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Abstract
We report the terahertz optical properties of vanadium doped (100) β-Ga2O3 using terahertz time-domain spectroscopy (THz-TDS). The V-doped β-Ga2O3 crystal shows strong birefringence in the 0.2-2.4 THz range. Further, phase retardation by the V-doped β-Ga2O3 has been measured over the whole THz range by terahertz time-domain polarimetry (THz-TDP). It is observed that the V-doped β-Ga2O3 crystal behaves both as a quarter waveplate (QWP) at 0.38, 1.08, 1.71, 2.28 THz, and a half waveplate (HWP) at 0.74 and 1.94 THz, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years β-Ga2O3 has been extensively studied due to its material properties such as wideband gap (4.9 eV), high electric field breakdown (8 MV/cm), and good thermal and chemical stability [1,2]. These properties make β-Ga2O3 a promising candidate for many semiconductor devices like Schottky barrier diodes [3], UV photodetectors [4], field-effect transistors [5], etc. In addition to these applications, the high-frequency applications of β-Ga2O3 are also under active investigation, and a proper understanding of material properties at high frequencies is required. Over the last two decades, advances in the generation and detection of Terahertz (THz) radiation enabled researchers to investigate a wide range of material properties in this wavelength range [6]. In particular, Terahertz time-domain spectroscopy (THz-TDS) has evolved into an effective tool for characterizing the optical properties of materials at THz frequencies [7]. It is a non-destructive, contactless technique suitable even for examining highly fragile materials like thin films [8], biological tissues [9], etc. Many semiconductors such as ZnO [10], GaN [11,12], and Graphene [13–15] have been characterized extensively using THz-TDS. However, there are only a few studies on the THz optical properties of the doped and undoped β-Ga2O3 [16–20].
In this work, we used the THz-TDS to report the optical properties of Vanadium doped β-Ga2O3 at THz frequencies. Furthermore, we employed the THz polarimetry (TDP) technique to determine the phase retardation and polarization of the THz wave transmitted through the V-doped β-Ga2O3 crystal. We show that the V-doped β-Ga2O3 behaves as a QWP and an HWP at different THz frequencies. To the best of our knowledge, the Terahertz optical properties of V-doped β-Ga2O3 crystal have never been investigated before.
2. Materials and methods
Single Crystals of (100) oriented Vanadium doped β-Ga2O3 were grown at TIFR using the optical float zone technique [21]. $\beta $-Ga2O3 has a base-centered monoclinic structure with C2/m space group symmetry and the corresponding a, b, c are 12.21Ǻ, 3.03 Ǻ, 5.79 Ǻ respectively, and $\beta $=103.83°. Electrically resistive V-doped β-Ga2O3 single crystals can be grown by carefully tuning the growth parameters. Vanadium atoms generate deep-level states within the gap, resulting in non-radiative recombination pathways [22]. These V-doped crystals have significantly different optical properties compared to the undoped crystal ones, details of which are given in the supplementary information. A cleaved slice of the V-doped β-Ga2O3 crystal was used in this study, with a thickness of ∼0.822 mm. The refractive index of the crystal is in general a complex number and the permittivity of the crystal can be calculated using well-known relations [7]. The permittivity of a crystal is a direct measure of the polarizability of the constituent atomic lattice of the crystal and the electron charge distribution in it under an externally applied electric field. The frequency of this field can be from DC to THz and beyond. The low-symmetry (C2/m) of monoclinic β-Ga2O3 results in strongly anisotropic dielectric permittivity parameters along with different crystal directions [18,19,23]. Thus, it is imperative to study the response of this crystal under different orientations with respect to the incident THz polarization direction. We have extensively studied the effect of polarizability in changing the polarization state of the transmitted THz signal through the crystal.
A THz-TDS setup as shown in Fig. 1 is used for measuring the THz transmission and state of polarization through the V-doped crystal. The setup consists of a femtosecond (fs) pulsed laser (FemtoSource Synergy, 800 nm, 80 MHz, 10 fs) and a standard four-parabolic mirror configuration. The laser beam is divided into a pump and probe beam. The pump beam generates THz radiation using an LT-GaAs-based photoconductive antenna (BATOP GmbH). The probe beam is optically delayed and is used for detection purpose. A 2 mm thick ZnTe crystal with <110 > orientation is used for detecting the generated THz using the standard electro-optic technique. The entire setup is purged with nitrogen to eliminate any unwanted absorption of the THz due to the water vapor present in the ambient air.
Fig. 1. THz-TDS setup. M: Mirror, BS: Beam Splitter, PCA: Photoconducting Antenna, PM: Parabolic Mirror, ITO: Indium Tin Oxide, ZnTe: Zinc Telluride, QWP: Quarter Wave Plate, WP: Wollaston Prism, BPD: Balanced Photo-Detectors.
3. Results and discussion
The V-doped crystal was oriented with the b-axis perpendicular to the incident electric field (θ=0°), and the transmitted THz field was measured. After that, the V-doped crystal was rotated by 90° in the sample plane (b-axis being parallel to the incident electric field) and the transmitted THz field was measured. Figure 2 (a, b) illustrates the transmitted THz electric fields. Figure 2 (a) shows that the transmitted temporal THz field along θ=90° is shifted by 0.62 ps compared to the one along θ=0°, suggesting a strong birefringence in the V-doped Ga2O3 crystal. Furthermore, Fig. 2 (b) illustrates the frequency domain THz spectrum.
Fig. 2. (a) The transmitted time-domain THz electric field along the b-axis of V-doped crystal for θ=0° and θ=90°, (b) Corresponding frequency domain spectra for θ=0° and θ=90°.
The complex refractive index is given as $\tilde{n} = n - i\kappa $,
where d is the thickness of the sample, c is the speed of light in vacuum, ω is the frequency, $\phi (\omega )$ is the phase difference and $\rho (\omega )$ is the transmittance amplitude. Detailed derivation is provided in the supplementary information.The refractive index and extinction coefficient are calculated to get a better insight into the birefringence of the V-doped crystal. The THz time-domain signals are Fourier transformed to obtain the corresponding frequency domain spectra. The complex-valued transfer function is calculated by normalizing the sample spectrum with the reference spectrum which is then used to determine the complex refractive index given by Eq. (1) (detailed derivation is provided in the supplementary information). Figure 3 (a, b) shows the refractive indices and extinction coefficients for θ=0° and θ=90° with respect to the frequency. As seen from the figure two different refractive indices are observed along the two directions suggesting different path lengths. The refractive index along θ=0° and θ=90° at 1 THz is 3.40 ± 0.01 and 3.10 ± 0.01, respectively. The overall contrast in the refractive index across the frequency range is evaluated to be |0.3 ± 0.02|. Table 1 compares the THz optical properties of some of the different wideband semiconductors. As seen from the table the V-doped has the highest birefringence. Moreover, the extinction coefficient is extremely low (order of 10−2) throughout the frequency range, indicating that the V-doped crystal has a minimal loss. The high transmittance and minimal loss make such V-doped $\beta $-Ga2O3 crystals promising candidates for further research into THz frequency applications, especially in the design of polarizing optical elements.
Fig. 3. (a) The refractive index for θ=0° and θ=90°, (b) The corresponding extinction coefficient for θ=0° and θ=90°.
Table 1. Comparison of THz optical properties of different semiconductors.
To map the polarisation of the THz field modified by the V-doped crystal, a THz-Time Domain Polarimetry [25] method is employed. Figure 4(a) shows a simplified schematic of the setup. The incident THz field is parallel to the x-axis. The V-doped crystal is mounted on a motorized rotating stage and is oriented with the b-axis being perpendicular to the electric field. The V-doped crystal is followed by a pair of linear THz wire grid polarisers (Tydex) in a Polarizer-Analyzer configuration. The Polarizer is oriented at an angle ϕ with respect to the x-axis and is mounted on a motorized rotation stage. The Analyzer is fixed and positioned along the x-axis. This technique allows us to precisely determine the phase retardation induced by the V-doped crystal without rotating the ZnTe. When the incident THz field is transmitted through the V-doped crystal, the electric field can be expressed as
Where a, b, and $\delta $ are co-polarisation, cross-polarisation, and phase retardation, respectively. As shown in Fig. 4 (b), the THz field after passing through the V-doped crystal is successively projected along with the Polarizer and Analyzer [24]. The resulting electric field on the ZnTe detector is given asFig. 4. (a) THz TDP setup schematic. (b) Electric field E projections leading to the measured signal S(ϕ). (c) Simulated amplitude S(ϕ), for the co-and cross-linear polarization (CoLP, CLP), circular polarization (CP) and elliptical polarization (b/a).
The polarization parameters are obtained by measuring S ($\phi $) as a function of the polarizer angle $\phi $. If the crystal acts as a QWP, then a = b, $\delta $ = $\pi $/2, and the Eq. (4) will be simplified to $S(\phi )\; = \; a|{cos\phi } |$. However, if the crystal acts as an HWP then for an x-polarised incident electric field, we will have a y-polarised electric field at the output; thus a = 0, $\delta $ = $\pi ,$ and the Eq. (4) will be simplified to $S(\phi )= b/2|{sin2\phi } |$. Furthermore, we will have elliptically polarized light for a ≠ b and $\delta $ = $\pi $/2. All of the preceding cases are demonstrated in Fig. 4 (c).
For each value of θ, a full scan over 360° rotation of the Polarizer is performed (in 10° steps), and the corresponding THz field is measured. Polarization parameters of the THz field transmitted from the V-doped Ga2O3 crystal are obtained by fitting the measured data to Eq. (4). The normalized polar plots for the measured data and corresponding fitting are shown in Fig. 5. As seen from Fig. 5 (a, b), the V-doped crystal behaves as a QWP at 0.38, 1.08, 1.71, and 2.28 THz and as an HWP at 0.74, 1.94 THz for θ = 40° (see Fig. 4 (c) for reference). There is a slight mismatch between the fit and measured data at 1.71 and 2.28 THz due to the presence of water lines at these frequencies. Furthermore, polar plots for θ = 50° are plotted as illustrated in Fig. 5 (c, d), which shows a similar trend at the corresponding frequencies. The transition from left to right-handedness is observed in the transmitted THz wave for the linear polarization case. Correspondingly, a slight right tilt in the circular polarization case is also seen for θ = 50° with respect to θ = 40°. Figure 5 (e, g) illustrates the amplitude ratio and phase retardation profile at θ = 40° and θ = 50°, respectively. The limit for both the phase tolerance and amplitude ratio (b/a) lies within ± 10%. The amplitude ratio and phase retardation values are within the tolerance limit at the frequencies where the V-doped crystal behaves as a QWP and HWP, as shown in Fig. 5 (e, g). In addition to this, a polar plot at 1.4 THz where the elliptical polarisation behaviour dominates is given at both θ = 40° and θ = 50° in Fig. 5 (f).
Fig. 5. Polar map for normalized amplitude S(ϕ) at various THz frequencies. (a, b) 0.38, 0.74, 1.08, 1.71, 1.94, and 2.28 THz for θ = 40°. (c, d) 0.38, 0.74, 1.08, 1.71, 1.94, and 2.28 THz for θ = 50°. (e, g) As a function of frequency, the corresponding fitted polarization parameters are plotted. The black curve represents the amplitude ratio b/a, while the red curve illustrates phase retardation $\mathrm{\delta }/\mathrm{\pi }$. (f) Polar map at 1.40 THz for θ = 40° and θ = 50°.
Figure 6 (a, b) illustrates the calculated co- and cross-polarization parameters as a function of azimuthal angle with respect to frequency. Figure 6 shows that the co- and cross-polarization parameters follow a complementary pattern across the frequency range, i.e., when co-polarization is maximum, cross-polarization is minimum, and vice versa. The crystal behaves as an HWP at 0.74 and 1.94 THz, where the co-polarization is minimum and cross-polarization is maximum. Moreover, the QWP type behaviour is seen at 0.38, 1.08, 1.71, and 2.28 THz when the co and cross-polarization are equal, and the phase retardation is $\delta $=$\pi $ /2 as seen previously. For further investigating the polarization state of the transmitted THz wave, we calculated the polarization orientation angle ψ and ellipticity angle χ using the Stokes parameters.
WhereFig. 6. (a, b) Experimental co- and cross-polarization parameter as a function of azimuthal angle with respect to the frequency, respectively.
And
Figure 7 (a) shows the ellipticity ($\chi $) as a function of frequency, as the azimuth angle is varied over 90°. For certain azimuth angles (θ=45°), the V-doped crystal acts as a QWP at 0.38, 1.08, 1.71, and 2.28 THz. Furthermore, in between these frequencies, a linear polarization state is also observed at 0.74 and 1.94 THz, where it behaves as a half-wave plate. Figure 7 (b) shows the evolution of the orientation angle ($\Psi $) as a function of frequency, as the azimuth angle is varied over 90°. Here, the transition from left-hand polarization to right-hand polarization of the transmitted THz field is clearly visible, which is consistent with the previous findings (see Fig. 5 (a, b, c and d)) [25–27].
Fig. 7. (a) Ellipticity ($\mathrm{\chi }$) as a function of azimuthal angle with respect to the frequency. (b) Orientation angle ($\mathrm{\Psi }$) as a function of azimuthal angle with respect to the frequency.
4. Conclusion
In conclusion, we report the first Terahertz optical study on V-doped β-Ga2O3 using the THz-TDS technique. It was observed that V-doped β-Ga2O3 has significant THz transmission and shows a strong birefringence in the 0.2-2.4 THz range. In addition, a THz polarimetry technique was used to accurately determine the phase retardation and polarization of the transmitted THz field through the V-doped β-Ga2O3 crystal. The V-doped β-Ga2O3 crystal behaves as a QWP at 0.38, 1.08, 1.71, and 2.28 THz, while an HWP type behavior is observed between these frequencies at 0.74 and 1.94 THz, respectively. Due to its high transmission and low losses, V-doped β-Ga2O3 opens up new possibilities for developing THz QWP, HWP, segmented waveplates, etc., and new opportunities for device integration requiring intrinsic polarisation control of THz light.
Funding
Department of Atomic Energy (DAE) and Tata Institute of Fundamental Research (TIFR), Mumbai (RTI4003).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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