## Abstract

The spectral reflectance and responsivity of Ge- and InGaAs-photodiodes at (nearly) normal and oblique incidence (45°) were investigated. The derived data allow a calculation of the photodiodes responsivities for any incident angle. The measurements were carried out with *s*-
and *p*-polarized radiation in the wavelength range from 1260 to
$1640\text{\hspace{0.17em} nm}$. The spectral reflectance of the photodiodes was modeled by using the matrix approach developed for thin-film optical assemblies. The comparison between the calculated and measured reflectance shows a difference of less than 2% for the Ge-photodiode. For the InGaAs-photodiode, the differences between measured and calculated reflectance are larger, i.e., up to 6% for wavelengths between 1380 and
$\text{1580 \hspace{0.17em} nm}$. Despite the larger differences between calculated and measured spectral reflectances for the InGaAs-photodiode, the difference between calculated and measured spectral responsivity is even smaller for the InGaAs-photodiode than for the Ge-photodiode, i.e.,
$\le \text{1.2\%}$ for the InGaAs-photodiode compared to
$\le \text{2.2\%}$ for the Ge-photodiode. This is because the difference in responsivity is strongly correlated to the absolute spectral reflectance level, which is much lower for the InGaAs-photodiode. This observation also shows the importance of having small reflectances, i.e.,
appropriate antireflection coatings for the photodiodes. The relative standard uncertainty associated with the modeled spectral responsivity is about 2.2% for the Ge-photodiode and about 1.2% for the InGaAs-photodiode for any incident angle over the whole spectral range measured. The data obtained for the photodiodes allow the calculation of the spectral responsivity of Ge- and InGaAs-trap detectors and the comparison with experimental results.

© 2007 Optical Society of America

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### Equations (15)

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(1)
$$Y=\frac{H}{E}=\frac{C}{B}\text{,}$$
(2)
$$\left[\begin{array}{c}B\\ C\end{array}\right]=\left\{{\displaystyle \prod _{r=1}^{q}\text{\hspace{0.17em}}\left[\begin{array}{cc}\mathrm{cos}\text{\hspace{0.17em}}{\delta}_{r}& \left(i\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\delta}_{r}\right)/{\eta}_{r}\\ i{\eta}_{r}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\delta}_{r}& \mathrm{cos}\text{\hspace{0.17em}}{\delta}_{r}\end{array}\right]}\right\}\left[\begin{array}{c}1\\ {\eta}_{m}\end{array}\right]\text{,}$$
(3)
$${\eta}_{{p}_{r}}=\frac{{N}_{r}}{\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{r}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{for \hspace{0.17em}}p\text{-polorization}\right)\text{,}$$
(4)
$${\eta}_{{s}_{r}}={N}_{r}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{r}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{for \hspace{0.17em}}s\text{-polarization}\right)\text{,}$$
(5)
$${N}_{0}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{0}={N}_{r}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{r}={N}_{m}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{m}\text{.}$$
(6)
$$\rho =\frac{{\eta}_{0}-Y}{{\eta}_{0}+Y}\text{,}$$
(7)
$$R{\left(\lambda ,{\theta}_{0}\right)}_{s\text{,}p}={\left|\rho \right|}^{2}\text{.}$$
(8)
$${n}_{1}{\left(\lambda \right)}_{\text{AR-coating}}={x}_{1}+\frac{{x}_{2}}{{\lambda}^{2}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}$$
(9)
$$\left(\text{for \hspace{0.17em} the \hspace{0.17em} Ge- \hspace{0.17em} and \hspace{0.17em} the \hspace{0.17em} InGaAs-photodiode}\right)\text{,}$$
(10)
$${n}_{2}{\left(\lambda \right)}_{\text{InP:Zn}}={x}_{3}+\frac{{x}_{4}}{{\lambda}^{2}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{for \hspace{0.17em} the \hspace{0.17em} InGaAs-photodiode}\right)\text{,}$$
(11)
$${n}_{4}{\left(\lambda \right)}_{\mathrm{ln}\text{P:S}}={x}_{5}+\frac{{x}_{6}}{{\lambda}^{2}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(\text{for \hspace{0.17em} the \hspace{0.17em} InGaAs-photodiode}\right)\text{,}$$
(12)
$$\sum _{{\lambda}_{\mathrm{min}}}^{{\lambda}_{\mathrm{max}}}\left[{\left[{R}_{s\text{,meas}}\left(\lambda ,\theta \right)-{R}_{s\text{,}\mathrm{mod}}\left(\lambda ,\theta \right)\right]}^{2}+{\left[{R}_{p\text{,meas}}\left(\lambda ,\theta \right)\text{\hspace{1em}}-{R}_{p\text{,}\mathrm{mod}}\left(\lambda ,\theta \right)\right]}^{2}\right]\to \text{minimum}}\text{.$$
(13)
$${S}_{\mathrm{mod}}{\left(\lambda ,\theta \right)}_{s\text{,}p}=\frac{en\lambda}{hc}\u3008{\eta}_{i}\left(\lambda ,\theta \right)\u3009\left(1-{R}_{\mathrm{mod}}{\left(\lambda ,\theta \right)}_{s\text{,}p}\right)\text{,}$$
(14)
$${\eta}_{i}\left(\lambda ,\theta \right)=\frac{hc}{en\lambda}\text{\hspace{0.17em}}{S}_{\text{meas}}{\left(\lambda ,\theta \right)}_{i}\text{\hspace{0.17em}}\frac{1}{\left(1-{R}_{\text{meas}}{\left(\lambda ,\theta \right)}_{i}\right)}\text{,}$$
(15)
$$S{\left(\lambda \right)}_{\text{Trap}}=\frac{en\lambda}{hc}\u3008{\eta}_{i}(\lambda ,\theta )\u3009\left[1-\left(R{\left(\lambda ,45\xb0,s\right)}_{\text{Diode \hspace{0.17em} 1}}^{2}\times R{\left(\lambda ,45\xb0,p\right)}_{\text{Diode \hspace{0.17em}}2}^{2}R{\left(\lambda ,0\right)}_{\text{Diode \hspace{0.17em}}3}\right)\right],$$