Optical phonon behaviors in ZnGeP2 single crystals from temperature dependent far-infrared reflectance spectra

Vibrational Spectroscopy 80 (2015) 1–5

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Optical phonon behaviors in ZnGeP2 single crystals from temperature dependent far-infrared reflectance spectra K.V. Shportko* V.E Lashkaryov Institute for semiconductor physics of NAS of Ukraine, Nauki av. 41, Kyiv, Ukraine

A R T I C L E I N F O

A B S T R A C T

Article history: Received 6 March 2015 Received in revised form 16 May 2015 Accepted 28 May 2015 Available online 30 May 2015

Lattice vibration behaviors of ZnGeP2 single crystals derived from the far-infrared (FIR) reflectance spectra in the temperature range of 4–300 K are reported in this study. Dielectric permittivity dispersion is obtained for the polarization along the a- and c-axes of a single crystal. Phonon modes are described by the Lorentz oscillator model. Temperature dependence of the parameters of Lorentz oscillator model and their influence on the imaginary dielectric permittivity dispersion is discussed. Optical phonon behaviors are ascribed to thermal expansion of the lattice. ã2015 Elsevier B.V. All rights reserved.

Keywords: Lorentz oscillator Reststrahlen Dielectric permittivity dispersion Low temperatures Single crystal Reflectance

1. Introduction Zinc germanium diphosphide ZnGeP2 belongs to AIIBIVCV2 compounds with great values of the coefficients of the nonlinear susceptibility and birefringence [1]. Good thermal conductivity, mechanical stability, resistance to moisture and aggressive environments [1] make ZnGeP2 attractive and promising functional material for different devices of the optoelectronics. Reliable data for the dielectric properties in the FIR range at different temperatures are crucial for the industrial applications of ZnGeP2. Vibration properties of ZnGeP2 have been investigated in [3–6] at room temperature. In [5], the Raman spectra of ZnGeP2 were discussed. Authors [6] performed Kramers–Kronig analysis of the reflectance spectra of ZnGeP2, obtained dispersion of the dielectric permittivity and refractive index of ZnGeP2 in the IR. Theoretical concepts of the temperature dependence of the phonon selfenergy are discussed in [7]. Results of FIR transmittance measurements of ZnGeP2 at low temperatures were presented in [8]. However, the quality of the fit of experimental data shows some improving potential, so the values of epsilon infinity and parameters of the oscillators used to model phonon contribution slightly differs from [3–6]. The presented in [8] temperature dependences of the strength of oscillators were shown with linear trend line; however, experimental points show rather parabolic

* Tel.: +38 95 3968060; fax: +38 44 463 8994. E-mail address: [email protected] (K.V. Shportko). http://dx.doi.org/10.1016/j.vibspec.2015.05.005 0924-2031/ ã 2015 Elsevier B.V. All rights reserved.

dependence. Moreover, the same dependences in ZnP2 and CdP2 reported in [9,10] are also not linear. The coefficient of thermal expansion of ZnGeP2 is anisotropic and should have a different impact on the dispersion of the dielectric permittivity for E||c and E?c polarizations. The goal of this study is to obtain and explain the temperature dependences of the parameters of the phonon contribution to the dielectric permittivity of ZnGeP2 single crystals in the FIR for the polarization parallel to the a- and c-axes in the wide temperature range. 2. Experimental ZnGeP2 has a chalcopyrite structure with body centered tetragonal unit cell belonging to the space symmetry group I42d ðD12 2d Þ (Fig. 1). The lattice constants are a = 0.5465 nm and c = 1.0771 nm [2]. A set of samples of single crystals of ZnGeP2 cut into plates of size 5  5  1 mm was used for the FIR reflectance measurements. The samples of ZnGeP2 were oriented to (0 0 1) and (1 0 0) crystallographic planes. Samples were polished mechanically. Room temperature reflectance spectra ZnGeP2 single crystals were measured in the 40–550 cm1 range. Temperature dependent reflectance spectra of ZnGeP2 were measured at 4, 10, 50, 100, 200, and 250 K in the 190–550 cm1 range. We used a Bruker IFS 66 v/s spectrometer with Hg lamp as source of radiation and DTGS detector with a resolution of 2 cm1 employing polarized radiation, 256 scans per 20 s were collected in each experiment.

2

K.V. Shportko / Vibrational Spectroscopy 80 (2015) 1–5 Table 1 Parameters used to model the reflectance spectra of ZnGeP2 at 300 K. E||c

e1 = 10.70 e1 = 140 cm1 B2modes Peak

(n), cm-1

(g), cm-1

S

A B C

115.9 342 400

4.75 2.49 2.26

0.13 1.32 0.34

Peak

(n), cm-1

(g), cm-1

S

D E F G H

142 202 327 368.4 386

7 7 5.62 2.05 2.25

0.05 0.12 0.37 0.89 0.67

E||c

e1 = 10.42 e1 = 360 E modes

The polarizer used in our experiments was a grid of metal strips on a window material which was mounted on special holder and was rotated by step motor to obtain different polarization of the IR beam. For each temperature, reflectance spectra have been measured 3 times. The spectrometer was equipped by Cryovac cryostat, which can vary the temperature of the sample in the range 4–300 K. Gold mirror (300 nm thick layer of gold, deposited on glass) with reflectance index of 0.99 in the FIR, used as a reference for reflectance measurements. The angle of incidence of radiation is about 10 and taken into account in the calculation of the reflectance spectra. Reflectance spectra of reference and investigated sample were measured right after another. After

Reflectance

Fig. 1. The unit cell of tetragonal ZnGeP2.

1

H

G

B

C

0.8

0.6

1 2

0.4

F E

0.2

D

A

3 4

0 540

440

340

240

140 40 -1 Wavenumber, cm

Fig. 2. IR reflectance spectra (300 K) of tetragonal ZnGeP2, E||c: 1( ) – experimental, 2 – theoretical spectrum, E?c: 3( ) – experimental, 4 – theoretical spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Reflectance

K.V. Shportko / Vibrational Spectroscopy 80 (2015) 1–5

1

Table 2 Relative temperature shift of the phonon peaks in the reflectance spectra of ZnGeP2.

B

C

0.8

0.6 2 0.4

3

1

0.2

Peak

Dn/DT

B C Average

1.35E–02 1.40E–02 1.38E–02

Peak

Dn/DT

E F G H Average

6.76E–03 5.00E–03 8.14E–03 9.73E–03 7.41E–03

0 450

400

1

350

H

G

300

250

Wavenumber, cm

-1

plasmon contributions:

0.4

Reflectance

Reflectance

500

E

eðnÞ ¼ e1 ðnÞ þ ie2 ðnÞ ! N X Sj n2j n2p ¼ e1 1  þ 2 nðn þ ig p Þ n  n 2  ig j n j¼1 j

0.3

0.8

0.2 213

0.6

203 193 -1 Wavenu mber, cm

F 0.4

3 4

0.2

0 500

450

400

350

300

250

Wavenumber, cm

-1

Fig. 3. Experimental IR reflectance spectra of ZnGeP2, E||c: 1( ) – 300 K, 2( ) – 4 K, E?c: 3 ( ) – 300 K, ( ) – 4 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

division sample’s spectrum by the spectrum of reference final spectrum was obtained. 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. 3. Results and discussion In ZnGeP2 allowed vibrations are distributed into following symmetries: A1 + 2A2 + 3B1 + 4B2 + 7E, B2 and E modes are allowed to be infrared active [11]. B2 modes can be observed employing the radiation polarized parallel to the c-axis, the radiation polarized normal to the c-axis used to detect E modes. Before starting studying the temperature effects, room temperature spectra have been recorded and analyzed. The anisotropy of ZnGeP2 impacts on the reflectance data at room temperature. In the spectra measured for E||c (curve 1,Fig. 2), we observed 3 peaks assigned to B2 modes, marked as A–C, at around 115, 350, and 403 cm1. For E?c polarization reflection, spectrum (curve 3, Fig. 2) shows 5 peaks, marked as D–H, at around 141, 202, 327, 370, and 390 cm1. In the new experimental data, we observe increase of the reflectance below 80 cm1, which we attributed to the contribution of the charge carriers. These data are in a good agreement with results from [3–6]. The analysis of the reflectivity curves was performed by classical dispersion theory. We have used a DrudeLorentz permittivity dispersion model e(n) (for the case of j oscillators), which is presented as a sum of the phonon and

(1)

here e1(n) is the real part of the permittivity, while e2(n) is the imaginary part of the permittivity, nj and g j (np and g p) are the frequency and damping coefficient of the j-th oscillator (plasmon), respectively; Sj is the oscillator strength. The parameters of the best-match calculated reflectance spectra, obtained by minimizing mean-square deviation, are collected in the Table 1. The high value of e1 can be explained by the contributions of the electron transitions from the impurity levels situated in the band gap. Relatively small phonon contribution into the permittivity caused by covalent nature of the chemical bonding in ZnGeP2. Unlike [8], we have observed the shift of the phonon peaks at low temperatures. We have presented experimental reflectance spectra recorded at 300 K and 4 K for both polarizations in Fig. 3. Relative temperature shift of the phonon peaks Dn/DT in the reflectance spectra of ZnGeP2 is presented in the Table 2. The shift of the phonon peaks at low temperatures is ascribed to thermal expansion of the lattice. The coefficient of thermal expansion of ZnGeP2 is anisotropic [12] and shows different impact on the reflectance spectra of ZnGeP2 for E||c and E?c polarizations at 4 K (Table 2). Reflectance spectra of ZnGeP2 of both polarizations recorded at 4, 10, 50, 100, 200 and 250 K have been analyzed. Corresponding dispersion of the imaginary part of the dielectric permittivity is shown in the Fig. 4 to show the qualitative evolution of the phonons contributions at different temperatures. In addition to the temperature shift, phonon peaks are getting narrower and higher at low temperatures. To look into quantitative changes of the parameters of harmonic oscillators used to model the reflectance spectra of ZnGeP2 the Table 3 was composed. The resonant frequency nT decreases, the oscillators’ strength S and the damping coefficient g increase, while the temperature increases. Fig. 5 provides a clear view of dependences of the above mentioned parameters. The dependence of all parameters shows parabolic behavior bT2, where the coefficient b is negative in the case of the resonant frequency nT and positive for the damping coefficient g and oscillators’ strength S. The damping coefficient g and oscillators’ strength S affect the width of “windows” of negative values of e1. Since these parameters are temperature dependent, width of “windows” of negative values of e1 (Table 4), where the surface polaritons can be excited, changes at low temperatures.

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K.V. Shportko / Vibrational Spectroscopy 80 (2015) 1–5

Fig. 4. The temperature dependence of e2(n) of ZnGeP2 in the Reststrahlen band, E||c and E?c: 1 ( ) – 4 K, 2 ( ) – 10 K, 3 ( ) – 100 K, 4 ( ) – 100 K, 5 ( ) – 200 K, 6( ) – 250 K, 7 ( ) – 300 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 3 Parameters of harmonic oscillators used to model the reflectance spectra of ZnGeP2 at different temperatures. T,K

300 250 200 100 50 10 4 T,K

B

C

(n), cm1

(g ), cm1

S

(n), cm1

(g ), cm1

S

342.0 342.6 343.0 343.6 343.8 344.0 344.1

2.49 2.00 1.60 1.20 0.98 0.95 1.11

1.32 1.30 1.28 1.27 1.25 1.24 1.24

400.0 401.0 401.6 402.8 403.5 403.8 403.8

2.26 2.00 1.51 1.50 1.40 1.10 1.11

0.34 0.33 0.31 0.31 0.30 0.29 0.29

E

cm

-1

C

380

G 340

F

(n), cm1

(g ), cm1

S

(n), cm1

(g ), cm1

S

300 250 200 100 50 10 4

202.0 202.4 202.8 203.4 204.0 204.5 204.5

7.00 6.00 6.00 5.50 5.40 5.10 5.00

0.12 0.12 0.11 0.11 0.11 0.11 0.10

327.0 327.2 328.0 328.6 329.0 329.0 329.0

5.62 5.30 5.21 4.50 4.30 4.10 4.00

0.37 0.37 0.37 0.36 0.36 0.36 0.36

T,K

G

300 250 200 100 50 10 4

420 ν Tj ,

γj ,

cm

-1

3 2 1

1.0

Sj

H

(n), cm1

(g ), cm1

S

(n), cm1

(g ), cm1

S

369.0 369.4 369.8 370.5 370.9 371.0 371.0

1.26 1.19 0.98 0.74 0.84 0.81 0.80

0.59 0.59 0.58 0.57 0.56 0.57 0.56

386.0 387.0 388.5 389.0 389.5 390.0 390.0

1.40 0.94 0.80 0.45 0.40 0.33 0.30

0.53 0.53 0.52 0.52 0.52 0.52 0.52

0.5 0.0 0

100

200

300

Temperature, K

Fig. 5. Temperature dependence of the parameters used to model phonon band C (E||c) and G (E?c) in the reflectance spectra of ZnGeP2.

K.V. Shportko / Vibrational Spectroscopy 80 (2015) 1–5

Acknowledgement

Table 4 Temperature dependence of the width of Reststrahlen band of ZnGeP2. T,K

B

C

v1, cm1

n2, cm1

Dn, cm1

n1, cm1

n2, cm1

Dn, cm1

300 4

342.2 344

361.5 361.5

19.3 17.5

400.1 404.6

410.2 411.2

10.1 6.6

T,K

G

300 4

n1, cm

n2, cm

368.8 371.2

375.0 377.4

1

Dn, cm 6.2 6.2

1

n1, cm 386.6 390.0

1

n2, cm

Dn, cm

404.1 406.0

17.5 16.0

1

Author gratefully acknowledges the support from the DAAD (German Academic Exchange Service). References

H 1

5

1

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4. Conclusions Thus, a Drude-Lorentz model is used to describe the plasmon and phonon contributions to the dielectric permittivity of ZnGeP2 at different temperatures. Dispersion analysis of reflectance spectra of ZnGeP2 was performed for both polarizations in the infrared range at different temperatures in this study. The phonons in ZnGeP2 show the same temperature behavior. Resonant frequency nt decrease upon increasing the temperature, while damping coefficient g and oscillator strength S increase. Optical phonon behaviors are ascribed to thermal expansion of the lattice.

[8] [9] [10] [11] [12]

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