Calculation of Cu2O thin film optical constants using the transmittance data

F. Hajakbari1, A. Hojabri1, M. Gholami1 and M. Ghoranneviss 1, 2

1Physics Department, Islamic Azad University, Karaj Branch, Iran.

2Plasma Physics Research Center, Science and Research Campus of Islamic Azad University, Tehran, Iran.

Abstract: In the present work the interference transmission spectrum T (λ) of Cu2O thin film was used for determination of the optical constants of the film. The complex refractive index, n (λ) of film is calculated by use of a Swanepoel model theoritically. The optical band gap energy Eg at the edge of absorption band has been determined by the Tauc relation. The dispersion of n is discussed in terms of the Cauchy model and has been compared with refractive index calculated using Swanepoel model.

Keywords: Transmission spectrum, Optical properties, Energy band gap

1. Introduction The optical properties of thin films have been investigated by various analytical and numerical methods [1-3]. In these methods for calculation of optical constant of thin film such as the refractive index n ( )λ , extinction

coefficient k ( )λ and the thickness of film, the transmittance or reflectance data can be used. In this study we used the transmittance data and the swanepoel’s method in a computer program which has been developed and tested for optical characterization of the Cu2O film deposited on the glass substrat. 2. Theory Consider the optical system consist of a thin homogeneous film deposited on a transparent substrate with thickness several orders of magnitude greater than that of the film. The film and the substrate are surrounded by air with refractive index n.≈1 and the incident light from the spectrophotometer is normal to the substrate. The film has a complex refractive index n=n-ik where n is the refractive index and k is the extinction coefficient which can be expressed in terms of the absorption coefficient α by k=αλ/4π. The transmission spectrum will contain interference fring that obey the basic formula: 2nd = m λ Where m is the interference order that is an integer for maxima points and half integer for

minima points in the transmission spectrum, and d is the film thickness. The transmission spectrum can roughly be divided into three regions: The transparent region: (α=0), the weak and medium absorption (α is small) .The strong absorption region that the transmission decreases drastically due to the influence of α .For the case of k2«n2 the transmittance, T, for normal incidence is given by:

2DxxCcosBAxT

+−=

ϕ (1)

Where:

αd)exp(x)s(n1)(nD

λnd4π

)s1)(n2(nCs)(n1)(nB

s16nA

23

222

23

2

−=−−=

=

−−=

++=

=

ϕ

The values of the transmission at the extremes of the interference fringes can be obtained from Eq. (1) by substituting cosφ=+1 for maxima and cosφ=-1 for minima.

2M DxCxBAxT+−

=

2m DxCxBAxT++

=

In the medium and weak absorption refractive index of film can be calculated by the expression [1]: 2/12/122 ])([ SNNn −+= (2) Where

Where TM and Tm are the transmission maximum and the corresponding minimum at a certain wavelength λ .The refractive index of substrate and the thickness of film are s and d respectively which the film thickness is given by:

)(2 122

2

1

1

nnd

λλ

λλ

−= (3)

Where n1 and n2 are the refractive indices at two adjacent maxima (or minima) at 1λ and 2λ .

3. Result and discussion We used the transmission spectrum of the Cu2O film deposited on the glass substrate using DC magnetron sputtering technique in fig.1 [4] and then optical constant of film were calculated by swanepoel method in a computer program. Fig.1 shows the transmission spectrum of the Cu2O film.

Fig.1.The Cu2O film transmission spectrum. The variation of the refractive index n with the wavelengths is shown in fig.2.The refractive index is found to decrease with increase in wavelength of the incident photon and then at

higher wavelength of the incident photon, the refractive index tends to be constant.

Fig.2. Refractive index versus wavelength for the Cu2O film in swanepoel model. The values of refractive index can be fitted to the Cauchy dispersion that well suited to the transparent materials through the following relationship:[5]

2)(λ

λ nn

BAn += (4)

Where the An, Bn are the fitting parameters. For our investigation the fitting parameters are An=2.28, Bn=6.5*104

Fig.3. Refractive index versus wavelength for the Cu2O film in Cauchy model. We can observe that from Fig2 and Fig3 there is a good agreement between the results obtained by swanepoel method and Cauchy method. To determine the film thickness, d, a number of thicknesses are calculated using equation (3) and then the average of d is calculated which is about 798nm.

21s

TT

TT2sN

2

mM

mM ++

⋅=

⋅

−

The absorption coefficient α in the weak and medium absorption was calculated by:

( ) ( )[ ]( ) ( ) ⎥

⎥

⎦

⎤

⎢⎢

⎣

⎡

−−−−−−

−= 23

21

42322

11ln1

snnsnnEE

dMMα (5)

Where

( )( )2222

18 snnT

snEM

M −−+=

In the strong absorption region, the refractive index is determined by extrapolating the plot of n versus λ in Eq. (4) and in this region mM TT , converge to a single curve T and the absorption coefficient can be calculated by:

( ) ( )⎥⎦

⎤⎢⎣

⎡ ++−=

snsnnT

d 2

23

161ln1α (6)

For determination of the optical band gap, we used the Tauc relationship as follow:

2/1)( gEhAh −= ννα (7)

Where νh is the photon energy, A is a constant, and gE is the optical band gap of film, by

extrapolating the linear portion of the plot of ( )2ναh versus ( )νh to ( )2ναh =0 was calculated. Fig.4. shows the plot of ( )2ναh versus photon energy of the Cu2O film.

Fig.4. Plot of ( )2ναh versus νh of Cu2O film. This fig. shows that the Cu2O film has direct band gap which is about 1.97 eV that is in good agreement with results of Ref. [6]. 4. Conclusion

In this work the transmittance data were used in a computer program which has been developed and tested for optical characterization of the Cu2O film deposited on the glass substrate. The film refractive index in this study is constant in the long wavelength range and increase in

short wavelength that shows the good agreement with Cauchy dispersion model. The film optical band gap energy as well as average thickness was investigated. Acknowledgement This work has been supported by the Islamic Azad University, Karaj Branch. References [1] Swanepole, R., J. Phys. E: Sci. Instrum., 19, 1214 (1984). [2] Ventura, S. D., Birgin, E. G., Martinez, J. M. and Chambouleyron, I., J. Appl. Phys. 97, 043512-1 (2005). [3] Poelman, D. and Smet, P. F., J. Phys. D: Appl. Phys. 36, 1850 (2003). [4] Sivasankar Reddy, A., Uthanna, S. and Sreedhara Reddy, P., Appl. Surf. Sci. 253, 5287 (2007). [5] Jenkins, F. A. and White, H. E., fundamentals of Optics (Auckland: McGraw-hill) pp 482 (1981). [6] Sivasankar Reddy, A., Venkata Rao, G., Uthanna, S. and Sreedhara Reddy, P., Mater. Lett. 60, 1617 (2006).