Download Gain and Bandwidth in Semiconductor Detectors

Gain and Bandwidth in
Semiconductor Photodetectors
S W McKnight and C A DiMarzio
Photoconductivity
length=l
Area=A
Φp = photon flux (photon/sec)
η = quantum efficiency
Photoconductor Responsivity
Photoconductor Detectivity and
Bandwidth
•
•
•
•
Sample thickness ~ absorption length
Photoconductive Gain ~ τn
Bandwidth ~ 1/ τn
Gain/Bandwidth product ~ constant
Photovoltaic Detection
E
Jdrift
Jdiffusion
Ec
Vo
Junction “built-in”
voltage
Ef
Ev
- +
Depletion
Region
x
Photovoltaic Detection: Gain
and Bandwidth
•
•
•
•
Transit across depletion region fast (vdrift)
Diffusion to depletion region slow (vdiff < <vthermal)
Highest η if absorption is within depletion region
Bandwidth
– Transit time of electrons ~ W / (μ
– Electrical bandwidth ~ 1/RCj
– Cj ~ ε A/d ~ 1/W
)
Diffusion and Drift Velocity
Jdiff = q Dn dn/dx = n q vdiff
vdiff = Dn 1/n dn/dx = Dn d/dx [ln(n)]
~ Dn ln(gop τ) / (1/α) < < vthermal = sqrt (kT/m)
vdrift = μn
Carrier Conductivity Mass
Conductivity mass:
Silicon Conductivity Mass
b
y
a
c
a
z
b
x
Silicon Conductivity Mass
Thermal vs. Drift Velocity
Carrier Saturation Velocities
Electrons
Holes
Photovoltaic Sensing Circuit
+
Vph
-
Photoconductive Sensing Circuit
Iph
-
+
Vd
Photoconductive Detection
E
Jdrift
Ec
Vo+ Vd
Ev
Ef
- +
Depletion
Region
x
Depletion Region Width
Absorption Length for
Semiconductor
Absorption Length vs. Wavelength
100
Absorption Length
(microns)
90
80
70
60
Silicon
50
GaAs
40
30
20
10
0
400
500
600
700
800
900
Wavelength (nm)
1000
1100
1200
Junction Capacitance
P-I-N Diode Detector
P-N Junction
E
- +
electrons
“holes”
Ef
Depletion
Region
x
Abrupt Junction
ρ
P-side
N-side
-xop
qNd
xon
-qNa
Charge conservation → q Na xop = q Nd xon
x
Electric Field Calculation
Poisson’s Equation:
1D Junction:
Abrupt Junction
P-side
N-side
-xop
xon
x
P-I-N Junction
E
+
Ef
electrons
“holes”
Ef
Depletion
Region
x
P-I-N Junction
E
Ec
Ef
electrons
“holes”
Ev
-
+
Depletion
Region
x
P-I-N Junction
P-side
I-region
xpo
N-side
xno
x
~ Va/W
Depletion width = W
Silicon pin diode
• W ~ 1/α ~ 10 μ at λ=600 nm
• Ebreakdown ~ 106 V/cm
• Maximum reverse bias ~ Ebreakdown/W ~ 1000V