- Nano Express
- Open Access
Dispersion of Phonon Surface Polaritons in ZnGeP_{2}: Anisotropy and Temperature Impacts
- K. V. Shportko^{1}Email author,
- A. Otto^{2} and
- E. F. Venger^{1}
- Received: 30 November 2015
- Accepted: 20 January 2016
- Published: 9 February 2016
Abstract
Zinc germanium diphosphide (ZnGeP_{2}) is an attractive and promising functional material for different devices of the nano- and optoelectronics. In this paper, dispersion of phonon surface polaritons (PSPs) in ZnGeP_{2} has been studied in the 200–500-cm^{−1} spectral range at 4 and 300 K. Dispersion of “real” and “virtual” PSPs were calculated for C-axis being normal and parallel to the surface. Anisotropy in ZnGeP_{2} leads to the different numbers of PSP dispersion branches for different orientations of the sample. The temperature-dependent phonon contributions in the dielectric permittivity shift dispersion of the surface polaritons in ZnGeP_{2} to the higher wavenumbers at 4 K. We have shown that experimental dispersion of PSP is in agreement with theory.
Keywords
- Single crystal
- Phonon
- Surface polariton
- Anisotropy
- Low temperature
Background
In this study, we report on the impact of anisotropy and low temperature on the dispersion of surface polaritons in zinc germanium diphosphide (ZnGeP_{2}), which is a promising material for the nano- and optoelectronics.
Introduction
Among other ternary A^{II}B^{IV}C^{V} _{2} compounds, ZnGeP_{2} stands out for its properties, such as great values of the coefficients of the nonlinear susceptibility and birefringence, which attract interest of researches.
Mechanical stability, resistance to moisture, aggressive environments, and good thermal conductivity characterize ZnGeP_{2} as an attractive and promising functional material for different devices of the nano- and optoelectronics. In [1], it has been discussed that diphosphides can be used in infrared converter systems. Experimental results of [2] prove that replacing CdTe by diphosphides can increase efficiency of the solar converters and simplify their mass deployment.
Therefore, the study of optical properties of ZnGeP_{2} is crucial for industrial applications of this material.
In the previous paper [3], we have reported on the lattice vibration behaviors of ZnGeP_{2} single crystals derived from the far-infrared (FIR) reflectance spectra in the temperature range of 4–300 K. From [3], one can notice that optical phonon behaviors in ZnGeP_{2} at low temperatures are similar to those in other diphosphides [4, 5]. These results show that surface polaritons in ZnGeP_{2} can be excited in the number of spectral ranges. However, for ZnGeP_{2}, the surface polaritons practically have not been studied yet. Results of [6] have shown that temperature has an impact on the dispersion of surface phonon polaritons in binary diphosphide Zn_{3}P_{2}.
Here, we present the results of our study of the dispersion of the surface polaritons in ZnGeP_{2} at different temperatures.
Methods
In the experiments, a set of samples of single crystals of ZnGeP_{2} cut into plates of size 2 × 4 × 0.5 mm was used. The samples of ZnGeP_{2} were oriented to (001) and (100) crystallographic planes. The orientation of the crystallographic planes was controlled by X-ray diffraction.
As an input data for the calculations of the dispersion of phonon surface polariton (PSP), we used reflectance data of ZnGeP_{2} from our study [3]. These spectra were measured at 300 K in the 200–500-cm^{−1} range, using a Bruker IFS 66v/s spectrometer with Hg lamp as the source of radiation with a resolution of 0.5 cm^{−1}, 256 scans per 20 s employing polarized radiation were collected in each experiment. The temperature of sample varied in the 4–300-K temperature range. The angle of incidence of radiation was less than 10°. Spectra were measured at two orientations of the electrical vector E of the IR radiation with respect to the crystal: E||c and E˩c.
The method of attenuated total reflection (ATR) was firstly used for the excitation of surface waves in metals [7]. Since general principles of excitation of PSP by ATR have been described in [8], this method remains the easiest and the most reliable for excitation of surface polaritons.
We obtained the ATR spectra of PSP for ZnGeP_{2} in the 300–500-cm^{−1} frequency range using polarized radiation. To measure these data, we used FTIR spectrometer Bruker IFS 66 with accessory with grazing angle of the incidence equipped by Ge hemisphere as ATR element. The air gap between the investigated sample and the hemisphere varied from 1.5 to 2 μ.
Results and Discussion
Input data for ZnGeP_{2}
B _{2} modes | ||||||||
4 K | 300 K | |||||||
ε _{∞} | 10.68 | ε _{∞} | 10.04 | |||||
ν _{ L }, cm^{−1} | γ _{ L }, cm^{−1} | ν _{ T }, cm^{−1} | γ _{ T }, cm^{−1} | ν _{ L }, cm^{−1} | γ _{ L }, cm^{−1} | ν _{ T }, cm^{−1} | γ _{ T }, cm^{−1} | |
1 | 362 | 2.0 | 343 | 1.9 | 361 | 2.1 | 340 | 3.5 |
2 | 412 | 2.2 | 403 | 1.1 | 409 | 2.8 | 400 | 1.8 |
E modes | ||||||||
4 K | 300 K | |||||||
ε _{∞} | 10.05 | ε _{∞} | 10.04 | |||||
ν _{ L }, cm^{−1} | γ _{ L }, cm^{−1} | ν _{ T }, cm^{−1} | γ _{ T }, cm^{−1} | ν _{ L }, cm^{−1} | γ _{ L }, cm^{−1} | ν _{ T }, cm^{−1} | γ _{ T }, cm^{−1} | |
1 | 205 | 12.0 | 205 | 16.0 | 203 | 5.7 | 203 | 6.8 |
2 | 334 | 5.8 | 329 | 3.6 | 332 | 4.8 | 328 | 6.2 |
3 | 378 | 2.4 | 371 | 0.9 | 375 | 2.1 | 368 | 0.7 |
4 | 403 | 1.5 | 388 | 1.1 | 399 | 2.7 | 385 | 1.3 |
Ranges of existence of PSP in ZnGeP_{2}
C||x | C||y | C||z | |
---|---|---|---|
SPP 1 | 4 K | ||
ν = 404 ÷ 406 cm^{−1} | ν = 329 ÷ 332 cm^{−1} | ν = 400 ÷ 403 cm^{−1} | |
ν = 369 ÷ 374 cm^{−1} | |||
ν = 386 ÷ 401 cm^{−1} | |||
300 K | |||
ν = 400 ÷ 403 cm^{−1} | ν = 327 ÷ 331 cm^{−1} | ν = 404 ÷ 406 cm^{−1} | |
ν = 371 ÷ 376 cm^{−1} | |||
ν = 390 ÷ 404 cm^{−1} | |||
SPP 2 | 4 K | ||
ν = 344 ÷ 363 cm^{−1} | ν = 201 ÷ 203 cm^{−1} | ||
ν = 406 ÷ 409 cm^{−1} | ν = 327 ÷ 331 cm^{−1} | ||
ν = 369 ÷ 374 cm^{−1} | |||
ν = 386 ÷ 399 cm^{−1} | |||
300 K | |||
ν = 342 ÷ 360 cm^{−1} | ν = 204 ÷ 205 cm^{−1} | ||
ν = 408 ÷ 412 cm^{−1} | ν = 329 ÷ 333 cm^{−1} | ||
ν = 371 ÷ 377 cm^{−1} | |||
ν = 390 ÷ 403 cm^{−1} |
This dispersion relation involves only ε _{⊥}, and it is of the same form as for PSP dispersion in isotropic media.
- 1.
412 cm^{−1}, 4 K; 409 cm^{−1}, 300 K;
- 2.
362 cm^{−1}, 4 K; 361 cm^{−1}, 300 K.
As already mentioned, for C||y, the dispersion relation is similar to the isotropic case, since only ε _{⊥} is involved in Eq. (2). Therefore, the quantity of dispersion branches is equal to the quantity of the Reststrahlen bands for E˩c. We obtained three dispersion branches of “real” PSP for C||y orientation.
- 1.
203 cm^{−1}, 4 K; 205 cm^{−1}, 300 K;
- 2.
332 cm^{−1}, 4 K; 334 cm^{−1}, 300 K;
- 3.
375 cm^{−1}, 4 K; 378 cm^{−1}, 300 K;
- 4.
399 cm^{−1}, 4 K; 403 cm^{−1}, 300 K.
Due to the temperature shift of the phonon frequencies of ZnGeP_{2} to the higher wave numbers [3], almost all branches of the 4 K dispersion lay above the corresponding branches at 300 K. The temperature-dependent phonon contributions in the dielectric permittivity, which are described by frequency, damping, and strength in frames of Lorentz model [3], affect dispersion of the surface polaritons in ZnGeP_{2}.
As one can notice in Figs. 4, 5, and 6, experimental PSP dispersion at 300 K calculated using Eq. (5) and shown in dots is a good agreement with the corresponding calculated dispersion branches. This agreement serves as a confirmation of 4 K PSP dispersion branches in ZnGeP_{2} which were calculated in the same manner.
Conclusions
Thus, in this paper, dispersion of PSP in ZnGeP_{2} has been studied in the 200–500-cm^{−1} spectral range at 4 and 300 K. Dispersion of “real” and “virtual” PSP were calculated for C-axis being normal and parallel to the surface. Anisotropy in ZnGeP_{2} leads to the different numbers of PSP dispersion branches for different orientations of the sample. The temperature-dependent phonon contributions in the dielectric permittivity shift dispersion of the surface polaritons in ZnGeP_{2} to the higher wave numbers at 4 K. Experimental dispersion of PSP is in agreement with theory.
Declarations
Acknowledgements
One of the authors (KS) gratefully acknowledges the support from the DAAD (German Academic Exchange Service).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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