Prospects of Colloidal Nanocrystals for Electronic - Computer Science

424 Chemical Reviews, 2010, Vol. 110, No. 1 Talapin et al.
Photoconductive gain is determined by the ratio between
the free carrier lifetime (τ) and transit time (Tt):
G i ) τ
T t
Gi is a very important parameter, which is determined by
the number of electrons flowing through the external circuit
per each absorbed photon or, in other words, the number of
cycles the majority carriers can make before recombining.
Gi e 1 represents the case of a primary photoconductor.
Gi > 1 indicates the presence of the secondary photoconductivity,
when more carries flow through the circuit than
the number of photons absorbed per unit time. Photoconductive
gain can be efficiently controlled by adjusting both τ
and Tt. The former is mainly controlled by engineering
trapping states, whereas the latter is determined by device
design and electronic properties of material. In the presence
of long-living traps, the carrier lifetime is effectively
prolonged, and the majority carriers can cycle in the circuit
until they recombine with trapped carriers. The secondary
photocurrent, induced by traps, can in principle last for hours
and days; its duration is determined by the release rate of
minority carriers from the trap states. This situation typically
results in a slow decay of the photocurrent after illumination
turn off.
Equation 38 demonstrates the main trade-off for photoconductive
detectors. If the fast response is the goal, the
carrier lifetime must be short. This leads to a low gain and
lower sensitivity. On the other hand, very sensitive photoconductors
are slow and have a long response time. With
respect to the NC photodetectors, this situation will be
illustrated in the following sections. Gi can generally take
values from much less than unity to the upper limit of ∼106 given by the restrictions imposed by the charge-limited
current flow, impact ionization, and dielectric breakdown. 434
Lifetime τ can range from 10-13 s to many seconds
depending on the particular material. For example, in highly
sensitive photodetectors based on PbS NC solids, τ was
reported to lie in the millisecond-to-second time scale, and
Gi was estimated to be about 102-104 . 265,435 Transit time Tt
depends on the device length of conducting channel L,
electric field E, and carrier mobility µ:
T t ) L
µE
Taking into account eq 37, E ) V/L (where V is applied
voltage), and Nλ ) Pin/hν, we can express the photocurrent
as:
iph ) ηe( Pin hν)( µτV
L
(38)
(39)
Noise. The main noise sources in photoconductors are
Johnson noise, generation-recombination, and 1/f noise. The
Johnson noise ij originates from the fluctuations induced by
the thermal motion of the charge carriers, which causes the
fluctuating charge gradients. It is expressed through the noiseequivalent
bandwidth ∆f and detector resistance R as shown
by eq 41:
i j ) � 4kT∆f
R
2 )
(40)
(41)
Johnson noise is independent of the applied bias; all other
kinds of noise are bias dependent. Generation-recombination
noise igr originates from the statistical fluctuations in the
generation and recombination rates of nonequilibrium charge
carriers. 1/f noise is given by:
i 1/f ) � i2 ∆f
f
where f is the electrical frequency, ∆f is the electrical
bandwidth, and i is the dc current. The 1/f noise is affected
by the nonohmic contancts and surface traps. Therefore,
reduction of 1/f noise is rather an experimental art. Usually,
1/f noise is significant at low modulation frequencies, while
at higher frequencies its amplitude drops below that of
Johnson noise or generation-recombination noise.
7.2.3. Photoconductivity Measurements
(42)
Figure 39 shows a typical setup for photoconductivity
measurements. Very similar designs were used for measuring
NC-based samples. 265,436-438 This setup allows one to obtain
spectral responsivity and all other figures of merits described
in section 7.2.1. A very similar setup is used for characterization
of solar cells (see section 7.3), and we will describe
it here in more detail.
A suitable light source (typically quartz, tungsten, xenon
lamp) is used depending on the spectral region of interest.
The light is dispersed by a monochromator and focused onto
the sample. The optical flux at the wavelength of interest
can be measured by placing a power meter or calibrated
detector in the place of sample. The input optical power is
then calculated taking into account the actual area of tested
photodetector. The sample has to be biased using low-noise
source, and its I-V characteristics are recorded under
illumination and in the dark. To obtain a high signal-to-noise
ratio, the photocurrent response is usually measured using a
lock-in amplification; the incident light is modulated by a
mechanical chopper, and the modulation frequency and phase
are used as a reference for lock-in amplifier of chopping.
The use of lock-in technique allows for the measuring of
very weak photocurrents in the presence of a noise signal.
Figure 39. Typical experimental setup for photoconductivity
measurements.