Theoretically the tantalum STJ has a remarkable efficiency to the absorption of photons ranging in wavelength from the ultraviolet to the near infrared. Currently an actual experimental measurement with a calibrated light source is experimentally not possible. Indirect methods can however be used to verify the theoretical data. Figure 5 (click here) (inset) illustrates schematically the principal sources of photon loss.
Figure 5: The theoretical quantum efficiency and reflectivity for the current
tantalum based STJ. The total reflectivity of both the vacuum-sapphire
and sapphire- tantalum 
) interfaces are included in the overall
reflectivity which includes multiple reflections, while in addition the
attenuation in the sapphire 
is included in the estimate of the
quantum efficiency. The 92 nm thick base tantalum film transmits 
) only
at a peak wavelength of 600 nm of all photons not reflected at this
interface. The inset illustrates the optical configuration where the quantum
efficiency is simply defined as 
. Here the
reflectivity and attenuation takes into account the case of multiple
reflections between the sapphire and tantalum interfaces and the associated
attenuation of the light in the sapphire
For 
nm the most significant factor effecting the detector quantum
efficiency is the reflection of photons from the vacuum - sapphire
and sapphire-tantalum )
interfaces in the back-illuminated mode.
Figure 5 (click here) shows the total reflectivity resulting from reflections,
including multiple reflections, at both these interfaces. These data are
based on the optical constants for Sapphire and Tantalum from
Palik
(1985) and Weaver et al. (1981).
Between 
nm the
reflectivity is always 
. The reflectivity of the sapphire substrate
as well as the substrate to tantalum interface can of-course be reduced
through the use of anti-reflection coatings, albeit at the expense on
bandwidth. The absorption 
) of the photon flux through the 0.5 mm
thick R-plane sapphire is dramatic at short wavelengths 
nm)
while the reflectivity of the tantalum film ) increases
significantly at the long wavelengths 
nm). These effects
therefore limit the overall quantum efficiency of the device. It can be
seen from Fig. 5 (click here) that the actual photon flux entering the thin epitaxial
tantalum film (thickness 
nm) is above 50% from nm.
Nearly all the photons entering the base epitaxial tantalum film will be
absorbed. To demonstrate this the transmission through a 0.5 mm thick
sapphire substrate covered by a 92 nm thick tantalum epitaxial film has
been measured at 300 K and is shown in Fig. 6 (click here) together with the
theoretical transmission based on the optical constants of Weaver et al.
(1981). Some deviation exists probably due to the fact that the optical
constants are derived for strain and oxide free bulk tantalum samples,
while the experimental data is derived for an epitaxial thin film known
to be coated with a few nanometers 
nm) of native tantalum oxide and
sub-oxides. Even with this uncertainty the measured peak transmission is
only at 
nm. Also this small number of photons is not totally
lost but rather are absorbed in the top polycrystalline film of the STJ
thereby still contributing to the overall response.
Figure 6: The measured transmission (+) through a sample of 0.5 mm thick
sapphire substrate coated with a 92 nm epitaxial tantalum film similar to
the base film of the current STJ. For comparison the theoretical
transmission for a 92 nm film deposited on a sapphire substrate is also
shown
Figure 7: The theoretical quantum efficiency and reflectivity for the current
tantalum based STJ if deposited on a substrate of magnesium fluoride. The
reflectivity of both the vacuum
and 
- tantalum interfaces are
included in the overall reflectivity together with any multiple reflections,
while in addition the overall attenuation in the MgF2 is included in the
estimate of the quantum efficiency
While a quantum efficiency predicted theoretically to be over 50% from
nm, peaking at 
at (peak 
nm, is more than
adequate for ground-based astronomical applications, the UV response is
inadequate due to the cut-off of the sapphire substrate below 
nm. An
alternative for a space based telescope taking advantage of the UV
response, would be to replace the sapphire substrate with one of
magnesium fluoride. Figure 7 (click here) illustrates the system reflectivity (vacuum -
and - Tantalum including multiple reflections) together with
the predicted quantum efficiency assuming a 0.5 mm thick
substrate.
The short wavelength response has now been extended down to the cut-off of
the (
nm) while the long wavelength optical response is largely
unchanged. As yet no devices have been fabricated on although
initial depositions of epitaxial tantalum films have been successful.
Any application of a superconducting tunnel junction for optical astronomy
must also consider the effect of infrared background radiation. For
wavelengths greater than a few microns the infrared flux from room
temperature components could be considerable. These photons can still
break Cooper pairs effectively increasing the thermal current in the
device. This is equivalent to raising the operating temperature of the
device. Naturally this flux can be reduced in any practical application
through careful optical design. The current device does however have a
significant intrinsic infrared rejection capability through the reflection
properties of the sapphire and tantalum. Figure 8 (click here) illustrates the measured
reflectivity 
of a sample (sapphire 
mm
thick plus a 92 nm thick
tantalum film) at 300 K as a function of wavelength. The theoretical
reflectivity 
is also shown highlighting the decreased
reflectivity
between 5 and 12 
m, although this is also accompanied by an increased
absorption. The measured reflectivity also shows such a window
which, although it reaches close to 100% for 
, is significantly
lower than calculated at 
and 
). For
comparison the normalised photon flux from a blackbody at 20 C is also
shown [BB(20C)]. The total efficiency 
to infrared photon detection
is also shown in Fig. 8 (click here). This efficiency contains the reflection from both
the sapphire and tantalum interfaces (including multiple reflections) as
well as absorption in the sapphire. Convolving the overall IR rejection
efficiency with the 20 C blackbody photon spectrum between 
indicates that 
of this blackbody radiation will enter the tantalum
STJ. The situation is however not quite so favourable for
substrates.
Figure 8: The infrared reflectivity 
(+) as measured with an IR
reflectometer of a representative sapphire plus 92 nm tantalum film as a
function of wavelength. For illustrative purposes the photon flux from a
blackbody at 20 C [BB(20C)] normalised such that the photon number spectral
integral equals one is also shown, together with the theoretical
reflectivity 
and overall infrared detection efficiency . The
convolution of the rejection efficiency 
with the photon flux from the
blackbody [BB(20C)] is also shown 
*BB]