The optical properties of Ag2Te crystals from THz to UV

Accepted Manuscript The optical properties of Ag2Te crystals from THz to UV Tien-Tien Yeh, Wen Hao Lin, Wen-Yen Tzeng, Phuoc Huu Le, Chih-Wei Luo, Teodor I. Milenov PII:

S0925-8388(17)32529-X

DOI:

10.1016/j.jallcom.2017.07.153

Reference:

JALCOM 42569

To appear in:

Journal of Alloys and Compounds

Received Date: 17 February 2017 Revised Date:

14 July 2017

Accepted Date: 15 July 2017

Please cite this article as: T.-T. Yeh, W.H. Lin, W.-Y. Tzeng, P.H. Le, C.-W. Luo, T.I. Milenov, The optical properties of Ag2Te crystals from THz to UV, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.07.153. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT The optical properties of Ag2Te crystals from THz to UV Tien-Tien Yeh,a Wen Hao Lin,a Wen-Yen Tzeng,a Phuoc Huu Le,b Chih-Wei Luo,a,*

Department of Electrophysics, National Chiao Tung University, Hsinchu 300,

Taiwan b

Faculty of Basic Sciences, Can Tho University of Medicine and Pharmacy, 179

c

M AN U

Nguyen Van Cu Street, Can Tho, Vietnam

SC

a

RI PT

Teodor I. Milenovc

“E. Djakov“ Institute of Electronics- Bulgarian Academy of Sciences, 72

Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria

Abstract

TE D

*[email protected] Tel:+886-3-5712121-56196

The optical properties of monoclinic Ag2Te crystals are studied in a wide

EP

range (3.7 meV - 6.2 eV) of photon energies. The measured reflectivity spectra from

AC C

THz to UV allow unambiguous a photon energy-dependent complex dielectric function, complex refractive index and absorption coefficient to be obtained. The spectral structure in these optical parameters further indicates the coexistence of an indirect transition with a bandgap energy of about 10 meV and a direct transition with a bandgap energy of about 1.84 eV. Keywords: Optical properties, Ag2Te, Spectroscopy, Semiconductors

ACCEPTED MANUSCRIPT

1. Introduction

RI PT

Silver telluride (Ag2Te), a so-called Hessite mineral, has recently attracted attention because of its potential applications in megagauss sensors [1] and in infrared (IR) optical devices that operate in telecommunication regions [2], which are similar

SC

to the applications of some metal- and metal oxide-based semiconducting materials with their promising electronic, optical, and magnetic properties [3-7]. Ag2Te exhibits

M AN U

a structural phase transition from β to α phase at around 421 K, i.e., from a monoclinic structure to a face-centered cubic structure [8]. In the low-temperature monoclinic structure, Ag2Te nanowires behave as a narrow bandgap semiconductor

TE D

with a high electron mobility of more than 22,000 cm2/Vs [9] and a low lattice thermal conductivity of 0.93 W/mK at 300 K [10]. Additionally, when the structure phase changes from monoclinic to cubic, the resistance increases and the absolute

EP

Seebeck coefficient value decreases due to the increase of density of states in

AC C

nanowire structure [11]. Ag2Te also possesses a large magnetoresistance [12], which extends the materials of GMR/CMR from manganite perovskites to non-magnetic compounds. Recently, theoretical calculations have shown that low-temperature β-Ag2Te is a binary topological insulator with a highly anisotropic Dirac-cone surface state [13], which has been experimentally demonstrated through the periodic quantum interference effect [14]. By the same means, large electric field tunability has been further observed on topological surface states [15]. Therefore, β-Ag2Te is a potential

ACCEPTED MANUSCRIPT topological insulator for applications in spintronics. Very recently, the preparations of thin, light-weight, and flexible thermoelectric devices have been reported [16], and glutathione capped Ag2Te nanoparticles offer great potential for developing

RI PT

cytochrome C biosensors [17].

Besides, Ag2Te also shows interesting optical properties such as optical filters

SC

based on Ag2Te thin films, enhancement of Raman scattering efficiency in β-Ag2Te nanotubes, and study of polarized Raman spectroscopy in β-Ag2Te crystals [18-20].

M AN U

Particularly, the fundamental optical properties, e.g., the bandgap energy, etc., of Ag2Te are also crucial parameters for developing optoelectronic devices. In 1966, Dalven et al. [21] estimated the optical bandgap energy of Ag2Te to be less than 0.064 eV using the transmission spectra. Later on, Prabhune and Fulari [22] reported an

TE D

optical bandgap of 1.72 eV in Ag2Te thin films prepared by electro-deposition. Furthermore, ellipsometric spectroscopy was performed to identify the optical

EP

bandgap of Ag2Te films with various thicknesses, i.e., the optical bandgap energy

AC C

varies from 1.33 eV to 1.64 eV as the thickness of Ag2Te films increase from 45 nm to 145 nm [23]. The disagreement between the above studies in terms of the value for the optical bandgap energy of Ag2Te might be caused by the limitation of the probe photon energy, e.g., this energy only falls in the far-IR or in the visible region. Surprisingly, the broadband reflectivity spectrum (from THz to UV) of Ag2Te crystals, especially for β-Ag2Te, has not yet been completely investigated.

ACCEPTED MANUSCRIPT Here we report the optical reflectivity spectra of β-Ag2Te crystals from 3.7 meV to 6.2 eV, which covers three orders of magnitude in the photon energy. The

RI PT

broadband reflectivity spectra are further used to determine various optical constants, e.g., the complex dielectric function, complex refractive index and absorption coefficient. Additionally, the plasma frequency and optical bandgap are respectively

M AN U

2. Crystals and experimental methods

SC

determined using the dielectric constant and absorption coefficient.

The β-Ag2Te crystals used in this study were grown by the Bridgman method. The crystal ingot has a diameter of about 21 mm and contains of few grains of (3-5) × (3-5) mm2 on a cross section. The size of the sample used in this study is ~10×10×1

TE D

mm. For the electrical transport measurements, the van der Pauw method was applied because it does not need to etch a sample to a required pattern as in traditional

EP

transport measurements. On the other hand, the van der Pauw method can only be applied when the samples satisfy the following required conditions: (1) The surface of

AC C

the sample is singly connected, i.e., the sample does not have isolated holes. (2) The sample is homogeneous in thickness. (3) The contacts are at the circumference of the sample. (4) The contacts are sufficiently small. Since our Ag2Te sample met the above required conditions, we applied the van der Pauw method in this study to avoid sample damage. The optical reflectivity spectra of β-Ag2Te crystals in the far-, mid- and near-IR regions (3.7 meV – 1.5 eV) were measured using a Fourier transform infrared

ACCEPTED MANUSCRIPT (FTIR) spectrometer (Accuracy: > 98.1 %, VERTEX 70v; Bruker Corp.), with a spectral resolution of 1 cm-1, which corresponds to 0.1 meV. For the region from

RI PT

near-IR to ultraviolet (from 1.37 eV to 6.2 eV), the optical reflectivity spectra were measured using a UV-VIS spectrometer (Accuracy: > 99.3 %, U-3310; Hitachi Corp), with a spectral resolution of 1 nm. All of the experiments were performed at room 293

K.

From

the

optical

reflectivity

spectra,

the

photon

SC

temperature,

M AN U

energy-dependent complex dielectric function, the complex refractive index and the absorption coefficient of β-Ag2Te crystals can be further estimated using the free carrier absorption model.

TE D

3. Results and discussion

3.1 Structure and chemical composition analyses and electrical properties Ag2Te is very soft material and problems with successful surface processing

EP

(mechanical and chemical lapping and polishing) remain unsolved. On the other hand,

AC C

only small single crystals (smaller than 1×3 mm2 and irregular thickness) can be cleaved. For that reason, we used a deeply lapped wafer with the size of ~10×10×1 mm (see the inset of Fig. 1) for further measurements. Fig. 1 shows the X-ray diffraction θ-2θ pattern for an Ag2Te crystal (see the inset of Fig. 1), which was measured by a diffractometer (D2 PHASER; Bruker Corp.) with a Cu kα line (λ=1.5406 Å). All of the diffraction peaks in Fig. 1 can be assigned to the β-phase

ACCEPTED MANUSCRIPT Ag2Te, which is in agreement with the diffraction pattern in the database of JCPDF81-1820. Therefore, the crystals used in this study are polycrystalline and possess monoclinic structure. Furthermore, the room-temperature carrier mobility (µ)

RI PT

of 3543 cm2/Vs, concentration (Ne) of -1.16×1018 cm-3 (n-type), and resistivity (ρ) of 1.52×10-3 Ω˗cm were determined by Hall measurements (PPMS; Quantum Design

SC

Corp.). The SEM (SU8000; Hitachi Corp.) image in the secondary electron image

M AN U

(SEI) mode of the mechanically polished surface of a β-Ag2Te crystal (see the inset of Fig. 1) is shown in Fig. 2(a), which confirms a void-free surface. The energy-dispersive X-ray spectroscopy (EDS, EMAX; Horiba Corp.) spectrum in Fig. 2(b) shows that the sample only consists of the elements Ag and Te. Additionally, the

TE D

quantitative analysis of Ag Lα and Te Lα in the EDS spectrum indicates that the atomic ratio of Ag to Te is ~2.00, which is within the realm of experimental deviation.

EP

3.2 Reflectivity spectra

AC C

Fig. 3 shows the reflectivity spectrum of a β-Ag2Te crystal as a function of photon energies from 3.7 meV to 6.2 eV, which corresponds to wavelengths from 335 µm to 0.2 µm. The reflectivity remains almost constant when the photon energy increases from 3.0 meV to 10 meV. However, the decrease in the reflectivity becomes more pronounced in the range of photon energy from 10 meV to 50 meV, as shown in Fig. 3. Interestingly, the reflectivity increases slightly as the photon energy increases

ACCEPTED MANUSCRIPT from 50 meV to 100 meV. Above 100 meV, the reflectivity monotonically decreases as the photon energy increases from 100 meV to 6.2 eV, which is consistent with the

RI PT

results of common semiconductors. Additionally, the p- and s-polarized reflectivity spectra (Rp, Rs) with incident angles of 11° were also measured (see the left inset of Fig. 3(a)). As shown in the left and middle insets of Fig. 3(a), there is no significant

SC

difference between the spectrum structure of non-, p- and s-polarized reflectivity

M AN U

according to the isotropic polycrystalline sample. The non-polarized reflectivity spectrum can be obtained by simply combining Rp and Rs as shown in the middle inset of Fig. 3(a).

3.3 The complex dielectric function and the refractive index

TE D

According to the Fresnel equation, we can find the relation between reflectivity (Rs: s-polarization, Rp: p-polarization, R: unpolarized) and refractive

EP

index/dielectric function as: 2

=

cosθ i − nc2 − sin 2 θ i

AC C

E Rs = rs Eis

Rp =

E rp Eip

2

=

cosθ i + nc2 − sin 2 θ i

2

=

nc2 cosθ i − nc2 − sin 2 θ i nc2 cosθ i + nc2 − sin 2 θ i

R = (R s + R p ) / 2

cosθ − ε − sin 2 θ i

2

(1)

cosθ + ε − sin 2 θ i 2

=

ε cosθ − ε − sin 2 θ i ε cosθ + ε − sin 2 θ i

2

(2)

(3)

where Eis and Eip stand for incident electric field with s-polarization and p-polarization, respectively, at the incident angle of θi = 11°. Ers and Erp represent reflective electric

ACCEPTED MANUSCRIPT fields with s-polarization and p-polarization, respectively. nc means the complex refractive index, and ε(ω) is complex dielectric function, which is expressed as:

ω 2p ω 2 + iΓω

+∑ i

ω 2p × S i ω02i + ω 2 + iΓ iω

(4)

RI PT

ε (ω ) = ε ∞ −

where ε∞ is the high-frequency limit of the dielectric function. The second term of Eq.

SC

(4) is the so-called Drude term, where ω0 is the natural frequency, ωp is the plasma frequency, Si is related to the oscillation strengths, and Г is the damping coefficient.

M AN U

The third term of Eq. (4) is the so-called Lorentz term, where ω0i is the natural frequency of the ith resonator, Si is related to the oscillator strengths, and Гi is the damping coefficient. Using the optical reflectivity spectrum in Fig. 3, the complex

TE D

dielectric function can be further determined by fitting the spectrum with Eqs. (1) and (2). The results are shown in Table 1 and Fig. 4 were obtained using the free program, RefFIT [24].

EP

According to the definition of plasma frequency (ωp) in the Drude model, ωp

AC C

is described as ωp = (Nee2/ε0m*)0.5, where Ne is the number of electrons per unit volume, which can be determined by Hall measurements, e is the electron charge, m* (= 0.05m0) is the effective mass of an electron [25] and ε0 is the free-space permittivity.

The dielectric constants in the range of photon energies from near-IR to visible roughly decrease as the photon energy increases. This behavior is consistent with the results reported by Pandiaraman et al. [23] in the range of photon energies between

ACCEPTED MANUSCRIPT 1.77 eV (700 nm) and 4.13 eV (300 nm). In their results, the values of the dielectric constants are also close for both ε1 and ε2.

constants as: n=

1 2

ε12 + ε 22 + ε1

k=

and

1 2

ε12 + ε 22 − ε1

RI PT

The complex refractive index can be further calculated from the dielectric

(5)

SC

The calculated complex refractive index is plotted as a function of photon energy in

M AN U

Fig. 5. The extinction coefficient, k, is larger than the refractive index, n, when the photon energy is less than 33 meV. However, the extinction coefficient, k, is smaller than the refractive index, n, if the photon energy is higher than 33 meV. These results show that the β-Ag2Te crystals have a typically metallic character.

TE D

When the photon energy is higher than 33 meV, the value of n quickly rises from 2.6 to 3.8 and then slightly decreases to 3.0 in mid- and near-IR regions, which

EP

implies the coexistence of large positive dispersion in the mid-IR region and small negative dispersion in the near-IR region. On the other hand, the value of k quickly

AC C

decreases from 5.6 to 0.7 for photon energies of less than 60 meV and then stays constants as the photon energy increases in the mid- and near-IR regions. These results for n and k are close to the free carrier plasma behavior in metals below and above the plasma energy. When the photon energy is higher than the plasma energy of 50 meV, n gradually increases, which indicates anomalous dispersion. This could be explained by other mechanisms, such as the energy gap transition, which is discussed

ACCEPTED MANUSCRIPT in the next section. Fig. 5 also shows that the value of k rapidly decreases as the photon energy increases in the photon energy range from 20 meV to 100 meV. When

RI PT

the photon energy is more than 1.23 eV, k rapidly increases and reaches a local maximum at 2.21 eV. The values of n and k obtained in this study are consistent with the results of Pandiaraman et al. in the range of photon energies between 1.77 eV and

SC

4.13 eV [23]. The characteristics of n and k observed from 1.0 eV to 6.2 eV resemble

3.4 Absorption spectra

M AN U

those of general semiconductors, such as GaAs, above the bandgap [26].

In order to completely determine the photon energy (E) dependence of k in the mid- and near-IR regions, as shown in Fig. 5, the absorption coefficient, α(E), is

TE D

calculated from k using the relationship between k and the absorption coefficient, i.e., α = 4πk/λ (cm-1), which is of the order of 103-105 at photon energies between 0.003

EP

eV and 6.2 eV. In particular, the calculated value of α in the range of photon energies

AC C

between 1 eV and 4 eV agrees with those obtained from thin films [23]. There is an absorption minimum at a photon energy of about 0.05 eV. When the photon energy is less than 0.05 eV, the absorption coefficient rapidly rises until 0.02 eV, which is due to the absorption of free carriers [27]. Further insight into the optical bandgap of Ag2Te is provided by the absorption coefficient spectra. From Tauc’s relationship [28], α varies with photon energy as αE = A(E-Eg)m, where E is the photon energy, Eg is the bandgap, m is 0.5

ACCEPTED MANUSCRIPT for the direct allowed transition and 2 for the indirect allowed transition. Fig. 6(b) shows a plot of (αE)0.5 versus photon energy (E) and a linear fit, which shows that the indirect bandgap energy is 10 meV. A possible indirect bandgap transition is

RI PT

illustrated by the inset of Fig. 6(b). Additionally, a closer look at the experimental data in Fig. 6(b) actually shows a deviation from the fitting line of (αE)0.5 at ~60 meV.

SC

This result is close to the value determined by previous studies [29] for Ag2Te with a bandgap energy of 64 meV. Besides, Vassilev et al. [30] also observed an indirect

M AN U

bandgap energy of 80 meV in Ag2Te films. Therefore, the finite value of (αE)0.5 below 60 meV in Fig. 6(b) is probably due to the Dirac surface state within the bulk bandgap [13].

The direct bandgap energy is estimated to be 1.84 eV, from the plot of (αE)2

TE D

versus the photon energy between 1 eV and 2 eV (see Fig. 6(c)), which is illustrated by the inset of Fig. 6(c). Prabhune and Fulari’s studies [22] observed an optical direct

EP

bandgap of 1.72 eV in an Ag2Te film at room temperature. Recently, Pandiaraman

AC C

[23] has reported that the bandgap of Ag2Te films is thickness-dependent, as shown by ellipsometric spectroscopy, and their results show that the direct bandgap energy varies from 1.33 eV to 1.64 eV as the film thickness decreases from 145 nm to 45 nm. Fig. 6(c) shows a clear tail in the (αE)2 spectrum when the photon energy is

less than 1.84 eV. The (αE)2 value increases exponentially between photon energies of 1 eV to 2.25 eV, which can be described by the Urbach tail equation: α(E)=α0 exp((E-Eg)/Eu) [31], where α0 and Eu are the fitting constant and tail width,

ACCEPTED MANUSCRIPT respectively. The semi-log plot of α in Fig. 6(d) is fitted by the Urbach tail equation and the value of Eu = 1.67 eV is obtained for a β-Ag2Te crystal. In general, the value

RI PT

of Eu depends on the amount of defects and disorders in samples. This large value for Eu strongly implies that the β-Ag2Te crystals are typical semiconductors with defects or disorders. Consequently, the wide Urbach tail, due to defects and disorders, results

SC

in uncertainty in determining the bandgap energy and further leads disagreement with

M AN U

the results of earlier studies, in terms of the bandgap energy [21-23]. Similar phenomenon of the bandgap variation was also observed in ZnO [32]. This kind of varying bandgap in ZnO is associated with the intrinsic defects, which further

in (αE)2 spectra. 4. Conclusions

TE D

introduce defect states in the bandgap to reduce the bandgap energy and form the tail

EP

We reported the studies of reflectivity spectra of β-Ag2Te crystals in the

AC C

broadband photon energy range from 3.7 meV to 6.2 eV. The photon energy-dependent optical parameters, such as the complex dielectric constant (ε1, ε2), the refractive index (n), the extinction coefficient (k) and the absorption coefficient (α), are determined from the reflectivity spectra by using the free carrier model. The crossing point between ε1 and ε2 shows that the plasma energy is 50 meV. Moreover, the complex refractive index spectra show n > k at photon energies of higher than 33

ACCEPTED MANUSCRIPT meV, which is similar to most semiconductors. From the absorption spectra and Tauc’s relation, it is found that β-Ag2Te crystals have an indirect bandgap energy of

RI PT

10 meV and a direct bandgap energy of 1.84 eV, with a wide Urbach tail (Eu =1.67 eV). Due to the indirect bandgap energy of 10 meV, a free carrier absorption is only observed at photon energies of less than 100 meV. Finally, all of the fundamental

SC

optical properties of β-Ag2Te crystals identified by this study may provide key

Acknowledgments

M AN U

information for future applications in optoelectronic devices.

This work was supported by the Ministry of Science and Technology of the Republic

of

China,

Taiwan

TE D

102-2112-M-009-006-MY3,

(Grant

Nos.

101-2112-M-009-016-MY2, 103-2923-M-009-001-MY3,

103-2628-M-009-002-MY3, and 103-2119-M-009-004-MY3) and the Grant MOE

EP

ATU Program at NCTU. The authors would like to thank Mr. C. C. Hung for his help.

AC C

The work is performed in the framework of MPNS COST Action MP1204TERRA-MIR Radiation: Materials, Generation, Detection and Applications.

ACCEPTED MANUSCRIPT

Table 1. The fitting parameters of Eqs. (1) and (2) in Fig. 3.

ε∞

The 2nd term of Eq. (4)

-

ωp (eV)

-

0.05

ω0i (eV)

Lorentz term -

1

0.57

The 3rd term of Eq. (4)

2

Γi (eV)

1.93

2.42

1.25

0.48

0.24

2.93

7

5.05

AC C

EP

TE D

3

0.01

Si

M AN U

i

Γ (eV)

SC

Drude term -

RI PT

3.94

ACCEPTED MANUSCRIPT References [1]

A. Husmann, J.B. Betts, G.S. Boebinger, A. Migliori, T.F. Rosenbaum, M.L. Saboungi, Megagauss sensors, Nature 417 (2002) 421-424.

[2]

M. Yarema, S. Pichler, M. Sytnyk, R. Seyrkammer, R.T. Lechner, G.

RI PT

Fritz-Popovski, D. Jarzab, K. Szendrei, R. Resel, O. Korovyanko, M.A. Loi, O. Paris, G. Hesser, W. Heiss, Infrared Emitting and Photoconducting Colloidal Silver Chalcogenide Nanocrystal Quantum Dots from a Silylamide-Promoted Synthesis, ACS Nano 5 (2011) 3758–3765. J. Kennedy, J. Leveneur, GV. Williams, DR. Mitchell , A. Markwitz, Fabrication of surface magnetic nanoclusters using low energy ion implantation and electron beam annealing, Nanotechnology 22 (2011) 115602.

[4]

J. Kennedy, P.P. Murmu, E. Manikandan, S.Y. Lee, Investigation of structural and photoluminescence properties of gas and metal ions doped zinc oxide

M AN U

SC

[3]

single crystals, J. Alloys Compd. 616 (2014) 614-617.

J. Kennedy, B. Sundrakannan, R.S. Katiyar, A. Markwitz, Z. Li, W. Gao, Curr. Raman scattering investigation of hydrogen and nitrogen ion implanted ZnO thin films, Appl. Phys. 8 (2008) 291-294.

[6]

P. Couture, G.V.M. Williams, J. Kennedy, J. Leveneur, P.P. Murmu, S.V. Chong, S. Rubanov, Nanocrystalline multiferroic BiFeO3 thin films made by room temperature sputtering and thermal annealing, and formation of an iron oxide-induced exchange bias, J. Alloys Compd. 695 (2017) 3061-3068.

EP

TE D

[5]

Y. Wang, L.T. Tseng, P.P. Murmu, N. Bao, J. Kennedy, M. Ionesc, J. Ding, K. Suzuki, S. Li, J. Yi, Defects engineering induced room temperature ferromagnetism in transition metal doped MoS2, Mater. Des. 121 (2017) 77-84.

AC C

[7]

[8]

M.D. Banus, M.C. Finn, Polymorphism in Silver Telluride at High Pressures and Temperatures, J. Electrochem. Soc. 116 (1969) 91-94.

[9]

S. Lee, J. In, Y. Yoo, Y. Jo, Y.C. Park, H.J. Kim, H.C. Kim, J. Kim, B. Kim, K.L. Wang, Single Crystalline β-Ag2Te Nanowire as a New Topological Insulator, Nano. Lett. 12 (2012) 4194–4199.

[10] M. Fujikane, K. Kurosaki, H. Muta, S. Yamanaka, Thermoelectric properties of α- and β-Ag2Te, J. Alloys Compd. 393 (2005) 299-301.

ACCEPTED MANUSCRIPT [11] S. Lee, H.S. Shin, J.Y. Song, M.-H. Jung, Thermoelectric Properties of a Single Crystalline Ag2Te Nanowire, J Nanomater 2017 (2017) 4308968. [12] R. Xu, A. Husmann, T.F. Rosenbaum, M.L. Saboungi, J.E. Enderby, P.B. Littlewood, Large magnetoresistance in non-magnetic silver chalcogenides, Nature 390 (1997) 57-60. W. Zhang, R. Yu, W. Feng, Y. Yao, H. Weng, X. Dai, Z. Fang, Topological Aspect and Quantum Magnetoresistance of β−Ag2Te, Phys. Rev. Lett. 106 (2011) 156808.

RI PT

[13]

SC

[14] A. Sulaev, P. Ren, B. Xia, Q.H. Lin, T. Yu, C. Qiu, S.-Y. Zhang, M.Y. Han, Z.-P. Li, W.-G. Zhu, Q. Wu, Y.-P. Feng, L. Shen, S.Q. Shen, L. Wang, Experimental evidences of topological surface states of β-Ag2Te, AIP

M AN U

Advances 3 (2013) 032123. [15]

A. Sulaev, W. Zhu, K.L. Teo, L. Wang, Gate-tuned quantum oscillations of topological surface states in β-Ag2Te, Sci. Rep. 5 (2015) 8062.

[16]

Y.-T. Jao, Y.-C. Li, Y. Xie, Z.-H. Lin, A Self-Powered Temperature Sensor Based on Silver Telluride Nanowires, ECS J. Solid State Sci. Technol. 6 (2017) N3055-N3057.

TE D

[17] S. Yan, D. Deng, L. Li, Y. Chen, H. Song, Y. Lv, Glutathione modified Ag2Te

EP

nanoparticles as a resonance Rayleigh scattering sensor for highly sensitive and selective determination of cytochrome C, Sens. Actuator B-Chem. 228 (2016) 458–464. [18] Sh.M. Alekperova, A.A. Aliyev, Kh. D. Jalilova, I.A. Ahmedov, Optical filters on the basis of α-Ag2Te thin films, Proc. of SPIE 5834 (2005) 384-387.

AC C

[19] A. Qin, Y.P. Fang, P.F. Tao, J.Y. Zhang, C.Y. Su, Silver Telluride Nanotubes Prepared by the Hydrothermal Method, Inorganic Chem. 46 (2007) 7403-7409. [20] T.I. Milenov, T. Tenev, I. Miloushev, G.V. Avdeev, C.-W. Luo, W.-C. Chou, Preliminary studies of the Raman spectra of Ag2Te and Ag5Te3, Opt. Quant. Electron. 46 (2013) 573-580. [21] R. Dalven, Fundamental Optical Absorption in β-Silver Telluride, Phys. Rev. Lett. 16 (1966) 311-312. [22] V.B. Prabhune, V.J. Fulari, Measurement of properties of silver telluride thin films using holography, Opt. Commun. 282 (2009) 2118-2122.

ACCEPTED MANUSCRIPT [23] M. Pandiaraman, N. Soundararajan, C. Kumar, R. Ganesan, Ellipsometric Studies on Silver Telluride Thin Films, J. Nano-Electron. Phys. 3 (2011) 32-42. [24] A. Kuzmenko, RefFIT https://sites.google.com/site/reffitprogram/home.

(2014),

[25] V.D. Damodara, D. Karunakaran, Semiconducting behavior of Ag2Te thin

RI PT

films and the dependence of band gap on thickness, J. Appl. Phys. 54 (1983) 5252-5255.

SC

[26] D.E. Aspnes, A.A. Studna, Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV, Phys. Rev. B 27 (1983) 985-1009.

Sci. Rep. 7 (2017) 40492.

M AN U

[27] T.-T. Yeh, H. Shirai, C.-M. Tu, T. Fuji, T. Kobayashi, C.-W. Luo, Ultrafast carrier dynamics in Ge by ultra-broadband mid-infrared probe spectroscopy,

[28] J. Tauc, R. Grigorovici, A. Vancu, Optical Properties and Electronic Structure of Amorphous Germanium, Phys. Status Solidi 15 (1966) 627-637.

[30]

TE D

[29] R. Dalven and R. Gill, Energy Gap in β−Ag2Te, Phys. Rev. 143 (1966) 666-670. V. Vassilev, P. Petkov, V. Vachkov, S. Boycheva, Electrical and optical properties of thin films in the Ag2Te–CdTe system, Mater. Lett. 41 (1999) 278-282.

EP

[31] F. Urbach, The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids, Phys. Rev. 92 (1953) 1324.

AC C

[32] J. Kennedy, P.P. Murmu, J. Leveneur, A. Markwitz, J. Futter, Controlling preferred orientation and electrical conductivity of zinc oxide thin films by post growth annealing treatment, Applied Surface Science 367 (2016) 52–58.

ACCEPTED MANUSCRIPT Figure Captions

Fig. 1.

The X-ray diffraction θ - 2θ pattern of a β-Ag2Te crystal. Inset: the

Fig. 2.

RI PT

photograph of a β-Ag2Te crystal wafer with the thickness of ~1 mm.

(a) The top view SEM image in (secondary electron image) SEI mode of a β-Ag2Te crystal. (b) The energy-dispersive X-ray spectroscopy (EDS)

SC

spectrum for an Ag2Te crystal within the area marked by the pink

M AN U

rectangle in (a). Inset: the composition pie-chart for the β-Ag2Te crystal in (a), which shows Ag and Te in an atomic ratio of 2.00:0.99. (c),(d) The concentration distribution of Ag and Te on the choose area (marked

Fig. 3.

TE D

by the pink rectangle) in (a).

The broadband reflectivity spectra of a β-Ag2Te crystal in the range of

EP

photon energies from 3.7 meV to 6.2 eV. The left inset in (a) shows the p-polarized (Rp) and s-polarized (Rs) reflectivity spectra. The middle

AC C

inset in (a) shows the non-polarized (R) and the (Rp+Rs)/2 reflectivity

spectra. The right inset in (a) shows the enlarged part below 0.01 eV.

Fig. 4.

The complex dielectric function in the range of photon energy from 20 meV to 6.2 eV. ε1 is the real part (red) and ε2 is the imaginary part (blue)

ACCEPTED MANUSCRIPT with its error bars of the complex dielectric function. Inset shows a part of ε1 and ε2 on an enlarged scale.

The complex refractive index in the range of photon energies from 20

RI PT

Fig. 5.

meV to 6.2 eV. n is the refractive index (red) and k is the extinction

n and k on an enlarged scale.

(a) The photon energy dependence of absorption coefficient α, (b) (αE)0.5

M AN U

Fig. 6.

SC

coefficient (blue). Both of them have its error bars. Inset shows a part of

as a function of photon energy (blue open squares) and (c) the (αE)2 as a function of photon energy (blue open squares). The red solid lines in (b)

TE D

and (c) are linear fitting curves. The insets in (b) and (c) are the schematic diagram of possible indirect and direct bandgap transitions in

EP

Ag2Te crystals, respectively [13]. (d) The semi-log plot of α versus

AC C

photon energy (blue open squares) and Urbach tail width fitting (red solid line).

M AN US C

3500

3000

2500

2000

1500

1000

500

0 10

RI

Intensity (a.u.)

(1 0 0)

20

(-1 0 2)

30

(-2 0 2) (2 0 0) (-1 1 2)

(-2 1 2)

(1 1 2) (-3 1 2) (3 0 0) (-3 1 3) (-1 2 1) (-1 0 4) (-4 0 2) (-3 1 4) (-1 1 4) (1 1 3) (-2 2 3) (4 0 0) (-5 0 4) (1 0 4) (-4 2 2) (-5 1 4) (-4 2 1) (-2 0 6) (-2 2 5)

CC

10 mm

10 mm

70

(2 2 3) (5 1 0)

1 mm

60

EP

50

TE

D

40

2T (degree)

(-2 1 3)

(1 1 1)

D

Te (33.3Ʋ1.8%)

Ag

500

Ag (66.7Ʋ1.8%)

400

EP

300

Te

200

Te

100 0 2.0

Ag

M AN US C

(b)

2.5

CC

Intensity (a.u.)

600

TE

700

RI P

(a)

3.0

3.5

Energy (keV)

Te 4.0

4.5

5.0

Te

RI P

Wavelength (Pm) 2.48

6.2

12.4

300 1.0

1.24

Wavelength (Pm)

Rs 0.3

Rp 0.1

0.4

0.2

0.3

0.4

0.5

0.2

0.2

0.3

0.4

0.3

0.4

0.5

0.6

200

150

0.6 0.4 0.2

0.5

0.0 0.004

Photon energy (eV)

0.2

0.1

300 250

0.8

0.3

0.1

Photon energy (eV)

0.0

1.0

R (Rp+Rs)/2

M AN US C

0.6

0.6

Reflectivity

Reflectivity

0.8

Reflectivity

0.6

Reflectivity

(a)

0.7

0.006

0.008

0.010

Photon energy (eV)

0.8

0.9

1.0

Photon energy (eV) Wavelength (Pm)

1

0.8

0.6

EP

0.2

0.1

1

AC C

Reflectivity

0.3

0.0

0.2

TE

(b)

0.4

D

0.4

1.2

2

3

4

Photon energy (eV)

5

6

WavelengthPm) 12.4

6.2

2.48

(a)

H

1

10

M AN US C

Dielectric function

20

H

0

30

2

-10

1.24

RI P

62

15

0

-15

-20

-30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.05 0.8

0.10

0.15

0.9

1.0

Photon energy (eV)

WavelengthPm)

1

0.8

0.6

0.4

TE

(b)

H

1

EP

10 0 -10 -20

1

CC

Dielectric function

20

-30

0.2

D

30

1.2

2

H

2

3

4

Photon energy (eV)

5

6

6

6.2

12.4

RI P

Wavelength (Pm) 62

2.48

(a)

4

M AN US C

Refractive index

5

n

3 2

1.24

6 5 4 3 2 1 0

0.05

0.10

0.15

k

1 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Photon energy (eV) Wavelength (Pm)

3 2 1

1

D

CC

EP

4

0

0.2

0.4

(b)

5

Refractive index

0.8

TE

6

1.2

2

n k 3

4

Photon energy (eV)

5

6

3

(c)

M AN US C

(a)

(DE) x 10 (eV/cm)

2

5

10

-1

1

2

D(



40

0 0.00

0.05

EP

20

0.10

0.15

Photon energy (eV)

2.0

2.5

(d)

D

3.0

3.5

0.20

0.3

1.00

0.2

-1

0.01 (eV)

1.5

Photon energy (eV)

TE

0.5

60

1.84 (eV)

0 1.0

3

80

(b)

20

0.1 0.37 0.0

0.25

0.5

1.0

1.5

Photon energy (eV)

2.0

Deviation

0

Photon energy (eV)

(eV/cm)

40

5

0

60

2

1

D x10 (cm )

D x10 (cm )

2

80

ACCEPTED MANUSCRIPT Highlights:

The reflectivity spectra of β-Ag2Te crystals were measured from 3.7 meV to 6.2 eV.

RI PT

The complex refractive index spectra show n > k at photon energy > 33 meV.

An indirect bandgap (~10 meV) and a direct bandgap (~1.84 eV) coexist in

AC C

EP

TE D

M AN U

SC

β-Ag2Te.