OPTOELECTRONIC and PHOTOVOLTAIC DEVICES · OPTOELECTRONIC and PHOTOVOLTAIC DEVICES 1. ... III – V...

OPTOELECTRONIC and PHOTOVOLTAIC

DEVICES

1. Introduction to the (semiconductor) physics: energy bands, charge carriers, semiconductors, p-n

junction, materials, etc.

2. Light emitting diodes Light emitting devices

3. Semiconductor lasers (displays, illumination)

4. Photodetectors Light absorbing devices

5. Photovoltaic solar cells (Photodiodes)

Outline

• Principles of operation (physical background)

• Design and structure

• Fabrication

http://www.lht.ovgu.de/studium/Lehrveranstaltungen.html

1

OPTOELECTRONIC and PHOTOVOLTAIC

DEVICES

[1] B. G. STREETMANN, S. K. BANERJEE: Solid state

electronic devices 6th ed.

[2] S. M. SZE: Physics of semiconductors devices

[3] Ch. KITTEL: Introduction to solid state physics

Technology

[4] J. D. PLUMMER, M. D. DEAL, P. B. GRIFFIN: Silicon VLSI

technology: fundamentals, practice and modeling

[5] S. K. GHANDHI: CLSI fabrication principles: silicon and

gallium arsenide

[6] S. A. CAMPBELL: The science and engineering of

microelectronic fabrication

[7] P.MOTTIER: LEDs for lighting applications

Literature recommendation

http://www.lht.ovgu.de/studium/Lehrveranstaltungen.html

2

1. Introduction

charge transport in solids depends not only on the properties

of the electron but also on the arrangement of atoms.

SEMICONDUCTORS:

electric conductivities intermediate between metals and

insulators

conductivity can be varied over orders of magnitude by

changes in temperature

optical excitation

impurity content

1.1. Overview of Semiconductors

3

1. Introduction

SEMICONDUCTORS:

found in

column IV and

neighboring of

periodic table


[1]

4

1. Introduction

SEMICONDUCTORS:

Band gap decreases with increasing temperature (thermal expansion of lattice)

elemental (300K) C – 5.5 eV =225nm

Si – 1.12 eV =1107nm

Ge – 0.67 eV =1850nm

Compound

two – element (binary): III-V GaN 3.37 eV =368nm

GaP 2.26 eV =549nm

GaAS 1.42 eV =873nm

three – element (ternary): GaAsSb

four – element (quaternary): InGaAsP :variety of material properties for

semiconductor devices


5

1. Introduction

SEMICONDUCTORS:

Binary, ternary, quaternary:

:variety of material properties

for semiconductors devices


[1]

6

1. Introduction

SEMICONDUCTORS:

Compound

II-VI: Fluorescent materials: ZnS (phosphors)

Light detectors: CdSe

InSb (III – V)

most important characteristic of semiconductors band gap


7

1. Introduction

ATOMS electrons restricted to sets of discrete energy levels

QUANTUM MECHANICS

SOLIDS same expected, will see: discrete energy levels spread into

BANDS

wave functions of electrons overlap, electrons are not localized

1.2. Bonding forces

8

1. Introduction Ionic bonding no loosely

bound electrons good

insulator (Fig 3-1a)

Metallic bonding sea of

free electrons free to move

under influence of electric

field

Covalent bonding bonding

force from shared electrons

(Fig. 3-1b)

Ge, Si, C covalent (quantum

mechanical interaction) diamond

lattice

no free electron at 0K!

excitation possible: thermal,

optical

mixed bonding ionic/covalent

compound semiconductors

III – V II – IV (more ionic)

1.2. Bonding forces

[1] 9

1. Introduction

Atoms brought together interactions

Result: balance of attraction and repulsion

Lattice spacing (equilibrium)

Electron energy level configuration

Result of PAULI exclusion principle:

no atomic interaction: identical electronic structures

spacing smaller: overlapping of wave functions

no two electrons of the system may have the same quantum state

splitting of discrete levels

bands

1.3. Energy bands

10

1. Introduction EXAMPLE: two atoms

interacting: Quantum mechanics

(solving Schrödinger equation)

composite two – electron wave

functions are linear combinations

of the individual atomic orbitals

LCAO (Fig. 3-2)

bonding orbital/antibonding

orbital higher value of wave

function higher e- probability

density between atoms

bonding energy level lower than

antibonding (and single level

before)

cohesion of crystal

MANY ATOMS: number of

energy levels depend on number

of atoms

lowest level: totally symmetric

LCAO

highest level: totally

antisymmetric LCAO

1.3. Energy bands

[1]

11

1. Introduction 1.3. Energy bands

EXAMPLE

Imaginary formation of Si

crystal (Fig. 3-3)

Si atom structure

bands grow (smaller

distance)

bands split

repulsive forces

conduction band

energy gap (forbidden

band)

valence band

Characteristic for

semiconductors

[1]

12

1. Introduction 1.4. Metals, semiconductors, and insulators

Completely filled band (at 0 K): no net charge transport possible (Fig. 3-4)

even when electric field applied

Metal: band overlap and/or partly filled bands

Semiconductor: gap < 5 eV (diamond)

Insulator: gap > 5eV

[1]

Room temp.

kT=0.026 eV (mean thermal

energy free of particle

at 300K)

13

1. Introduction

Conservation principle: for energy and momentum

Quantitative calculations can be made of band structures:

typical calculation: single electron travels trough perfectly periodic lattice

wave function of electron: plane wave

space dependent wave function (x-direction)

𝜓𝑘 𝑥 = 𝑈 𝑘𝑥, 𝑥 𝑒𝑖𝑘𝑥 𝑥

𝑘𝑥 =1

ℏ𝑝

𝑥 propagation constant (wave vector)

𝑈 𝑘𝑥, 𝑥 modulates the wave function according to the periodicity of

lattice (potential)

1.5. Direct and indirect semiconductors

Physical meaning: (absolute value)2

probability density

integral: prob. to

find electron at

location

14

1. Introduction

Allowed values of energy can be plotted vs 𝑘


[1]

15

1. Introduction 1.5. Direct and indirect semiconductors

Periodicity different in

various directions.

(E, 𝑘)diagram plotted for

various directions:

complex surface in 3d

[1] 16

1. Introduction

GaAs: minimum in conduction band and maximum in valence band for same

k value (k=0)

Electron makes smallest energy transition without change of k

(= direct)

Si: minimum in conduction band and maximum in valence band at

different values of k

Electron requires change of k!

(= indirect)


17

1. Introduction

band structure diagrams are difficult to handle and do not provide view of

variation of electron energy with distance in the sample (see Fig. 3.9)

simpler band

models often better

suited for device

discussion


[1] 18

1. Introduction

Electron – momentum in the crystal connected to k:

𝑝𝑥 = ℏ𝑘𝑥 (ℏ =ℎ

2𝜋)

GaAs: electron from conduction band can fall into empty state in valence

band

giving of energy difference Eg as a photon of light

Si: change of energy and momentum

for example: electron energy goes through defect states within band gap

energy is given up as heat to lattice (phonon) rather than as emitted photon

optical devices:

made of materials capable of direct band – to – band transitions

OR

indirect materials with vertical transitions between defect states


19

1. Introduction

Variation of alloy composition of

III – V ternary and quaternary

alloys

variation of their band

structure (Fig. 1-13)

1.6. Variation of energy bands with alloy

composition

[1] 20

1. Introduction

EXAMPLE:

Band structure of GaAs and AlAs


composition

GaAs

1.43 eV(room temp.)

Direct

AlAs

2.16 eV

Indirect

X=0.38

38% Al

GaAs

1.43 eV(room temp.)

Direct

GaP

2.26 eV

Indirect

X=0.45

45% P

(bigger lattice mismatch)

21

1. Introduction

! Light emission most efficient in direct semiconductors!

GaAs1-xPx best for X< 0,45 (RED LED´s: x = 0,4)

Eg 1,9 eV

650nm

(conversion between energy E of a photon of light in eV and its wavelength)

λ in nm : λ = 1240𝑛𝑚⋅𝑒𝑉

𝐸)


composition

22

1. Introduction

0 K and band gap valence band: completely filled

conduction band: empty

no free carriers insulator

EXCITATION by temperature: 𝑛 ~ 𝑒−𝐸𝑔

2𝑘𝑇 Room T : kT=0.0259eV

Temperature raised some electrons receive enough energy to be excited

across the band gap

1.7. Charge carriers in semiconductors

electron free to

move via many

available states

leave “holes” in

valence band

(positive charge

carriers) Electron-hole pair

(EHP)

[1] 23

1. Introduction

EHP (electronic hole pair)

(no net charge of semiconductors)

ROOM TEMP. : not much excitation: EXAMPLE Si

atom density: 51022 at/cm3

EHP´s 1.51010 EHP/cm3


electron free to

move via many

available states

leave “holes” in

valence band

(positive charge

carriers)

[1]

24

1. Introduction

INTRINSIC MATERIAL n=p=ni (electron/hole concentration [1/cm³])

Equilibrium: generation of EHP´s = recombination ri =gi

at any temperature the rate of recombination of electrons and holes (ri)

is proportional to equilibrium concentration n0,p0

ri = rn0p0=rni2=gi

r constant of proportionality for recombination


[1] 25

1. Introduction

INTRINSIC MATERIAL

n=p=ni


26 [1]

1. Introduction 1.7. Charge

carriers in semiconductors

EXTRINSIC MATERIAL

n type: P, As, Sb

p type: B, Al, Ga, In

Doping 1015 As at./cm3

Resistance from 2105 Ωcm to 5 Ωcm

[1] 27

1. Introduction 1.7. Charge

carriers in semiconductors

EXTRINSIC MATERIAL

Doping 1015 As at./cm3 Resistance from 2105 Ωcm to 5 Ωcm

[1] 28

1. Introduction 1.7. Charge carriers in semiconductors

FERMI – LEVEL: electrons in solid obey Fermi – Dirac statistics: • indistinguishability of electrons

• wave nature of electrons

• Pauli exclusion principle

distribution of electrons over a range of allowed energy levels at thermal

equilibrium:

f(𝐸) =1

1+ 𝑒(𝐸−𝐸𝐹)/𝑘𝑇

k : Boltzmann´s constant (8.6210-5 eV/K)

EF: Fermi level

Fermi – Dirac distribution function =

probability that an available energy state

E will be occupied by an electron at

temperature T

[1] 29

1. Introduction 1.7. Charge carriers in semiconductors

30 [1]

1. Introduction 1.7. Charge carriers

in semiconductors

[1]

31

1. Introduction

Usually single – valued (discrete) energy levels from doping and (quasi)

continuum of allowed states in valence and conduction bands

Discrete levels also possible by confinement in quantum wells:

growth of multilayer compound semiconductors by MBE (Molec. Beam Epitaxy) or

MOVPE (Metal Organic Vap. Phase Epitaxy)

adjacent layers with different band gaps (Fig. 3.13)

HETEROJUNCTIONS

1.8. Electrons and holes in quantum wells

32

1. Introduction 1.8. Electrons and holes in quantum wells

very thin layer treatment as particle in potential well problem

confinement to discrete quantum states

+ change of energy at which

photons are emitted:

Eg + El + Eh

shift to higher energies

(to red light for GaAs)

important for lasers

[1] 33

1. Introduction 1.8. Excess carriers in semiconductors

creation of charge carriers in excess of thermal equilibrium values

optical excitation

electron bombardment

carrier injection (forward – biased pn – junction)

Excess carriers can dominate the conduction of the semiconductor

34


OPTICAL ABSORPTION

important technique for measuring band gap energy

h = EPh Eg absorption excess carriers (Fig. 4.1)

h = EPh < Eg no absorption transmission

some materials

are transparent in

certain wavelength

ranges

[1] 35


OPTICAL ABSORPTION

possible to “see through” certain insulators: NaCl, SiO2 (crystalline)

Eg 2eV infrared and red part of visible spectrum transmitted

Eg 3eV infrared and all visible light transmitted

Ratio of transmitted to incident light intensity depend on wavelength,

(material), and thickness of the sample

[1] 36


OPTICAL ABSORPTION

probability of absorption in any dx is constant

decrease of intensity - 𝑑𝐼(𝑥)

𝑑𝑥 is proportional to remaining intensity at x

- 𝑑𝐼 𝑥

𝑑𝑥= 𝐼 𝑥

37 [1]


OPTICAL ABSORPTION

decrease of intensity - 𝑑𝐼(𝑥)

𝑑𝑥 is proportional to remaining intensity at x

-𝑑𝐼 𝑥

𝑑𝑥= 𝐼 𝑥

I of x (I as function of x)

𝐼 𝑥 = 𝐼0𝑒

−∝𝑥

intensity of light transmitted through sample of thickness l:

𝐼 = 𝐼0𝑒−∝𝑙

- absorption coefficient [] = cm-1

38


OPTICAL ABSORPTION

absorption edge

39 [1]


OPTICAL ABSORPTION

absorption edge depends on Eg

40

[1]

1. Introduction 1.9. Luminescence

recombination of EHPs or carriers excited into higher energy levels fall to

equilibrium states:

light can be given off the material

best for direct semiconductor

property of light emission luminescence

Depending on excitation mechanism:

photoluminescence: photon absorption

cathodoluminescence: high – energy electron bombardment

electroluminescence: introduction of current into sample

(most important)

different to incandescence! hot process (heated materials)

Luminescence

cold process (here: colder is better)

41

1. Introduction 1.9. Photoluminescence

Simplest example of light emission from Semiconductors:

direct excitation and recombination of EHPs by photon

Steady state excitation: same rate of generation and recombination

FLUORESCENCE

direct recombination FAST: mean lifetime of EHP 10-8 s or less.

emission stops within 10-8s after excitation turned off

PHOSPHORESCENCE

slow processes sec to minutes after excitation removed

(Materials =phosphors) ZnS

defect level with tendency to temporarily capture (trap) electron from

conduction band

42

1. Introduction 1.9. Photoluminescence: PHOSPHORESCENCE

a) absorption of photon EHP

b) excited electron looses energy to lattice (scattering) electron to bottom of

conduction band

c) electron trapped by impurity level

d) re – excitation possible (thermally)

e) recombination of electron with

Empty state in valence band light

Delay time can be long!

Impurity levels in phosphors

different colors of light (fluorescent lamps)

43 [1]

1. Introduction 1.9. Electroluminescence

ELECTROLUMINESCENCE

electrical energy to generate photon emission in solid

LED: electrical current causes injection of MINORITY CARRIERS into

regions where they recombine (with majority carriers)

recombination radiation

= injection electroluminescence

First electroluminescent effect observed:

emission of photons by certain phosphors in alternating electric field

ZnS in a binder materials (plastic, high – k)

44

1. Introduction 1.10. Electron transition

45 [2]

1) Interband transitions: a) intrinsic emission, b) higher – energy emission (hot carriers)

2) Transition involving impurity or defects: a) CB to acceptor type defect, b) donor –

type defect to VB, c) donor to acceptor emission (pair emission), d) band – to band

emission via deep

level traps

3) intraband

transition involving

hot carriers

(longer process)

not all radiative, not

all can occur in same

material under same

conditions

1. Introduction 1.10. Interaction between photon and electron

46

Three main optical process for interaction between photon and electron in solids:

1. Absorption of photon by excitation

of electrons from filled state in VB to

empty states in CB

PHOTODETECTOR/SOLAR CELL

2. Electron of CB can spontaneously

return to empty state in VB

(recombination with emission of photon)

LED

3. Incoming photon can stimulate

emission of similar photon by

recombination free photons

coherent LASER

[2]

1. Introduction 1.11. Carrier lifetime

47

excess carriers increase in conductivity

photoconductivity ()

𝐽 = 𝐸 = 𝑞(𝑛µ𝑛 + 𝑝µ𝑒)𝐸

= 𝑞(𝑛µ𝑛 + 𝑝µ𝑝) ,

(µ𝑛 = − <𝑣𝑥>

𝐸𝑥)

1. Introduction 1.11. Carrier lifetime

48

Mechanisms of recombination and recombination kinetics:

Direct recombination of electrons and holes

Indirect recombination

Direct recombination:

Excess electrons and holes decay by electrons falling from conduction band

to empty states (holes) in valence band

energy loss of electrons photon

• spontaneously: probability of recombination constant in time

Rate of decay of electrons at any time t is proportional to number of electrons remaining

at t and number of holes, with some constant of proportionality for recombination (𝑟).

1. Introduction 1.11. Carrier lifetime: direct recombination

49

Net rate of change in conduction band electron concentration:

Thermal generation rate – recombination rate

𝑑𝑛(𝑡)

𝑑𝑡= 𝑟𝑛𝑖

2 − 𝑟𝑛 𝑡 𝑝(𝑡)

(thermal generation =recombination, intrinsic material)

ASSUMPTION:

excess e- - h+ – population created at t = 0 (short flash of light)

initial excess e- and h+ concentration equal n = p

• e- and h+ recombine in pairs instantaneous concentrations of excess carriers also

equal • n(t) = p(t)

𝑑𝑛 𝑡


2 − 𝑟 𝑛0 + 𝑛 𝑡 𝑝0 + 𝑝 𝑡

: initial

: instantaneous

Degradation of

excess carriers

equilibrium value excess value


50

𝑑𝑛 𝑡


2 − 𝑟 𝑛0 + 𝑛 𝑡 𝑝0 + 𝑝 𝑡

(𝑛 = 𝑝) and 𝑛0𝑝0 = 𝑛𝑖2

𝑑𝑛 𝑡


2 − 𝑟 𝑛0 + 𝑛 𝑡 𝑝0 + 𝑝 𝑡 = −𝑟 (𝑛0+𝑝0 𝑛 𝑡 + 𝑛2 𝑡 ]

: excess

0: equilibrium

Degradation of

excess carriers equilibrium value excess value


51

𝑑𝑛 𝑡

𝑑𝑡= −𝑟 (𝑛0+𝑝0 𝑛 𝑡 + 𝑛2 𝑡 ]

Difficult to solve

simplification: excess carrier concentration small n2 to neglect

material is extrinsic neglect the term for minority carriers

example: p – type (p0 >> n0)

𝑑𝑛(𝑡)

𝑑𝑡 = - r𝑝0n(t)

n(t) = ∆n 𝑒−𝑟𝑝0𝑡 = ∆n 𝑒−𝑡/𝑛

𝑛 - recombination lifetime (= (𝑟𝑝0)

−1)

(minority carrier lifetime)

𝑝=(𝑟𝑛0)

−1) for excess holes in n – type

: excess

0: equilibrium


52

Approximation: extrinsic material

low – level injection n(t) n(t)

p(t) p0

more general expression for carrier lifetime

𝑛 = 1

𝑟(𝑛𝑜 + 𝑝0)

valid for n – or p – type if injection level is low


53

for direct recombination:

excess majority carriers

decay at same rate as

minority carriers

however: large percentage

change for minority carrier

concentration

small percentage

change for majority carrier

concentration

[1]

1. Introduction 1.11. Carrier lifetime: indirect recombination

54

Indirect recombination: trapping

column IV semiconductors and certain compounds

probability of direct recombination is small

majority of recombination in indirect material

via recombination levels within band gap

energy loss of electron given up to lattice as heat rather than photons

Any impurity or lattice defect can serve as recombination center if it is capable of:

1. receive carrier of one type

2. capture opposite type of carrier(subsequently)

annihilation of pair


55

Example: recombination level Er (below EF) filled with electrons (Fig. 4-8).

1. hole capture by Er (electron of Er to hole in VB heat)

2. electron capture by Er (electron of CB to Er heat)

[1]


56

Carrier lifetime from indirect recombination more complicated

• unequal times for capturing each type of carriers

recombination often delayed, captured carrier can be thermally reexcited

before capture of opposite carrier can occur

temporary trapping

Types of impurity or defect centers

1. trapping center (trap): after capture of one type of carrier, most probable next event

is reexcitation

2. recombination center: after capture of one type of carrier, most probable next event

is capture of opposite type of carrier


57

Trapping and recombination centers. (deep levels mostly slower)


58

• measurement of recombination and trapping: photoconductive decay (see previous

Fig. 4.7):

excess electrons and holes disappear with decay constant characteristic of particular

recombination process

conductivity during decay:

(t) = 𝑞[𝑛 𝑡 µ𝑛 + 𝑝 𝑡 µ𝑝]

sample resistance is function of time (Fig. 4-10)

[1]

1. Introduction 1.12. Steady state carrier generation

59

Recombination also important in samples at thermal equilibrium or steady state EHP

generation – recombination balance

• equilibrium: no external excitation, no net motion of charge (constant T, sample

in the dark, no fields applied)

• steady state: non equilibrium condition in which all processes are constant and

balanced by opposing processes (constant current or constant optical generation

of EHP´s)

• in equilibrium: thermal generation of EHP`s at rate

g(T) = gi

balanced by recombination so that equilibrium concentrations n0 and p0 maintained:

g(T) =rni2 = rn0p0

can include generation

from defect centers as

well as band – band

generation


60

• in steady state:

light: optical generation rate gop added to g(T)

carrier concentration n and p increase to new steady state values

g(T) + gop = rnp = r(n0 + 𝑛)(p0 + 𝑝)

Steady state recombination, no trapping 𝑛 = 𝑝

g(T) + gop = rn0p0 + r[(n0 + p0) 𝑛 + 𝑛 ²] g(T) = rn0p0

gop = r[(n0 + p0) 𝑛 ] = 𝑛

𝑛

𝑛 = 𝑝 = 𝑔𝑜𝑝 ∙ 𝑛

steady state excess carrier concentration

More general:

if 𝑛≠ 𝑝 (trapping)

𝑝 = 𝑔𝑜𝑝 ∙ 𝑝 and 𝑛 = 𝑔𝑜𝑝 ∙ 𝑛


61

DESIRABLE: to refer the steady state carrier concentration in terms of Fermi levels

which can be included in band diagrams

equilibrium: n0 = ni exp[(EF – Ei)/kT], p0 = ni exp[(Ei – EF)/kT]

separate quasi – Fermi levels for electrons and holes Fn, Fp

n = ni exp[(Fn – Ei) /kT], p = ni exp[(Ei – Fp)/kT]

n p ni2 ,when excess carriers

[1]

1. Introduction 1.13. p-n junction

62

Equilibrium conditions:

Contact potential (U0)

Drift and diffusion

Depletion region

Space charge


63

Equilibrium conditions:

Contact potential (U0)

Drift and diffusion

Depletion region

Space charge

[1]


64

Bias at p-n

[1]


65

I-V:

[1]

OPTOELECTRONIC and PHOTOVOLTAIC DEVICES · OPTOELECTRONIC and PHOTOVOLTAIC DEVICES 1. ... III – V...

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Transcript of OPTOELECTRONIC and PHOTOVOLTAIC DEVICES · OPTOELECTRONIC and PHOTOVOLTAIC DEVICES 1. ... III – V...