6.3 Spectral Response of Photodetectors
In photo detectors the efficiency as a function of wavelength l strongly depends on the absorption coefficient a(l) [210]. The struggle to improve individual devices as well as integrate a number of functions on a single chip has led to a need to better understand the associated material properties. Therefore, accurate values of the refractive index, n, and the absorption coefficient of the materials used in the device structure are needed for proper device tailoring. A knowledge of these properties and their variation with material composition and wavelength is fundamental to the understanding of almost any conceivable travelling wave device [211].
Since the optical properties of materials vary according to their composition, only the systems with demonstrated importance in optoelectronics and device performance i.e. technological relevance will be considered. In the case of AlGaAs/GaAs HBTs, the preferred system consists of 27% Al and 73% Ga in the high bandgap Al0.27Ga0.73As emitter which is lattice matched to the underlying GaAs base. On the other hand, InP/In0.53Ga0.47As HBTs are usually grown on Fe doped InP substrates. Hence, the collector and base materials have to be lattice matched to InP; the preferred composition in this case is 53% In and 47% Ga in the In0.53Ga0.47As cap, base, collector and sub-collector layers.
In this section the refractive indices of the materials are first presented followed by the respective absorption coefficients. A table showing the minority carrier diffusion lengths in each of these materials is also shown. A model, to simulate the measured spectral response, Sl, based on the principles of light transmission, absorption and reflection in different semiconductor materials is presented for the first time and shown to have extremely good correlation with the experimental data.
Device parameters such as the doping concentrations, the semiconductor layer thickness as
well as the material properties such as the absorption coefficients, a, and the refractive indices,
n, were used from the literature for the purpose of simulation
[212-215]. A 100%
collection efficiency is assumed for any electron-hole pairs photo generated inside the
depletion region or within a diffusion length from it in the bulk material.
Figure 6.49 shows a plot of the experimentally measured refractive
indices vs. wavelength for GaAs, AlGaAs, InP and InGaAs materials; the relevant data was
obtained from the literature. It is clearly seen that for the AlGaAs/GaAs system, the refractive
index for the narrower bandgap material is greater than that of the large bandgap counterpart.
This is property is often used to design solid state optical waveguides, rather like optical fibers,
to confine light inside a narrow bandgap material which is inserted between two layers of large
bandgap material. The same can be noticed for the InP/InGaAs system. Indeed, this property
is often a prime advantage for edge coupled optical detectors such as double heterojunction
phototransistors made from the latter system.
Figure 6.49: A comparison of the refractive indices for various semiconductor materials as a
function of wavelength. (After ref.
[212-215])
The optical data used for GaAs and Al0.27Ga0.73As layers were obtained from the work by
Aspnes et al [216]. 2 to 3 mm thick layers of AlGaAs were grown on Cr doped semi-insulating
GaAs substrates by LPE. This work provides room-temperature pseudo-dielectric and related
optical function data for AlxGa1-xAs alloys for compositions x from 0.00 to 0.80 in steps of
approximately 0.10. Hence, for the data used in the model in the case of GaAs, x is assumed
to be zero and in the case of AlGaAs, x is assumed to be 0.3. The data was measured using an
automatic rotating analyser spectro-ellipsometer. The authors report that the detailed analysis
of similar samples showed that typical differences between actual and target Al compositions
do not exceed 0.03. Furthermore, they conclude that the data are accurate to within 2% of
peak values for x £ 0.5, the region of relevance for this study.
The optical data for InP is obtained from the work by Forouhi et al
[213]. These spectral
functions are deduced by indirect methods: they are determined through measurements of one
or more extrinsic optical parameters which depend on them such as reflectance, transmittance
and phase angle. Typical methods for determining the functions include: Kramers-Kronig
analysis, comparison of measured and theoretical reflectance values, spectroscopic
ellipsiometry and modulation spectroscopy.
Finally, the data for InGaAs lattice matched to InP is based on the table by Adachi
[214] for l £ 0.83 mm and the work by Jenkins et
al [215] for 1.0mm £ l £ 1.7mm. The table by
Adachi relies on high precision pseudo-dielectric function spectra ellipsiometrical
measurements at room temperatures on LPE grown InGaAs materials.
Figure 6.50: A comparison of the absorption co-efficients, a, versus the wavelength for
various semiconductor materials. (After ref.
[212-215])
Figure 6.50 shows the optical absorption co-efficients, a, for GaAs,
AlGaAs, InP and InGaAs materials as a function of wavelength. From these plots, it is
apparent that the absorption drops sharply at the edge of the respective bandgaps of each
of these materials.
In addition to considering the optical properties, it is instructive to consider the electrical
diffusion properties of these materials since almost all photo detection significantly depends on
the diffusion fields in the absorption volumes. These are listed in
Table 6.28:
6.3.1 Spectral Properties of Relevant Materials
