minority carriers for n-type material is:
0
'' )(
p
pn
tpRR
==
• where po is the minority carrier holes lifetime.
Generation-Recombination Rates
so,
no = (p)-1 and po = (n)-1
[For high injections which is in the case of LASER and LED
operations, n >> no and p >> po ]
• During recombination process if photons are emitted (usually in direct bandgap semiconductors), the process is called radiative (important for the operation of optical devices), otherwise is called nonradiative recombination (takes place via surface or bulk defects and traps).
Generation-Recombination Rates
• In any carrier-decay process the total lifetime can be expressed as
nrr
111=
where r and nr are the radiative and nonradiative lifetimes
respectively.
The total recombination rate is given by
Where Rr and Rnr are radiative and nonradiative recombination rates
per unit volume respectively and Rsp is called the spontaneous
recombination rate.
spnrrtotal RRRR ==
pn Junction
The entire semiconductor is a single-
crystal material:
-- p region doped with acceptor
impurity atoms
--n region doped with donor
atoms
--the n and p region are separated
by the metallurgical junction.
eNa
eNd
x
B
h+
p n
M
As+
e
W
Neutral n-regionNeutral p-region
Space charge region
Metallurgical Junction(a)
(b)
xp
xn(c)
E
E (x)
eVbi
e x)
x
x0
Eo
M
xn
xn
xp
xp
(e)
(f)
(d)
(x)
Hole PE(x)
Electron PE(x)
- the potential barrier :
- keeps the large concentration
of electrons from flowing from
the n region into the p region;
- keeps the large concentration
of holes from flowing from the
p region into the n region;
=> The potential barrier maintains thermal equilibrium.
PN junction under equilibrium (zero biased)
- the potential of the n region is positive
with respect to the p region => the
Fermi energy in the n region – lower
than the Fermi energy in the p region;
- the total potential barrier – larger than
in the zero-bias case;
- still essentially no charge flow and
hence essentially no current;
PN junction under reverse biased
-a positive voltage is applied to the p region with
respect to the n region;
- the Fermi energy level – lower in the p region than
in the n region;
- the total potential barrier – reduced => the electric
field in the depletion region – reduced;
diffusion of holes from the p region across the
depletion region into the n region;
diffusion of electrons from the n region across the
depletion region into the p region;
- diffusion of carriers => diffusion currents;
PN junction under forward biased
=
2ln
i
datbi
n
NNVV
-in thermal equilibrium :
- the n region contains many
more electrons in the
conduction band than the p
region;
- the built-in potential barrier
prevents the large density of
electrons from flowing into the
p region;
- the built-in potential barrier
maintains equilibrium between
the carrier distribution on either
side of the junction;
-=
kT
qVnn bi
np exp00
- the electric field Eapp induced by Va – in
opposite direction to the electric field in
depletion region for the thermal equilibrium;
- the net electric field in the depletion region is
reduced below the equilibrium value;
- majority carrier electrons from the n side ->
injected across the depletion region into the p
region;
- majority carrier holes from the p region ->
injected across the depletion region into the n
region;
- Va applied => injection of carriers across the
depletion regions-> a current is created in the
pn junction;
2/1
max
2/1
max
2/1
2
)(2)(2
)(2
-
-=
-=
==
da
da
s
R
biR
Rbi
da
da
s
Rbi
da
daRbispn
NN
NNeVE
VV
W
VV
NN
NNVVeE
NN
NN
e
VVxxW
e
e
e
212
==
da
dabisnp
NN
NN
e
VxxW
eFor zero bias
For reverse biased
W
VE bi2
max
-=
For reverse
biased
For zero bias
When there is no voltage applied across the pn junction the
junction is in thermal equilibrium => the Fermi energy level –
constant throughout the entire system.
FpFnbiV =
=
=
=
p
n
n
p
i
dab i
n
n
e
k T
p
p
e
k T
n
NN
e
k TV lnln
2
=--==
i
d
i
aFiFnFpFinpbi
n
N
e
kT
n
N
e
kTeEEeEEV lnln/)(/)(
dx
xdEx
dx
xd
EquationsPoisson
s
)()()(
'
2
2
-=-
=e
px-
+
_
ρ(C/cm³)
deN
aeN-
nx
E
x =0
-=x
xs p
dxxxE )(1
)( e
nn
s
d
pp
s
a
xxxxeN
E
xxxxeN
E
--
=
--
=
0),(
0),(
e
e
cmFSiFor rs /)1085.8)(7.11( 140
-== eee
ndpa xNxN =
Charge neutrality:
The peak electric field Is at x = 0
s
pa
s
ndxeNxeN
Eee
-=-=max
nxpx-
Emax
=
n
pn
p
np
sL
nqD
L
pqDJ
00
-
= 1exp
kT
qVJJ a
s - ideal-diode equation;
The bipolar transistor:
- three separately doped regions
- two pn junctions;
The width of the base region – small compared to the minority carrier diffusion length;
The emitter – largest doping concentration;
The collector – smallest doping concentration;
- the bipolar semiconductor – not a
symmetrical device;
-the transistor – may contain two n regions
or two p regions -> the impurity doping
concentrations in the emitter and collector =
different;
-- the geometry of the two regions – can be
vastly different;
MOSFET
Electromagnetic Spectrum
• Three basic bands; infrared (wavelengths above 0.7m), visible (wavelengths between 0.4-0.7m), and ultraviolet light (wavelengths below 0.4m).
• E = h = hc/ ; c = (μm) =1.24 /E(eV)
• An emitted light from a semiconductor optical device has a wavelength proportional to the semiconductor band-gap.
• Longer wavelengths for communication systems; Eg 1m. (lower Fiber loss).
• Shorter wavelengths for printers, image processing,… Eg > 1m.
• Semiconductor materials used to fabricate optical devices depend on the wavelengths required for the operating systems.
Photoluminescence & Electroluminescence
• The recombination of excess carries in direct bandgap semiconductors may result in the emission of photon. This property is generally referred to as luminescence.
• If the excess electrons and holes are created by photon absorption, then the photon emission from the recombination process is called photoluminescence.
• If the excess carries are generated by an electric current, then the photon emission from the recombination process is called electroluminescence.
PhotoluminescenceOptical Absorption
Consider a two-level energy states of E1 and E2. Also consider that E1 is populated with N1 electron density, and E2 with N2 electron density.
E1; N1
E2; N2
Absorption
• dN1 states are raised from E1 to E2 i.e dN1 photons are absorbed.
Electrons are created in conduction band and holes in valence band.
• When photons with an intensity of I (x) are traveling through a semiconductor, going from x position to x + dx position (in 1-D system), the energy absorbed by semiconductor per unit of time is given by
I (x)dx, where is the absorption coefficient; the relative number of
photons absorbed per unit distance (cm-1).
dxxIdxdx
xdIxIdxxI )(.
)()()(
-==-
)()(
xIdx
xdI
-=xeIxI
-= 0)(
where I(0) = I0
Absorption
• Intensity of the photon flux decreases exponentially with distance.
• The absorption coefficient in semiconductor is strong function of photon energy and band gap energy.
• The absorption coefficient for h < Eg is very small, so the semiconductor appears transparent to photons in this energy range.
PhotoluminescenceOptical Absorption
• When semiconductors are illuminated with light, the photons may be absorbed (for Eph = hEg= E2 – E1)or they may propagate through the semiconductors (for EphEg).
• There is a finite probability that electrons in the lower level absorb energy from incoming electromagnetic field (light) with frequency of (E2 – E1)/h and jump to the upper level.
• B12 is proportionality constant, = 2 - 1 and = I is the photon density in the frequency range of .
1121 )( NB
dt
dN
ab
-=
Photon Emission in Semiconductors
• When electrons in semiconductors fall from the conduction band to the valence band, called recombination process, release their energy in form of light (photon), and/or heat (lattice vibration, phonon).
• N1 and N2 are the concentrations of occupied states in level 1 (E1) and level 2 (E2) respectively.
Basic Transitions
Radiative
Intrinsic emission
Energetic carriers
Nonradiative
Impurities and defect center involvement
Auger process
Photon Emission in Semiconductors
Photon Emission in Semiconductors
Photon Emission in Semiconductors
Spontaneous Emission
Photon Emission in Semiconductors
Photon Emission in Semiconductors
Photon Emission in Semiconductors
Einstein Relationship
Einstein Relationship
These are the two fundamental conditions for lasing.
Wave attenuation
Internal Quantum Efficiency
Internal Quantum Efficiency