Lecture 15 optics

8/10/2019 Lecture 15 optics

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Lecture 15

Semiconductor Science and Light Emitting Diodes

! Semiconductor concepts and energy bands

!

Direct and indirect bandgap semiconductors

! The p-n junction principles and band diagram

! Light-emission processes in semiconductors

!

Light-emitting diodes (LEDs)





Mass Action Law valid along the whole device, through the pn junction.

p-n Junction

Depletion Widths nd pa W N W N = (conservation of total charge)



The electric field across the pn junction is found

by integrating !net.

p-n Junction

Built-in field

!

nd

o

W eN "=E

Built-in voltage

!

" )(net x

dx

d =

E

Field (E ) and net space charge density

! "=

x

W p

dx x x )(1

)( net # $

E

Field in depletion region

V o =

kT

e

ln N

a N

d

ni

2

!

" #

$

% & V

o = !

1

2

E 0W

0



p-n Junction

Law of the Junction

Boltzmann Statistics (only to be usedwith nondegenerate semiconductors)

!"

#$%

& ''=

T k

E E

N

N

B

)(exp 12

1

2

n po

nno

= exp ! eV o

k BT

"

#$

%

&'

nno = N d & n po =

ni

2

N a

V o =k BT

e

ln nno

n po

!

" #

$

% & =

k BT

e

ln N a N d

ni

2

!

" #

$

% &



Forward Bias: Diffusion Current




n p0

nn0

=

exp !

eV 0

k BT

"

#$

%

&'

n p (0)

nn0

=

exp ! e(V 0 !V )

k BT

"

#$

%

&'



Law of the Junction: Minority Carrier Concentrations and Voltage

n p 0( ) = n po exp eV

k BT

! " #

$ % &

pn 0( ) = pno exp eV

k BT

!

" #

$

% &




Law of the Junction: Minority Carrier Concentrations and Voltage

n p 0( ) = n po exp eV

k BT

! " #

$ % &

pn 0( ) = pno exp eV

k BT

!

" #

$

% &

n p(0) is the electron concentration just outside the depletion region on the p-side

pn(0) is the hole concentration just outside the depletion region on the n-side


!n p 0( ) = n po exp eV

k BT

" # $

% & ' (1

)

*+

,

-.

! pn 0( ) = pno exp eV k BT

" # $ % & ' (1)

*+ ,

-.



Ideal diode (Shockley) equation

J = J so exp

eV

k BT

! " #

$ % & '1

(

)*

+

,-

J so =

eDh

Lh N

d

! " #

$ % & +

eDe

Le N

a

! " #

$ % &

'

()

*

+,ni

2

Reverse saturation current

Shockley Equation

Intrinsic concentration:

ni depends strongly on the material

(e.g. bandgap) and temperature

ni

2= N c N v exp !

E g

k BT

"

#

$%

&

'





Forward Bias: Recombination Current

Forward biased pn junction, the injection of carriers and their recombination inthe SCL. Recombination of electrons and holes in the depletion region involves

the current supplying the carriers.




A symmetrical pn junction for calculating the recombination current.




n p0

nn0

=

exp !

eV 0

k BT

"

#$

%

&'

n p (0)

nn0

=

exp ! e(V 0 !V )

k BT

"

#$

%

&'




he

eBCDeABC J

! !

+"recom

n M

nno

= exp !e(V

o !V )

2k BT

"

#

$%

&

'

n M

= niexp

eV

2k BT

!

"#

$

%&

!!"

#$$%

&'(

)*+

,+-

T k

eV W W en J

Bh

n

e

pi

2exp

2recom

. .



Forward Bias: Recombination and Total Current

Recombination Current

J recom = J ro[exp eV / 2k

BT ( )!1]

!!"

#$$%

&+!!

"

#$$%

&=

T k

eV J

T k

eV J J

B

ro

B

so

2expexp

Total diode current = diffusion + recombination

e

T k V B>

The diode equation

!!"#

$$%& +=

h

n

e

piro

W W en J ' ' 2

where

J = J o exp

eV

!k BT

" # $

% & ' (1)

*+ ,

-.

where J o

is a new constant and ! is an ideality factor

General diodeequation



Typical I -V characteristics of Ge, Si and GaAs pn junctions as log( I ) vs. V . The slope

indicates e/(!k BT )

Typical I -V characteristics of Ge, Si and GaAs pn junctions



Reverse Bias

Energy band diagrams for a p-n junction under reverse biasLEFT: Shockley model

RIGHT: Thermal generation in the depletion region



Reverse Bias

J revdiff

=eDh

Lh N d +

eDe

Le N a

!

" #

$

% & ni

2 J revther

=

eWni

! g



Reverse BiasTotal Reverse Current

J rev

= eDh

Lh N d + eDe

Le N a! " #

$ % & ni

2+ eWni

' g

Mean thermal generation time0

Diffusion current in neutral regions

the Shockley reverse current

Thermal generation in depletion region

J = J o exp

eV

!k BT

"

# $

%

& ' (1

)

*+

,

-.



Heterojunctions

Two types of heterojunction and the definitions of band offsets, Type I and Type II between

two semiconductor crystals 1 and 2. Crystal 1 has a narrower bandgap E g 1 than E g 2 for

crystal 2. Note that the semiconductors are not in contact so that the Fermi level in each is

different. In this example, crystal 1 (GaAs) is p-type and crystal 2 (AlGaAs) is N-type.



! Under open circuit and equilibrium conditions, the Fermi level E F must be uniform, i.e.

continuous throughout the device.

! If E F is close to the conduction band (CB) edge, E c , it results in an n-type, and if it is close

to the valence band (VB) edge, E v , it results in a p-type semiconductor.

!

There is a discontinuity "E c in E c , and "E v in E v , right at the junction.

Heterojunctions



Heterojunctions

!

Under open circuit and equilibrium conditions, the Fermi level E F must be uniform, i.e.

continuous throughout the device.

! If E F is close to the conduction band (CB) edge, E c , it results in an n-type, and if it is close

to the valence band (VB) edge, E v , it results in a p-type semiconductor.

! There is a discontinuity "E c in E c , and "E v in E v , right at the junction.



Light Emitting Diodes

UV LED

Courtesy of Chris Collins (Photos by SK)





Heterostructure High Density LEDS

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Lecture 15 optics