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“A normal-incidence PtSi photoemissive detector with Black Silicon light-trapping”
Martin Steglich1, Matthias Zilk1, Astrid Bingel1,2, Christian Patzig3, Thomas Käsebier1, Frank
Schrempel1, Ernst-Bernhard Kley1,2 and Andreas Tünnermann1,2
1
Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University, Jena (Germany)
Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Jena (Germany)
3
Fraunhofer Institute for Mechanics of Materials IWM, Halle (Germany)
2
In our paper “A normal-incidence PtSi photoemissive detector with Black Silicon light-trapping” we
describe the beneficial effects of Black Silicon (b-Si) light-trapping on the absorptance of thin rear
PtSi layers with regard to an application in Schottky Barrier Photodiodes.
In this contribution, we also estimate the additional benefit by applying a SiO2/Al rear mirror to a
Si/PtSi device with PtSi thickness of 2.8 nm. Here, the underlying approximations and calculations are
presented in more detail.
The basic idea is that an additional SiO2/Al rear mirror yields an increased light absorptance in the
PtSi through reflecting the transmitted light T. The measured transmittance T is displayed in Figure 1.
Figure 1. Measured transmittance of sample with 2.8 nm PtSi with Black Silicon light-trapping.
Illumination is from the nanostructured b-Si side of the sample.
In order to estimate the rear mirror effect, additional measurements were conducted, in which the
sample was flipped; such that illumination is from the polished, PtSi coated sample side (Figure 2).
These spectra will be denoted with the superscript * in the following.
With help of the additional spectra A* and R*, the rear mirror benefit can be estimated under two
approximations.
Firstly, we assume that the transmitted light T propagates perpendicular to the sample, which means
that scattered transmission is neglected. This is reasonable since the large refractive index contrast
between PtSi and air (or SiO2, respectively) widely prevents the escape of light scattered into high
angles of propagation through strong internal reflection or even total internal reflection. Secondly,
interface reflectance and transmittance of the PtSi/SiO2 interface is assumed to be nearly equal to that
of the PtSi/air interface, which also stems from the comparably large refractive index of PtSi.
With these approximations, the rear mirror effect can be calculated with a rather simple round-trip
model (Figure 3). The transmitted part of light T that leaves the sample upon illumination from the bSi side hits the rear mirror at an angle of incidence of 0°. Given that Al exhibits a reflectance of RAl,
T∙RAl will be reflected at the rear mirror. Hitting the sample from the rear again, T∙RAl∙T* (with T*
being the measured transmittance upon illumination from the rear) will be transmitted and T∙RAl∙R*
will be reflected towards the mirror again. The latter part will undergo equivalent round-trips until the
light in the rear cavity is completely lost either in transmission or absorption.
Figure 2. Measured optical spectra of the same sample like in Figure 1 (2.8 nm PtSi, with b-Si
light-trapping), where light incidence is from the polished, PtSi coated sample side.
Figure 3. Schematic depiction of the optical cavity formed by the PtSi coated sample with b-Si
nanostructure and the rear mirror. The system is treated within a round-trip model. The
subsequent round-trips displayed from top to bottom.
Then, the additional absorptance Aadd can be written as:
2
3
Aadd  T  R Al  (1  R * T *)  T  R Al
 R * (1  R * T *)  T  R Al
 R *2 (1  R * T *)  
With (1-R*-T*)=A* this gives:
.

Aadd  T  R Al  A *  R * R Al .
n 0
Since R*∙RAl is a positive number smaller than 1, the last term can be calculated as a geometrical sum:
Aadd 
T  R Al  A *
 f reabs  T ,
1  R * R Al
where fre-abs is the fraction of the transmittance T that is re-absorbed through the application of a
SiO2/Al rear mirror.
Figure 4 shows the resulting fractions of re-absorption for an ideal mirror with RAl = 1 and a real
mirror with RAl = 0.975. Like expected, the real mirror yields a slightly lower fre-abs due to its
incomplete reflectance. Both curves decrease with increasing wavelength because of the slowly
decreasing absorptance A*.
For the estimation in our publication “A normal-incidence PtSi photoemissive detector with Black
Silicon light-trapping”, the curve for the real mirror has been used.
Figure 4. Estimated fraction of re-absorbed transmittance upon application of a rear mirror.
Curves for an ideal mirror with RAl = 1 and a real mirror with RAl = 0.975 are displayed.