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