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Depth profile determination of Si nanocrystals embedded in SiO2 films by spectroscopic ellipsometry Y. Liu*1, T. P. Chen1, M.S.Tse1, P.H.Ho1, T.B. Chong1, D. Gui2, J. H. Hsieh3 *1 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 2 Institute of Microelectronics, Singapore 117685 3 School of Mechanical and Production Engineering Nanyang Technological University, Singapore, 639798 Abstract report an approach to determination of depth profiles of both optical constants and excess Si nc fraction in SiO2 films. In this approach, the depth profiles are quantified in an inexpensive and nondestructive way that is based on spectroscopic elliposmetry (SE). The results of the depth profile of excess Si fraction are in good agreement with secondary ion mass spectroscopy (SIMS) analysis, indicating that the approach is reliable. 100 No Implantation Dose=2x1016/cm2 Dose=6x1016/cm2 Dose=1x102/cm2 80 60 degree) In this paper, we report an approach to determine the depth profiles of Si nanocrytals fraction distributed in SiO2 films based on spectroscopic ellipsometry (SE). In the SE analysis, a Si implanted SiO2 film is divided into m sub-layers with equal thickness (a better depth resolution for a larger m), and an effective medium approximation (EMA) is used to convert the depth profile of the complex refractive index to the depth profile of the excess Si fraction. With this approach, the depth profiles of both excess Si nanocrystal (nc) fraction and optical constants are determined quantitatively in a inexpensive and non-destructive way. The depth profiles of excess Si nc fraction obtained are in good agreement with secondary ion mass spectroscopy (SIMS), indicating that the approach is reliable. 40 20 Introduction 0 * Corresponding author. Email: p150531616@ntu.edu.sg 200 400 600 800 1000 1200 1400 Wavelength (nm) 180 No implantation Dose=2x1016/cm2 Dose=6x1016/cm2 Dose=1x1017/cm2 160 140 120 (degree) SiO2 films containing Si nanocrystals (nc-Si) have recently attracted much attention because of their light-emitting ability that can be used for Si-based optoelectronic applications [1]. In addition, they have also regained the interest as a possible candidate for the application of single electron memory devices or other single electron devices [2-5]. One of the promising techniques being used to elaborate nc-Si is the implantation of Si ions into SiO2 films that are thermally grown on Si substrates [6-8]. The SiO2 has proven to be a robust matrix that provides good chemical and electrical passivation of the nanocrystals. In addition, the fabrication is fully compatible with the mainstream CMOS processes, and this allows the integration of the optoelectronic devices into the Si circuits. Therefore, this technique is very attractive. For applications such as light-emitting structures, single-electron memories, optical storage devices or wave guides, it is essential to have detailed information on the exact depth distribution of the excess Si concentration and of optical properties of the Si-doped SiO2 films. In this paper, we 100 80 60 40 20 0 200 400 600 800 1000 1200 1400 Wavelength (nm) Fig1. Measured and as a function of wavelength. Experiment 550nm-thick SiO2 films were grown on ptype Si (100) substrates by wet oxidation of Si at 1000 oC. The SiO2 films were implanted with doses from 21016 to 11017 atoms/cm2 of Si+ at 50 keV. Thermal annealing at 1000 oC for 1 hour led to the crystallization of the implanted Si ions in nano-size. As revealed by the SE analysis and SIMS measurements discussed below, the excess Si atoms distribute from the surface to a depth of about 250 nm. SE measurements before and after Si implantation were carried out in the wavelength range of 400 to 1200 nm. A continuous significant change in the ellipsometric angles and with the implant dose was observed as shown in Fig.1. As discussed below, the depth profiles of the excess Si nc fraction in the SiO2 films were determined from these SE measurements. SE analysis and results As the concentration of excess Si atoms in the SiOx films varies with the depth, namely, the x is a function of the depth; the optical properties of the films will also vary with the depth. To model the SiOx films, the films are divided into m sublayers with equal thickness d = Tox / m where Tox is the total thickness of the films, i.e., layers 1, 2, ...m from the surface to the SiO2/Si interface. The x (2) is considered constant within each sublayer, and the corresponding x for the m layers are x1, x2, ...xm, respectively. Actually, the depth profile of x can be translated into the depth profile of excess Si fraction in the films. Each sub-layer has its own complex refractive index. For example, for the ith sub-layer, its complex refractive index is Ni = ni + jki (i=1, 2, ...m) where ni and ki are the refractive index and extinction coefficient for the ith sub-layer, respectively. Note that Ni is also a function of wavelength. For SE analysis, an appropriate optical model is required. Based on the above discussions, we can use a (m + 2)-phase model, i.e., air/sub-layer 1/.../sub-layer m/Si substrate to describe the system of Si implanted SiO2 film on Si substrate. Each phase is characterized by its complex refractive index, namely, Ni (i=0, 1, ...m, m+1). Note that N0 = 1 for air and Nm+1 = NSi for the Si substrate. For the total system, the ratio of the complex reflection coefficients for the p and s polarizations is given by [10] Rp / Rs tan( ) exp( j ) , (1) where and are the ellipsometric angles . The complex reflection coefficient R ( =p, s) for the p and s polarizations is given by R =( r0,1 + R1,2 X1)/ (1+ r0,1 R1,2X1) , (2) where X1=exp(-j4 N1d cos 1 / ) , R1,2=(r1,2+R2,3X2)/(1+r1,2R2,3X2) , X2=exp (-j4 N 2d cos 2 / ) , ... R (m-1),m=(r(m-1),m+rm,(m+1)Xm)/(1+r(m-1),mrm,(m+1)Xm), Xm=exp (-j4 N m d cos m / ). In the above equations, is the freespace wavelength of light; ri,(i+1) (i =O, 1, ...m) is the Fresnel complex-amplitude reflection coefficient for - (=p, s) polarized light at the interface between the ith phase and the (i+1)th phase[11]; and the angles i and the complex refractive index Ni (i=0, 1, ...m, m+1) are related by Snell’s law. In the present study, 0 is fixed at 75o. As N0 (=1) and Nm+1 (= Si complex refractive index) are known, for a given d, from the above equations, and can be symbolically written as = f1(N1, N2, …Nm, ) and = f2(N1, N2, …Nm, ). The functions f1 and f2 cannot be expressed as analytical formulae, but the and can be calculated numerically. To determine the depth profile of the optical constants, one can search for one set of the parameters (N1, N2, ...Nm) which are dependent of wavelength , by comparing the calculated (, ) with the experimental (, ). To obtain the definite values of the complex refractive indices of the m sublayers at various wavelengths, an appropriate constraint that is independent of wavelength, is required. . Fig2. Comparison of theoretical computation (solid lines) with experimental (* and o) data for dose=0. i h h vi a i 2 h a 2 h (3) where i is the volume fraction (it will be converted to atom percentage later) of the excess Si atoms in the ith sub-layer, h is the dielectric function of host material SiO2, and a is the dielectric function of the Si inclusion. With (3), the depth profile of the complex refractive index is converted to the depth profile of the volume fraction (i). Note that the i is independent of the wavelength. Therefore, there are only m (the number of the sub-layers) unknown parameters, i.e., 1, 2, ...m in the spectral fitting of experimental (, ), which greatly reduces the complexity of the fitting. Obviously, a larger m means a better depth resolution but a longer computation time more complicated compared with that of pure SiO2 film on Si substrate. However, the fitting procedure is also able to produce a very good fitting over the whole spectral range. One typical example is shown in Fig.3. As can be seen in this figure, all the complicated spectral features of both and can be fitted excellently. Such a fitting can yield the depth profile of the volume fraction of the excess Si atoms in the SiO2 films. The volume fraction can be simply converted to the atom percentage that can be compared with the SIMS analysis. One example of the depth profile of the excess Si atom percentage obtained is shown in Fig.4. As shown in this figure, the depth profile obtained agrees well with the SIMS result. This indicates that our approach is reliable. On the other hand, as revealed by the TRIM simulation, the depth profile follows a Gaussian distribution approximately. 10 SE calculation Normalized SIMS 8 Excess Si fraction (at %) The constraint can be established by using an effective medium approximation (EMA) to relate the depth profile of the complex refractive index to the depth profile of the excess Si fraction that is independent of wavelength. According to the EMA [10,12], the effective complex dielectric function of each sub-layer, i (=Ni2, i=1, 2, ...m), can be approximately calculated using the following expression 6 4 2 0 0 200 100 150 200 250 300 350 measurement measurement calculation calculation 160 140 Fig.4. Comparison of the depth profiles of excess Si nanocrystal fraction obtained with the SE and SIMS analysis. The Si implant dose is 11017 atoms/cm2. 120 Degrees 50 Depth (nm) 180 100 80 60 40 Conclusion 20 0 200 400 600 800 1000 1200 1400 (nm) Fig.3. Typical example of spectral fitting of and with the (m+2)-phase model and the constraint that uses the EMA to convert the depth profile of the complex refractive index to the depth profile of the Si nanocrystal fraction. The Si implant dose is 11017 atoms/cm2. The above models and the fitting procedure are proven correct and effective by applying them to a system of pure SiO2 film on Si substrate. The fitting yields i =0 (i=1, 2, ...m) and the calculated (, ) fit the experimental (, ) perfectly over the whole spectral range (400 1200nm), as illustrated in Fig2. For Si implanted SiO2 films on Si substrate, the situation is much In conclusion, we have developed an approach to determination of depth profiles of the excess Si nc fraction distributed in SiO2 films based on the SE. In the SE analysis, a Si implanted SiO2 film is divided into m sub-layers with equal thickness (a better depth profile resolution for a larger m), and an optical model of (m+2) phases is used. 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