Electron Energy,

E

Free electron Vacuum level 3

p

3

s

2

p

2

s

2

s

Band 3s Band 2

p

Band

E

= 0 Overlapping energy bands Electrons 1

s

ATOM 1

s

SOLID In a metal the various energy bands overlap to give a single band of energies that is only partially full of electrons. There are states with energies up to the vacuum level where the electron is free.

© 1999 S.O. Kasap,

Optoelectronics

Covalent bond Si ion core (+4

e

) Electron energy,

E E c

+  Conduction Band (CB) Empty of electrons at 0 K.

E c

Band gap =

E g E v

Valence Band (VB) Full of electrons at 0 K.

0

(a) (b)

(a) A simplified two dimensional view of a region of the Si crystal showing covalent bonds. (b) The energy band diagram of electrons in the Si crystal at absolute zero of temperature.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Electron energy,

E E c

+  CB

h

 >

E g E c

Free

e

– Hole

h

+

E g h

 hole

e

–

E v

VB 0

(a) (b)

(a) A photon with an energy greater than

E g

can excite an electron from the VB to the CB.

(b) Each line between Si-Si atoms is a valence electron in a bond. When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

E c

+  CB

E c E F E v

VB

(a)

E

(b)

g

(

E

)  (

E

–

E c

) 1/2

E

(c)

[1–

f

(

E

)] For electrons

E F

For holes

E

(d)

E c

Area =

•

n E (E)dE

=

n n E

(

E

)

E v p E

(

E

) Area =

p

0

g

(

E

)

fE

)

n E

(

E

) or

p E

(

E

) (a) Energy band diagram. (b) Density of states (number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a state). (d) The product of

g

(

E

) and

f

(

E

) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under

n E

(

E

) vs.

E

is the electron concentration.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

e–

As + (a) (b)

Electron Energy

CB

E c

~0.05 eV

E d

As + As + As + As + (a) The four valence electrons of As allow it to bond just like Si but the fifth electron is left orbiting the As site. The energy required to release to free fifth electron into the CB is very small.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

E v x

Distance into crystal As atom sites every 10 6 Si atoms (b) Energy band diagram for an with 1 ppm As. There are donor energy levels just below

E c

around As + sites.

n

-type Si doped

Electron energy B atom sites every 10 6 Si atoms

E c x

Distance into crystal

h

+

B –

E a E v

B –

h

+ B – B – B – ~ 0.05 eV VB

(a) (b)

(a) Boron doped Si crystal. B has only three valence electrons. When it substitutes for a Si atom one of its bonds has an electron missing and therefore a hole. (b) Energy band diagram for a

p

-type Si doped with 1 ppm B. There are acceptor energy levels just above

E v

around B – sites. These acceptor levels accept electrons from the VB and therefore create holes in the VB.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

CB

E c E Fi E v

VB

E c E Fn E v E c E Fp E v

(a) (b) (c)

Energy band diagrams for (a) intrinsic (b) -type and (c)

p

-type semiconductors. In all cases,

np

=

n i

2

. Note that donor and acceptor energy levels are not shown.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Impurities forming a band

g

(

E

) CB

E E F n E c E v

CB

E c E v E Fp

VB

(a)

(a) Degenerate

n

-type semiconductor. Large number of donors form a band that overlaps the CB. (b) Degenerate

p

-type semiconductor.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

(b)

V

(

x

),

PE

(

x

)

V

(

x

)

x PE

(

x

) = –

eV

Electron Energy

E E c E F E v A n

-Type Semiconductor

B E c



eV E F



eV E v



eV V

Energy band diagram of an voltage supply of

V n

-type semiconductor connected to a volts. The whole energy diagram tilts because the electron now has an electrostatic potential energy as well © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

PE

(

r

)

r PE

of the electron around an isolated atom When

N

atoms are arranged to form the crystal then there is an overlap of individual electron

PE

functions.

0

V

(

x

)

a a x

= 0 Surface

a

2

a

3

a

Crystal

x

=

L

Surface

x PE

of the electron, period

a

.

V

(

x

), inside the crystal is periodic with a The electron potential energy (

PE

),

V

(

x

), inside the crystal is periodic with the same periodicity as that of the crystal,

a

. Far away outside the crystal, by choice,

V

= 0 (the electron is free and

PE

= 0).

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

E E E

CB Direct Bandgap

E g

–

k

VB (a) GaAs

E c

Photon

E v k

–

k

Indirect Bandgap,

Eg

CB

k cb E c E v

VB

k vb k

–

k

(b) Si

E r

VB CB

E c

Phonon

E v

(c) Si with a recombination center

k

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is therefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced from the maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination of an electron and a hole in Si involves a recombination center .

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

p n

B-

h+

Neutral

p M

Metallurgical Junction -region

E o

Neutral

n

-region As+

e–

(a)

E

(

x

)

M –W p

0

W n

(b)

– E o V

(

x

) log(

n

), log(

p

)

p po W p M W n

Space charge region

n po



net x

= 0

M n no n i p no x

(c)

eN d –W p x

(d)

W n -eN a PE

(

x

)

Properties of the

pn

junction.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

V o x

(e)

x

(f)

eV

o Hole

PE

(x)

x

(g)

Electron

PE

(

x

) –

eV

o

J p

-region SCL

n

-region Majority carrier diffusion and drift current

J

elec

J

hole

Total current

J =

J

elec + J hole

Minority carrier diffusion current The total current anywhere in the device is constant. Just outside the depletion region it is due to the diffusion of minority carriers.

x –W p W n

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

I I

=

I o

[exp(

eV

/ 

k B T

)  1] mA Shockley equation Space charge layer generation.

nA © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

V

Reverse

I-V

characteristics of a

pn

junction (the positive and negative current axes have different scales)

Reverse diode current (A) at 10 10 -4 -6

V

=  5 V Ge Photodiode 323 K 0.63 eV 10 -8 10 -10 0.33 eV 10 -12 10 -14 238 K 10 -16 0.002

0.004

0.006

0.008

1/Temperature (1/K) © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall) Reverse d iode current in a Ge a ln(

I

rev ) vs. 1/

T pn

junction as a function of temperature in plot. Above 238 K,

I

rev is controlled by

n

i

2 and below 238 K it is controlled by Kasap,

n

i

. The vertical axis is a logarithmic scale with actual current values. (From D. Scansen and S.O.

Cn d. J. Physics.

70

, 1070-1075, 1992.)

E c E Fp E v p p E o M n E c E Fn eV o n E v

(a)

E c E Fp E v p E o

–

E

(b)

eV E c E Fn e

(

V o

–

V

)

E v n E c E Fp E v p

SCL

I V E o

+

E

(c)

E c E c E Fn e

(

V o

+

V r

)

E Fp E v E

Thermal generation

o

+

E n E v p

(d)

n E c E Fn e

(

V o

+

V r

)

E v V r V r I

= Very Small Energy band diagrams for a

pn

junction under (a) open circuit, (b) forward bias and (c) reverse bias conditions. (d) Thermal generation of electron hole pairs in the depletion region results in a small reverse current.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Electron energy

E c E g p eV o

(a)

E F E v n

+

E c E F E g p n

+

h

  -

E g eV o E v

Distance into device Electron in CB Hole in VB

V

(a) The energy band diagram of a

p-n

+ (heavily

n

-type doped) junction without any bias.

Built-in potential

V o

prevents electrons from diffusing from

n

+ to

p

side. (b) The applied bias reduces

p V o

and thereby allows electrons to diffuse, be injected, into the -side leads to photon emission.

p

-side.

Recombination around the junction and within the diffusion length of the electrons in the © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

(b)

Light output

p n

+

n

+ Substrate Epitaxial layers Light output

p n

+

n

+ Substrate Insulator (oxide) Epitaxial layer

(a)

Metal electrode

(b)

A schematic illustration of typical planar surface emitting LED devices. (a) grown epitaxially on an

n

+ substrate. (b) First

n

+ is epitaxially grown and then is formed by dopant diffusion into the epitaxial layer.

p

-layer

p

region © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

(a)

Light output

(b)

Light Domed semiconductor Plastic dome

(c)

p n

+

pn

Junction

n

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

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Indirect bandgap GaAs 1-

y

P

y x

= 0.43

Al

x

Ga 1-

x

As In 0.49

Al

x

Ga 0.51-

x

P In 1-

x

Ga

x

As 1-

y

P

y

0.4

0.5

0.6

0.7

0.8

Infrared 0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

 Free space wavelength coverage by different LED materials from the visible spectrum to the infrared including wavelengths used in optical communications. Hatched region and dashed lines are indirect

E g

materials.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

(a)

n

+ AlGaAs

p

GaAs ~ 0.2  m (b) Electrons in CB

E F E c

2 eV

E v eV o

1.4 eV (c) (d)

n

+

p p

AlGaAs 

E c

Holes in VB

E c

2 eV

E F E v

No bias (a) A double heterostructure diode has two junctions which are between two different bandgap semiconductors (GaAs and AlGaAs) (b) A simplified energy band diagram with exaggerated features.

E F

must be uniform.

p

With forward bias (c) Forward biased simplified energy band diagram.

(d) Forward biased LED.

Schematic illustration of photons escaping reabsorption in the AlGaAs layer and being emitted from the device.

AlGaAs GaAs AlGaAs © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

(a) CB

E c

1 2 3

E g E v

VB

E

(b)

Electrons in CB 2

k B T

1/ 2

k B T

Holes in VB Carrier concentration per unit energy

(c) (d)

Relative intensity

E g

+

k B T

1 (2.5-3)

k B T



h

 0

h

 

E g h

 

h

 

h

 Relative intensity 1 0        (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)

k B T

above

E c

. (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).

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall) 

Relative intensity 1.0

(a)

655nm

(b)

Relative light intensity

V

(c)

2 0.5

  24 nm 1 0 600 650 700  0 0 20 40

I

(mA) 0 0 20 40

I

(mA) (a) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED.

(b) Typical output light power vs. forward current. (c) Typical I-V characteristics of a red LED. The turn-on voltage is around 1.5V.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Light Double heterostructure (a) Surface emitting LED (b) Edge emitting LED © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall) Light

Fiber (multimode) Epoxy resin Fiber Microlens (Ti 2 O 3 :SiO 2 glass) Electrode (a) Etched well Double heterostructure SiO 2 (insulator) Electrode Light is coupled from a surface emitting LED into a multimode fiber using an index matching epoxy. The fiber is bonded to the LED structure.

(b) A microlens focuses diverging light from a surface emitting LED into a multimode optical fiber.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

60-70  m

L

Stripe electrode Insulation

p

+ -InP (

E g

= 1.35 eV, Cladding layer)

p

+ -InGaAsP (

E g

 1 eV, Confining layer)

n

-InGaAs (

E g

= 0.83 eV, Active layer)

n

+ -InGaAsP (

E g

 1 eV, Confining layer)

n

+ -InP (

E g

= 1.35 eV, Cladding/Substrate) Electrode 2 Current 1 3 200-300  m Active region (emission region) Light beam Schematic illustration of the the structure of a double heterojunction stripe contact edge emitting LED © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

ELED Lens Multimode fiber ELED GRIN-rod lens Single mode fiber Active layer (a) (b) Light from an edge emitting LED is coupled into a fiber typically by using a lens or a GRIN rod lens.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

Relative spectral output power 1 –40°C 25°C 85°C The output spectrum from AlGaAs LED. Values normalized to peak emission at 25°C.

0 740 800 840 Wavelength (nm) 880 900 © 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)

E g

(eV) 2.6

2.4

GaP 2.2

2 1.8

1.6

Quaternary alloys with indirect bandgap Direct bandgap Indirect bandgap Quaternary alloys with direct bandgap InP 1.4

1.2

1 0.8

0.6

0.4

0.2

0.54

GaAs In1-

x

Ga

x

As In0.535Ga

0.465

As 0.55 0.56 0.57 0.58

X

0.59

Lattice constant,

a

(nm) 0.6

InAs 0.61

0.62

Bandgap energy

E g

and lattice constant

a

for various III-V alloys of GaP, GaAs, InP and InAs. A line represents a ternary alloy formed with compounds from the end points of the line. Solid lines are for direct bandgap alloys whereas dashed lines for indirect bandgap alloys.

Regions between lines represent quaternary alloys. The line from

X

to InP represents quaternary alloys In 1-

x

Ga

x

As 1-

y

P

y

made from In 0.535

Ga 0.465

As and InP which are lattice matched to InP.

© 1999 S.O. Kasap,

Optoelectronics

(Prentice Hall)