Gain and Bandwidth in Semiconductor Photodetectors
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Transcript of Gain and Bandwidth in Semiconductor Photodetectors
Gain and Bandwidth in Semiconductor Photodetectors
S W McKnight and C A DiMarzio
Photoconductivity
Φp = photon flux (photon/sec)
Area=A
length=l
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
Ef
E
x
+-Depletion Region
Ev
Ec
JdiffusionJdrift
Junction “built-in” voltage
Vo
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 VelocityJdiff = 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
x
y
za a
b
b
c
Silicon Conductivity Mass
Thermal vs. Drift Velocity
Carrier Saturation Velocities
Electrons Holes
Photovoltaic Sensing Circuit
Vph
+
-
Photoconductive Sensing Circuit
Vd
+ -Iph
Photoconductive Detection
Ef
E
x
+-Depletion Region
Ev
Ec
Jdrift
Vo+ Vd
Depletion Region Width
Absorption Length for Semiconductor
Absorption Length vs. Wavelength
0
10
20
30
40
50
60
70
80
90
100
400 500 600 700 800 900 1000 1100 1200
Wavelength (nm)
Abs
orpt
ion
Leng
th
(mic
rons
)
Silicon
GaAs
Junction Capacitance
P-I-N Diode Detector
P-N Junction
Ef
electrons“holes”
E
x
+-
Depletion Region
Abrupt Junction
x
ρ
-qNa
qNd
P-side N-side
-xop
xon
Charge conservation → q Na xop = q Nd xon
Electric Field CalculationPoisson’s Equation:
1D Junction:
Abrupt Junction
x
P-side N-side
-xop
xon
P-I-N Junction
Ef
electrons“holes”
E
x
+-
Depletion Region
Ef
P-I-N Junction
Ef
electrons“holes”
E
x
+-Depletion Region
Ev
Ec
P-I-N Junction
x
P-side N-side
xpo xno
I-region
~ 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