One of a number of ways of detecting the excess
quasiparticles produced as a result of the photoabsorption process is by
ensuring that they tunnel from one thin superconducting film in which
they are created into another
through a thin insulator (I). To maximise
the tunnel probability this insulating barrier must be very thin, of order
1 nm (i.e. only a few atomic layers). This
superconductor-insulator-superconductor (or SIS) structure is in essence a
superconducting tunnel junction (STJ) or Josephson junction (Giaever 1960;
Josephson 1962). A small magnetic field is applied parallel to the junction
barrier, as shown in Fig. 2 (click here), so as to suppress the Josephson current which
results from the tunnelling of Cooper pairs at zero bias voltage. Applying a
bias voltage
ensures that the only allowed tunnel processes
involve the transfer of quasiparticles from one film to the other.
The flow of quasiparticles in a time t produces a measurable
excess electric current, with the amplitude of the current pulse being
directly proportional to the incident photon energy.
Figure 2:
A schematic of a typical symmetrical tunnel junction deposited on a sapphire
substrate together with its orientation in a parallel magnetic field so as to
suppress the Josephson current. Such a device was used by
Peacock et al. (1996
a,b) to demonstrate single photon counting from . Back or front
illumination is possible
For the case where two tunnel processes exist (Gray
1978). In the first process an electron tunnels from film
to
film
(the direction depends simply on the polarity of
) and
effectively a quasiparticle is exchanged, while in the second process
an electron tunnels again from film
to
while a
quasiparticle is exchanged between films
and
. The
combination of these two processes in series leads to an effect known
as multiple tunnelling, which can be viewed as equivalent to an
amplification of the initial charge
created
in the superconducting film i. If each quasiparticle originally
created in the film is transferred across the barrier on average of
n times then, in the absence of loss processes, the average total
electrical charge detected would be
. In this time-dependent
process, recombination, diffusion losses and quasiparticle trapping
will all reduce
(Booth 1987;
Verhoeve et al. 1996).
This charge amplification will however degrade the Fano-limited
resolution of the STJ by adding in quadrature the variance on this
tunnel process, a contribution referred to as the tunnel noise (Goldie
et al. 1994). On the assumption of a perfectly symmetrical junction
(with equal probabilities of tunnelling from to
and from
to
) the resolution is given by:
This limiting resolution for a perfectly symmetrical STJ is also shown
in Fig. 1 (click here) for the case n=5. This choice of n is based on the
experimental determination by Peacock et al. (1996a) for a
symmetrical Nb-based device. Figure 1 (click here) shows that a resolution of
nm and
nm is achievable for simple Nb and Al based
devices respectively when illuminated by photons of wavelength
. The degradation due to an equivalent
amplification through multiple tunnelling is not a basic limitation,
since the need for such amplification is dependent on the
signal-to-noise ratio and hence on the noise of the readout
electronics. Provided the initial charge is sufficiently large
compared to the electronic noise then such an amplification is not
essential, and the contribution of the tunnel noise to the overall
resolution can be reduced. Naturally, this requirement affects the
basic design of the STJ and, depending on the materials used, its
operating temperature. For these reasons we show the limiting
resolution in Fig. 1 (click here) as a band ranging from
to
, for the case
.
Effects of the quasiparticle lifetime and the role of
various recombination mechanisms were considered by Perryman, et al.
(1993). For a typical device with a film
thickness of 100 nm, i.e. a film volume
, the number
of thermal quasiparticles can be written:
where N(0) is the single spin electronic density of states at the
Fermi energy. From Eq. (3) a photon of
wavelength 500 nm will produce an initial number of quasiparticles
of order
,
and
for Nb, Al and Hf
respectively. Combining Eqs. (3) and (6):
It is reasonable to require that the thermal population is
at least an order of magnitude lower than . This means
that, in the absence of additional barrier leakage mechanisms (thermal
regime), the
operating temperature T has to be less than
,
and
for
Nb, Al and Hf respectively (i.e.
, 170 or 30 mK) to detect
500 nm photons. In the event of multiple tunnelling, these
requirements may be somewhat modified.