Chapter 4b

pn-junction principles

pn junction open circuit

• Consider a sample of Si is doped n-type and the other p-type.– Assume there is an abrupt discontinuity between

the p and n regions, called metallurgical junction, M.

– the fixed ionized donors and free electrons in the n-region

– fixed ionized acceptors and holes in the p region.

Depletion region

• Due to the hole concentration gradient from the p-side (p= ppo) to then n-side (p= pno)– Holes diffuse towards n-region and recombine with the

electrons in this region. – The n-side near the junction becomes depleted of majority

carriers and therefore has exposed positive donor ions (As+) of concentration Nd.

• Similarly, the electron concentration gradient drives the electrons by diffusion towards the p-side, which exposes acceptor ions (B–) of concentration Nd in the region.

Depletion Region

Depletion region

Space charge layer (SCL)

Figs (a) & (b): The regions on both sides of the junction M consequently becomes depleted of free carriers in comparison with the bulk p and n regions far away from the junction.– There is therefore a space charge layer around M.– Also known as the depletion region around M.

Fig (c): the hole & electron concentration profilesFig (d): the net space charge density across the semiconductorFig (e): the variation of the electric field across the pn-junctionFig (f): taking the potential on the p-side far away form M as

zero, then V(x) increases in the depletion region towards the n-side.

nno

xx = 0

pno

ppo

npo

log(n), log(p)

-eNa

eNd

M

x

E (x)

B-

h+

p n

M

As+

e–

Wp Wn

Neutral n-regionNeutral p-region

Space charge regionVo

V(x)

x

PE (x)

Electron PE (x)

Metallurgical Junction

(a )

(b )

(c )

(e )

( f )

x

–Wp

Wn

(d)

0

eVo

x (g)

–eVo

H ole PE(x)

–Eo

Eo

M

r net

M

Wn–Wp

ni

pn-junction band diagram

Ec

Ev

Ec

EFp

M

EFn

eVo

p nEo

Evnp

(a)

VI

np

Eo–E

e(Vo–V)

eV

Ec

EFn

Ev

Ev

Ec

EFp

(b)

Energy band diagrams for a pn junction under (a) open circuit, (b) forwardbias

SCL

Energy band diagrams for a pn junction under(c) reverse bias conditions. (d) Thermal generation of electron holepairs in the depletion region results in a small reverse current.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

(c)

Vr

np

e(Vo+Vr)

EcEFn

Ev

Ev

Ec

EFp

Eo+E (d)

I = Very SmallVr

np

Thermalgeneration

EcEFn

Ev

Ec

EFp

Ev

e(Vo+Vr)

Eo+E

Open Circuit• Given EFp and EFn are the Fermi levels in the p and n

sides, then in equilibrium and in the dark, the energy band diagram for open circuit is shown Fig (a):– The Fermi level must be uniform through the two

materials– Far from the metallurgical junction M, we should still have

an n-type semiconductor and (Ec– EFn) should be the same as in the isolated n-type material

– Similarly, (EFn– Ev) far away from M inside the p-type material should also be same as in the isolated p-type material

– Keeping EFp and EFn the same & the band gap Ec– Ev the same.

– To draw the band diagram, we have to bend the bands Ec and Ev near the junction at M

Forward Bias

• When the pn-junction is forward biased, majority of the applied voltage drops across the depletion region, Fig (b) shows the effect of forward bias:– The applied voltage is in opposition to the built-in potential to

reduce the PE barrier from eVo to e(Vo – V)

– The electrons at Ec in the n-side can now readily overcome the PE barrier and diffuse to the p-side

– The diffusing electron from the n-side can be replenished easily by the negative terminal of the battery and the positive terminal of the battery can replenish those holes diffusing away from the p-side.

– There is therefore a current flow through the junction and around the circuit.

Reverse Bias

• When a reverse bias, V= -Vr, is applied to the pn-junction the voltage again drops across the SCL.– Vr adds to the built-in potential Vo so that the PE barrier

becomes e(Vo+Vr) as shown in Fig (c).– The field in the SCL at M increases to Eo+E where E is the

applied field– There is hardly any reverse current because if an electron

were to leave the n-side to travel the positive terminal, it cannot be replenished from the p-side.

• Virtually no electrons on the p-side– However, there is a small reverse current arising from

thermal generation of Electron-Hole Pairs (EHP) in the SCL as shown in Fig (d).

• The generated electron falls down the PE hill to the n-side to be collected by the battery.

• Similarly the generated hole makes it to the p-side.

Light Emitting Diode

Introduction

• One of the most popular optoelectronics sources– Inexpensive, consumes very little power & easily

adaptable to electronics circuitry• In an LED, the semiconductor has a high energy

gap and the junction is constructed so that radiation from the junction can escape– In a normal Si diode, the radiated wavelength is long

(infrared range), the radiation is absorbed by the surrounding semiconductor materials

Electrical characteristic

• LED is a semiconductor diode.– Its characteristics and limitation are similar

to a normal p-n junction diode• The breaking voltage is about 1.2 to 2V

depending on the semiconductor material. – Dynamic resistance ranges from a few ohms

to tens of ohms.

I–V characteristic of a p-n junction.

LED types

Infrared - 1.6VRed - 1.8 to 2.1VOrange - 2.2VYellow - 2.4VGreen - 2.6VBlue - 3.0 to 3.5V (White same as blue)UltraViolet - 3.5V

Principles of LED

Principles of LED

• A LED is typically made from a direct band gap semiconductor e.g. GaAs– in which the Electron-Hole Pairs (EHP) recombination

results in the emission of a photon– The emitted photon energy is approximately equal to

the band gap energy, h Eg.

Energy band diagram of unbiased pn+-junction device in Fig.1(1)

• n side is more heavily doped than p side• The band diagram is drawn to keep the Fermi level uniform

through the device, – which is a requirement of equilibrium without bias.

• The depletion region extends mainly into the p-side• There is a Potential Energy (PE) barrier eVo from EC on the n -side

to EC on the p-side, Vo is the built-in voltage• The higher concentration of conduction electrons in the n-side

encourages the diffusion from the n to the p side.• The net electron diffusion is prevented by the electron PE barrier,

eVo.

hu Eg

Eg (2)

V

(1)

p n+

Eg

eVo

EF

p n+

Electron in CBHole in VB

Ec

Ev

Ec

Ev

EF

eVo

Electron energy

Distance into device

(1) The energy band diagram of p-n+ (heavily n-type doped) junction without any bias.Built-in potential Vo prevents electrons from diffusing from n+ to p side. (2) The appliedbias reduces Vo and thereby allows electrons to diffuse, be injected, into the p-side.Recombination around the junction and within the diffusion length of the electrons in thep-side leads to photon emission.


Fig.1: Principles of LED

Energy band diagram of pn+-junction device with a forward bias V in Fig.1(2)

• As soon as a forward bias V is applied, this voltage drops across the depletion region – since this is the most resistive part of the device.

• The built-in potential Vo is reduced to Vo – V

• Allows the electrons from the n+ side to be injected into the p-side– The hole injection component from p into n+ side is much smaller than

electron injection component from n+ to p side

• The recombination of injected electrons in the depletion region & p-side results in the spontaneous emission of photons

Injection Electroluminescence

• Recombination primarily occurs within the depletion region and within a volume extending over the diffusion length of the electron in the p-side– This recombination zone is frequently called the active region

• The phenomenon of light emission from EHP recombination as a result of minority carrier injection is called injection electroluminescence

• Because of the statistical nature of the recombination process between electrons and holes, the emitted photons are in random direction– They result from spontaneous processes in contrast to stimulated

emission

Device structures

Light output

Insulator (oxide)p

n+ Epitaxial layer

A schematic illustration of typical planar surface emitting LED devices. (a) p -layergrown epitaxially on an n + substrate. (b) First n + is epitaxially grown and then p regionis formed by dopant diffusion into the epitaxial layer.

Light output

pEpitaxial layers

(a) (b)

n+

Substrate Substrate

n +

n +

Metal electrode


Fig 2: Device structures

Device structures of LED

• In its simplest technological form, LEDs are typically fabricated by epitaxially growing doped semiconductor layers on a suitable substrate (e.g. GaAs or GaP) as shown in Fig.2(a).– It is formed by the epitaxial growth of first the n-layer and then the

p-layer• The substrate is essentially a mechanical support for the pn-

junction device and can be of different material• The p-side is on the surface

– from which light is emitted – it is also made narrow (a few microns) so that photons is allowed to

escape without reabsorbed

GaP: Gallium Phosphide GaAs: Gallium Arsenide

Low pressure chemical vapor deposition (LPCVD) reactor for Epitaxially Growing DopedNot only a film is deposited, but single crystal growth must also be maintained

Light output

Insulator (oxide)p

n+ Epitaxial layer

A schematic illustration of typical planar surface emitting LED devices. (a) p -layergrown epitaxially on an n + substrate. (b) First n + is epitaxially grown and then p regionis formed by dopant diffusion into the epitaxial layer.

Light output

pEpitaxial layers

(a) (b)

n+

Substrate Substrate

n +

n +

Metal electrode


Fig 2: Device structures

Device structures, cont

• To ensure that most of the recombination takes place in the p-side, the n-side is heavily doped– Those photons that are emitted towards the n-side become

either absorbed or reflected back.– In Fig 2(a), the use of a segmented back electrode will

encourage reflections from the semiconductor-air interface.• It is also possible to form the p-side by diffusing

dopants into the epitaxial n+-layer, which is diffused junction planar LED as shown in Fig 2(b).

Defect of Device structures

• If the epitaxial layer and the substrate crystals have different crystal lattice parameters– Mismatch between the two crystal structures will exist– This causes lattice strain in the layer and leads to crystal defects.– Such defects encourage radiationless EHP recombination acting as

recombination center• Such defects are reduced by lattice matching the LED epitaxial

layer to the substrate crystal– AlGaAs alloys is a direct bandgap semiconductor in the red emission

region.– It can be grown on GaAs substrate with excellent lattice match to

produce high efficiency LED devices.

Light output

p

Electrodes

LightPlastic dome

Electrodes

Domedsemiconductor

pn Junction

(a) (b) (c)

n+n+

(a) Some light suffers total internal reflection and cannot escape. (b) Internal reflectionscan be reduced and hence more light can be collected by shaping the semiconductor into adome so that the angles of incidence at the semiconductor-air surface are smaller than thecritical angle. (c) An economic method of allowing more light to escape from the LED isto encapsulate it in a transparent plastic dome.

Substrate


Fig. 3: Optical design

Optical Design of LED

• Figs. 2(a) & 2(b) show the planar pn-junction based simple LED structures. – Not all light rays reaching the semiconductor-air interface can

escape because of Total Internal Reflection (TIR)– Those rays with incidence angle > critical angle (c) will be

reflected back as shown in Fig.3(a)– For GaAs-air interface, c is only 16

• It is possible to shape the surface of the semiconductor into a dome/hemisphere– So that light strikes the surface at angles less than c and

therefore do not experience TIR as shown in Fig.3(b).

Encapsulation of LED

• The main drawback is – the additional difficult process in fabricating such domed LEDs

and – the associated increase in expense

• An inexpensive and common procedure that reduces TIR is the encapsulation of the semiconductor junction within a transparent plastic medium (epoxy)– has higher reflective index than air– has a domed surface on one side of pn-junction as shown in

Fig.3(c)

LED materials

• There are various direct bandgap semiconductor materials that can be readily doped to make commercial pn-junction LEDs that emit radiation in the red & infrared range of wavelength– In visible spectrum is III-V ternary alloys based on

alloying GaAs & GaP donated as GaAs1–yPy.– In this compound, As & P atoms (Group V) are

distributed randomly at normal As sites in the GaAs crystal structure.

Band gaps of some common semiconductors relative to the optical spectrum.

Direct & Indirect bandgap semiconductor

• When y <0.45, the alloy GaAs1–yPy is a direct bandgap semiconductor and hence the EHP recombination process is direct.– The rate of recombination the product of electron and hole

concentration– The emitted wavelength range from 630nm (red) for y=0.45

(GaAs0.55P0.45) to 870nm (Infrared) for y = 0 (GaAs)• When y >0.45, the alloy GaAs1–yPy is a indirect bandgap

semiconductor.– The EHP recombination processes occur through recombination

centers – It involves lattice vibrations rather than photon emission

Isoelectronic Impurites

• If isoelectronic impurites, N atoms (Group V), is added into semiconductor crystal, some of N atoms substitute for P atoms to form the same number of bonds.

• The positive nucleus of N is less shielded by electrons compared with that of the P atom.– A conduction electron in the neighborhood will be attracted

and trapped at this site – Therefore N atoms introduce localized energy level (electron

traps), EN near the conduction band.

Ec

Ev

EN

(b) N doped GaP

Eg

(a) GaAs1-yPy

y < 0.45

(a) Photon emission in a direct bandgap semiconductor. (b). GaP is anindirect bandgap semiconductor. When doped with nitrogen there is anelectron trap at EN. Direct recombination between a trapped electron at ENand a hole emits a photon. (c) In Al doped SiC, EHP recombination isthrough an acceptor level like Ea.

Ec

Ev

Ea

(c) Al doped SiC


Fig.4: LED materials

Isoelectronic Impurites, cont

• When the electron is captured at EN, it can attract a hole in its vicinity by Coulombic attraction – Eventually recombine with it directly and emit a photon.– The emitted photon energy is slightly less than Eg.

• The recombination process depends on N doping, it is not as efficient as direct recombination– Thus the efficiency of LEDs from N doped indirect band gap

GaAs1–yPy semiconductors is less than those from direct band gap semiconductor

• N doped with indirect band gap alloys are widely used in inexpensive green, yellow and orange LEDs.

Two types of blue LED materials

1. GaN is a direct bandgap semiconductor with Eg of 3.4eV– The blue GaN LEDs actually use the GaN alloy– InGaAs has a bandgap of about 2.7eV, which corresponds to blue

emission.2. The less efficient type is the Al doped SiC, which is an indirect

bandgap semiconductor– The acceptor type localized energy level captures a hole from the

valence band – A conduction electron then recombines with this hole to emit a photon– As the recombination process is not direct and therefore not as efficient,

the brightness of blue SiC LEDs is limited.

GaN: Gallium Nitride

SiC: Silicon Carbide

Commercially important direct bandgap semiconductor materials

• Ternary (3 elements) and Quarternary (4 elements) alloys based on III & V elements (III-V alloys)

• Ternary alloy, Al1–xGaxAs, in which x <0.43 are direct bandgap semiconductors

– The composition can be varied to adjust the bandgap and hence the emitted radiation from 640nm-870nm (deep red-infrared light)

• InGaAlP is a quarternary III-V alloy that has a direct bandgap variation with composition over the visible range

– It can be lattice-matched to GaAs substrate when in the composition range In0.49Al0.17Ga0.34P to In0.49Al0.058Ga0.452P

• This LED material is likely to dominate high intensity visible range.

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Blu

eG

reen

Ora

nge

Yel

low

Red

1.7

Infrared

Vio

let

GaA

s

GaA

s 0.55

P 0.45

GaAs1-yPyIn

P

In0.

14G

a 0.86

As

In1-xGaxAs1-yPy

AlxGa1-xAs

x = 0.43

GaP

(N)

GaS

b

Indirectbandgap

InG

aNS

iC(A

l)

In0.

7Ga 0.

3As 0.

66P 0.

34

In0.

57G

a 0.43

As 0.

95P 0.

05

Free space wavelength coverage by different LED materials from the visible spectrum to theinfrared including wavelengths used in optical communications. Hatched region and dashedlines are indirect Eg materials.

In0.49AlxGa0.51-xP


Fig.5: Spectrum range

External efficiency

• External efficiency ext of an LED quantifies the efficiency of conversion of electrical energy into an emitted external optical energy

– The input of electrical power into an LED is simply the diode current and diode voltage product (IV).

– Pout is the optical power emitted by the device.

• For indirect bandgap semiconductor ext are generally less than 1%, but for direct band gap semiconductor with the right device structure, ext can be larger.

%100

opticalext

IV

Pout

Heterojunction high intensity LEDs

• A junction between 2 differently doped semiconductor that are of the same material (same band gap) is called a homojunction.

• A junction between 2 different band gap semiconductors is called a heterojunction

• A semiconductor device structure that has junctions between different band gap materials is called a heterostructure device (HD)

Refractive index and band gap

• The refractive index of a semiconductor materials depends on its band gap.– Wider band gap semiconductor has a lower refractive

index

• This means that by constructing LEDs from heterostructures, we can engineer a dielectric waveguide within the device – Thereby channel photons out from the recombination

region.

The homojunction LED has two drawbacks.

1. The p-region must be narrow to allow the photons to escape without much re-absorption

– When p side is narrow, some of the injected electrons in the p side reach the surface by diffusion and recombine through crystal defects near the surface

– The radiationless recombination process decreases the light output2. If the recombination occurs over a relatively large volume

(distance), due to long electron diffusion length, then the chances of re-absorption of emitted photons becomes higher.

– The amount of re-absorption increases with the material volume

Double Heterostructure

• LED constructions for increasing the intensity of the output light make use of the Double Heterostructure (DH) structure.– Two junctions between different semiconductor materials with different

band gaps• In Fig 6(a), DH consists of AlGaAs with Eg2eV and GaAs with

Eg1.4eV. – DH has an n+p heterojunction between n+-AlGaAs and p-GaAs– Another heterojucntion between p-GaAs and p-AlGaAs.– The p-GaAs region is a thin layer (a fraction of micron) and is lightly doped

Fig. 6: Double Heterostructure

2 eV

2 eVeVo

Holes in VB

Electrons in CB1.4 eV

No bias

Ec

EvEc

Ev

EFEF

(a)

(b)

pn+ p

DEc

~ 0.2 mm

AlGaAsAlGaAs

(a) A doubleheterostructure diode hastwo junctions which arebetween two differentbandgap semiconductors(GaAs and AlGaAs)

(b) A simplified energyband diagram withexaggerated features. EF

must be uniform.

GaAs

Withforwardbias(c)

(d)

GaAs AlGaAsAlGaAs

ppn+

(c) Forward biasedsimplified energy banddiagram.

(d) Forward biased LED.Schematic illustration ofphotons escapingreabsorption in theAlGaAs layer and beingemitted from the device.

Fig. 6: Double Heterostructure

Band Diagram of Double Heterostructure

• The simplifies energy band diagram for the whole device in the absence of an applied voltage is shown in Fig.6(b)– The Fermi level EF is continuous through the whole structure– There is potential energy barrier eVo for electrons in the CB of

n+-AlGaAs against diffusion into p-GaAs.– There is a band gap change at the junction between p-GaAs

and p-AlGaAs that results in a step change, Ec.– Ec is effectively a potential energy barrier that prevents any

electrons in the CB in p-GaAs passing to the CB of p-AlGaAs

When a forward bias is applied, majority of this voltage drops between n+-AlGaAs and p-GaAs

• Reduces the potential barrier eVo • This allows electrons in the CB of n+-AlGaAs to be injected into p-

GaAs as shown in Fig.6(c)• These electrons are confined to the CB of p-GaAs since there is a

barrier between p-GaAs and p-AlGaAs.• The wide bandgap AlGaAs layers act as confining layers that

restrict injection electron to the p-GaAs layer• The recombination of injected electrons and the holes already

present in this p-GaAs layer results in spontaneous photon emission.

• Since the bandgap Eg of AlGaAs is greater than GaAs, the emitted photon do not get reabsorbed as they escape the active region and can reach the surface of the device as shown in Fig.6(d)

Defect of Double Heterostructure

• Since light is also not absorbed in p-AlGaAs, it can be reflected to increase the light output

• There is no lattice mismatch between the two crystal structure in AlGaAs/GaAs heterojunction.

• Negligible strain induced interfacial defects (e.g. dislocation) in the device compared with the defects at the surface of the semiconductor in conventional homojunction LED structure.

• The DH LED is much more efficient than the homojunction LED.

LED characteristics• The energy of an emitted photon from LED is not

simply equal to band gap energy Eg – because electrons in the CB are distributed in energy and so

are holes in the valence band.• Fig.7(a) and 7(b) illustrate the energy band diagram

and the energy distribution of electrons and holes in the CB and VB respectively

• The energy concentration per unit energy in CB is given by g(E)f(E) – g(E) is the density of states– f(E) is the Fermi Dirac function

LED characteristics, 1• In Fig 7(b), the electron concentration in the CB

as a function of energy is asymmetrical – has a peak at ½kBT above Ec.– The energy spread of these electrons is typically

about 2kBT from Ec.

– Similarly, hole concentration spread from Ev in the VB

Fig.7: LED characteristics

(a) Energy band diagram with possible recombination paths. (b) Energy distribution of electrons in the CB and holes in the VB. The highest electron concentration is (1/2)kBT above Ec

E

Ec

Ev

Carrier concentrationper unit energy

Electrons in CB

Holes in VB

CB

VB

(a) (b)

1/2kBT

Eg1 2 3

2kBT


hu

1

0

Eg

hu1 hu2 hu3

l

Relative intensity

1

0l1l2l3

DlDhu

Relative intensity

(c) (d)

Eg + kBT

(2.5-3)kBT

(c) The relative light intensity as a function of photon energy based on (b). (d) Relative intensity as a function of wavelength in the output spectrum based on (b) and (c).

The rate of direct recombination is proportional to both electron and hole concentrations

1. The transition, which is identified as 1 in Fig 7(a), has the relative small intensity of light with photon energy hv1.– The carrier concentrations near the band edges are very

small and hence does not occur frequently2. The relative intensity of light corresponding to

transition hv2 is maximum – The transitions that involve the largest electron and hole

concentration occur most frequently.3. The light intensity at the relative high photon energies

hv3 occurred through transition 3 is small. – The energetic electron and hole concentrations are small

Output Spectrum

• The relative light intensity vs photon energy characteristic of the output spectrum is shown in Fig 7(c).– It represents an important LED characteristic

• Given the spectrum in Fig 7(c), we can also obtain the relative light intensity vs wavelength characteristic as shown in Fig (d) because =c/– The linewidth of the output spectrum, or , is defined as

width between half-intensity points.

V

2

1

(g)

0 20 40I (mA)0

(e)

600 650 700

0

0.5

1.0

l

Relativeintensity

24 nm

Dl

655nm

(f )

0 20 40I (mA)0

Relative light intensity

(e) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED.(f ) Typical output light power vs. forward current. (g) Typical I-V characteristics of ared LED. The turn-on voltage is around 1.5V.



Output Spectrum, 2• The wavelength for the peak intensity and the

linewidth of the spectrum are obviously related to – Energy distributions of the electrons and holes in the CB

and VB – Density of states in these bands (individual semiconductor

properties) • The photon energy for the peak emission is roughly

Eg+kBT– It corresponds to peak-to-peak transitions in the energy

distributions of the electrons and holes– The linewidth (h) is typically between 2.5kBT to 3kBT as

shown in Fig.7(c)

Output spectrum, 3

• The output spectrum (relative intensity vs wavelength characteristics) from an LED depends – The semiconductor material– The structure of the pn-junction diode including the

dopant concentration levels• The spectrum in Fig 7(d) represents an idealized

spectrum without including the effects of heavy doping on the energy bands

Red LED characteristics

• Typical characteristics of a red LED (655nm) are shown in Fig 7(e) to 7(g).– The output spectrum exhibits less asymmetry than

the idealized spectrum– The width of the spectrum is about 24 nm, which

corresponds to a width of about 2.7kBT in the energy distribution of the emitted photons

LED current

• As the LED current increases, so does the injected minority carrier concentration, – thus the rate of recombination and hence the output light

intensity– However, the increase in the output power is not linear with

the LED current -> Fig.7(f)• At high current levels, strong injection of minority

carriers leads to the recombination time depending on the injected carrier concentration – Hence on the current itself; this leads to a non-linear

recombination rate with current

Current-Voltage Characteristics

• Typical current-voltage characteristics are shown in Fig 7(g)– It can be seen that the turn-on or cut-in voltage is about 1.5V

(current increases sharply with voltage)• The turn-on voltage depends on the semiconductor and

generally increases with energy bandgap Eg

– For example, typically it is about 3.5-4.5V for a blue LED– It is about 2V for a yellow LED– It is around 1V for a GaAs infrared LED

Example LED output spectrum

• Given that the width of the relative light intensity vs photon energy spectrum of an LED is typically about ~3kBT, what is the linewidth ½ in the output spectrum in terms of wavelength ?

• Given = 870 nm, 1300 nm, 1550 nm• T = 300 K

Solution

structure LED on the depend esexact valu theand values typicalare linewidths These

149 ,1550

105 ,1300

47 ,870at Thus,

3

find, we of in terms for ngsubstituti andlatter theusing Then,

.3 spectrum,output theofth energy wid given the are We

then/ / e.g.

atedifferentiby )(or intervalsor changes smallrepresent can We

get weenergy photon respect to with atedifferenti weIf

by energy photon the torelated is h wavelengtemitted that thenote We

2

2

2

nmnm

nmnm

nmnmhc

Tk

E

TkhE

EE

hc

dEdE

E

hc

dE

d

E

E

hcc

E

B

ph

Bph

phph

phph

phph

ph

ph

ph

Example: LED output wavelength variations

• Consider a GaAs LED. The band gap of GaAs at 300K is 1.42eV, which changes (decreases) with temperature as dEg/dT= – 4.510–4 eVK–1. What is the change in the emitted wavelength if the temperature change is 10C?

Solution

books. data

in quoted LEDs GaAsfor values typicalof 10% within is change calculated This

erature. with tempincreasesh wavelengt theerature, with tempdecreases Eg Since

8.2100.277nmK

is C10 for h wavelengtin the change The

0.277nmKor 1077.2 that,So

106.1105.4106.142.1

10310626.6

,have we/ takingand term theNeglecting

1

1110

194219

834

2

nmKTdT

d

T

mKdT

d

dT

dE

E

hc

dT

d

EhcTk

g

g

gB

Example: InGaAs on InP substrate

• The ternary alloy In1–xGaxAsyP1–y grown on an InP crystal substrate is a suitable commercial semiconductor material for infrared wavelength LED and laser diode applications. The device requires that the InGaAsP layer is lattice matched to the InP crystal substrate to avoid crystal defects in the InGaAsP layer. This in turn requires that y 2.2x. The bandgap Eg of the ternary alloy in eV is then given by the empirical relationship,

• Eg 1.35 – 0.72y + 0.12y2; 0x0.47• Calculate the compositions of InGaAsP ternary alloys for

peak emission at a wavelength of 1.3 m

Solution

0.340.660.30.7

2

619

348

g

6

PAsGaIn isalloy y quarternar The

0.3.2.2/66.0Then .66.0 gives calculator aon equation quadratic thisSolving

12.072.035.1928.0

,satisfying havemust then InGaAsP The

928.00259.0103.1106.1

10626.6103

, taking,103.1at and

olts,electron vin Then ./ isemission peak at energy photon The

.interest ofh wavelengtat the bandgap required theneed that wenotefirst We

xy

yy

y

eVeVE

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Chapter 4b

Science

Transcript of Chapter 4b