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nanocrystalline Si multilayers studied using spectroscopic ellipsometry
Thin Solid Films 476 (2005) 196 – 200 www.elsevier.com/locate/tsf
Optical properties of SiO2/nanocrystalline Si multilayers studied using spectroscopic ellipsometry Kang-Ju Leea, Tae-Dong Kanga, Hosun Leea,*, Seung Hui Honga, Suk-Ho Choia, Tae-Yeon Seongb, Kyung Joong Kimc, Dae Won Moonc b
a Department of Physics and Institute of Natural Sciences, Kyung Hee University, Suwon 449-701, Korea Department of Materials Science and Engineering, Kwangju Institute of Science and Technology, Kwangju 500-712, Korea c Nano Surface Group, Korea Research Institute of Standards and Science, PO Box 102, Yusong, Taejon 305-600, Korea
Received 26 May 2004; received in revised form 18 August 2004; accepted 21 September 2004
Abstract Using variable-angle spectroscopic ellipsometry, we measure the pseudo-dielectric functions of as-deposited and annealed SiO2/SiOx multilayers. The SiO2(2 nm)/SiOx (2 nm) multilayers are prepared under various deposition temperatures by ion beam sputtering. Annealing at temperatures above 1100 8C leads to the formation of Si nanocrystals (nc-Si) in the SiOx layer of multilayers. Transmission electron microscopy images clearly demonstrate the existence of nc-Si. We assume a Tauc–Lorentz lineshape for the dielectric function of nc-Si, and use an effective medium approximation for SiO2/nc-Si multilayers as a mixture of nc-Si and SiO2. We successfully estimate the dielectric function of nc-Si and its volume fraction. We find that the volume fraction of nc-Si decreases after annealing, with increasing x in asdeposited SiOx layer. This result is compared to expected nc-Si volume fraction, which is estimated from the stoichiometry of SiOx . D 2004 Elsevier B.V. All rights reserved. PACS: 68.65.Hb; 73.21.La; 78.20.Ci; 78.40.Fy; 78.67.Hc Keywords: Nanostructures; Silicon; Ellipsometry; Transmission electron microscopy
1. Introduction In order to realize light-emitting diode using siliconbased materials, intensive investigations on nanocrystalline silicon (nc-Si) have been carried out. Due to the confinement of electron and hole carriers in nanoscale volumes, we expect enhanced luminescence efficiency due to the increasing recombination rate of carriers as well as the visible luminescence arising from quantum confinement effect [1]. Notably, superlattices composed of alternating nc-Si and SiO2 layers have been given much attention due to a large volume fraction of nc-Si and the controllability of the size and density of nc-Si crystallites [2,3]. One promising method of SiO2/nc-Si multilayers relies on the growth of * Corresponding author. Tel.: +82 312012412; fax: +82 312732411. E-mail address: [email protected] (H. Lee). 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.09.037
SiO2/SiOx multilayers and subsequent heat treatment [4]. We used the ion beam sputtering deposition method to grow SiO2/SiOx multilayers. Ion beam sputtering deposition has the advantage of low operational pressure of the ion sources and precise control of the ion beam parameters, compared to plasma-based radiofrequency (RF) sputtering techniques. Defect densities are relatively low because a neutralized ion beam is used for sputtering and a substrate is not immersed in the plasma [5,6]. In order to optimize SiO2/nc-Si multilayers for optoelectronic devices, we need various structural and optical characterization methods [2,3,5,7]. Using spectroscopic ellipsometry, we can characterize the structural and optical properties at the same time. We can also estimate the thickness of the nc-Si and SiO2 layers and the volume fraction of nc-Si, as well as the dielectric function of nc-Si in detail. Recently, several researchers successfully adopted the Tauc–Lorentz (TL) model for the dielectric function of
K.-J. Lee et al. / Thin Solid Films 476 (2005) 196–200
nc-Si for diameters of 1–3 nm [8,9]. Transmission electron microscopy (TEM) is a direct method to verify the formation of nc-Si. However, it cannot represent the average physical property of a material system because it is only a local probe. Using ellipsometry, we can determine the average property, such as the volume fraction and the dielectric function of nc-Si. In this work, we measure the pseudo-dielectric functions of as-deposited single thick-layer SiOx and its annealed ncSi embedded in SiO2 matrix, as well as as-deposited (SiO2/ SiOx )50 and annealed (SiO2/nc-Si) multilayers, by using variable-angle spectroscopic ellipsometry at room temperature (RT). Using the TL model for the dielectric function of nc-Si and the Bruggeman effective medium approximation (BEMA), we determine the dielectric function of nc-Si and the volume fraction of nc-Si phase.
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ion beam mill. The sample was rotated and thinned from both sides using Ar+ ion beams until a hole appeared in the center of the bar, giving electron-transparent material. A liquid N2 cold stage was used to cool the sample during ion beam milling. The milling conditions were ion beam energy 4 kV, gun current 0.4 mA, and angle of beam to the sample surface 158. TEM examination was performed using a JEM 2010 instrument operated at 200 kV. Spectroscopic ellipsometry measurements were performed on samples with incidence angles of 708 and 758 using a variable-angle ellipsometer (Woollam VASE model) with and without an autoretarder in the spectral range of 1.0–6.0 eV. The capability of multiple angles of incidence increases the accuracy in determining the layer dielectric function of pseudo-dielectric functions. The pseudo-dielectric functions were fitted using nonlinear Levenberg– Marquardt algorithm using WVASE32 software.
2. Experimental details 3. Results and discussion Two sets of SiO2/nc-Si samples were grown. First, alternating multilayers composed of 2-nm-thick SiOx and 2-nm-thick SiO2 thin films with 50 periods were grown on ptype (100) Si wafers at temperatures of RT, 100 8C, 200 8C, and 300 8C by reactive ion beam sputtering deposition using a Kaufmann-type direct current ion gun and Ar+ beam with ion energy of 750 eVand a Si target. Second, a single layer of 80nm-thick SiOx was grown under identical conditions, for comparison. The deposition chamber was evacuated to a pressure of 2.0108 Torr before introducing argon gas into the system. Details of the system are described elsewhere [5]. We controlled the relative oxygen content by varying both the sputtering rate and the oxygen gas pressure. After deposition, the samples were annealed at 1100 8C for 20 min in an ultra-pure nitrogen ambient using a horizontal furnace to form Si nanocrystals in the SiOx layers. In order to passivate Si dangling bonds, the samples were hydrogenated for 1 h at 650 8C under hydrogen gas flow. The stoichiometry of the SiOx layers was analyzed by in situ Xray photoelectron spectroscopy (XPS) using Al Ka line of 1486.6 eV, thereby sidestepping the problem of surface contamination and oxidation. A stoichiometric SiO2 film was used as a reference to determine the relative sensitivity factors of Si 2p and O 1s. Because the XPS analysis depth of SiO2 is longer than 10 nm, we determined the stoichiometry of SiOx layers in the SiOx /SiO2 multilayers cautiously. We measured the oxygen compositions (denoted as X 1 and X 2, respectively) of SiOx - and SiO2-terminated multilayers and the composition x of SiOx was determined as x=X 1+X 22. For more details on the stoichiometry of SiOx , we refer to Ref. [10]. For cross-sectional TEM examination, the sample was cleaved into two bars, which were glued together surface to surface. The sample was mechanically ground using SiC papers until it was about 40 Am thick. The sample was then glued to a Cu TEM grid, which was placed in a Gatan dual-
Fig. 1 shows TEM images of nc-Si in the annealed multilayer SiO2/SiOx samples for (a) x=1.0 and (b) x=1.2. The TEM results clearly revealed the formation of nc-Si in both single-layer and multilayer SiO2/SiOx samples, when annealed. Due to the interdiffusion of Si and O atoms, the multilayer structures are not evident for x=1. The average
Fig. 1. TEM image of the (SiO2)50/(SiOx )50 multilayers for (a) x=1.0 and (b) x=1.2, which was annealed at high temperature. For visibility, a few Si nanocrystallites were marked.
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diameter of their nc-Si was about 4 nm for x=1. This size information is consistent with the quantum confinement effect, which was verified by photoluminescence results in Ref. [10]. In general, the size of nc-Si decreased with increasing oxygen concentration (x), whereas the number of nanocrystallites increased. However, the total volume of ncSi should have decreased with increasing x. Fig. 2a–d plots the real part of pseudo-dielectric functions (discrete symbols) and their curve fits (solid lines) for as-deposited and annealed (SiO2)50/(nc-Si)50 multilayers, which were grown at RT at a 708 angle of incidence. The imaginary parts of the pseudo-dielectric functions were simultaneously fitted. Note that the H-passivation did not change the pseudo-dielectric function of annealed multilayers. We also measured and fitted the pseudo-dielectric function for the multilayers, which were grown at 100, 200, and 300 8C. For simplicity, the data and fitting are not shown here. We adopted the TL lineshape model for the dielectric function of nc-Si [11,12]. We successfully fitted the pseudo-dielectric function by using BEMA [13]. We assumed a mixture of nc-Si and SiO2 for the multilayers. The equation for BEMA is given by: fnc-Si
enc-Si hei eSiO2 hei þ fSiO2 ¼0 enc-Si þ 2hei eSiO2 þ 2hei
where e nc-Si and e SiO2 are the dielectric functions of nc-Si and SiO2, respectively; hei is the effective dielectric
function of multilayer; and f nc-Si and f SiO2 are the volume fractions of nc-Si and SiO2, respectively. In the TL model, the imaginary dielectric function e 2 is determined by multiplying the Tauc joint density of states by the e 2 obtained from the Lorentz oscillator model. Thus, e 2 is given by: " 2 # AE0 C E Eg 1 e2 ð E Þ ¼ for ENEg E E2 E2 2 þ C 2 E2 0
¼0
for EbEg
where A, E, E g, and C are the four parameters used to describe the spectral dependence of e 2(E) [11,12]. The real part of the dielectric function e 1(E) is then obtained using Kramers–Kronig transformation, with an additional parameter of e 1l. Fig. 3 shows the fitted dielectric function of nc-Si of annealed multilayers and SiOx of as-deposited multilayers for x=1 from Fig. 2. The peak from nc-Si is much more pronounced than that of SiOx , as expected, because of crystallization. The dielectric functions of both SiOx and nc-Si were fitted using the TL model. Note that there is a very small change of the dielectric function at a low-energy region between nc-Si and SiOx . The fitted dielectric function of nc-Si is similar to that of Ref. [8]. The average diameter of their nc-Si was about 1.5 nm, whereas those of nc-Si in this work were 3 nm (x=1.2) and 4 nm (x=1).
Fig. 2. Plots of the real part of pseudo-dielectric functions (discrete symbols) and their curve fits (solid lines) for as-deposited (circles) and annealed (rectangles) (SiO2)50/(nc-Si)50 multilayers, which were grown at room temperature. The oxygen composition x was (a) 1.0, (b) 1.2, (c) 1.4, and (d) 1.6.
K.-J. Lee et al. / Thin Solid Films 476 (2005) 196–200
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into SiO2 and nc-Si after annealing. We estimated the volume fraction of nc-Si for SiO2/nc-Si multilayers after annealing, using the equations: fnc-Si ¼
Vnc-Si t ¼ 1þt VSiO2 þ Vnc-Si
Vnc-Si 2x t¼ ¼ 2þx VSiO2
Fig. 3. Plot of the fitted dielectric functions of nc-Si of annealed multilayers and SiOx of as-deposited multilayers for x=1 from Fig. 1(a).
Compared to the dielectric function of bulk Si, the values of dielectric function decreased. For example, the maximum of e 2 of bulk Si near E 2 (4.270 eV) band gap energy is about 45. In general, the dielectric functions of silicon semiconductors in the form of quantum well and bulk show main peaks associated with E 1 (3.396 eV) and E 2 (4.270 eV) critical points. However, in the case of nc-Si, the dielectric function shows only a single peak in the experimental range, possibility because of large broadening of the E 1 and E 2 band gaps and the weakening of the exciton effect of the E 1 transition. This phenomenon may also be attributed to the inadequacy of band structure in nanocrystallites due to their extremely small volume and increased surface effect. We note that the BEMA fitting gave a more successful fitting for annealed SiO2/nc-Si multilayer rather than the same fitting for single-layer annealed SiO2/nc-Si. This suggests that the size uniformity of nc-Si in annealed SiO2/nc-Si multilayer is better than that of nc-Si in a single layer. This is reasonable because SiOx and SiO2 layers are periodically distributed in multilayer, and SiOx will decompose into SiO2 and nc-Si phase after high-temperature annealing. Therefore, in order to get a narrow size distribution of nc-Si, multilayer growing of SiO2/SiOx is much better than the single layer growing of SiOx . Fig. 4a and b shows the fitted volume fraction of nc-Si in the multilayers and in the single layer. We also plotted an expected curve from the consideration of the stoichiometry of SiOx (solid lines) in Fig. 4a and b. In Fig. 4a, we observe that the volume fraction of nc-Si decreased with increasing x in as-deposited SiOx layer due to annealing is the driving force for the formation of Si nanocrystals. The decrease of the nc-Si volume fraction with increasing x, in other words approaching x=2.0, can be explained with the consideration of stoichiometry of SiOx layer. The amount of the precipitated nc-Si can be estimated by assuming that all the SiOx will decompose
mSi mSiO2
qSiO2 qSi
;
where m Si and m SiO2 are the molecular weights of Si and SiO2 molecules; and q Si (2.329 g/cm3) and q SiO2 (2.2 g/ cm3) are the mass density of nc-Si and SiO2 phases, respectively [14,15]. Note that we assumed that the SiO2 and SiOx layers in the as-grown multilayers have the same number of Si atoms. Similarly, the volume fraction of SiO2/nc-Si single layer can be estimated using: Vnc-Si ¼ t¼ VSiO2
2 1 x
mSi mSiO2
qSiO2 : qSi
The calculated volume fraction of nc-Si ( f nc-Si) is shown in Fig. 4.
Fig. 4. Plot of the fitted volume fraction of nc-Si (a) in the multilayers and (b) in the thick single layer.
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In Fig. 4a and b, the fitted volume fraction of nc-Si by SE matches reasonably well with calculated values. In the case of multilayers, the fitted volume fractions of nc-Si from the deposition temperatures of 100 and 300 8C match the calculated curve, whereas those from other deposition temperatures are higher than that. The discrepancy between the calculation and experimental data can be attributed to the simplified model. We assumed that SiO2 and SiOx layers in the as-grown multilayers have the same number of Si atoms. However, the number of Si atoms in the SiOx layer should be larger than that of the SiO2 layer, assuming the same thickness for both layers. This will increase the calculated V nc-Si, especially in the low x region in Fig. 4a. In the case of single layers of deposition temperature RT in Fig. 4b, the fitted values are higher than the calculated ones, which is similar to the case of multilayers with the same deposition temperature RT. According to TEM data in Fig. 1, the size of nc-Si appeared to decrease with oxygen concentration (x) approaching 2. Due to the increasing ratio of surface to volume in nc-Si, we may expect a decrease of the dielectric function of nc-Si. However, our ellipsometric data gave no clear correlation between the size of nc-Si and their dielectric functions.
4. Conclusion Using variable-angle spectroscopic ellipsometry, we measured the pseudo-dielectric functions of as-deposited and annealed SiO2/SiOx multilayers and single layers. The SiO2(2 nm)/SiOx (2 nm) multilayers with period 50 were prepared under various deposition temperatures by ion beam sputtering deposition. Annealing at temperatures larger than 1100 8C leads to the formation of nc-Si in the SiOx layer of multilayers, which was verified by TEM. Using TL lineshape analysis for the dielectric function of nc-Si, and assuming SiO2/nc-Si multilayers to be a mixture of nc-Si and SiO2, we successfully estimated the dielectric function of ncSi and its volume fraction. The volume fraction of nc-Si decreased after annealing, with increasing x in as-deposited SiOx layer. The formation of nc-Si was verified by TEM. The
fitted nc-Si volume fraction was compared to the estimated value from stoichiometry of SiOx .
Acknowledgement H. Lee acknowledges partial support of 2003 Special Research Fund of Kyung Hee University. S.H. Choi acknowledges partial support from the National research program for the 0.1 Terabit Non-Volatile Memory Development sponsored by Korea Ministry of Science & Technology.
References [1] D.J. Lockwood, Light Emission in Silicon: From Physics to Devices, Semiconductors and Semimetals, vol. 49, Academic Press, San Diego, 1998. [2] D.J. Lockwood, Z.H. Lu, J.-M. Baribeau, Phys. Rev. Lett. 76 (1996) 539. [3] P. Photopoulos, A.G. Nassiopoulou, D.N. Kouvatsos, Appl. Phys. Lett. 76 (2000) 3588. [4] Y.Q. Wang, G.L. Kong, W.D. Chen, H.W. Diao, C.Y. Chen, S.B. Zhang, X.B. Liao, Appl. Phys. Lett. 81 (2002) 4174. [5] J.-S. Bae, S.-H. Choi, K.J. Kim, D.W. Moon, J. Korean Phys. Soc. 43 (2003) 557. [6] C. Saha, S. Das, S.K. Ray, S.K. Lahiri, J. Appl. Phys. 83 (1998) 4472. [7] L. Khriachtchev, S. Nivikov, O. Kilpel7, J. Appl. Phys. 87 (2000) 7805. [8] M. Losurdo, M.M. Giangregorio, P. Capezzuto, G. Bruno, M.F. Cerqueira, E. Alves, M. Stepikhova, Appl. Phys. Lett. 82 (2003) 2992. [9] D. Amans, S. Callard, A. Gagnaire, J. Joseph, G. Ledoux, F. Huisken, J. Appl. Phys. 93 (2003) 4173. [10] S.H. Hong, S. Kim, S.H. Choi, K.J. Lee, H. Lee, K.J. Kim, D.W. Moon, J. Korean Phys. Soc. 45 (2004) 116. [11] G.E. Jellison Jr., F.A. Modine, Appl. Phys. Lett. 69 (1996) 371. [12] G.E. Jellison Jr., F.A. Modine, Appl. Phys. Lett. 69 (1996) 2137. [13] D.E. Aspnes, Thin Solid Films 89 (1982) 249. [14] S. Wolf, R.N. Tauber, Silicon Processing for the VLSI Era, Process Technology, vol. 1, Lattice Press, 1986. [15] O. Madelung, Semiconductors; group IV elements and III–V compounds, in: R. Poerschke (Ed.), Data in Science and Technology, Springer-Verlag, Berlin, 1991.
Optical properties of SiO2/nanocrystalline Si multilayers studied using spectroscopic ellipsometry Kang-Ju Leea, Tae-Dong Kanga, Hosun Leea,*, Seung Hui Honga, Suk-Ho Choia, Tae-Yeon Seongb, Kyung Joong Kimc, Dae Won Moonc b
a Department of Physics and Institute of Natural Sciences, Kyung Hee University, Suwon 449-701, Korea Department of Materials Science and Engineering, Kwangju Institute of Science and Technology, Kwangju 500-712, Korea c Nano Surface Group, Korea Research Institute of Standards and Science, PO Box 102, Yusong, Taejon 305-600, Korea
Received 26 May 2004; received in revised form 18 August 2004; accepted 21 September 2004
Abstract Using variable-angle spectroscopic ellipsometry, we measure the pseudo-dielectric functions of as-deposited and annealed SiO2/SiOx multilayers. The SiO2(2 nm)/SiOx (2 nm) multilayers are prepared under various deposition temperatures by ion beam sputtering. Annealing at temperatures above 1100 8C leads to the formation of Si nanocrystals (nc-Si) in the SiOx layer of multilayers. Transmission electron microscopy images clearly demonstrate the existence of nc-Si. We assume a Tauc–Lorentz lineshape for the dielectric function of nc-Si, and use an effective medium approximation for SiO2/nc-Si multilayers as a mixture of nc-Si and SiO2. We successfully estimate the dielectric function of nc-Si and its volume fraction. We find that the volume fraction of nc-Si decreases after annealing, with increasing x in asdeposited SiOx layer. This result is compared to expected nc-Si volume fraction, which is estimated from the stoichiometry of SiOx . D 2004 Elsevier B.V. All rights reserved. PACS: 68.65.Hb; 73.21.La; 78.20.Ci; 78.40.Fy; 78.67.Hc Keywords: Nanostructures; Silicon; Ellipsometry; Transmission electron microscopy
1. Introduction In order to realize light-emitting diode using siliconbased materials, intensive investigations on nanocrystalline silicon (nc-Si) have been carried out. Due to the confinement of electron and hole carriers in nanoscale volumes, we expect enhanced luminescence efficiency due to the increasing recombination rate of carriers as well as the visible luminescence arising from quantum confinement effect [1]. Notably, superlattices composed of alternating nc-Si and SiO2 layers have been given much attention due to a large volume fraction of nc-Si and the controllability of the size and density of nc-Si crystallites [2,3]. One promising method of SiO2/nc-Si multilayers relies on the growth of * Corresponding author. Tel.: +82 312012412; fax: +82 312732411. E-mail address: [email protected] (H. Lee). 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.09.037
SiO2/SiOx multilayers and subsequent heat treatment [4]. We used the ion beam sputtering deposition method to grow SiO2/SiOx multilayers. Ion beam sputtering deposition has the advantage of low operational pressure of the ion sources and precise control of the ion beam parameters, compared to plasma-based radiofrequency (RF) sputtering techniques. Defect densities are relatively low because a neutralized ion beam is used for sputtering and a substrate is not immersed in the plasma [5,6]. In order to optimize SiO2/nc-Si multilayers for optoelectronic devices, we need various structural and optical characterization methods [2,3,5,7]. Using spectroscopic ellipsometry, we can characterize the structural and optical properties at the same time. We can also estimate the thickness of the nc-Si and SiO2 layers and the volume fraction of nc-Si, as well as the dielectric function of nc-Si in detail. Recently, several researchers successfully adopted the Tauc–Lorentz (TL) model for the dielectric function of
K.-J. Lee et al. / Thin Solid Films 476 (2005) 196–200
nc-Si for diameters of 1–3 nm [8,9]. Transmission electron microscopy (TEM) is a direct method to verify the formation of nc-Si. However, it cannot represent the average physical property of a material system because it is only a local probe. Using ellipsometry, we can determine the average property, such as the volume fraction and the dielectric function of nc-Si. In this work, we measure the pseudo-dielectric functions of as-deposited single thick-layer SiOx and its annealed ncSi embedded in SiO2 matrix, as well as as-deposited (SiO2/ SiOx )50 and annealed (SiO2/nc-Si) multilayers, by using variable-angle spectroscopic ellipsometry at room temperature (RT). Using the TL model for the dielectric function of nc-Si and the Bruggeman effective medium approximation (BEMA), we determine the dielectric function of nc-Si and the volume fraction of nc-Si phase.
197
ion beam mill. The sample was rotated and thinned from both sides using Ar+ ion beams until a hole appeared in the center of the bar, giving electron-transparent material. A liquid N2 cold stage was used to cool the sample during ion beam milling. The milling conditions were ion beam energy 4 kV, gun current 0.4 mA, and angle of beam to the sample surface 158. TEM examination was performed using a JEM 2010 instrument operated at 200 kV. Spectroscopic ellipsometry measurements were performed on samples with incidence angles of 708 and 758 using a variable-angle ellipsometer (Woollam VASE model) with and without an autoretarder in the spectral range of 1.0–6.0 eV. The capability of multiple angles of incidence increases the accuracy in determining the layer dielectric function of pseudo-dielectric functions. The pseudo-dielectric functions were fitted using nonlinear Levenberg– Marquardt algorithm using WVASE32 software.
2. Experimental details 3. Results and discussion Two sets of SiO2/nc-Si samples were grown. First, alternating multilayers composed of 2-nm-thick SiOx and 2-nm-thick SiO2 thin films with 50 periods were grown on ptype (100) Si wafers at temperatures of RT, 100 8C, 200 8C, and 300 8C by reactive ion beam sputtering deposition using a Kaufmann-type direct current ion gun and Ar+ beam with ion energy of 750 eVand a Si target. Second, a single layer of 80nm-thick SiOx was grown under identical conditions, for comparison. The deposition chamber was evacuated to a pressure of 2.0108 Torr before introducing argon gas into the system. Details of the system are described elsewhere [5]. We controlled the relative oxygen content by varying both the sputtering rate and the oxygen gas pressure. After deposition, the samples were annealed at 1100 8C for 20 min in an ultra-pure nitrogen ambient using a horizontal furnace to form Si nanocrystals in the SiOx layers. In order to passivate Si dangling bonds, the samples were hydrogenated for 1 h at 650 8C under hydrogen gas flow. The stoichiometry of the SiOx layers was analyzed by in situ Xray photoelectron spectroscopy (XPS) using Al Ka line of 1486.6 eV, thereby sidestepping the problem of surface contamination and oxidation. A stoichiometric SiO2 film was used as a reference to determine the relative sensitivity factors of Si 2p and O 1s. Because the XPS analysis depth of SiO2 is longer than 10 nm, we determined the stoichiometry of SiOx layers in the SiOx /SiO2 multilayers cautiously. We measured the oxygen compositions (denoted as X 1 and X 2, respectively) of SiOx - and SiO2-terminated multilayers and the composition x of SiOx was determined as x=X 1+X 22. For more details on the stoichiometry of SiOx , we refer to Ref. [10]. For cross-sectional TEM examination, the sample was cleaved into two bars, which were glued together surface to surface. The sample was mechanically ground using SiC papers until it was about 40 Am thick. The sample was then glued to a Cu TEM grid, which was placed in a Gatan dual-
Fig. 1 shows TEM images of nc-Si in the annealed multilayer SiO2/SiOx samples for (a) x=1.0 and (b) x=1.2. The TEM results clearly revealed the formation of nc-Si in both single-layer and multilayer SiO2/SiOx samples, when annealed. Due to the interdiffusion of Si and O atoms, the multilayer structures are not evident for x=1. The average
Fig. 1. TEM image of the (SiO2)50/(SiOx )50 multilayers for (a) x=1.0 and (b) x=1.2, which was annealed at high temperature. For visibility, a few Si nanocrystallites were marked.
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diameter of their nc-Si was about 4 nm for x=1. This size information is consistent with the quantum confinement effect, which was verified by photoluminescence results in Ref. [10]. In general, the size of nc-Si decreased with increasing oxygen concentration (x), whereas the number of nanocrystallites increased. However, the total volume of ncSi should have decreased with increasing x. Fig. 2a–d plots the real part of pseudo-dielectric functions (discrete symbols) and their curve fits (solid lines) for as-deposited and annealed (SiO2)50/(nc-Si)50 multilayers, which were grown at RT at a 708 angle of incidence. The imaginary parts of the pseudo-dielectric functions were simultaneously fitted. Note that the H-passivation did not change the pseudo-dielectric function of annealed multilayers. We also measured and fitted the pseudo-dielectric function for the multilayers, which were grown at 100, 200, and 300 8C. For simplicity, the data and fitting are not shown here. We adopted the TL lineshape model for the dielectric function of nc-Si [11,12]. We successfully fitted the pseudo-dielectric function by using BEMA [13]. We assumed a mixture of nc-Si and SiO2 for the multilayers. The equation for BEMA is given by: fnc-Si
enc-Si hei eSiO2 hei þ fSiO2 ¼0 enc-Si þ 2hei eSiO2 þ 2hei
where e nc-Si and e SiO2 are the dielectric functions of nc-Si and SiO2, respectively; hei is the effective dielectric
function of multilayer; and f nc-Si and f SiO2 are the volume fractions of nc-Si and SiO2, respectively. In the TL model, the imaginary dielectric function e 2 is determined by multiplying the Tauc joint density of states by the e 2 obtained from the Lorentz oscillator model. Thus, e 2 is given by: " 2 # AE0 C E Eg 1 e2 ð E Þ ¼ for ENEg E E2 E2 2 þ C 2 E2 0
¼0
for EbEg
where A, E, E g, and C are the four parameters used to describe the spectral dependence of e 2(E) [11,12]. The real part of the dielectric function e 1(E) is then obtained using Kramers–Kronig transformation, with an additional parameter of e 1l. Fig. 3 shows the fitted dielectric function of nc-Si of annealed multilayers and SiOx of as-deposited multilayers for x=1 from Fig. 2. The peak from nc-Si is much more pronounced than that of SiOx , as expected, because of crystallization. The dielectric functions of both SiOx and nc-Si were fitted using the TL model. Note that there is a very small change of the dielectric function at a low-energy region between nc-Si and SiOx . The fitted dielectric function of nc-Si is similar to that of Ref. [8]. The average diameter of their nc-Si was about 1.5 nm, whereas those of nc-Si in this work were 3 nm (x=1.2) and 4 nm (x=1).
Fig. 2. Plots of the real part of pseudo-dielectric functions (discrete symbols) and their curve fits (solid lines) for as-deposited (circles) and annealed (rectangles) (SiO2)50/(nc-Si)50 multilayers, which were grown at room temperature. The oxygen composition x was (a) 1.0, (b) 1.2, (c) 1.4, and (d) 1.6.
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into SiO2 and nc-Si after annealing. We estimated the volume fraction of nc-Si for SiO2/nc-Si multilayers after annealing, using the equations: fnc-Si ¼
Vnc-Si t ¼ 1þt VSiO2 þ Vnc-Si
Vnc-Si 2x t¼ ¼ 2þx VSiO2
Fig. 3. Plot of the fitted dielectric functions of nc-Si of annealed multilayers and SiOx of as-deposited multilayers for x=1 from Fig. 1(a).
Compared to the dielectric function of bulk Si, the values of dielectric function decreased. For example, the maximum of e 2 of bulk Si near E 2 (4.270 eV) band gap energy is about 45. In general, the dielectric functions of silicon semiconductors in the form of quantum well and bulk show main peaks associated with E 1 (3.396 eV) and E 2 (4.270 eV) critical points. However, in the case of nc-Si, the dielectric function shows only a single peak in the experimental range, possibility because of large broadening of the E 1 and E 2 band gaps and the weakening of the exciton effect of the E 1 transition. This phenomenon may also be attributed to the inadequacy of band structure in nanocrystallites due to their extremely small volume and increased surface effect. We note that the BEMA fitting gave a more successful fitting for annealed SiO2/nc-Si multilayer rather than the same fitting for single-layer annealed SiO2/nc-Si. This suggests that the size uniformity of nc-Si in annealed SiO2/nc-Si multilayer is better than that of nc-Si in a single layer. This is reasonable because SiOx and SiO2 layers are periodically distributed in multilayer, and SiOx will decompose into SiO2 and nc-Si phase after high-temperature annealing. Therefore, in order to get a narrow size distribution of nc-Si, multilayer growing of SiO2/SiOx is much better than the single layer growing of SiOx . Fig. 4a and b shows the fitted volume fraction of nc-Si in the multilayers and in the single layer. We also plotted an expected curve from the consideration of the stoichiometry of SiOx (solid lines) in Fig. 4a and b. In Fig. 4a, we observe that the volume fraction of nc-Si decreased with increasing x in as-deposited SiOx layer due to annealing is the driving force for the formation of Si nanocrystals. The decrease of the nc-Si volume fraction with increasing x, in other words approaching x=2.0, can be explained with the consideration of stoichiometry of SiOx layer. The amount of the precipitated nc-Si can be estimated by assuming that all the SiOx will decompose
mSi mSiO2
qSiO2 qSi
;
where m Si and m SiO2 are the molecular weights of Si and SiO2 molecules; and q Si (2.329 g/cm3) and q SiO2 (2.2 g/ cm3) are the mass density of nc-Si and SiO2 phases, respectively [14,15]. Note that we assumed that the SiO2 and SiOx layers in the as-grown multilayers have the same number of Si atoms. Similarly, the volume fraction of SiO2/nc-Si single layer can be estimated using: Vnc-Si ¼ t¼ VSiO2
2 1 x
mSi mSiO2
qSiO2 : qSi
The calculated volume fraction of nc-Si ( f nc-Si) is shown in Fig. 4.
Fig. 4. Plot of the fitted volume fraction of nc-Si (a) in the multilayers and (b) in the thick single layer.
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K.-J. Lee et al. / Thin Solid Films 476 (2005) 196–200
In Fig. 4a and b, the fitted volume fraction of nc-Si by SE matches reasonably well with calculated values. In the case of multilayers, the fitted volume fractions of nc-Si from the deposition temperatures of 100 and 300 8C match the calculated curve, whereas those from other deposition temperatures are higher than that. The discrepancy between the calculation and experimental data can be attributed to the simplified model. We assumed that SiO2 and SiOx layers in the as-grown multilayers have the same number of Si atoms. However, the number of Si atoms in the SiOx layer should be larger than that of the SiO2 layer, assuming the same thickness for both layers. This will increase the calculated V nc-Si, especially in the low x region in Fig. 4a. In the case of single layers of deposition temperature RT in Fig. 4b, the fitted values are higher than the calculated ones, which is similar to the case of multilayers with the same deposition temperature RT. According to TEM data in Fig. 1, the size of nc-Si appeared to decrease with oxygen concentration (x) approaching 2. Due to the increasing ratio of surface to volume in nc-Si, we may expect a decrease of the dielectric function of nc-Si. However, our ellipsometric data gave no clear correlation between the size of nc-Si and their dielectric functions.
4. Conclusion Using variable-angle spectroscopic ellipsometry, we measured the pseudo-dielectric functions of as-deposited and annealed SiO2/SiOx multilayers and single layers. The SiO2(2 nm)/SiOx (2 nm) multilayers with period 50 were prepared under various deposition temperatures by ion beam sputtering deposition. Annealing at temperatures larger than 1100 8C leads to the formation of nc-Si in the SiOx layer of multilayers, which was verified by TEM. Using TL lineshape analysis for the dielectric function of nc-Si, and assuming SiO2/nc-Si multilayers to be a mixture of nc-Si and SiO2, we successfully estimated the dielectric function of ncSi and its volume fraction. The volume fraction of nc-Si decreased after annealing, with increasing x in as-deposited SiOx layer. The formation of nc-Si was verified by TEM. The
fitted nc-Si volume fraction was compared to the estimated value from stoichiometry of SiOx .
Acknowledgement H. Lee acknowledges partial support of 2003 Special Research Fund of Kyung Hee University. S.H. Choi acknowledges partial support from the National research program for the 0.1 Terabit Non-Volatile Memory Development sponsored by Korea Ministry of Science & Technology.
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