XRR and FE-SEM Studies of Nano-Multi-Layer Ceramic Thin Films with Periodic Structures

Jong-Hong Lu and Bo-Ying Chen Department of Materials Engineering Ming Chi University of Technology

Taipei, Taiwan

Hua-Chung Tzou Nanotechnology Research Center

Industrial Technology Research Institute Hsinchu, Taiwan

Abstract—Nano-multi-layer (NML) ceramic thin films with the periodic (ITO/AlON)n and (ITO/SiOx)m structures were fabricated by the magnetron sputtering. The nano-size of film thickness was characterized by x-ray reflection (XRR) technique and field emission scanning electron microscopy (FE-SEM). The non-destructive XRR technique was able to analyze the NML films under sub-nano-meter-grade resolution quickly and precisely. From the XRR theoretical studies, two methods were used to simulate the characterization result in this study, the multiple-beam-interference (MBI) recursive method and the characteristic matrix method. Both methods show same calculation results. Finally, the periodic thickness and uniformity of NML thin films were compared by XRR and FE-SEM.

Keywords-Nano-multi-layer thin film; XRR; FE-SEM

I. INTRODUCTION The nano-multi-layer structure has been paid much

attention for manipulating the positions of the electron energy band in optoelectronic applications [1,2], and also for designing the optical refractive indices of the transparent conductive thin films [3]. For the thin film with a nano-multi-layer (NML) structure, thickness in each layer strongly affects electrical and optical properties. In general, the film thickness was measured by the field emission scanning electron microscopy (FE-SEM), but the analysis is off-line and needed to break the sample. X-ray reflection (XRR) technique is non-destructive which is suitable for in-line thickness inspection in industries [4] with a sub-nano-meter resolution. In this study, the periodic NML ceramic thin films with conductive-dielectric alternately structures were fabricated and characterized by XRR and FE-SEM. We compare the measurement results by the XRR technique and FE-SEM to explore the average thickness in large area and the distributions in local thickness uniformity, respectively. For the electromagnetic reflection theories of the multi-layer films, the characteristic matrix method is applied in the visible spectra range [5,6], and the “recursion formula” is famed at XRR calculation derived by Parratt [7]. In this work, we propose a multiple-beam-interference (MBI) recursive method, and the MBI recursive method has more clearly physical picture than the “recursion formula” during derivation. Moreover, we show that both the characteristic matrix method and the MBI recursive method have same simulation results for the XRR of NML films.

Figure 1. Sketch of the m-layer thin film, in drawing with refractive index n, interface reflection coefficient r, layer thickness d, and incident angle .

Figure 2. The MBI recursive method, (a) starting from the mth layer with reflection coefficients rm+1 and rm, (b) replacing rm by the effective reflection coefficient reff,m to the (m-1)th layer, (c) sequentially recursive still to the 1st layer, finally (d) the total reflection coefficient of the m-layer thin film is reff,1.

II. XRR SIMULATION MODELS

A. Multiple-Beam-Interference Recursive Method With considering x-ray from free space (air or vacuum)

incident upon the m-layer thin film, the structure is shown

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Proceedings of the 2011 6th IEEE International Conference on Nano/Micro Engineered and Molecular Systems February 20-23, 2011, Kaohsiung, Taiwan

schematically in Fig. 1, the amplitude reflection coefficient and the reflectance of the sample are Er,0/Ei,0 and (Er,0/Ei,0)*(Er,0/Ei,0), respectively. The MBI recursive method starting from the mth layer to the 1st layer is shown in Fig. 2. Fig. 2a shows the x-ray from the (m-1)th layer film incident to the mth layer. X-ray is undergoing infinite times of reflection and transmission by the interference between the mth and the (m+1)th layers. By the multiple beam interference arrangement [4,5], an effective amplitude reflection coefficient reff,m of the mth layer is obtained and can be expressed as in

Where rm and rm+1 are the amplitude reflection coefficients of the mth and the (m+1)th interfaces defined by Fresnel equations (or called Fresnel formulae) [4,5], respectively. m = 4 nmdmcos m/ 0 is the phase difference due to optical path difference in the mth layer film. The parameters are refractive index nm, film thickness dm, incident angle m, and free space wavelength 0. The x-ray from the (m-2)th layer film incident to the (m-1)th layer film is shown in Fig. 2b. Similarly, an effective amplitude reflection coefficient reff,m-1 of the (m-1)th layer can be rewritten as in

Where rm-1 is the amplitude reflection coefficients of the (m-1)th interface and m-1 is the phase difference due to path difference in the (m-1)th layer film. Following above recursive procedure of the effective amplitude reflection coefficients, x-ray from free space is incident to the 1st layer film shown in Fig. 2c, an effective amplitude reflection coefficient reff,1 of the 1st layer shown in Fig. 2d can be described as in

Where r1 is the amplitude reflection coefficients of the 1st interface, reff,2 the effective amplitude reflection coefficient of the 2nd layer film, and 1 the phase change due to path difference in the 1st layer film. By using the multiple-beam-interference recursive method, the amplitude reflection coefficient of the sample Er,0/Ei,0 is equal to the effective amplitude reflection coefficient reff,1. Therefore, the reflectance R = (reff,1 )*reff,1 could be achieved.

B. Characteristic Matrix Method For a m-layer structure, the relationship of electric field E

and magnetic field H at the boundary of the film can be described as the following equation with a characteristic matrix method [4,5]:

Figure 3. The simulation results of the MBI recursive method and the

characteristic matrix method with a 10-period layer structure of periodic thickness 15 nm.

Where E1 and H1 are the electric and magnetic fields at the boundary between free space and film, and E(m+1) and H(m+1) are the fields at the boundary between film and substrate. Mm is the characteristic matrix of the mth layer film, and M1M2 Mm = M represents the stacked films. With incident angle of 0, the first film with thickness of d1 and refractive index of n1, the second film with d2 and n2, the film characteristic matrices of M1 and M2 can be expressed respectively as:

Where k0 = 2 / 0, h1 = n1d1cos 1, h2 = n2d2cos 2, 1 and 2 are refractive angles in the first layer and the second layer films. For TE mode with the electric field normal to the incident plane, Y1 = ( 0/ 0)1/2n1cos 1 and 2 = ( 0/ 0)1/2n2cos 2 with 0,

0, 0 being wavelength, permittivity, and permeability constant in the free space, respectively. For TM mode with the electric field parallel to the incident plane, 1 = ( 0/ 0)1/2n1/cos 1 and 2 = ( 0/ 0)1/2n2/cos 2. Therefore, the reflectance RM = r*r and the amplitude reflection coefficient of the stacked films on substrate can be written as:

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For TE mode, 0 = ( 0/ 0)1/2n0cos 0 and s = ( 0/ 0)1/2nscos m+1, n0 is the air refractive index, m+1 is the refractive angle in the substrate, and ns = nm+1 is substrate refractive index. For TM mode, 0 and s are changed to 0 = ( 0/ 0)1/2n0/cos 0 and s = ( 0/ 0)1/2ns/cos m+1, respectively.

Fig.3 shows the simulation results of the MBI recursive method and the characteristic matrix method with a 10-period layer structure. It is found that both calculation results are consistent.

III. EXPERIMENTAL Indium tin oxide (ITO)/aluminum oxide nitride (AlON) and

ITO/SiOx (silicon oxide) periodic NML thin films were prepared on Si substrate by reactive DC/RF magnetron sputtering. The sputtering guns were set in parallel and a rotating substrate-holder plate was placed above the sputtering guns. Two sets of targets, Al-ITO or Si-ITO, were used at the same time during depositing the NML films. The film growth of NML structure was layer by layer sequentially by controlling the substrate-holder rotation speed and sputtering power. Additionally, the film uniformities along the rotational direction of substrate-holder plate are better than that of radial directions.

XRR were obtained with Philips X,Pert Pro (MRD) instrument. FE-SEM, model JSM-6701F, was used for secondary electron and backscattered electron images.

IV. RESULTS AND DISCUSSION

A. ITO/AlON NML Thin Films The XRR results of ITO/AlON NML samples with various

periodic thicknesses fitted by the MBI recursive method are shown in Fig. 4. The thicknesses ratios of ITO and AlON of samples (a), (b), (c), and (d) are 1.55/0.96, 3.60/2.40, 7.05/3.90, and 16.45/8.05, respectively. For the sample (d), the third, 6th, 9th, etc., x-ray intensities are decreased due to the thickness ratio about 2:1. For the sample (a) with a 200-layer structure, the periodic thickness of 2.51 nm is too thin and can not be observed its by FE-SEM, but the infrared absorption of the inter-subband transition phenomenon was measured due to super-lattice structure with quantum well ITO of 1.55 nm and barrier AlON of 0.96 nm. The profiles of samples (b) with 100 layers, (c) 50 layers, and (d) 22 layers could be observed directly by FE-SEM without any pre-coating Au or Pt on the samples. In this work, ITO/AlON NML structures have alternately conducting/insulating electric properties and high/low atomic densities, which would improve the observable capability of FE-SEM. Therefore, the secondary electron image of the sample (b) with an average periodic thickness 5.85 nm and the backscattering electron image of sample (c) with an average periodic thickness 10.99 nm could be clearly observed, as shown in Fig. 5 and Fig. 6, respectively.

Figure 4. The XRR results of ITO/AlON NML samples with varing periodic thicknesses of (a) 2.51 nm, (b) 6.00 nm, (c) 10.95 nm, and (d) 24.50 nm and fitted by the MBI recursive method.

Figure 5. FE-SEM secondary electron image of ITO/AlON NML sample (b). The sample is 100 layers and the average periodic thickness of 5.85 nm.

Figure 6. FE-SEM backscattered electron image of ITO/AlON NML sample (c). The sample is 50 layers and the average periodic thickness of 10.99 nm.

Avg. period : 5.85 nm

ITO/AlON NML sample (b)

Avg. period : 5.85 nm

ITO/AlON NML sample (b)

Avg. period 10.99 nm

ITO/AlON NML sample (c)

Avg. period 10.99 nm

ITO/AlON NML sample (c)

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B. ITO/SiOx NML Thin Films To demonstrate the nano-meter resolution of the XRR,

ITO/SiOx NML samples were made of 10 periods (20 layers) with periodic thicknesses of (a) 26.70 nm, (b) 27.10 nm, (c) 27.60 nm, and (d) 28.70 nm. Because XRR is measured with a large area at small incident angles, and there are better and less uniform at the rotational and radial directions as the mention of section III, the NML film uniformity was checked again at rotating sample 90 degree shown in Fig. 7. The broader peaks of XRR were indicating the less uniform distribution. Additionally, we observed the thickness distributions by FE-SEM along the less uniform direction. The XRR result and the FE-SEM images of the local periodic thickness distributions in the ITO/SiOx NML sample (d) are shown in Fig. 8 and 9, respectively. For FE-SEM measurement with high resolutions, screen image drift during measurement will interrupt vertical distance accuracy, so we arrange the periodic thickness measurements along the horizontal direction as shown in Fig. 9 that is able to reduce the interruption by the screen image drift.

Figure 7. The XRR results of ITO/SiOx NML samples with varing periodic thicknesses of (a) 26.70 nm, (b) 27.10 nm, (c) 27.60 nm, and (d) 28.70 nm fitted by the MBI recursive method. Two different explored directions with a rotation angle 90 degrees were measured.

Figure 8. XRR simulation result of ITO/SiOx NML sample (d) of periodic thickness 28.70 nm with layer thicknesses of ITO 14.70 nm and SiOx 14.00 nm.

Figure 9. FE-SEM images with local periodic thickness distributions in ITO/SiOx NML sample (d). The average periodic thicknesses are 28.34 nm, 28.86 nm, 28.81 nm, and 28.31 nm for position 1, 2, 3, and 4, respectively.

V. CONCLUSIONS We have successively fabricated the ITO/AlON and

ITO/SiOx periodic NML (nano-multi-layer) structured thin films with reactive magnetron sputtering. For the XRR simulation, we prove that the MBI (multiple-beam-interference) recursive method is consistent with the characteristic matrix method. Finally, the NML periodic thickness uniformity is compared by XRR and FE-SEM for large average area measurement and tiny local observation, respectively.

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