Introduction

Transparent electrodes (TE) are important for many optoelectronic devices including solar cells, detectors, touch screens, displays, and smart windows. A large group of well-investigated TE materials are transparent conductive oxides (TCOs), which are heavily doped wide bandgap semiconductors. Indium tin oxide (ITO), as the most widely used TCO, has high optical transparency within the visible light range [1]. However, ITO films become highly reflective above 1.5 μm due to its plasma frequency in the near infrared (IR) [2] (similar to other TCOs), which makes it impractical for mid-IR optoelectronic applications. In addition, the deposition of ITO films can be complicated and usually requires post deposition treatment [3]. Mid-IR optoelectronic devices operating in the 1.5-10 μm range offer a broad range of functionality for a variety of applications such as free space optical communication (using atmospheric transmission windows at 1.5-1.8 μm and at 3-5 μm), environmental gas monitoring, thermal imaging and IR countermeasures, and many others. Alternative options for mid-IR TE materials include carbon nanotube (CNT) films [4,5], ultrathin metal films [3], graphene films [6], metal nanostructures in the form of metal nanogrids/ nanowires/ nanofibers [7,8], and highly conductive polymers [9]. CNT films exhibit significant transparency (over 80%) over the IR range (1-22μm). However, the resistivity of CNT is relatively high, at around 200 Ω/□ [5]. Ultrathin metal films have an extremely sensitive dependence on thickness in terms of the tradeoff between transmittance and resistivity. For example, in the IR range (2.5-25 μm), a 2 nm Ni film has a mean transmittance above 80% but a resistivity of around 1000 Ω/□; while a 10 nm Ni film has a resistivity at 30 Ω/□ but its mean transmittance falls to 40% [3]. In addition, according to the growth stages of thin metal films, a continuous metal film will not form until the thickness is above 20 nm; irregular metal islands only begin to touch each other at a thickness around 10 nm [10]. Metal nanostructures could achieve high transparency as well as good electrical properties. However, the process of building metal grids or meshes remains complicated and expensive [7,8]. Graphene and conductive polymers offer ideal mechanical properties for flexible electronics, but both the transparency and conductivity of these TEs are inferior to most of the aforementioned technologies [6,8].

There has been significant interest in the use of highly doped semiconductors for mid-IR optoelectronic applications. Recent works have shown that at mid-IR frequencies, highly doped semiconductors can act as epsilon-near-zero materials, or are able to support localized surface plasmon modes [11,12]. Previously, we have demonstrated InGaBiAs as a new material for the mid-IR optoelectronics [13,14]. In this paper, we report degenerately doped InGaBiAs:Si as a novel TE candidate in the mid-IR range. InGaBiAs:Si is able to achieve very high doping concentration as well as good mobility. As a result, InGaBiAs:Si has very high electrical conductivity of up to 4850 S/cm [15]. Although electrical properties of heavily-doped InGaAs:Si and InP:Si have been reported before, optical properties were not included [16,17]. In our own work, InGaBiAs was able to be doped more heavily than InGaAs, and the mobility was significantly higher [15]. Degenerately doped InGaBiAs:Si, exhibits high transparency in the mid-IR region (1.3 −12.5 μm, with the transparency from 1.3 −1.7 μm due to an increased band gap from the Burstein-Moss shift [15,18,19]). The combination of large electrical conductivity and high transparency in the mid-IR region makes InGaBiAs:Si a promising new mid-IR TE material. Another advantage of the InGaBiAs system is that it can be produced as a single crystal and grown under ultra-high vacuum conditions with few impurities and lattice matched to the underlying optoelectronic device.

Experiment

Samples were grown by MBE on double side polished InP:Fe substrates by first depositing a 90 nm In_0.52Ga_0.48As buffer layer followed by a 500 nm In_0.52Ga_0.48Bi_0.016As_0.984:Si film at relatively low growth temperature of approximately 300 °C. The carrier concentrations were controlled by varying the temperature of the Si cell, while the fluxes from the other cells were kept constant. Degenerately doped InGaBiAs:Si films can exhibit very high conductivity (up to 4850 S/cm) for two reasons. First, the doping concentration level can be very high due to the low growth temperature (the sticking coefficient of Si atoms is higher at low growth temperature, and higher carrier concentrations at low-temperatures is well-established in epitaxial growth [16]) and a large density of step edges provided by bismuth as reported previously [15]. Second, a small amount of bismuth can behave as a surfactant, improving the crystalline quality of the film, which keeps the mobility relatively high even at a low growth temperature. More detailed descriptions of growth conditions have been reported previously [13–15]. For comparison, a 300 nm ITO film was deposited by sputtering a commercially available ITO target onto double side polished Si substrates. Previous work has shown that the carrier concentration of ITO can be tuned by adjusting the oxygen flow during the production, but the mobility of ITO remains relatively constant for carrier concentrations between 10¹⁸ and 10²⁰ cm⁻³. In terms of conductivity, the ITO sample we chose has superior electrical performance compared to other ITOs with varied carrier concentrations [20]. While it may be possible to tune the optical properties somewhat by reducing the carrier concentration, the electrical conductivity would necessarily suffer. Transmission spectra in the mid-IR were measured at room temperature using a Thermo-Nicolet Nexus 670 Fourier transform infrared (FTIR) from 5000 to 833 cm⁻¹ (2-12 μm) at a resolution at 4cm⁻¹ with 128 average scans. For the experimental transmission set-up, we used the combination of a KBr beam-splitter and a deuterated triglycine sulfate (DTGS) detector. The data were processed with OMNIC software. Transmission measurements of the thin films were all normalized to a background of open air with the effect from the InP substrate subtracted. Due to the poor sensitivity of the DTGS detector from 1 to 2 μm, the transmission spectra in this range were measured using a Perkin-Elmer Lambda-750 UV-visible-IR spectrophotometer equipped with a Peltier-cooled PbS detector. The reflection spectra were collected using a Bruker IRII infrared microscope coupled to a V80V FTIR spectrometer and normalized to reflection from a flat gold surface. The electrical measurements were carried at room temperature using a custom-built Hall effect system in the Van der Pauw configuration.

Results and discussion

Figures 1(a) and 1(b) show the transmission and reflection spectra as a function of wavelength for InGaBiAs:Si films with different doping concentration levels. The transmittance of ITO is included as a comparison. In Fig. 1(a), data measured by spectrophotometer (1-2 μm) are indicated by dashed lines, by FTIR are shown (above 2 μm) as solid lines and the calculations for the transmittance through a normalization to the substrate are indicated in dashed dot lines. In Fig. 1(b), the directly measured reflectance spectra are indicated by solid lines, and the transmittance spectra calculated from the complex dielectric constant (shown in Fig. 3) extracted from the FTIR fitting parameters (given in Table 1) are noted by dashed lines. In Fig. 1(a), the measured transmission (dashed and solid lines) slightly over 100% is a result of our normalization process, in which our transmission is normalized to a bare InP wafer. Thus, at certain wavelengths, the highly transparent InGaBiAs:Si layers are acting like an anti-reflective coating, improving transmission over the bare InP wafer. Such effects are to be expected when using the substrate transmission as a reference. This method of normalizing the transmission to the substrate is widely used for transparent contacts [3,4,7], but it intrinsically neglects the front surface reflection, and the resulting transmittance is overestimated. One method to directly measure the transmittance requires separating the InGaBiAs:Si film and the InP substrate, but this is highly impractical. Instead, we choose to utilize the experimentally-extracted complex dielectric constant and calculate the amount of light that is transmitted into the InP substrate. This value (dashed line in Fig. 1(b)) is the truest representation of the transparency of the contact for the purposes of an optoelectronic device, and is therefore the transmittance we use for the Figure of Merit (FOM) calculations shown in Table 2 and Fig. 4.

 

Fig. 1 (a) and (b) show the transmittance and reflection spectra of InGaBiAs:Si films and the ITO film as a function of wavelength. The inset shows the carrier concentration of each InGaBiAs:Si sample. In Fig. 1 (a), data measured by spectrophotometer (1-2 μm) are indicated by dashed lines, by FTIR are shown (above 2 μm) as solid lines, and the calculations for the transmittance calculated from FTIR data normalized to the substrate are indicated in dashed dot lines. In Fig. 1 (b), the directly measured reflectance are indicated by solid lines and the transmittance calculated from the complex dielectric constant extracted from the FTIR fitting parameters are noted by dashed lines.

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Table 1. Experimental and fitting parameters for the transmission spectra

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Table 2. Comparison of figure of merit for InGaBiAs:Si and ITO

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Figure 1(a) shows that at the long wavelength end, the transition point where samples start to become highly transparent blue shifts with the increase of the carrier concentration. This transition point is determined by the plasma frequency. For light of frequencies below the plasma frequency, the phase difference between the vibration of the electrons and the oscillation of the electric field in the light wave is 1/4 of the period, and the light will be reflected. For light of frequency above plasma frequency, the free electrons in the material cannot oscillate as fast as the electrical field in the light wave; therefore the material becomes transparent at this wavelength. Figure 1(a) also indicates that at the short wavelength end, the cutoff wavelength of the high transmittance region blue shifts with the increases in the carrier concentration. This is mainly due to the increase in the effective band gap for absorption caused by the so-called Burstein-Moss shift. As the degenerate doping increases, the conduction band is filled with electrons, preventing transitions from the valence band to these filled states [18,19]. This has been discussed in detail in previous work [15]. Previously, we have utilized Burstein-Moss model to fit the band gaps of our doped samples using an In_0.52Ga_0.48As effect mass of m* = 0.041 [15]. However, a more accurate approach requires that the non-parabolicity of the InGaAs conduction band be taken into account. As doping increases and electrons fill higher states in the conduction band, an increase in the electron effective mass is expected. In Fig. 2, we plot the experimental effective band-gap (determined by the absorption coefficient using the so-called Tauc plot method) against the calculated bandgap of our material for two values of m*. As one can see, at low doping concentrations, the experimental data matches closely to the uncorrected m*, as would be expected for electrons near the InGaAs conduction band edge. However, as doping increases, our experimental data fits more closely with the effective bandgap calculated with a larger m*, as would be expected from the effects of non-parobolicity at higher doping levels and thus higher energies in the conduction band. Figure 1(b) shows the reflection spectra from our samples. They remain around 30% for a wide range of mid-IR wavelengths, and exhibit transitions to high values at wavelengths depending on carrier concentrations. The reflection spectra confirm that our samples are not only highly transmitting but also have low losses. As clearly shown in Fig. 1(a), the transmittance of the ITO film falls quickly for wavelengths longer than 1.5 μm, which demonstrates that in terms of transparency, InGaBiAs:Si films are better candidates for mid-IR contact materials than ITO.

 

Fig. 2 Shown above is a plot of the samples’ measured band gaps versus carrier concentration. The dashed and solid curve represent the range of the fitting effective mass m* from 0.041 to 0.062. The dots [15] and open squares (samples we have adopted in the previous discussion) represent the experimentally measured bandgap.

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We calculated the transmission spectra using the Drude model formalism. The complex dielectric constant can be expressed as:

Table 1 lists the electrical properties, the theoretical _{${\omega }_{\text{p}}$} and _$\text{Г}$ calculated from the mobility and carrier concentration (i.e. free electron concentration), and the fitting _{${\omega }_{\text{p}}$} and _$\text{Г}$we used in our calculation.

In Fig. 1(a), the transmission spectra are calculated using a method described here [12]. The fitting results indicate that the simulations match with the experimental spectra very well in terms of both the spectral behavior and the amplitude.

Figures 3(a) and 3(b) exhibit the calculated real component _{${\text{ε}}_{\text{r}}$}and imaginary component _{${\text{ε}}_{\text{i}}$} of the extracted dielectric constants _{$\text{ε}(\omega )$} from Eq. (1). The transition point where the InGaBiAs:Si film becomes highly transparent is indicated by the position where _{${\text{ε}}_{\text{r}}$}becomes negative, as shown in Fig. 3(a). With an increase in the carrier concentration, the transition point blue shifts, as discussed above. This shows the wavelength-flexibility of these materials; the highly transparent spectral region can be adjusted through control of the carrier concentration. Figure 3(b) describes_{${\text{ε}}_{\text{i}}$}, largely related to the radio absorption coefficient, as a function of wavelength. A large _{${\text{ε}}_{\text{i}}$} indicates a small power absorption skin depth. The uncertainty of _{${\text{ε}}_{\text{r}}$} and _{${\text{ε}}_{\text{i}}$} originates from the fact that the transmission data fitting process is an indirect measurement of permittivity, and there is some freedom in choosing the scattering rate in order to get a well-matched fitting.

 

Fig. 3 (a) and (b) exhibit the calculated real component ε_r and the imaginary component ε_i of the extracted dielectric constants ε(ω). The error bars of ε_r and ε_i come from the uncertainty in the fitted scattering rate Γ.

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In order to optimize the electrical and optical coating parameters, researchers have defined an empirically instructive figure of merit (FOM) (T¹⁰/Rs, T is either the average transmittance in the desired wavelength range or at the exact wavelength of interest, and Rs is the sheet resistivity) to compare contacts [22]. It should be noted that the material we studied here is somewhat thicker than typical contact layers, and the FOM can be improved by optimizing the thickness. Due to the potential importance of interference effects, contact layers should be optimized for a particular device's wavelength and contact requirements. Figure 4 compares the FOM and the high transmittance window of InGaBiAs:Si films and the ITO film. The length of each bar represents the high transmittance region (T% > 65%) in wavelength. From Fig. 4, we could conclude that each InGaBiAs:Si sample shown here has a FOM several orders of magnitude larger than ITO, and the transparent region of the InGaBiAs:Si samples extends farther into the IR range than ITO with shifts depending on carrier concentrations. Table 2 lists the sheet resistivity, the average transmission and the FOM for both InGaBiAs:Si and ITO.

 

Fig. 4 Comparison of the transparent windows (transmittance> 65%) of InGaBiAs:Si films and the ITO film as well as FOM. The FOM of ITO is 2.9x10⁻⁷ □/ Ω, very close to zero. It is noted in the figure for clear comparison. In the inset, the numbers by the bars indicate the carrier concentration.

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Conclusion

In conclusion, we have measured, calculated and compared the transmittance of degenerately doped InGaBiAs:Si films with an ITO film. Our films exhibit a clear advantage in terms of transparency at wavelengths above 1.5 μm when compared to ITO film. The high transmittance regions for our films start from 1.3 μm and extend into the mid-IR, with the long-wavelength transmission cut-off depending on the doping levels. InGaBiAs:Si films also have higher conductivity when compared to ITO by degrees varying from 20% to 48% more. In addition, the deposition technique of InGaBiAs:Si films offers the possibility to epitaxially deposit single crystalline, lattice matched samples with fewer impurities on InP-based mid-IR optoelectronic devices, which makes the process much easier and cost-effective. Therefore, InGaBiAs:Si is a potentially ideal candidate for near-IR to mid-IR contact materials.