6-2 Spectroscopic ellipsometric spectra

Figures 6.11 and 6.12 show two independently measured experimental data of monolayer WS2

and WSe2 thin films at 70^o and 75^o incidence angles and the model curves are in good agreement. We

fitted the ellipsometric spectra using the stacked layer model consisting of sapphire structure / thin

film / surface roughness / air ambient structure (Fig. 6.13). First, we constructed the c-sapphire

substrate and set its thickness about 0.5 mm. Second, we added the Cauchy model and fitted the data

in the range of 650 ~ 1700 nm (0.73 ~ 1.9 eV). Thickness of a monolayer WS2 thin film was mainly

determined by using the Cauchy model. The Cauchy model can be described by

( )

^B₂ ^C₄ where n is the refractive index, k is the extinction coefficient, A, B and C are the Cauchy parameters.

Third, we fitted the data in the range of 180 ~ 650 nm (1.9 ~ 6.9 eV) by using the Tauc-Lorentz

oscillator model. Tauc-Lorentz model describes the function of the complex dielectric constants near

the band gap. The complex dielectric function is ε ε= +₁ iε₂. The optical constants ( , n k ) are related to the real and imaginary part of the dielectric constants (ε ε₁, ₂) at each wavelength by Eqs.

(6.2.3) and (6.2.4).

2 2

1 n k

ε = − , (6.2.3)

and ε₂ =2nk . (6.2.4)

The Tauc-Lorentz model can be described by the imaginary part Eq. (6.2.5) and the real part Eq.

(6.2.6). The real part of the dielectric function is obtained by the Kramers-Kronig integration of ε₂ [73].

is the broadening parameter, and ε_∞ normally equals to 1. Finally, we added the surface roughness and air ambient structure. Table 6.5 contains a list of fitting parameters of the stacked layer model.

The complex optical constants of monolayer WS2 and WSe2 thin films derived from the

ellipsometric parameters of Ψ and ∆ are shown in Figs. 6.14 and 6.15. The complex optical

constants can reasonably be divided into three different regions. No anomalous dispersion was

observed in the near-infrared region. The visible wavelength region was dominated by excitonic

transitions. Several structures were observed in the ultraviolet region. They were associated with the

interband transitions.

Figures 6.16 and 6.17 show the room-temperature absorption spectra of monolayer WS₂ and

WSe2 thin films. The absorption spectrum can reasonably be divided into a region at low energy,

which is dominated by excitonic transition on an otherwise relatively low absorption background,

and a region of strong absorption at higher energy. Two low-energy peaks are assigned to A and B

excitons [145,146]. Their positions in a monolayer WS2 thin film are approximately 2.01 and 2.41

eV and are red shifted to 1.65 and 2.08 eV in a monolayer WSe2 thin film. These position values

were determined by the broadened Lorentzian line shape. Our experimental values are in good

agreement with those reported by B. Zhu et al. and K. Xu et al. [147,148] B. Zhu's et al. studied the

transmission spectra of mechanical exfoliated monolayer WS₂. The A and B exciton positions of

monolayer WS2 are 2.020 and 2.403 eV. K. Xu's et al. examined the photoluminescence spectra of

vapor-liquid-solid (VLS) grown monolayer WSe2. The A and B exciton positions of single-layer

WSe2 are 1.65 and 2.02 eV.

The discrete states of the exciton observed in monolayer WS2 and WSe2 thin films can be

described by using the broadened Lorentzian line shape [149].

0

fitting parameters is given in Table 6.6. The first-principle calculations [68,150-152] predicted

monolayer WS2 and WSe2 exhibit a direct band gap at K point. Furthermore, the direct gap

transitions at K point between the top of the split valence bands and bottom of the conduction band

are called A and B excitons. At room-temperature, the direct band gap values of monolayer WS2 and

monolayer WSe₂ thin films are 2.1 and 1.72 eV. The results of our experimental band-gap values are

consistent with the reported earlier by Z. Ye et al. [153] and S. Tongay et al. [154] Z. Ye's et al.

studied the absorption spectrum of mechanical exfoliated single-layer WS₂. The band gap value of

the single-layer WS2 is 2.22 eV. S. Tongay's et al. examined the photoluminescence spectrum of

mechanical exfoliated monolayer WSe2. The band gap value of monolayer WSe2 is 1.73 eV.

Using the effective mass approximations, Figure 6.18a proposes that the Coulomb interaction

between electron and hole. The Coulomb interaction leads to a hydrogen-like problem with a

Coulomb potential term, which can be described by

2

Indeed, excitons in semiconductors form a hydrogen or positronium like series of states below the

gap. For the direct band gap semiconductor, one can separate the relative motion of electron and hole

and the motion of the center of mass. This leads to the dispersion relation of excitons [155,163] :

( )

^{2 2 2}

reduced exciton mass, ε is the dielectric constant, K

is the wave vector of the exciton, and M is the translational mass. When going from three-dimensional to two-dimensional system, N is

related to the confluent hypergeometric function [156]. In the three-dimensional, the function

satisfies the condition at infinity. But, the function satisfies the condition at finity in the

two-dimensional. So the function reduces to a finite polynomial. Thus we arrive at the condition 1 3 5

considered. The Eqs. (6.2.8) was moified as follows :

( )

²

The exciton binding energy can be described by Eqs. (6.2.10)

2

WSe2 thin films were estimated to be 0.33 and 0.24 eV. Our experimental values are in good

agreement with the reported by A. Chernikov et al. [157] and C. J. Docherty et al. [158] A.

Chernikov's et al. examined the mechanical exfoliated monolayer WS2. The exciton binding energy

value of a monolayer WS₂ is 0.32 eV. C. J. Docherty 's et al. studied the chemical vapor deposition

(CVD) grown monolayer WSe2. The exciton binding energy value of monolayer WSe2 is 0.24 eV.

Notably, the exciton binding energy of monolayer WS2 and WSe2 is approximately four or five times

than that of bulk WS2 and WSe2 (57 meV for bulk WS2 [164,165] and 55 meV for bulk WSe2 [164]).

This phenomenon can be explained that the electrons, holes, and excitons increases the Coulomb

interaction between electrons and holes with a increase in dimension [163], which leads to exciton

binding energies of monolayer materials four or five times larger than that of bulk materials.

Figures 6.19 and 6.20 show the temperature-dependent absorption spectra of monolayer WS2

and WSe2 thin films. The temperature-dependent positions and linewidths of excitonic transitions of

monolayer WS2 and WSe2 thin films are shown in Figs. 6.21 ~ 6.24. With an increase in the

temperature, we observed the positions of A and B excitons are red shifted for both materials. The

linewidths of A and B excitons are broadening. The changes of positions and linewidths with

increasing temperature are due to contributions from thermal expansion and electron-phonon

interactions [159].

Figures 6.25 and 6.26 show the temperature dependence of energy gap and exciton binding

energy of monolayer WS2 and WSe2 thin films. The direct band gap of monolayer WS2 thin film is

2.12 eV at 240 K and 2.01 eV at 500 K. The exciton binding energy of monolayer WS2 thin film is

0.348 eV at 240 K and 0.276 eV at 500 K. The direct band gap of monolayer WSe2 thin film is 1.75

eV at 240 K and 1.62 eV at 500 K. The exciton binding energy of monolayer WSe₂ thin film is 0.264

eV at 240 K and 0.192 eV at 500 K. Notably, the band-gap narrowing coefficient of monolayer WS2

and WSe₂ thin films can be obtained by using the formula β =dE_g/dT, and the results are

approximately -6.3 × 10^-4 eV / K and -3.75 × 10^-4 eV / K at 300 K, respectively. These values are

comparable to those of other semiconductor materials; for example, GaN is -6.14 × 10^-4 eV / K and

GaAs is -4.76 × 10^-4 eV / K [120]. The exciton binding energy narrowing coefficient of monolayer WS2 and WSe2 thin films can be obtained by using the formula β =dE_b /dT, and the results are

approximately -2.4 × 10^-4 eV / K and -1.8 × 10^-4 eV / K at 300 K. The negative band-gap narrowing

coefficient can be explained by two reasons: (i) thermal expansion of the lattice and renormalization

of the band structure by electron- phonon interaction, and (ii) lattice vibration, leading to a deviation

of atoms or ions from balance sites, would destroy the lattice periodic field, gives rise to an addition

potential as a perturbation of electron energy and transition, even changes the chemical bond length,

and further renormalize these bond structure and band-gap energy [120,121]. The energy gap with

elevating temperature can be described using the Bose-Einstein model [124]

( ) ( )

Θ is average phonon temperature. In our fitting results, the band-gap energy of monolayer WSB 2

and WSe2 thin films toward 0 K are approximately 2.18 ± 0.05 and 1.81 ± 0.05 eV. The strength of electron-phonon interaction a of monolayer WS_B 2 and WSe2 thin films are 59 and 63 meV. The

average phonon temperature Θ of monolayer WS_B 2 and WSe2 thin films are 260 and 254 K. These

values are comparable to those of other semiconductor materials; such as Ge material, a = 52 meV _B

and Θ = 253 K [160]. _B

The temperature shift of Eg

( )

^T contains contributions from both thermal expansion and electron-phonon coupling effects. The energy shift ∆E_th due to the thermal expansion can be

described by [161]

3 T

th th

E aα

∆ = − , (6.2.13)

where a is the hydrostatic deformation potential (this value of monolayer WS₂ and WSe₂ thin films are approximately -0.074 and -0.048 eV); and α is the linear thermal expansion coefficient. This _th

equation can combine with the Bose-Einstein model. Equation (6.2.11) can be rewritten as

( ) ( )

comparable to those of other semiconductor materials; for example, In_0.06Ga_0.94As is 6.69 × 10^-6

(1 / K) [162].

6-3 Summary

In summary, Raman scattering and spectroscopiec ellipsometry spectra of monolayer WS2 and

WSe2 thin films provide us several important information.

First, Raman scattering spectra of monolayer WS₂ and WSe₂ thin films excited by a 532-nm

laser line show full phonon modes including first-order mode, second-order mode, and

combinational mode.

Second, the complex optical constant spectra of monolayer WS2 and WSe2 thin films show that

the visible region was dominated by excitonic transition and the ultraviolet range was dominated by

interband transition. The room-temperature absorption spectra of monolayer WS2 and WSe2 thin

films show emerging A and B excitons in the low-energy region. These spectra display direct band

gaps of monolayer WS₂ and WSe₂ thin films to be 2.1 and 1.72 eV at 300 K. Importantly, this studies

identify the exciton binding energy of monolayer WS₂ and WSe₂ thin films are approximately 0.33

and 0.24 eV at 300 K.

Third, variable temperature absorption spectra of monolayer WS2 and WSe2 thin films show

that the positions of A and B excitons positions are red shifted with elevated temperature from 240 to

500 K. The temperature dependent of direct band gap of monolayer WS2 and WSe2 thin films shows

a redshift, which can be elucidated by thermal expansion and electron-phonon interaction.

Table 6.1 Parameters of a Lorentzian fit for the Raman scattering spectrum of a monolayer WS2 thin film excited by a 532-nm laser line. All units are cm^-1.

Monolayer WS2 Monolayer WS2

ωp1 550.6 ωp9 810.4

Table 6.2 Parameters of lattice vibrations of WX2 (X = S, Se) [139].

Irreducible representation

Transformation

properties Activity Direction

of vibration Atoms involved

A2u T_z acoustical c axis W + X

2

B2 g inactive c axis W + X

A2u T_z infrared (E c ) c axis W + X

1

B2 g inactive c axis W + X

A1g α_xx+α_yy, α_zz Raman c axis X

B1u inactive c axis X

E1u T_x, T_y acoustical basal plane W + X

2

E2 g α_xx−α_yy, α_xy Raman basal plane W + X

E1u T_x, T_y infrared (E⊥c) basal plane W + X

1

E2 g α_xx−α_yy, α_xy Raman basal plane W + X

E1g α_yz, α _zx Raman basal plane X

E2u inactive basal plane X

Table 6.3 Correlation chart relating the irreducible representations of the site groups D_3h and C_3v

to those of the factor group D_6h [139].

W atom (S, Se) atoms

D3h D_6h C_3v

A1g A T1

( )

z

( )

Tz A2^'' A_2u A T1

( )

z

B1u A T1

( )

z

( )

Tz A2^'' B_{2 g} A T1

( )

z

E1g ^{E T}

(

^{x, Ty}

) (

^{Tx, Ty}

)

^{E' E1u E T}

(

^{x, Ty}

) (

^{Tx, Ty}

)

^{E' E2 g E T}

(

^{x, Ty}

)

E2u ^{E T}

(

^{x, Ty}

)

在文檔中 摻雜鑭系元素(鏑,釓)氧化鋅與單層二(硫,硒)化鎢薄膜的光譜性質研究 (頁 189-200)