Page 248 - Organic Electronics in Sensors and Biotechnology

An Intr oduction to Or ganic Photodetectors 225

statistics and consequently applies only when the electrons behave as
independent particles. Interactions between particles can lead to
more or less noise than predicted by the shot expression. An impor-
tant example in inorganic semiconductor devices is the so-called
flicker noise, which has a spectral energy density that varies as f α
where α≤ 1; its precise origin is poorly understood and remains a
subject of considerable debate. The effect of flicker noise is to increase
50
the noise level above the shot limit at frequencies less than a few hun-
dred hertz, and whenever possible, it is advisable to work at appre-
ciably higher frequencies. We are aware of no studies investigating
the existence of flicker noise in organic photodiodes.
Noise Equivalent Power
The noise equivalent power (NEP) is a useful means of characterizing
the sensitivity of a detector. The NEP is the minimum detectable
power and is formally defined as the incident power required to
achieve a signal-to-noise ratio of 1. In a system dominated by shot
and thermal noise, the total noise current per square root of band-
width is
4 kT
V +
V + 2
σ = 2 eI () eI () B (6.42)
I dark ph
R
To generate a photocurrent of equal size would require an incident
σ
λ
power P()λ = ()/ S()λ , and hence we obtain for the noise equiva-
I
lent power per square root of hertz

NEP = 1 2 eI () eI () 4 kT (6.43)
V +
B
V + 2
λ
S() dark ph R
6.5 Measuring a Current
The simplest way to measure a small current is to pass it through a
large “sense” resistor and measure the associated voltage drop across
the resistor (Fig. 6.17a). The current can then be determined by simple
application of Ohm’s law. There are several problems with this
approach, however. To obtain a reasonably sized voltage from a small
current, a very large sense resistor is required; e.g., a gigaohm resis-
tance is required to generate a millivolt from a picoampere. The high
resistance combines with the high capacitance of the photodiode to
create a large RC time constant, which results in a sluggish response.
For instance, a photodiode capacitance of 100 pF coupled to a gigaohm
sense resistance yields a time constant of 100 ms, making it difficult to
measure signals above 10 Hz. A faster response can be obtained by
reducing the sense resistor, but the increased speed comes at the
expense of reduced gain. The use of a large sense resistor also limits