Improvement of Swanepoel method for deriving the thickness and the optical properties of chalcogenide thin films

Youliang Jin; Baoan Song; Zhitai Jia; Yinan Zhang; Changgui Lin; Xunsi Wang; Shixun Dai

doi:10.1364/OE.25.000440

1. Introduction

Chalcogenide glasses (ChGs) are infrared transparent semiconductors formed primarily from chalcogen elements such as sulphur, selenium or tellurium. In contrast with silica, ChGs are highly nonlinear and photosensitive. ChGs in the form of flexible thin films have been widely used in the phase-change memories, highly efficient solar cells, on-chip optical circuits, active matrix display, image sensors, laser-induced films waveguides, photovoltaic devices, etc [1–3]. Over the past few decades the optical properties of ChGs films have been the subject of intense study. The accurate knowledge of optical properties (refractive index, absorption coefficient, dispersion parameter, etc.) of the ChGs films is critical important for fabricating high-quality optical devices for researchers and technologists.

Great efforts have been made to develop the method for determining the refractive index, absorption coefficient, dispersion parameter, etc. of the films. Many methods have been developed including ellipsometry [4–6], fitting method [7, 8], reflection spectrum method [9–11]. The most common method was proposed by Swanepoel [12]. Swanepoel obtained the refractive index, thickness and absorption coefficient of the films only from their transmission spectrum. Therefore, Swanepoel method has been employed by numerous researchers to analyze the optical properties of the films [13–18]. On the basic of Swanepoel method some researchers have presented some different analytical algorithms for determining the thickness and optical parameters of the films [19–25]. However, Swanepoel method would lead to obvious abnormal values of the film thickness in the region of strong absorption which were rejected by Swanepoel. Therefore, more precise method is highly desired to determine the thickness and optical properties of the chalcogenide thin films in the whole transmission spectrum.

In the present paper, we proposed TPM to solve the problem of abnormal value of the film thickness obtained by the Swanepoel method. Firstly, it is theoretically proved that the tangencypoints really are at the position of transmission curve where the interference order is an integer or semi-integer. Then we obtained the thickness and refractive index of the ChGs films by the TPM. Furthermore, we compared TPM and Swanepoel method based on the same simulation and experimental data. Finally, the dispersion and absorption coefficient of the ChGs thin films were accurately obtained by using the TPM.

2. Theory

2.1 The TPM

The TPM is the improvement of Swanepoel method for deriving the thickness and the optical properties of ChGs thin films. The key for determining the thickness and refractive index of the films is to find the position of the transmission curve where the interference order is an integer or semi-integer. The corresponding transmission and light wavelength at the position are used to calculate the thickness and refractive index of the films. Swanepoel method would lead to some abnormal results obviously in the region of strong absorption because the refractive index and thickness of the films were calculated by using the transmission and light wavelength at two adjacent peaks or valleys of the transmission curve. However the peaks and valleys are not exactly located at the position of the transmission curve where the interference order is an integer or semi-integer especially in the strong absorption region. Thus we improved Swanepoel method and proposed the TPM. In the TPM we solved the problem of the abnormal value of thickness in the strong absorption region obtained by Swanepoel method. The light wavelength and transmission at the tangency points of transmission curve and its envelopes were used to calculate the thickness and refractive index of ChGs thin films. Furthermore, it is proved to be more accurate theoretically.

2.2 Expressions used in the TPM

The optical schematic is shown in Fig. 1 with a ChGs thin film on a transparent thick silica substrate. The film parameters include: thickness d, absorption coefficient α and complex refractive index N = n-ik, where n is the real part of the refractive index and k is the imaginary part which can be expressed in terms of the absorption coefficient by k = αλ/4π where λ is light wavelength. The thickness of transparent substrate with refractive index s and absorption coefficient α_s = 0 is more than two orders of magnitude than the film thickness d. The refractive index of surrounding air is n₀ = 1.

Fig. 1 Schematic of an absorbing thin film on a thick finite transparent substrate

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The transmission T for the case of Fig. 1 is expressed as:

T = \frac{A x}{B - C x \cos φ + D x^{2}}

where A = 16n²s, B = (n + 1)³(n + s²), C = 2(n²-1)(n²-s²), D = (n-1)³(n-s²), φ = 4πnd/λ, x = exp(-αd). The refractive index s of the substrate is acquired based on the data from the transmission spectrum of the substrate alone. λ is light wavelength. φ is phase. x is a parameter related to thickness d and absorption coefficient α of the film. There are only two independent variables n and x in the above equation. In order to get these two variables two independent equations are needed. The extremes of the interference fringes can be expressed as

T_{M} = \frac{A x}{B - C x + D x^{2}}

T_{m} = \frac{A x}{B + C x + D x^{2}}

where T_M and T_m really are the upper and lower tangent envelopes of the transmission spectrum, respectively, rather than the peaks and valleys envelopes. Solving Eqs. (2) and (3), we can get n at any wavelength

n = \sqrt{2 s \frac{T_{M} - T_{m}}{T_{M} T_{m}} + \frac{s^{2} + 1}{2} + \sqrt{{(2 s \frac{T_{M} - T_{m}}{T_{M} T_{m}} + \frac{s^{2} + 1}{2})}^{2} - s^{2}}}

Additionally, the basic equation for the interference fringes is

2 n d = m λ

where m is the interference order. The film thickness d is given by:

d = \frac{λ_{1} λ_{2}}{2 (λ_{1} n_{2} - λ_{2} n_{1})}

where n₁ and n₂ are the refractive index at two adjacent interference fringes whose interference order is an integer or semi-integer at λ₁ and λ₂. Then the average value

\bar{d_{1}}

of d and n are used to get the interference order m₀ by Eq. (5). Now the parameters n and d are recalculated using Eq. (5) with higher accuracy after m₀ is approached to m (integer or semi-integer).

The Eqs. (1)-(3) are corresponding to the transmission curve, upper and lower envelopes, respectively. The parameters A, B, C, D, φ and x in three equations are only related to the variables λ, n, d and α. In addition, n and α are only related to λ. Therefore, T, T_m and T_M are now considered to be continuous function of λ. Solving the first derivative of T, T_m and T_M versus λ yields Eqs. (7)-(9) respectively:

T^{'} = \frac{{(A x)}^{'} (B - C x \cos φ + D x^{2}) - (A x) [B^{'} - {(C x \cos φ)}^{'} + {(D x^{2})}^{'}]}{{(B - C x \cos φ + D x^{2})}^{2}}

where

{(C x \cos φ)}^{'} = {(C x)}^{'} \cos φ - (C x) \frac{4 π n^{'} d λ - 4 π n d}{λ^{2}} \sin φ

.

T_{M}^{'} = \frac{{(A x)}^{'} (B - C x + D x^{2}) - (A x) [B^{'} - {(C x)}^{'} + {(D x)}^{'}]}{{(B - C x + D x^{2})}^{2}}

T_{m}^{'} = \frac{{(A x)}^{'} (B + C x + D x^{2}) - (A x) [B^{'} + {(C x)}^{'} + {(D x)}^{'}]}{{(B + C x + D x^{2})}^{2}}

Only if φ = 2kπ (where k is an integer or semi-integer) we can get

T^{'} = T_{M}^{'}

and

T^{'} = T_{m}^{'}

, respectively. Besides, we know φ = 4πnd/λ from the Eq. (1). So 4πnd/λ = 2kπ and solving it yields

λ = \frac{2 n d}{k}

Substituting

λ = \frac{2 n d}{k}

into Eq. (1) yields

T = T_{M}

and

T = T_{m}

. As we know, two curves intersect in one point and they have the same slope in the point of intersection. So these two curves are tangent in the point. Consequently, we can conclude that the transmission curve is tangent to its envelope only if φ = 2kπ (where k is an integer or semi-integer). The Eq. (10) has the same form as the basic equation for the interference fringes 2nd = mλ (where m is an integer or semi-integer). It shows the tangent points of the transmission curve and its envelopes are the point of transmission curve where the interference order m is an integer or semi-integer.

3 Simulation and experiments

3.1 Numerical simulation

To test the accuracy of TPM, a film with the following properties postulated in the paper “Determination of the thickness and optical constants of amorphous silicon” is used [12]. The properties of the film are as follows: s = 1.51, d = 1000 nm, $n = \frac{3 \times 10^{5}}{λ^{2}} + 2.6$ , $\lg α = \frac{1.5 \times 10^{6}}{λ^{2}} - 8$ . The full curve in Fig. 2 is a plot of T as calculated by Eq. (1) using the above postulated properties of the film and the broken curve T_M and T_m are the upper and lower envelopes of the transmission spectrum, respectively.

Fig. 2 Transmission curve of a 1 µm film of Si-H on a finite glass substrate

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3.2 Experimental

ChGs films (Ge-Sb-Se film) were deposited by radio frequency (RF) magnetron sputtering the targets prepared by using conventional melt-quenching vacuum method onto a clean glass slide substrate. The sputtering was carried out at a pressure of 0.5 Pa. and a low RF power in the range of 20-40 W. The substrate was rotated at a speed of 5 r/min and maintained at 25°C during the deposition. The films were annealed after the deposition. The transmission spectrums with high frequency noises were obtained by using a double-beam UV-VIS-NIR spectrophotometer (Perkin-Elmer Lamda-950) with the wavelength range of 400-2500 nm. The Savitzky-Golay filter was used to filter out the noises of transmission curve [26, 27] which are five times more than the frequency of the signal to obtain the smooth full curve as shown in Fig. 3. The transmission measurements had a good reproducibility in various parts of the films. In addition it was unnecessary to make slit width correction because the instrument was set with a slit width of smaller than 2 nm. In order to compare with the results deduced from the transmission spectrum a surface profilometer (Veeco Dektak 150) with the accuracy of 0.1 nm was used to measure the thickness of the films directly. Both results agree with each other.

Fig. 3 The transmission curve with upper and lower tangent envelopes obtained by P-E 950 experimentally

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4 Results and discussion

4.1 The thickness and refractive index obtained from simulation

To get simulation results of thickness and refractive index of the postulated film we substituted $n = \frac{3 \times 10^{5}}{λ^{2}} + 2.6$ , d = 1000 into 2nd = mλ and solving λ yields wavelength values at the position where the order number m is an integer or semi-integer. Then the values of T_M and T_m were obtained respectively by substituting these wavelength values into Eqs. (2) and (3). The thickness and refractive index of the film are obtained by TPM listed in Table 1 using these values of T_M, T_m and corresponding wavelengths. And the values of the thickness and refractive index in Table 2 are obtained by Swanepoel method.

Table 1. Values of λ, T_M and T_m obtained from Fig. 2 and the n and d values calculated by TPM.

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Table 2. Values of λ, T_M and T_m obtained from Fig. 2 and the n and d values calculated by Swanepoel method.

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The inset of Fig. 2 is the transmission curve ranging from 561 nm to 568 nm in the region of strong absorption. Obviously the valley and tangent points are not in the same position. There has a difference of a few nanometers. The calculation accuracy of n and d is more sensitive to values of λ, T_M and T_m in the region of strong absorption than in the region of medium, weak and transparent absorption. Swanepoel calculated the values of n and d by using the data of λ, T_M and T_m at peaks and valleys of the transmission curve. So there is a significant difference between the calculated values n₁, d₁ and m₀ in Table 2 obtained by Swanepoel method and the theoretical values n_tr, d = 1000 nm and m respectively at the wavelengths of 564 nm and 555 nm. However, n₁, d₁ and m₀ calculated by TPM as shown in Table 1 are in good agreement with the theoretical values n_tr, d = 1000 nm and m, respectively. And after the interference order m₀ is approached to m (integer or semi-integer), n₂ and d₂ are exactly consistent with their theoretical values. The calculation accuracy of refractive index and thickness of the film are improved to 0.5% by using TPM.

The wavelength values are generally not an integer when the interference order m, the thickness d and the refractive index n are constants according to the interference Eq. (2)nd = mλ. However, the wavelength values read from the spectrophotometer are an integer in fact. In order to increase the calculation accuracy of the refractive index n and the thickness d the cubic spline interpolation is used for processing the discrete experimental data [28, 29] to get the continuous transmission curve at any λ which is accurate to a digit after a decimal point with the unit of nanometer. Calculation of n, d and m₀ are listed in Table 3. The results show that the calculated values of n, d and m₀ is more accurate after such a data processing.

Table 3. Values of λ, T_M and T_m from Fig. 2 and the n and d values calculated by TPM after improving the accuracy of λ, T_M and T_m.

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4.2 The thickness and refractive index of Ge-Sb-Se film obtained from experiments

The thickness and refractive index of Ge-Sb-Se films were obtained by TPM and Swanepoel method, respectively. And the calculation accuracy of the thickness and refractive index is better than 0.5% by TPM which is higher than that of Swanepoel method. The calculation of n and d obtained by TPM based on Fig. 3 are shown in Table 4. And n and d in Table 5 are acquired by Swanepoel method.

Table 4. Values of λ, T_M and T_m from Fig. 3 and the n and d values calculated by TPM.

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Table 5. Values of λ, T_M and T_m from Fig. 3 and the n and d values calculated by Swanepoel method.

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There are two values of d₁ in the region of strong absorption deviate considerably from the other values in Table 5. These values must be rejected in Swanepoel's view. The values of n₂ in the region of the strong absorption have to be estimated by extrapolating the values calculated in the other parts of spectrum. But the estimation is not accurate enough. Obviously, there are no abnormal values of d₁ and d₂ in whole spectrum region in Table 4 and the value σ₁ and σ₂ in Table 4 are less than the value σ₁ and σ₂ in Table 5. In addition, the values m₀ are much closer to the value of m in Table 4 than in Table 5 in the strong absorption region. It indicates that TPM is more accurate than Swanepoel method especially for the strong absorption region. During the process of measuring the transmission spectrum, the high-frequency noise generated by switching grating is mainly in the wavelength region of 840-900 nm which caused the values d₁ at the wavelength of 793.5 nm and 751.5 nm were slightly smaller. And the high-frequency noise generated by the noise of detector which caused the values d₁ at the wavelength of 1413.7 nm and 1264.2 were slightly larger.

4.3 The dispersion and absorption coefficient of Ge-Sb-Se film

Now substituting n₂ in Table 4 into Eq. (2) and solving for x yields

x = \frac{\frac{8 n^{2} s}{T_{M}} + (n^{2} - 1) (n^{2} - s^{2}) + {{[\frac{8 n^{2} s}{T_{M}} + (n^{2} - 1) (n^{2} - s^{2})]}^{2} - {(n^{2} - 1)}^{3} (n^{2} - s^{4})}^{1 / 2}}{{(n - 1)}^{3} (n - s^{2})}

The absorption coefficient α can be calculated from x and d by using x = exp(-αd). It is given by

α =- \frac{\ln x}{\bar{d_{2}}}

And then we get a curve of the absorption coefficient α versus the wavelength λ by the method of interpolation as shown in Fig. 4(a). According to the results transmission spectrum are divided into three regions, namely the strong absorption region from 400 to 720 nm, the weak and medium absorption region 720-1200 nm and the transparent region with the wavelength larger than 1200 nm. The relationships between the absorption coefficient and the photon energy in the region of strong absorption is given by Tauc [30] as

{(α E)}^{1 / 2} = k (E - E_{g})

where k is a constant which is almost independent of the chemical composition of the film, E is the photon energy and E_g is the optical band gap. The optical band gap is defined as the E axis intercept of the linear part of the plot of (αE)^½ vs E. Through the linear fitting of the experimental data the following equation was got: (αE)^½ = 247 × (E−1.623) and we got E_g = 1.623 eV with (αE) ^½ = 0. The corresponding wavelength was 764 nm.

Fig. 4 The absorption characteristic s of chalcogenide film (a) the absorption coefficient vs the wavelength; (b) Square root of the product of the absorption coefficient and photon energy vs the photon energy in the strong absorption region

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We get $n = \frac{4.76 \times 10^{4}}{λ^{2}} + \frac{3.04 \times 10^{10}}{λ^{4}} + 2.3234$ and a continuous curve of refractive index as shown in Fig. 5(a) by using a well-known Cauchy dispersion formula of the form $n = \frac{a}{λ^{2}} + \frac{b}{λ^{4}} + c$ for fitting the refractive index n₂ in Table 4. Then the group refractive index and dispersion parameter of the film were obtained. The group refractive index n_g is given by

n_{g} = n - λ n^{'}

where n' is the first-order derivative of the refractive index n versus λ. And the dispersion parameter D_λ can be expressed as

D_{λ} = c^{- 1} {n^{'}}_{g}

where c is the velocity of the light and n_g' is the first-order derivative of n_g versus λ. And the unit of D_λ is ps/km•nm. The dependence of the group refractive index and the dispersion coefficient of the film on the wavelength are shown in Figs. 5(b) and 5(c), respectively. In this spectral range, n'< 0 for any wavelength. Ge-Sb-Se film has normal phase-velocity dispersion in the entire spectral region around λ = 600-1900 nm. And the dispersion parameter D_λ is negative in the spectral range so longer wavelengths travel faster than shorter wavelengths in Ge-Sb-Se films.

Fig. 5 Dependence of the refractive index, group refractive index and group dispersion of Ge-Sb-Se film on the light wavelength

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5. Conclusion

TPM is presented to calculate the refractive index n and the thickness d based on the data λ, T_M and T_m at the tangent points of the transmission curve and its envelopes, which achieves an accuracy of higher than 0.5%. It is proven theoretically that tangency point really locates at the position where the interference order is an integer or semi-integer. This method corrects the abnormal value of d in the region of strong absorption. The transmission spectrum of the chalcogenide thin film was obtained by using the spectrophotometer and the refractive index and thickness of the film were derived by TPM and Swanepoel method, respectively. The results indicated that there are no abnormal values of d in the whole spectrum region and the results are more accurate and precise by using TPM. Finally, we obtained the dispersion, absorption coefficient and group refractive index of the ChGs thin film by TPM.

Funding

The work was supported by the Natural Science Foundation of Zhejiang Province (Grant No. LY14F050001), State Key Laboratory of Crystal Material (Shandong University) (Grant No. KF1204), and K.C. Wong Magna Fund in Ningbo University.

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λ		T_M	T_m	n₁	d₁	m₀	m	d₂	n₂	n_tr
859		0.919	0.480	3.006		6.97	7	1000	3.008	3.006
814		0.918	0.470	3.051		7.47	7.5	1001	3.054	3.053
775		0.917	0.459	3.101	998	7.97	8	1000	3.102	3.099
740		0.913	0.448	3.149	985	8.48	8.5	999	3.147	3.148
710		0.908	0.438	3.193	1008	8.96	9	1001	3.197	3.195
683		0.899	0.426	3.244	1012	9.46	9.5	1000	3.246	3.243
658		0.881	0.413	3.292	987	9.97	10	999	3.292	3.293
636		0.853	0.398	3.342	989	10.47	10.5	999	3.341	3.341
616		0.804	0.379	3.392	993	10.97	11	999	3.390	3.391
598		0.728	0.354	3.443	996	11.47	11.5	999	3.441	3.439
581		0.610	0.318	3.491	997	11.97	12	999	3.488	3.489
566		0.461	0.268	3.540	1005	12.46	12.5	999	3.540	3.536
552		0.292	0.198	3.595	991	12.97	13	998	3.590	3.585
	$\bar{d_{1}} =996$ ;σ₁ = 8; $\bar{d_{2}} =999$ ;σ₂ = 1

λ		T_M	T_m	n₁	d₁	m₀	m	d₂	n₂	n_tr
859		0.919	0.478	3.015		7.08	7	997	3.007	3.006
814		0.919	0.470	3.052		7.56	7.5	1000	3.053	3.053
775		0.916	0.460	3.095	1035	8.05	8	1002	3.100	3.099
740		0.913	0.448	3.149	988	8.58	8.5	999	3.145	3.147
710		0.908	0.437	3.198	979	9.08	9	999	3.195	3.195
683		0.896	0.426	3.240	1023	9.56	9.5	1001	3.244	3.243
659		0.882	0.413	3.293	1013	10.08	10	1000	3.295	3.291
636		0.847	0.398	3.335	1002	10.57	10.5	1001	3.339	3.341
617		0.805	0.378	3.400	975	11.11	11	998	3.394	3.389
598		0.715	0.354	3.420	1049	11.53	11.5	1005	3.439	3.439
582		0.616	0.319	3.496	1006	12.11	12	999	3.492	3.484
564		0.433	0.256	3.570	819	12.76	12.5			3.542
555		0.328	0.210	3.668	830	13.33	13			3.573
	$\bar{d_{1}} =1008$ ; σ₁ = 25; $\bar{d_{2}} =1000$ ; σ₂ = 2

λ	T_M	T_m	n₁	d₁	m₀	m	d₂	n₂	n_tr
859.0	0.9193	0.4801	3.0064		6.999	7	1000.0	3.0064	3.0066
814.1	0.9183	0.4697	3.0524		7.498	7.5	1000.1	3.0528	3.0527
774.9	0.9165	0.4591	3.0998	999.2	8.000	8	999.9	3.0995	3.0996
740.5	0.9134	0.4485	3.1471	998.9	8.499	8.5	1000.0	3.1471	3.1471
710.0	0.9080	0.4376	3.1949	1000.8	8.999	9	1000.0	3.1949	3.1951
682.8	0.8984	0.4260	3.2433	1000.1	9.499	9.5	1000.0	3.2432	3.2435
658.4	0.8818	0.4132	3.2921	999.5	9.999	10	1000.0	3.2919	3.2921
636.4	0.8532	0.3983	3.3408	1000.8	10.498	10.5	1000.1	3.3410	3.3407
616.3	0.8050	0.3796	3.3897	1000.1	10.999	11	1000.0	3.3896	3.3898
598.0	0.7277	0.3545	3.4388	998.1	11.500	11.5	999.9	3.4384	3.4389
581.3	0.6127	0.3191	3.4875	1001.1	11.998	12	1000.1	3.4877	3.4878
565.9	0.4595	0.2678	3.5366	1002.1	12.498	12.5	1000.1	3.5368	3.5368
551.7	0.2879	0.1965	3.5863	998.3	12.999	13	999.9	3.5860	3.5856
	$\bar{d_{1}} =999 .9$ ; σ₁ = 1.16; $\bar{d_{2}} =1000 .0$ ; σ₂ = 0.06

λ	T_M	T_m	n₁	d₁	m₀	m	d₂	n₂
1871.8	0.9469	0.6303	2.3517		2.98	3	1193.9	2.3379
1610.0	0.9478	0.6339	2.3418		3.45	3.5	1203.1	2.3461
1413.7	0.9481	0.6377	2.3301	1276.0	3.91	4	1213.4	2.3543
1264.2	0.9467	0.6391	2.3236	1304.0	4.36	4.5	1224.2	2.3685
1142.9	0.9441	0.6319	2.3428	1245.1	4.86	5	1219.6	2.3792
1045.3	0.9409	0.6234	2.3653	1176.8	5.37	5.5	1215.3	2.3936
963.6	0.9367	0.6164	2.3822	1184.0	5.86	6	1213.5	2.4071
896.0	0.9318	0.6068	2.4070	1180.5	6.37	6.5	1209.8	2.4248
842.3	0.9270	0.5904	2.4557	1127.9	6.91	7	1200.5	2.4548
793.5	0.9208	0.5737	2.5053	1061.8	7.49	7.5	1187.7	2.4777
751.5	0.9102	0.5605	2.5380	1082.8	8.01	8	1184.4	2.5030
715.0	0.8831	0.5418	2.5698	1144.6	8.52	8.5	1182.5	2.5303
684.2	0.8061	0.5031	2.6078	1150.5	9.04	9	1180.5	2.5636
656.9	0.6651	0.4392	2.6369	1190.6	9.52	9.5	1183.3	2.5982
	$\bar{d_{1}} =1177$ ; σ₁ = 69.0; $\bar{d_{2}} =1200$ ; σ₂ = 14.7

λ	T_M	T_m	n₁	d₁	m₀	m	d₂	n₂
1871.9	0.9469	0.6222	2.3776		3.00	3	1180.9	2.3320
1610.8	0.9478	0.6339	2.3418		3.44	3.5	1203.8	2.3413
1413.8	0.9481	0.6413	2.3190	1351.1	3.88	4	1219.3	2.3484
1263.8	0.9471	0.6391	2.3242	1297.7	4.35	4.5	1223.4	2.3618
1143.0	0.9441	0.6306	2.3471	1210.2	4.86	5	1217.5	2.3733
1044.7	0.9408	0.6234	2.3652	1176.6	5.36	5.5	1214.6	2.3862
963.7	0.9367	0.6182	2.3763	1212.5	5.83	6	1216.6	2.4012
895.0	0.9319	0.6067	2.4075	1174.1	6.36	6.5	1208.2	2.4159
842.4	0.9270	0.5902	2.4565	1110.6	6.90	7	1200.3	2.4488
793.1	0.9204	0.5736	2.5049	1067.2	7.47	7.5	1187.3	2.4702
751.7	0.9102	0.5607	2.5375	1087.7	7.98	8	1184.9	2.4973
714.3	0.8824	0.5416	2.5695	1139.6	8.51	8.5	1181.5	2.5214
685.6	0.8089	0.5138	2.5663	1361.0	8.85	9
654.6	0.6375	0.4358	2.5839	1428.0	9.34	9.5
	$\bar{d_{1}} =1183$ ; σ₁ = 85.3; $\bar{d_{2}} =1203$ ;σ₂ = 15.2

Improvement of Swanepoel method for deriving the thickness and the optical properties of chalcogenide thin films

Abstract

1. Introduction

2. Theory

2.1 The TPM

2.2 Expressions used in the TPM

3 Simulation and experiments

3.1 Numerical simulation

3.2 Experimental

4 Results and discussion

4.1 The thickness and refractive index obtained from simulation

4.2 The thickness and refractive index of Ge-Sb-Se film obtained from experiments

4.3 The dispersion and absorption coefficient of Ge-Sb-Se film

5. Conclusion

Funding

Reference and links

Cited By

Figures (5)

Tables (5)

Equations (15)

Optics Express