592
22 Light-to-Electricity Conversion
(a)
se m ic on du ct or
ohmic
contact
d
w
L
ohmic
contact
I
h
(b)
Fig. 22.4 a Scheme of photoconductor. b Equivalent circuit of photoconductor
where t r = L/v d is the transit time through the photoconductor.
Now we consider a modulated light intensity
P(ω) = P opt
1 + m exp(iωt)
,
(22.5)
where m is between 0 and 1. For m = 0 it is a constant light power, for m = 1 the intensity is
sinusoidally modulated between 0 and P max = 2P opt . The rms optical power
2 is given by
√
2m P opt . In
the case of m = 1 this is equal to P max /
√
2.
The rms photocurrent (i
2
= =I
2
− −I
2 ) is
i ph ≈
e η m P opt
√
2hν
τ
t r
1
√
1 + ω 2 τ 2
.
(22.6)
Besides the photocurrent which is considered the signal, several sources of noise must be considered.
Noise is in this case a fluctuation current i n with n = 0 (see Appendix K).
The thermal noise (Appendix K.3.1) at a conductivity G = 1/R is
3
i
2
G = 4 k T G B ,
(22.7)
with B being the bandwidth over which the noise spectrum is integrated. The thermal noise at a resistor
was experimentally found by Johnson [1820, 1821] and theoretically explained by Nyquist [1822].
4
The statistical nature (Poisson statistics) of photon arrival (and absorption) and equally that of
recombination of (photo-) excited electrons leads to fluctuations of the carrier density and consequently
to fluctuating conductivity and gain. This so-called generation-recombination noise (Appendix K.3.4)
is given by [1823]
i
2
GR = 4 e I ph B g
1
1 + ω 2 τ 2
(22.8)
for the modulation frequency ω, I ph being the photocurrent in steady state (22.3). The equivalent circuit
with the ideal photocurrent source and the noise currents is depicted in Fig. 22.4b. A detailed treatment
can be found in [1824].
The signal-to-noise ratio of the power is then given by
2 The rms value is the square root of the time average of the square of the power,
P 2
3 For frequencies hν kT ; at room temperature kT / h is in the THz regime.
4 The formula for thermal noise (22.7) is the fluctuation-dissipation theorem in statistical physics, providing a general
relation between the response of an equilibrium system to small external perturbations and its spontaneous fluctuations.
22 Light-to-Electricity Conversion
(a)
se m ic on du ct or
ohmic
contact
d
w
L
ohmic
contact
I
h
(b)
Fig. 22.4 a Scheme of photoconductor. b Equivalent circuit of photoconductor
where t r = L/v d is the transit time through the photoconductor.
Now we consider a modulated light intensity
P(ω) = P opt
1 + m exp(iωt)
,
(22.5)
where m is between 0 and 1. For m = 0 it is a constant light power, for m = 1 the intensity is
sinusoidally modulated between 0 and P max = 2P opt . The rms optical power
2 is given by
√
2m P opt . In
the case of m = 1 this is equal to P max /
√
2.
The rms photocurrent (i
2
= =I
2
− −I
2 ) is
i ph ≈
e η m P opt
√
2hν
τ
t r
1
√
1 + ω 2 τ 2
.
(22.6)
Besides the photocurrent which is considered the signal, several sources of noise must be considered.
Noise is in this case a fluctuation current i n with n = 0 (see Appendix K).
The thermal noise (Appendix K.3.1) at a conductivity G = 1/R is
3
i
2
G = 4 k T G B ,
(22.7)
with B being the bandwidth over which the noise spectrum is integrated. The thermal noise at a resistor
was experimentally found by Johnson [1820, 1821] and theoretically explained by Nyquist [1822].
4
The statistical nature (Poisson statistics) of photon arrival (and absorption) and equally that of
recombination of (photo-) excited electrons leads to fluctuations of the carrier density and consequently
to fluctuating conductivity and gain. This so-called generation-recombination noise (Appendix K.3.4)
is given by [1823]
i
2
GR = 4 e I ph B g
1
1 + ω 2 τ 2
(22.8)
for the modulation frequency ω, I ph being the photocurrent in steady state (22.3). The equivalent circuit
with the ideal photocurrent source and the noise currents is depicted in Fig. 22.4b. A detailed treatment
can be found in [1824].
The signal-to-noise ratio of the power is then given by
2 The rms value is the square root of the time average of the square of the power,
P 2
3 For frequencies hν kT ; at room temperature kT / h is in the THz regime.
4 The formula for thermal noise (22.7) is the fluctuation-dissipation theorem in statistical physics, providing a general
relation between the response of an equilibrium system to small external perturbations and its spontaneous fluctuations.