3.46 PHOTONIC MATERIALS AND DEVICES
Lecture 17: Detectors—Part 2
Notes
Lecture
Detector Attributes
• efficiency
• noise
• speed
• linearity
“Digital” Sensitivity
1. Bit Error Rate
• charge carriers are created by photons in a Poisson random process a) probability that a pair is generated in time
interval dt = ρ(t)
RP(t)
dt
q
ηλ
=
P(t)dt
hc
ρ(t)dt =
b) average # carriers generated
ηλ t+T
∫ t P(t)dt
hc
ηλ
E
=
hc
Ν=
energy in pulse of width T
IL
T
t
c) probability the N = n charges in time interval T
(average value of N : N )
n
Ν e-Ν
P(Ν = n) =
n!
n
=
Ν exp (−ηλE hc )
n!
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 17: Detectors—Part 2
Page 1 of 5
Lecture
Notes
Example
What is E required such that P < 10-9 that a
logical “0” will be detected when a logical “1” is
transmitted?
• logical “0” ≡ no e- h+ pairs ⎡
ηλΕ ⎤
⎥ < 10−9
• P(N = 0) = exp ⎢−
⎢⎣ hc ⎦⎥
⇒ Ε > 21
⇒
hv
η
21
photons required
η
d) Each bit is TB seconds long
⇒ required power at detector
Pav =
21⋅ hν η
2TB
•
•
assumes only shot noise
quantum limit of the detection process
⎡ ηΕ ⎤
∴ exp ⎢− ⎥ ≤ BER
⎢⎣ hν ⎥⎦
2. Noise
iS2
S Psignal
=
= 2
N Pnoise
iN
a) Shot Noise
• quantization of charge q
• quantization of light hν
iN2 = 2qIB
I = average diode current
B = bandwidth of electronics
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 17: Detectors—Part 2
Page 2 of 5
Notes
Lecture
•
“white” noise
o independent of center frequency
• AC noise dependent on DC value of output current I = IL + Ibackground + Idark
• RMS noise current ≡
•
iN2
shot noise is multiplied by an APD
b) Thermal Noise
• attribute of any resistive load
iN2 =
4k B TB
R
R = resistive load
T = noise temperature of device
•
iN2 independent of signal
Example
M =
ID =
Ro =
RL =
T =
B =
PL =
APD
50
10 nA
0.6 A/W (unamplified)
50 Ω
300 K
10 MHz
5 nW
iS M=1 = RoPi =
3 nA = IL
S
=
N
iS2
M2
2q(IL +ID )M2B +
4k B TB
RL
5.9
c) APD: shot noise dominates
PIN: thermal noise dominates
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 17: Detectors—Part 2
Page 3 of 5
Lecture
Notes
3. Speed
e−
n+
+
−
p−
h+
xj
I, N
a) drift transit time (in depletion region)
Si:
e−
h+
107
ln(vd)
(cm/s)
105
JK
ln E ( V cm)
Δt =
w
s
≈ 10−7
×w
v d
cm
⇒ 10 μm = w,
Δt = 10-10 s
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 17: Detectors—Part 2
Page 4 of 5
Lecture
Notes
b) diffusion time (outside w)
Δt =
x2
Dn,p
⎛k T ⎞
Dn,p = ⎜⎜ B ⎟⎟⎟ μ n,p
⎜⎝ q ⎠
Dn (Si) 30 c
s
(10 )
2
−3 2
Δt ( x = 10 μm) =
30
= 3×10−8 s
● RC time constant εA
C = ≤ 1 pF
w
Detector Design Rules
a) η ↑ as w ↑ as C ↓
b) τ tr ↑ as w ↑
2
α
τ tr ≈ RC
c) design for w ≈
PIN limit ≡ τ tr
APD limit ≡ carriers drift to avalanche region
+ drift of multiplied carriers out
+ avalanche time
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 17: Detectors—Part 2
Page 5 of 5