lecture #21 photodetectors

EE 232: Lightwave Devices

Lecture #21 – Photodetectors

Instructor: Seth A. Fortuna

Dept. of Electrical Engineering and Computer Sciences

University of California, Berkeley

4/22/2019

2Fortuna – E3S Seminar

Absorption coefficient

H. Melchior, “Laser Handbook”, Vol. 1 pp 725-835 (1972).


Photoconductor

+ _

d

V

Light off

semiconductor0 0 0( )n pJ q n p E = +

Light on

0 0( )n pJ J q p En + +

(assuming p-type semiconductorand low-injection)

( )

0( )ph n

n n

n t

nI J J A q EA

dq A G

=

= −

=

Photocurrent

generationelectronlifetime

transit time

/# carriers injected

(V )o (lume)( ) )(s

opt hG

P

A d

= =

where (1 )(1 )t

i R e −−= −

surfacereflectance

absorption

t


Photoconductive gain

opt nph

t

PI

hq

=

photoconductivegain

Putting it all together,

injectedprimary

photocurrent

Illustration of photoconductive gain.An electron can contribute multipletimes to photocurrent.

Responsivity is Rh

q

=

and has units of amps / watt

Photogeneratedelectronexitssemiconductor

Second electronexits

Third electronexits

Second electronenters

Thirdelectronenters

Photo-generatedhole exits

Time

Positionx=0 x=d


Photoconductor high-frequency response

)( )

(n

d nnG t

dt

t

= −

0 [ ( )( ) Re ]i tn nt en −= +

0 [ ( )( ) Re ]i tG Gt eG −= +

/(

( ))

)(

opt

n

P hi

A d

nn

= −−

1

/ 1

( )( ) 1

1

n

opt n

p n

p n

opt t n

A d i

qv

h

hn

P

I nA

I q

v iP

=

=

−

=

−

Let,

Then,

Note:

etc…

/ 1n t =

/ 10n t =

/ 100n t =

/ 1000n t =

/ 10000n t =


p-i-n photodiode

+ _

d

p i n

-V

Ener

gyE-

fiel

d

Position

Position

p-i-n photodiode: Undoped orlightly doped semiconductorinserted between p and n-typesemiconductor. p and n-type regionsmay be higher bandgap than intrinsic region.Low noise and capable of high-speed.

cEvE

dark phI I I= +

0 1

h

qV

kTdark

opt

p

I I

P

hq

e

I

−

= −

(1 )(1 )d

i R e −−= −


p-i-n photodiodep-i-n photodiode: Undoped orlightly doped semiconductorinserted between p and n-typesemiconductor. p and n-type regionsmay be higher bandgap than intrinsic region.Low noise and capable of high-speed.

dark phI I I= +

0 1

h

qV

kTdark

opt

p

I I

P

hq

e

I

−

= −

(1 )(1 )d

i R e −−= −

I

VDark

0P

02P

p-i-n diode is usuallyreverse biased


Two types of p-i-n photodiodes

i

p

n

i

p

n

substratesubstrate

Surface illuminated p-i-n waveguide p-i-n

(1 )(1 )d

i R e −−= −

d

L

(1 )(1 )L

i R e −−= −

confinementfactor

d


p-i-n high-frequency response

Time constant of hole transit across intrinsic region:

RC time constant:

t

h

d

v =

RCd

AR =

Surface illuminated p-i-n waveguide p-i-n

Speed usually limited by hole transit time

3

1(1 )(1 )

2

1

2

/ 2

d hdB i

hi

i h

vf R e

v

d

v

dd

−

=

− − =

3

1

2

hdB

vf

d

Efficiency-bandwidth product

Speed usually limited by RC time

3

1(1 )(1 )

2

1

2

2

L

dB i

i

i

df

w

L

R eR

A

d

d

R

A

R

− =

=

− −

3

1

2dB

A

df

REfficiency-bandwidth product

w: waveguidewidth


BW-efficiency product(surface illuminated p-i-n)

Stephen B. Alexander. Optical communication receiver design. 1997.


Avalanche photodiode (APD)

+ _

p+ i n+

-V

Ener

gyE-

fiel

d

Position

Position

cEvE

p

absorption

gain

APD: High-field region acceleratescarriers resulting in impact ionizationand creation of new carriers (avalanchebreakdown). Unlike the p-i-n, the APDhas gain. A single e-h pair can createa cascade of several others.Downside is additional noise.

opt

ph MP

qIh

=

multiplicationfactor

(1 )(1 )ad

i R e −

−= −

ad gd


Impact ionization and multiplication factor

p

n

k

=

p

n

k

: electron ionization coefficient

: hole ionization coefficient

: ionization ratio

Usually k << 1 is desirable for good noise properties (more on this later).For example, silicon is an excellent material for APD.When only electrons are injected into the gain region, it can be shown:

(1 )

1n gkn d

k

e kM

− −

−=

−(electron multiplication factor)

MaterialSiGeInGaAs

k-value0.02-0.050.7-1.00.5-0.7


APD high-frequency response

High-frequency response limited by hole transit time and gain build-up time.

hole transit timea g a

h

h h

d d d

v v

+=

gain build-up time m

n

gnM kd

v =

n

m

n

g

h

M kd

v →Usually, 3

1

2

n

n

dB

g

fv

M kd

Gain-bandwidth product

32 2

n e edB

g gn

M v v

MM f

kd kd = Typical values are 100 to 200 GHz


Summary

Photodetector

Photoconductor

p-i-n

APD

Pros

Simple device,Gain,Very fast

Low noise,Fast

Gain,Fast,Increasedsensitivity(sometimes)

Cons

High noise

No gain

Complicated,Multiplication noise

phI

optq M

P

h

opt

hq

P

opt n

t

P

hq

Recommended reading: S.D. Personick, Optical Detectors and Receiver. J. Light. Technol. Vol. 26, No. 9, 2008.

lecture #21 photodetectors

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