"Study of Indium Tin Oxide (ITO) for Novel Optoelectronic Devices"
Ph.D. thesis by Shabbir A Bashar

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.

6.3.1 Spectral Properties of Relevant Materials

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:

Material Doping Concentration
Minority Carrier
Diff. Length [mm]
n - GaAs 2e16 (ND) 1.8 (hole) [217]
n+ - GaAs 2e18 (ND) 1.2 (hole) [217]
p+ - GaAs 1e19 (NA) 2.5 (electron) [218]
n - Al0.27Ga0.73As 1e17 (ND) 0.3 (hole) [219,220]
n - InP 3e17 (ND) 0.24 (hole) [221,222]
n - In0.53Ga0.47As 2e16 (ND) 0.4 (hole) [223,224]
p+ - In0.53Ga0.47As 1 - 4e19 (NA) 0.4 - 4.0 (electron) [223,225,226]

Table 6.28: Minority Carrier Diffusion Lengths of Various Materials.

The doping densities in the above table have been chosen to represent the actual layers in the detector devices as closely as possible. Wherever data for exact specification was not found, the closest value with respect to doping concentration or in case of ternary materials the percentage composition was selected.

It should be noted that the minority carrier diffusivity is much more difficult to determine than the majority-carrier mobility [227]. Workers often extrapolate majority carrier mobility values to minority carrier values at the same doping level. For example to estimate the minority electron mobility at doping level NA, one uses the electron mobility in n-type material at doping density ND.

6.3.2 Spectral Response Model for a Monolayer Detector

As discussed earlier in Chapter 2, a semiconductor photo detector is capable of detecting only radiation with photon energy, hn, greater than the bandgap, Wg, of the device material. If however, hn is much greater than Wg, then the absorption will take place entirely near the surface. This is because as the photon energy increases, their penetration depth decreases. Hence, the electron hole pairs created by absorbing the high energy photons near the surface of the detecting device (i.e., away from the junction or the adjacent diffusion fields) will recombine with majority carriers before diffusing into the depletion layer. This event does not contribute to the current flow and is not detectable.

Assuming the basic principles of optical detection are applicable, photo generation takes place where incident photons with super bandgap energies create electron-hope pairs; however, for these photo generated pairs to give rise to an external current, they must be collected before recombination leads to their annihilation. This can only occur if the photo generation takes place within the absorption volume which consists of the depletion region and the two diffusion regions on either side of it. As Table 6.28 demonstrates, the materials involved in this study, AlGaAs, GaAs, InP and InGaAs all have a diffusion length typically in the region of a few micrometers while the devices have active layers which have thicknesses usually a fraction of or smaller than these values. This means that in all cases the photo generation takes place within the absorption volume, hence justifying the assumption of a 100% collection efficiency. Let us consider one of the layers of the photo transistor, layer 2, bounded at 'A' by layer 1 and at 'B' by layer 3 as shown in Figure 6.51 below:

Figure 6.51: Schematic of optical flux propagation, absorption and reflection for a multilayered semiconductor device

Each of these layers is assumed to have homogenous material properties and constant doping concentration. Thus the flux absorbed as a function of the wavelength, l, for layer 2, Fabs2(l), can be expressed as:

Fabs2(l) = [F1(l) - FRef1(l)] x {exp-[aa2(l)] - exp-[ba2(l)]} (eqn. 6.17)

F1 = the incident flux from layer 1 at the layer1/layer 2 interface
a2 = the absorption coefficient of layer 2
a = the distance of the first boundary of layer 2 from the air/ITO interface
b = the distance of the second boundary of layer 2 from the air/ITO interface
Fref1 = the reflected flux from layer 1 at the layer1/layer 2 interface; this is given by

Fref1(l) = [(n2 - n1)/(n2 + n1)]2 (eqn. 6.18)

n1 = refractive index of layer 1 at a given l
n2 = refractive index of layer 2 at a given l

In the case of layer 1, here being the ITO contact, the incident flux is calculated from the measured transmission spectrum of the ITO layer and the two reflections at the air/ITO and ITO/cap interfaces.

Thus, for a given device made of a homogeneous material (e.g. GaAs), the thickness required to absorb a given fraction of the incident light increases sharply as its absorption co-efficient, a, drops (or as the penetration depth increases). As shown earlier in Figure 6.50, for most direct bandgap semiconductors, the absorption co-efficient sharply drops near the band edge. The effect of a change in a is clearly demonstrated in Figure 6.52 by plotting the fraction of the incident light absorbed vs. absorption layer thickness (difference between 'b' and 'a') using (eqn. 6.17) for three different values of the absorption coefficient.

Figure 6.52: Calculated effect of absorption thickness on the amount of light absorbed for different values of absorption co-efficients

Conversely, as the energy of the incident photons approaches the band edge of the semiconductor material, thicker and thicker absorption layers are required in order to produce a given number of photo generated electron hole pairs. Taking these factors into account, it follows that for a given material system at a given wavelength the response is greater for the structure which has the thicker absorption region. Figure 6.53 shows the simulated effect of altering only the absorption thickness on the spectral response of a photo detector.

Figure 6.53: Calculated effect of absorption layer thickness on the spectral response for a monolayer detector

It is seen from Figure 6.53 that not only is the overall peak of the response reduced as a result of having a thinner absorption layer, but there is also a distinct shift in its shape. Reducing the thickness by an order of magnitude shifts the peak to a lower wavelength corresponding to a higher energy. This is because for a thinner absorption layer, only the photons with high energy (or for which the material has higher absorption co-efficients) have the optimum match between the (low) penetration depth and the absorption thickness. Therefore there is a fundamental influence on the spectral response of a photo detecting device purely arising its geometrical dimensions. Hence, this model is able to exploit yet another design parameter for such a device to optimise and tailor its response according to specific requirements.

6.3.3 Spectral Response of an ITO/n-GaAs Schottky Diode

In order to demonstrate the model, the measured and simulated spectral responses of an ITO/n-GaAs Schottky photo diode will now be presented. This device is so chosen as it consists of a single material (n-GaAs) absorption layer. The structure of the device is the same as those presented earlier in section 6.1.2.

Figure 6.54 below shows the measured and simulated results of the spectral response of such an ITO/n-GaAs Schottky diode:

Figure 6.54: Comparison between measured and simulated Spectral Response of an ITO/n- GaAs Schottky Diode

This device is represented by modifying (eqn. 6.17) and using the basic principles to determine the amount of actual absorption in the active layer of the photo diode. Therefore, the responsivity, R as a function of the wavelength, l for the Schottky diode is given by:

R(l) = Fo(l) x [1 - R1(l)] x TITO (l) x (1-R2(l)) x Fabs(l) (eqn. 6.19)

where, at a given wavelength,
Fo = the flux incident at the air/ITO surface
R1 = reflection caused at the air/ITO interface
TITO = transmission of ITO
R2 = reflection caused at the ITO/GaAs interface
Fabs = flux absorbed in the semiconductor active layer (calculated using
(eqn. 6.17))

The spectral response, Sl, can thus be found by integrating over the entire operational wavelength range:

Sl = R(l)dl (eqn. 6.20)

6.3.4 Spectral Response of a HPT with ITO Emitter Contact

For the HPT the generic equation (eqn. 6.20) is used for each layer in succession with the appropriate values of a, n and the layer thickness to determine the theoretical absorption; in order to calculate the absorption in each layer, any reflection and absorption in previous interfaces and layers is thus accounted for. Subsequently, the device responsivity at a particular wavelength is given by:

RHPT(l) = Fcap(l) + Femitter(l) + Fcollector(l) + b[Fbase(l) + Fcollector(l)] (eqn. 6.21)

Fcap, Femitter, Fbase and Fcollector are the respective fluxes absorbed in the (n+-GaAs or n+- InGaAs) cap layer, the (n-AlGaAs or n-InP) emitter, the (p+-GaAs or p+-InGaAs) base and the (n-GaAs or n-InGaAs) collector at a given wavelength, while b is the common emitter current gain of the transistor.

Hence, the spectral response, Sl, is found by integrating (eqn. 6.21) over the entire operational wavelength range:

Sl = RHPT(l)dl (eqn. 6.22)

The simulated and measured spectral responses of the AlGaAs/GaAs (wafer no. 1-1408) HPTs are shown in Figure 6.55. The corresponding plot for the InP/InGaAs (wafer no. 3-089) devices was shown in section (see Figure 6.46).

Figure 6.55: Measured and simulated spectral response, Sl, for AlGaAs/GaAs HPT devices with ITO emitter contact (VCE = 2V)

Some of the apparent mismatch between the simulation and the measured data is due to the uncertainties in the literature, the lack of absolute device layer dimensions and non-linear effects of the monochromator around 800nm (for the AlGaAs/GaAs case) and the atmospheric absorption around 1400nm (for InP/InGaAs devices) as discussed in section

1998: Shabbir A. Bashar (in accordance with paragraph 8.2d, University of London Regulations for the Degrees of M.Phil. and Ph.D., October 1997). The Copyright of this thesis rests with the author, and no quotation from it or information derived from it may be published without the prior written consent of the author.
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