Introduction

Semiconductors are so common nowadays due to the wide applications such as the chipsets inside the cell-phones, the micro-FET components in the integrated circuits or the luminous semiconductor devices. Besides the well known applications in the electronics, semiconductors also play and important role in the applications of nonlinear optics, e.g. GaSe, ZnTe, etc.. In particular, the III-VI class semiconductors gallium selenide (GaSe) are the important nonlinear crystals for mid-IR generation, which have good characters such as the high nonlinear susceptibility χ⁽²⁾(𝑑₂₂ = 54 𝑝𝑚/𝑉) and anisotropy. Although there are four crystalline types in GaSe structure, ε-, β-, γ-, δ-type [1], the layered ε-type is the most stable structure among them for GaSe compound as shown by the SEM image in Fig. 1(a). Fig. 1(b) further illustrates that one layer comprises of four atomic planes (Se-Ga-Ga-Se along c-axis) and bound with each other by the ionic bonds (white bar). Also, these layers are bounded by the Van der Waals force to form a layered-structure crystal.

(a)

- 2 -

The pure III-VI gallium selenide crystals had been studied in the 1960s.

Until the 1970s, the optical and electrical characteristics of the pure or doped III-VI semiconductor were observed [2,3,4] because of the development of the instruments [5]. For instance, the mobility, the carrier concentration, the band structures, the band edge absorption, and the luminance properties were continuously reported in some journals [6,7,8,9]. After the quiet 1980 ages, the nonlinear effect in pure and doped GaSe crystals was attracted the researchers’

attention again [10,11,12,13,14,15] especially for the applications in phase-matching, e.g. the different frequency generation, the sum frequency emission, the optical parametric oscillator, or even the optical parametric amplifier.

Fig. 1 (a) SEM picture of the GaSe:Te layer structure;

(b) Atomic structure of ε-type GaSe;

(c) Atomic structure of β-type GaTe

(b) (c)

- 3 -

Dopant In Al S Te

Doping level (mass %) 0.01-3 0.01-3 0.01-3 0.01-3

Supposed predominant dopant introduction in the GaSe crystal

To Ga sites the crystal and Ga

sites: substitutes

Conduction type of the doped

crystals Hole Hole Hole Hole

Type of photoconductivity and its

main features - Microhardness rises up to (kg/𝑚𝑚²,

~8 for GaSe) 14 20 17 10

Table 1 Electrical and optical parameters of doped GaSe [16]

- 4 -

In order to compare the properties of GaSe:Te with other doping elements, some of the parameters have been listed in Table 1 [16, 17]. The transmittance of the Te-doped GaSe crystals in visible range is shown in Fig. 2. The optical absorption band edge of GaSe crystals locates at around 620 nm (photon energy of 2.00 eV), while the GaTe crystals locate at 753 nm (photon energy of 1.65 eV). Thus it is benefited that the band gap energy can be modified within the range of 1.65 eV~2.00 eV if the tellurium atoms are doped into the GaSe crystals or the selenium atoms are doped into the GaTe crystals. Indeed, the transmission edge significantly shifts to longer wavelength as increasing the concentration of Te in GaSe:Te crystals..

400 500 600 700 800

0 20 40 60

3 2.5 Photon Energy(eV)2 1.5

Transmission(%)

Wavelength(nm) x=0.0006

x=0.0012 x=0.006 x=0.012 x=0.022

GaSe

^1-x

Te

^x

Some important applications of the GaSe crystals are the type-I and the type-II phase-matching for the mid- to far-IR generation. In ref. [14], a BBO-based optical parametric oscillator and a Nd:YAG laser were used to perform the difference frequency generation of mid-infrared in pure ε-type GaSe crystals. In particular, the refractive indices of the pure GaSe at the far- and

Fig. 2 The transmittance of GaSe:Te

- 5 -

mid-infrared region were studied in order to assure the possibility of the system construction. In spite of its many attractive features, for generation from near to mid infrared and further to terahertz range, the GaSe crystals is difficult to be cut and polished along some arbitrarily chosen directions. For the applications in optics, further improvement in the optical and mechanical properties of the GaSe crystals is highly desirable. The doping of GaSe crystals seems to be the most economical way to radically improve its mechanical and other physical properties. Recent developments in the crystal growth technology indicated that GaSe can be doped with several elements, e.g. Er, Al, In, S, and Te, to strengthen the structural properties and noticeably modify the optical properties.

Comparing with Er-, Al-, In-, S-doping, the Te-doped GaSe crystals are benefited by the high power THz generation with type-II phase-matching in the mid-IR region [17]. Thus, we use the time-domain spectroscopy technique to investigate the characteristics of the Te-doped ε-type GaSe crystals in the far-infrared frequency region. Moreover, the temperature-dependent measurements in time-domain spectroscopy will provide us more information about the role of Te-doping in the GaSe crystals.

- 6 -

II. Principle

After obtaining the time-domain signals, it can be converted to the frequency domain spectra through the Fast-Fourier Transform. Owing to both amplitude and phase information have been simultaneously included in the time-domain signals [18], we can directly obtain the electromagnetic properties without Kramers-Kronig relations. In this chapter, we will describe the principle and procedure for calculating the complex refractive indices, the absorption coefficients, and the complex dielectric responses from time-domain signals.

2.1 Electromagnetic Waves in Crystals

When the electromagnetic wave straightly penetrates through the crystals, a time delay will be created due to its different optical path length between the crystals and the surrounding. The delay time is

∆𝑡 =^{(𝑛𝑆𝑎𝑚𝑝𝑙𝑒−1)𝑑}

𝑐 (2.1)

where 𝑛_{𝑆𝑎𝑚𝑝𝑙𝑒} is the refractive index of the sample, 𝑑 is the thickness of the sample, 𝑐 is the speed of light.

The propagation process can be described by the spectral components, either 𝑆(𝑡) in the time domain or 𝑆(𝜔) in the frequency domain. The propagation wave is influenced by the reflectance and the transmittance of both surfaces of a crystal,

- 7 -

𝑆_{𝑆𝑎𝑚𝑝𝑙𝑒}(𝜔) = 𝑡₁₂(𝜔) ∙ 𝑡₂₃(𝜔) ∙ 𝑝₂(𝜔, 𝐿)

∙ ∑^∞_𝑘=0*𝑟₂₃(𝜔) ∙ 𝑝₂²(𝜔, 𝐿) ∙ 𝑟₂₁(𝜔)+^𝑘 ∙ 𝐸(𝜔) (2.2) 𝑆_𝑅𝑒𝑓(𝜔) = 𝑡₁₃(𝜔)∙𝑝_1,3(𝜔, 𝐿)∙ 𝐸(𝜔) (2.3) where 𝑆_{𝑆𝑎𝑚𝑝𝑙𝑒}(𝜔) is the spectral component through sample; 𝑆_𝑅𝑒𝑓(𝜔) is the spectral component without sample; 𝑡₁₂(𝜔) and 𝑡₂₃(𝜔) are, respectively, the transmission coefficients through the surface and the rear surface (the suffixes 1, 2, and 3 represent medium 1, medium 2, and medium 3 respectively); 𝑟₂₃(𝜔) and 𝑟₂₁(𝜔) are, respectively, the backward reflection coefficients of the rear and the front surfaces; 𝑝₂(𝜔, 𝐿) and 𝑝_1,3(𝜔, 𝐿) are, respectively, the propagation coefficients inside and outside the sample over the distance 𝐿, 𝐸(𝜔) is the electric field of the propagation wave. In normal incidence electromagnetic wave, the transmissions, reflection, and propagation coefficients between medium a and medium b are derived to be

𝑡_𝑎𝑏(𝜔) = ^2𝑛̃𝑎

𝑛̃_𝑎+𝑛̃_𝑏 (2.4)

𝑟_𝑎𝑏(𝜔) = ^{𝑛̃𝑎−𝑛̃𝑏}

𝑛̃_𝑎+𝑛̃_𝑏 (2.5)

𝑝_𝑎(𝜔, 𝑑) = exp ,𝑖^{𝑛̃𝑎𝜔𝑑}

𝑐 - (2.6)

For the case of thick sample, the second reflection signal locates far from the primitive one, the multi-reflection and the summation effects of Fabry-Perot can be neglected.

- 8 -

2.2 Power Spectrum

The Fourier transform between the power spectra in the time domain and the frequency domain is represented by

𝑃̃(𝜔) = 𝐴(𝜔) 𝑒𝑥𝑝,−𝑖𝜑(𝜔)- = ∫ 𝑃(𝑡) 𝑒𝑥𝑝(−𝑖𝜔𝑡) 𝑑𝑡 (2.7) where 𝑃̃(𝜔) and 𝑃(𝑡) are, respectively, the power spectra in the frequency domain and the power spectra in time domain, meanwhile they are proportional to the spectral components 𝑆(𝜔) and 𝑆(𝑡) respectively; 𝐴(𝜔) and 𝜑(𝜔) are the amplitude and the phase of the power spectrum respectively.

2.3 The Complex Refractive Index

The ratio of the two spectral components, which means the total transmission coefficient of the samples, will lead the derivation to the complex refraction index,

𝑆_{𝑆𝑎𝑚𝑝𝑙𝑒}(𝜔)

𝑆_𝑅𝑒𝑓(𝜔) = 𝑡₁₂(𝜔)∙𝑡₂₃(𝜔)∙^𝑒

𝑖𝑛̃𝜔𝑑 𝑐 𝑒^𝑖

𝜔𝑑 𝑐

= 𝜌𝑒^𝑖∆𝜑 (2.8)

the ratio of the exponential terms corresponds to the delay time and 𝑡 = 𝑡₁₂(𝜔)∙𝑡₂₃(𝜔) is the transmittance of the samples; 𝜌 is the amplitude of the ratio and ∆𝜑 is the phase difference of spectral components. Medium 1 and 3 are free space or air, whose refractive indices are approximated to be 1. Medium 2, the sample, whose complex refractive index is represented by 𝑛̃ = 𝑛 + 𝑖𝑘.

Thus, some simplifications of the ratio can take place,

- 9 - imaginary part of the refractive indices can be obtained by comparison.

𝜌𝑒^𝑖∆𝜑 ≅ ^4𝑛

(𝑛+1)²∙ 𝑒^{−𝑘𝜔𝑑𝑐} ∙ 𝑒^{𝑖(𝑛−1)𝜔𝑑𝑐} (2.10)

Thus the real part of refractive index is n ≅ 1 +^𝑐∆𝜑

𝜔𝑑 (2.11)

and the imaginary part is k ≅ ^𝑐

𝜔𝑑ln , ^4𝑛

𝜌(𝑛+1)²- (2.12)

- 10 -

2.4 Absorption Coefficient

The strength of the penetration wave between two surfaces of a sample experiences a decay, which is

P₃^′(𝜔) = P₁^′(𝜔)exp,−αd- (2.13)

P₁^′(𝜔) here is the strength just behind the first incident surface. After the wave propagates and decays over a distance 𝑑 , the output strength is P₃^′(𝜔).

Moreover, α is defined as the absorption coefficient, whose unit is cm^-1 and magnitude is related to the transmittances as,

α = ¹

𝑑ln (^P1′(𝜔)

P_3′(𝜔)) = ¹

𝑑ln (𝑇₂₃𝑇₁₂^P1(𝜔)

P₃(𝜔)) (2.14)

For the transparent sample, the absorption coefficient can be estimated from the sample thickness and the transmittance.

2.5 Dielectric Responses

In the electromagnetism, the Maxwell equations for EM-wave propagating in the conducting material are different from those equations for EM-wave propagating in vacuum,

{

∇ ∙ 𝐸⃑ = 0

∇ ∙ 𝐵⃑ = 0

∇ × 𝐸⃑ = −𝜇^{𝜕𝐻⃑⃑}

𝜕𝑡

∇ × 𝐻⃑⃑ = 𝜍𝐸⃑ + 𝜀^𝜕𝐸⃑

𝜕𝑡

(2.15)

the Laplace equation is thus derived to be

−∇²𝐸⃑ = ∇ × ∇ × 𝐸⃑ − ∇ ∙ (∇ × 𝐸⃑ ) = ∇ × ∇ × 𝐸⃑ (2.16) And

- 11 -

∇ × ∇ × 𝐸⃑ = ∇ × .−𝜇^{𝜕𝐻⃑⃑}

𝜕𝑡/ = −𝜇 ^𝜕

𝜕𝑡(∇ × 𝐻⃑⃑ ) = −𝜇 ^𝜕

𝜕𝑡(𝜍𝐸⃑ + 𝜀^𝜕𝐸⃑

𝜕𝑡)

= −μσ^∂𝐸⃑

∂t − 𝜇𝜀^𝜕2𝐸⃑

𝜕𝑡² (2.17) The velocity relation of the propagating plane wave E = 𝐸₀𝑒^{−𝑖𝜔(𝑡−𝜔𝑣)} = 𝐸₀𝑒^{𝑖(𝑘𝑥−𝜔𝑡)} to the Laplace equation is

1

𝑣² = 𝜇𝜀 − 𝑖^𝜎𝜇

𝜔 (2.18)

The complex refractive index is related to the velocity of light and the wave propagation velocity in the medium; or it is related to the electric permittivity 𝜀̃

and the magnetic permeability 𝜇̃. Thus we can obtain the relation 𝑛̃² = 𝑐² ∙ ¹

𝑣²

and 𝑛̃² = 𝜀̃ ∙ 𝜇̃. For the GaSe sample which is the non-magnetic material with 𝜇̃ ≅ 1, it only relates to the dielectric function,

𝑛̃² = 𝑐²(𝜇_𝑟𝜀_𝑟𝜇₀𝜀₀+ 𝑖 𝜍𝜇_𝑟𝜇₀⁄ ) = 𝜇𝜔 _𝑟𝜀_𝑟 + 𝑖 𝜍𝜇_𝑟⁄𝜔𝜀₀

≅ 𝜀_𝑟 + 𝑖 𝜍 𝜔𝜀⁄ ₀ (2.19)

𝑛̃² = (𝑛 + 𝑖𝑘)² = (𝑛²− 𝑘²) + 𝑖2𝑛𝑘

≅ 𝜀̃ = 𝜀₁+ 𝑖𝜀₂ (2.20) By comparison to Eq. (2.19) and Eq. (2.20), the real part and the imaginary part of the dielectric function are respectively

𝜀₁ ≅ 𝑛²− 𝑘² ≅ 𝜀_𝑟 (2.21)

𝜀₂ ≅ 2𝑛𝑘 ≅ 𝜍 𝜔𝜀⁄ ₀ (2.22)

and thus the conductivity of the material for optical frequency concerned is

σ_𝑙 ≅ 2nkω𝜀₀ (2.23)

- 12 -

III. Experiments

3.1 Sample Preparation

The Te-doped GaSe crystals with ε -type stacks were grown by the Bridgman technique and were supplied by Professor Yury M. Andreev of the Institute of Monitoring of Climatic and Ecological Systems, SB RAS, Tomsk in Russia. In this study, we have six sorts of the crystals, one is the pure GaSe crystal and five of them are in various doping levels. The mass doping levels and the thicknesses of them are shown in Table. 2. All of the samples used in the ordinary incidence measurements are prepared by the z-cut cleavage.

A B C D E F

Doping level (mass %)

0.00 0.05 0.10 0.50 1.00 2.00

Thickness (mm) 1.30 1.38 1.22 1.39 0.96 0.75 0.00 0.0006 0.0012 0.006 0.012 0.022

3.2 THz Time-Domain Spectroscopy System

For the room temperature experiments, the THz time domain spectroscopy system can be divided mainly into three parts, i.e. the area for the samples, the area for THz wave propagation which is covered by a plastic box to keep the humidity below 6 %, and the area for laser pulses guiding as shown in the Fig. 3.

Table 2 Doping level and the thickness of GaSe:Te crystals

- 13 -

The input femtosecond laser pulses are split into two paths, one is the pump beam and the other is the signal beam. The THz wave is generated from the indium phosphor semiconductor antenna by the photoconductive switching effect with the pump beam. The THz wave propagates and is guided by two pairs of off-axis parabolic mirrors inside the box. The GaSe1-xTex crystals are illuminated by the THz beam right at the focus point. Then, the signal beam passes the delay stage which provides the time resolution for THz time-domain spectroscopy. At last, the THz and femtosecond laser beams are joined to the electro-optic sampling detection part. In order to avoid the absorption of water vapor in THz range [19], moreover, the box is purged with nitrogen gas to reduce the humidity lower than 6 %.

For the measurements at various temperatures, the samples are put inside a vacuum chamber which is sealed with Teflon windows. The chamber is provided a high vacuum level of 10⁻⁶ Torr to isolate the heat flow from the environments. The temperatures of samples can be controlled from room temperature to 40 K.

Fig. 3 Schematic diagram of THz time-domian spectroscopy system

- 14 -

3.3 The Principles for THz Generation and Detection

When a laser pulse of 800 nm irradiates on the indium phosphor antenna, many free carriers will be generated inside the illuminated area. With applying 180 V bias voltage to the antenna, an induced time-varying current flows between the electrodes. Then, the indium phosphor antenna radiates the electromagnetic wave [20] from the surface of antenna. The electric field of this radiated wave is proportional to the time-varying current density,

𝐸(𝑡) ∝^{𝜕𝐽(𝑡)}

𝜕𝑡 (3.1)

Finally, the THz pulse can be generated by the femtosecond laser pulse with the peak power of 2.31 nJ and the repetition rate of 80 MHz. Furthermore, the characteristics of THz pulse could be significantly affected by the material of the antenna, the electrodes’ distance, or even the pattern of the antenna.

The electro-optic sampling detection used in this system includes a birefringence ZnTe crystal, a quarter waveplate, a Wollaston prism and a pair of photodiodes.

The main idea [21] of the detecting method is that the electro-optic (or Pockels effect) and the phase retardation Γ occurs in the (110) face of a ZnTe crystal by the THz electric field at normal incidence. The phase retardation Γ can be expressed as,

Γ =^{𝜔𝑛03𝐸𝑇𝐻𝑧𝑟41𝐿}

𝑐 (3.2)

where 𝑛₀ is the refractive index of ZnTe crystal, 𝑟₄₁ is the electro-optic coefficient and 𝐿 is the thickness of ZnTe crystal. During the pass of the signal beam (or probe beam) in a ZnTe crystal, the signal beam will be modified by the phase retardation of the ZnTe crystal caused by the THz electric field 𝐸_𝑇𝐻𝑧. The polarization of probe beam will change from linear to circular through the 𝜆 4⁄

- 15 -

waveplate and the transmittance is linearly approximated with the retardation Γ.

The orthogonally polarizations of the probe beam are separated by the Wollaston prism to perform the retardation detection via the differential photo diodes. The final signal, which is in the form of ∆I = ΓI ∝ 𝑆_𝑇𝐻𝑧(𝜔), is sent to the lock-in amplifier with a reference frequency of 2.39 kHz.

8 10 12 14 16 18 20

Fig. 4 (a) Time-domain spectrum of various GaSe1-xTex samples;

(b) Time domain spectrum of a GaSe_0.9994Te_0.0006 crystal at various temperatures

(a)

(b)

- 16 -

The bold black line in Fig. 4(a) shows the typical THz signal with FWHM of about 400 fs in air. After passing through samples at room temperature, a dramatic delay related to the reference signal appears. Due to the thermo-expansion effect, e.g. the delay is also clearly observed in the signals from the GaSe0.9994Te0.0006 crystal measured at various temperatures as shown in Fig. 4(b).

- 17 -

IV. Results and Discussion

Thanks to the measurements of the time-domain spectroscopy system, and then the reliable parameters of the Te-doped gallium selenide crystals can be obtained or be calculated in the far-infrared region. The complex refractive indices, the absorption coefficient, and the dielectric responses at various temperatures will be presented and discussed in this chapter. Also, some structural behaviors like the interlayer vibration and the impurity influence are concerned.

4.1 The Characteristics of GaSe

1-x

Te

x

Crystals at Room Temperature

Figure 5 shows the power spectra in frequency domain of GaSe1-xTex

crystals, which are obtained from the Fig. 4(a) via the Fourier transform. The bandwidth of this spectrum is about 2.3 THz (1.4 mm), i.e. from far-infrared region 2.5 THz (0.12 mm) to micro-wave region 0.2 THz (1.5 mm). The signal to noise ratio is bad elsewhere due to the amplitude of the signal drops dramatically below 0.2THz and oscillates strongly beyond 2.5 THz. According to the real part of Eq. (2.9), the transmittance spectra of various samples are obtained from Fig. 5 and shown in Fig. 6. At room temperature, all of the transmittance spectra have the same tendency, namely decrease from 60 % down to about 10 % as increasing frequency.

- 18 -

Furthermore, we found a clearly deep in the transmittance spectra which indicates that certain absorption occurs around 0.58 THz (19.3 cm^-1). In general, this absorption deep is called rigid layer mode which characterizes the ε-type layered pure GaSe crystals. It is caused by the out of phase interlayer vibrations and the in-phase intralayer vibrations. The observed vibrational modes probably match with the vibrational modes indicated by the first principle calculations

Fig. 5 Frequency domain spectra of GaSe1-xTex crystals

Fig. 6 Transmittance spectra of GaSe1-xTex crystals

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

- 19 -

which study the physics of materials based on their compositions without experimental data. The configuration is derived by the Density Function Perturbation Theory to describe the atomic pseudo-potential variation and the different modes of phonon vibrations. The configuration of the rigid layer mode is shown in Fig. 7 [22]. There are other vibrational modes’ configurations versus different infrared vibrational frequencies and they are listed below in Table. 3

Fig. 7 (a) Configuration of the rigid layer vibrational mode at 19.3 cm^-1; (b) Configuration of the vibrational mode at 56.8 cm^-1

- 20 -

Mode First principle G Mode (cm^-1) First principle U Mode (cm^-1)

E’’

18.35 18.38

A1’ 33.58

E’

56.84 56.84

56.89 56.89

E’’ 58.74

58.81

A₂’’ 131.72

A1’ 136.26

E’

227.85 228.33

E’

230.74 230.74

231.26 231.26

E’’

231.65 232.17

A2’’ 253.48

A1’ 260.92

A1’ 322.18

A2’’ 322.62

This rigid layer mode can also be observed in low-doped GaSe_1-xTe_x crystals. The rigid layer mode of ε-type GaSe crystals at 0.58 THz (19.3 cm-1)

Table 3 Vibrational modes calculated by the First Principle

- 21 -

presents in both the frequency-domain spectra and the transmittance spectra including various Te-doping levels.

4.1.1 Complex Refractive Indices

Figure 8 shows the real part and the imaginary part of the ordinary refractive indices, which were calculated from the Eq. (2.11) and Eq. (2.12). The real part of refractive index is quite flat at low frequencies except phonon mode oscillations, and it rises slowly as increasing frequencies. The value is around 3.21 at low frequency range and rises towards 3.3 due to the Transverse Optical phonon mode oscillation at 6.40 THz (46.8 μm). The rigid layer phonon mode can be clearly observed in the refractive indices’ diagrams; and this mode induces an increment in the real part of refractive index while approaching the mode center from low frequency side and then drops just behind it.

Correspondingly, there is a peak appeared in the imaginary part of the ordinary refractive indices at where it represents absorption.

.

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 3.18

3.21 3.24 3.27 3.30

Real part of refractive index (a.u.)

Frequency (THz)

x=0.0000 x=0.0006 x=0.0012 x=0.006 x=0.012 x=0.022

GaSe1-xTex

(a)

- 22 -

The real part of refractive indices of thick GaSe1-xTex crystals increases as increasing the concentration of Te. For the thin GaSe1-xTex crystals, however, it shows neither any clear dependence of the Te-doping nor any absorption modes

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

imaginary part of refractive index (a.u.)

Frequency (THz)

Fig. 8 (a) Real part and (b) Imaginary part of the ordinary refractive indices in GaSe1-xTex crystals with thickness >0.75 mm at room temperature; (c) Real part of the ordinary refractive indices in the GaSe1-xTex thin crystals around 0.3 mm

Real part of refractive index (a.u.)

Frequency (THz)

- 23 -

as in Fig. 8(c). This may be caused by the non-uniform distribution of Te atoms in single crystal. The Sellmeier formula[10,23,24] is commonly used in the transparent region of most materials,

𝑛_𝑜² = 𝐴 + ^𝐵

this reciprocal wavelength (or frequency) polynomial is the experience formula related to the electronic transitions, which can fit the experimental refractive indices well at wide range photon energies. The 5^th and 6^th terms in the Sellmeier formula are attributed to certain phonon modes, i.e. the rigid layer mode at 0.58 THz (0.51 mm) and the TO mode at 6.40 THz (46.8 μm) expressed by the form of oscillators. The parameters 𝐴, 𝐵, 𝐶, 𝐷, 𝐸, 𝐹, 𝐺, 𝐻 were obtained by fitting the experimental data of refractive indices with the least square method, which are consistent with the early results in GaSe crystals [24,25]. Moreover, the last term in the Sellmeier formula is the new phonon mode proposed by us, which is caused via the tellurium impurity at 1.76 THz (0.170 μm). All of the parameters in the Sellmeier formula obtained from the fitting in Fig. 9 and are listed in the Table 4 for comparing with the results of ref. [10, 24].

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Real part of refractive index (a.u.)

Frequency (THz) Real part of the refractive index of pure GaSe crystal

Sellmeier formula fitted curve

(a)

- 24 - crystals in this work

Fitted parameters to GaSe0.9988Te0.0012

crystals in this work

A 7.443 7.37 7.19 7.22

Table 4 The fitting parameters used in the Sellmeier formula for the experimental data of refractive indices in GaSe1-xTex crystals

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Real part of refractive index (a.u.)

Frequency (THz) Real part of the refractive index of GaSe0.9988Te0.0012 crystal

Sellmeier formula fitted curve

(b)

Fig. 9 (a) Real part of the refractive index of pure ε-type GaSe crystal at room temperature and the Sellmeier formula fitting curve;(b) Real part of the refractive index of

GaSe0.9988Te0.0012 crystal at room temperature and the Sellmeier formula fitting curve

*Ref. [10] K. L. Vodopyanov, L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65-18 μm spectral region”, Opt. Commun., 118, 375 (1995)

#Ref. [23] C. W. Chen, T. T. Tang, S. H. Lin, J. Y. Huang, C. S. Chang, P. K. Chung, S. T. Yen, C. L. Ping,

“Optical properties and potential applications of ε-GaSe at terahertz frequencies”, J. Opt. Soc. Am. B, 26,

“Optical properties and potential applications of ε-GaSe at terahertz frequencies”, J. Opt. Soc. Am. B, 26,

在文檔中 利用兆赫波時析光譜研究摻碲硒化鎵晶體在不同温度下之電磁特性 (頁 12-0)