Some Concepts of Solid State Materials with Applications in …users.encs.concordia.ca/~mojtaba/Some Concepts (optical... · 2016-05-12 · Some Concepts of Solid State Materials

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


• 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.


• 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.


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).


• 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

-=


• 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




Spontaneous Emission




Einstein Relationship

Einstein Relationship

These are the two fundamental conditions for lasing.

Wave attenuation

Internal Quantum Efficiency

Internal Quantum Efficiency

Documents

Some Concepts of Solid State Materials with Applications in …users.encs.concordia.ca/~mojtaba/Some Concepts (optical... · 2016-05-12 · Some Concepts of Solid State Materials