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EE232 Lecture 21-1 Prof. Ming Wu
EE 232 Lightwave DevicesLecture 21: Avalanche Photodiode (APD)
Reading: Chuang 15.4 (2nd Ed)
Instructor: Ming C. Wu
University of California, BerkeleyElectrical Engineering and Computer Sciences Dept.
EE232 Lecture 21-2 Prof. Ming Wu
Avalanche Photodiode (APD)
2
EE232 Lecture 21-3 Prof. Ming Wu
Typical APD Structure:Separate Absorption and Multiplication (SAM) APD
EE232 Lecture 21-4 Prof. Ming Wu
Ideal APD: Injection Impact Ionization Only
1
( ) ( )
: electron ionization coefficient [cm ]
Electron current distribution along the field:( ) (0)
Multiplication factor:( )(0)
n
n
nn n
n
xn n
Wnn
n
dJ x J xdx
J x J e
J WM eJ
α
α
α
α −
=
=
= =
3
EE232 Lecture 21-5 Prof. Ming Wu
( )nJ x
Practical APD: Both Electron and Hole produce Impact Ionizations
( )
( )
1
1
( ) ( ) ( )
( )( ) ( )
: electron ionization coefficient [cm ]
: hole ionization coefficient [cm ]
( ) ( ) 0
( ) ( ) constant
( ) ( )
nn n p p
pn n p p
n
p
n p
n p
nn p n p
dJ x J x J xdxdJ x
J x J xdx
d J x J xdxJ x J x JdJ x J x Jdx
α β
α β
αβ
α β β
−
−
⎧ = +⎪⎪⎨⎪− = +⎪⎩
+ =
+ = =
− − =
EE232 Lecture 21-6 Prof. Ming Wu
Multiplication Factor
( )
( )( )( )
'
0
(1 )
Multiplication factor:1
(0)1 '
1
1 1
Define
1
n p
n p
n p
n
n Wxn
n
nWn
n p
n pW
n p
p
n
n k W
JMJ
dx e
Me
e
k
kMe k
α β
α β
α β
α
α
αα β
α β
α ββα
− −
− −
− −
− −
= =−
=− −
−
−=
−
=
−=−
∫
0 1 2 3 4 51
10
100
1 103×
1 104×
Mn 0 x, ( )
Mn 0.2 x, ( )
Mn 0.9 x, ( )
x
nM
nWα
0k =
0.2k =
0.9k =
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EE232 Lecture 21-7 Prof. Ming Wu
Response Time
Response time = transit time in absorption region + multiplication time
Usually
t m
n nm
e h e
abst
h
m t m
M kW M kWWv v v
Wv
τ τ τ
τ
τ
τ τ τ τ
= +
⎧ = + ≈⎪⎪⎨⎪ =⎪⎩
→ ≈?
Gain-Bandwidth Product:
1 12 2
constant2
en n
m n
e
vG BW M MM kW
vG BWkW
πτ π
π
× = ⋅ = ⋅
× = =
EE232 Lecture 21-8 Prof. Ming Wu
Noise Figure
2
2
Excess noise factor (due to fluctuation in gain) :
1(1 ) 2
Noise Figure:10log
Small has small under high gain Minimum noise figure = 3 dB occurs when 0
nn
n
F
MF k M k
MM
NF F
k F Mk
⎛ ⎞= = + − −⎜ ⎟⎜ ⎟⎝ ⎠
=
=
5
EE232 Lecture 21-9 Prof. Ming Wu
APD Noises
( )( )
222
2
2 2
2
2
Signal is amplified by the average gain :
12
Shot noise is amplified by :
2
2
: photocurrent;
: background photocurrent: dark current
4
p opt
S p B D
p B D
p
B
D
BT
M
qi P M
M
i e I I I M dv
e I I I F M dv
III
k T vi
ηω
⎛ ⎞= ⎜ ⎟⎝ ⎠
= + +
= + +
Δ=
h
( )
22
2
12
42
opt
Bp B D
RqP M
SNR k T ve I I I F M dvR
ηω
⎛ ⎞⎜ ⎟⎝ ⎠= Δ+ + +
h
1 10 6−× 1 10 5−× 1 10 4−× 1 10 3−× 0.01 0.1 11 104×
1 105×
1 106×
1 107×
1 108×
1 109×
1 1010×
1 1011×
1 1012×
SNR ip 100, 0.4, ( )
ip
Slope=2at low Ip
Slope=1at high Ip
Photocurrent, ipSNR
EE232 Lecture 21-10 Prof. Ming Wu
( )
( )
22
2
2
12APD: 42
p-i-n: set 1, 1
12
42
opt
Bp B D
opt
Bp B D
qP MSNR k T ve I I I F M dv
RM F
qPSNR k T ve I I I dv
R
ηω
ηω
⎛ ⎞⎜ ⎟⎝ ⎠= Δ+ + +
= =
⎛ ⎞⎜ ⎟⎝ ⎠= Δ+ + +
h
h
1 10 9−× 1 10 7−× 1 10 5−× 1 10 3−× 0.11 10 3−×
0.1
10
1 103×
1 105×
1 107×
1 109×
SNR ip 40, 0.4, ( )
ip
1 10 9−× 1 10 7−× 1 10 5−× 1 10 3−× 0.11
10
100
1 103×
1 104×
1 105×
1 106×
1 107×
1 108×
1 109×
1 1010×
SNR ip 40, 0.4, ( )
SNR ip 1, 0.4, ( )
ip
SNR Comparison of p-i-n and APD
Photocurrent, ip
SNR
APD
p-i-n
