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Investigation of phosphorus surface segregation by X-ray scattering measurements
Surface Science 580 (2005) 51–56 www.elsevier.com/locate/susc
Investigation of phosphorus surface segregation by X-ray scattering measurements J. Qin a, F. Xue a, L. Huang a, Y.L. Fan a, X.J. Yang a, Z.M. Jiang Q.J. Jia b, X.M. Jiang b b
a,*
,
a Surface Physics Laboratory (National Key Laboratory), Fudan University, Shanghai 200433, China Synchrotron Radiation Laboratory, Institute of High Energy Physics, Chinese Academy of Science, Beijing 100039, China
Received 5 November 2004; accepted for publication 1 February 2005
Abstract The surface segregation of phosphorus in silicon at low temperatures is studied by using d doping structures grown by molecular beam epitaxy. The samples are characterized by X-ray crystal truncation rod (CTR) scattering using synchrotron radiation as the light source. The 1/e decay length of P segregation and segregation barrier energy are obtained by fitting the CTR curves within kinematical approximation of X-ray diffraction theory. The surface segregation of P is strong at a growth temperature of 450 C, with a 1/e decay length of 14 nm, while for growth temperatures below 350 C, P segregation is negligible with a 1/e decay length not larger than 4 nm. The segregation barrier energy is determined to be 0.43 eV. 2005 Elsevier B.V. All rights reserved. Keywords: Molecular beam epitaxy (MBE); Surface segregation; Phosphorus; Silicon; X-ray scattering, diffraction, and reflection
1. Introduction With the further reduction of device dimensions to deep-submicron and nanometer scale, precise control of dopant profiles and diminishing unintentional doping are essential for the electronic perfor-
*
Corresponding author. Tel.: +86 21 65643827; fax: +86 21 65104949. E-mail address: [email protected] (Z.M. Jiang).
mance of devices [1]. Compared with p-type B doping in Si, n-type doping suffers severe donor segregation at typical Si molecular beam epitaxy (MBE) temperatures (P500 C) [2–6]. Most studies in this field have been concentrated on Sb [2,4–6] doping in Si, P doping and P segregation behavior were much less studied. In general, dopant segregation behavior can be divided into two regimes: equilibrium segregation at higher temperatures (>550 C) and kinetically limited segregation at lower temperatures. Nu¨tzel and Abstreiter
0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.02.002
52
J. Qin et al. / Surface Science 580 (2005) 51–56
[2] studied both P and Sb segregation in Si MBE by secondary-ion mass spectroscopy (SIMS) and electrochemical capacitance/voltage profiling. They found that P segregates in Si much less noticeably than Sb does: the decay length of P segregation in Si is about 2–3 orders lower than that of Sb at higher temperatures and more than a half order lower than that of Sb at lower temperatures. According to their results, however, the decay length of P segregation in Si is still as large as 10 nm even at a low temperature of 300 C. Whereas Lippert et al. [7] showed that above 450 C P segregation becomes crucial and at 350 C P segregation seems not significant by SIMS measurement. Further understanding of the segregation behavior of P in Si MBE is required. Moreover, the recent proposal of quantum computers based on the encapsulation of P dopant atoms in Si [8] leads to an increasing importance of controlling P doping profile in Si. For studying dopant segregation, d doping structures are often used and usually characterized by SIMS, Rutherford backscattering spectrometry (RBS), small angle X-ray reflectivity (XRR) and X-ray crystal truncation rod (CTR) scattering. X-ray crystal truncation rod is a line-like distribution of the diffracted intensity around a Bragg point in reciprocal space and is caused by abrupt truncation of a crystal lattice at the surface [9]. X-ray CTR scattering is very sensitive to the difference in average lattice constant across the interface, while XRR is sensitive to the difference in average electron density across the interface [10]. Moreover, with the help of intensive and highly collimated synchrotron X-ray beam, reflected or diffracted intensities as low as 107 (normalized by the intensity of incident X-ray beam) could be detected, resulting in a high depth resolution (1 nm) in characterizing the dopant depth distribution [5]. In this paper, the surface segregation of P atoms in Si in temperature range of 250–450 C is studied by synchrotron radiation X-ray CTR scattering measurement on d doping structures grown by MBE. The 1/e decay length and the barrier energy of P segregation in this temperature range are determined through fitting the CTR curves within the kinematical theory of X-ray diffraction.
2. Experimental The samples were grown by Si MBE in a Riber EVA-32 system with an electron beam evaporator for Si. A GaP decomposition cell was used as P source, which has a specially designed Ga-capture cap to separate the parasitic Ga atoms from P2 beams [11]. The flux density of the P source on sample surface was calibrated by SIMS and verified by the four-point-probe method. The base pressure of the system is better than 5 · 1010 Torr. The growth procedure is as follows: a 50 nm thick Si buffer layer was first deposited on a p-type Si(0 0 1) wafer (1–10 X cm) at 650 C, then a nominal amount of 0.41 ML (1 ML = 6.78 · 1014 atoms/cm2) P was deposited at a substrate temperature of 500 C. Finally a thin Si cap layer was grown at temperatures of 250, 350 and 450 C, respectively. The same growth procedure and parameters are used in the first two steps to keep the surface status as same as possible before Si capping for three samples. X-ray CTR scattering measurements were carried out at the beam line 17C of the Photon Factory in Japan using h 2h scan mode. The wavelength of the X-ray was set at 0.1118 nm. Sample morphology was measured by atomic force microscopy (AFM) in contact mode in air.
3. Results and discussion Fig. 1 shows the measured CTRs around the Si(0 0 4) reflection of the samples grown at different temperatures and the corresponding best simulations (solid lines). The abscissa in Fig. 1 is the scattering vector normalized by the reciprocal lattice vector of Si(0 0 1) reflection. In general, intensity oscillations appear on CTR curve due to the presence of a d doping layer which results in a phase shift between the X-rays reflected from top Si cap layers and those from substrate layers [6]. The oscillation period depends on the thickness of Si top layer [6]. The oscillation amplitudes are mainly determined by the difference of average lattice constant across the Si/P interface (Dd) caused by the incorporation of P atoms, and reduced in logarithmic scale by the surface and interface
J. Qin et al. / Surface Science 580 (2005) 51–56
53
12
P concentration
10
θ
θ
0
Intensity (arb. units)
Si cap 8
10
P
o
450 C
Si buffer
4
10
z
o
350 C Fig. 2. Schematic diagram of the sample structure and distribution of P atoms as a function of depth.
0
10
o
250 C -4
10
3.7
3.8
3.9
4.0
4.1
4.2
Q [G001(Si)] Fig. 1. Measured X-ray CTRs (scatters) of samples grown at different temperatures and the corresponding best fittings (solid curves).
roughness [6,10]. The reduction due to the surface and interface roughness become more and more significant with increasing diffraction vector deviation q = jQ QBraggj. Therefore, oscillation amplitudes in logarithmic scale at smaller q values on CTR curves directly reflect the amount of P atom at the interface, whereas the reduction of these amplitudes in logarithmic scale with increasing q is mainly determined by surface and interface roughness. For samples grown at 250 and 350 C, oscillation of CTR intensity is clearly seen between Q values of 3.7 and 4.2 as shown in Fig. 1. The oscillation amplitudes for the sample grown at 250 C are larger than those for the sample grown at 350 C, indicating a larger amount of P atoms at the interface for the former sample. In contrast, for the sample grown at 450 C the intensity oscillation is significantly reduced and only observed within a much smaller Q range, indicating much less P atoms remaining at the Si/P interface after Si capping at 450 C. This means that the depth distribution profile of P atoms is seriously broadened by P surface segregation at this temperature. In order to obtain quantitative information such as 1/e decay length and the barrier energy of P segregation, numerical simulations for X-ray CTR curves were carried out using kinematical approximation of X-ray diffraction theory as described in literatures [6,10,12]. The structural model
adopted here is schematically illustrated in Fig. 2. In simulation we include the decay length s of P segregation and the lattice constant change induced by P atoms substituting for Si atoms. The P distribution towards the sample surface is assumed to have an exponential decay profile with a decay length of s (we also tried other functions such as Gaussian function however the best fittings which can be obtained are inferior to that using the exponential functions). As we know, P incorporation in Si causes lattice contraction near the dopant atoms [13]. This lattice contraction is taken into account in our fitting model. The lattice constant change is obtained by the first-principles calculations using a supercell consisting of a 20-atomic-layer slab. We also calculated lattice constant changes induced by ddoped Sb and Ge in Si to check the correctness of our calculations. For ideal d doping in Si, 1 ML P, 1 ML Sb and 3 ML Ge are inserted in Si respectively and have the same in-plan lattice constant with Si. The corresponding lattice constant changes perpendicular to the plane are calculated to be 6.6%, 23.6% (for the atomic plane spacing nearest to the dopant layer), and 7.2% (for the atomic plane spacing of two adjacent Ge layers). The lattice constant change of 7.2% for strained coherent Ge layers in Si coincides quite well with the value of 7.3% calculated by using PoissonÕs ratio and elastic coefficients, confirming the correctness of our calculation. We then further assume a linear relationship between the lattice constant change and the P amount, and do the interpolation to obtain the lattice constant change induced by less than 1 ML d-doped P atoms. Table 1 summarizes the growth parameters and the fitting parameters for the best fittings shown in
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J. Qin et al. / Surface Science 580 (2005) 51–56
Table 1 Sample growth parameters and fitting parameters obtained by the best fittings to X-ray CTRs D1 (nm)
N (ML)
N1 (ML)
s (nm)
r (nm)
250 350 450
18.0 22.0 22.0
16.0 19.8 19.8
0.41 0.41 0.41
0.45 0.45 0.45
1.0 4.0 14.0
0.32 [0.233] 0.23 [0.175] 0.60 [0.254]
T is Si capping temperature. D and N are the thickness of the Si cap layer and the expected value of the total amount of P atoms in unit of monolayer, respectively; D1 and N1 are the corresponding values obtained by the best fittings. s is the 1/e decay length of P segregation towards the sample surface. r is the rms roughness of sample surface. The rms roughness data obtained by AFM (2 · 2 lm2) are shown in square brackets.
measured τ =0.01nm, N1=0.35 ML τ =0.3 nm, N1=0.6 ML
2
10
0
10
-2
10
3.7
3.8
3.9
4.0
4.1
4.2
Q [G001(Si)] Fig. 3. Measured X-ray CTRs (scatters) of samples grown at 250 C and the ‘‘best’’ fittings (solid curves) obtained with either N1 or s being fixed and much deviated from the optimal value, showing the uniqueness of N1 and s values for the best fitting.
0.10 20
o
250 C
0.08
o
350 C 15
o
450 C
0.06
10
0.04
5
0.02 0.00
P (%)
Fig. 1. The thickness of Si cap layer and the incorporated amount of P atoms obtained by fitting are very close to those expected for each sample, showing the reliability of our fitting. The rootmean-square (rms) roughness values given by AFM measurement (for 2 · 2 lm2 area) are also listed in square brackets in Table 1. They are quite smaller than those obtained by fitting CTR curves but the trend is consistent. This difference may be due to both different measurement techniques and correspondingly different detected surface sizes. AFM measures external roughness, CTR would likely include internal interface roughness. So the rms value obtained by fitting CTR data may be larger than that obtained by AFM. As mentioned earlier, although both Dd (which is determined by the incorporation of P atoms, i.e., N1, the amount of P and the decay length s) and surface roughness (r) affect the oscillation amplitudes, the fine features located just next to the Si substrate peak are most sensitive to Dd, while the surface roughness reduces the oscillation amplitudes in logarithm scale significantly at larger q values. Moreover, the fine features have different sensitivities to the variation of N1 and s. It is found that N1 and s values which give the best fitting are unique with certain errors. When either parameter (N1 or s) is much deviated from the optimal value, the ‘‘best’’ fitting obtained by changing all the other parameters is still far from satisfying as shown in Fig. 3. Fig. 4 shows the depth distribution profiles of P atoms in Si cap layer obtained from fitting CTR
Intensity (arb. units)
D (nm)
P (ML)
T (C)
4
10
0
5
10
152
0
0
Distance from the interface (nm) Fig. 4. Depth distribution profiles of P atoms obtained by fitting X-ray CTR curves.
curves. It can be seen that at 450 C most P atoms distribute in the whole Si cap layer, with about 19% of the total amount of P atoms having moved to the sample surface via segregation, while only 1% remain at the interface. The amount of P atoms at the interface is so small that only a very limited modification to the atomic plane spacing at the interface is induced, resulting in a very weak intensity oscillation on CTR curve as shown in Fig. 1. The segregation of many P atoms to the surface may have a great influence on surface morphology, which is confirmed by AFM observation as shown
J. Qin et al. / Surface Science 580 (2005) 51–56
55
Fig. 5. AFM images (2 · 2 lm2) of the samples grown at different temperatures.
in Fig. 5. It can be found from Fig. 5 that the surface of the sample grown at 450 C is obviously rougher than that of the other two samples. Fig. 6 gives the dependence of 1/e decay length (s) on Si capping temperature as determined by fitting CTR curves. For comparison, the results of Nu¨tzel and Abstreiter [2] are also plotted. They studied P segregation and concluded that in the kinetically limited region P segregation obeys the following formula [2]: rffiffiffiffiffi R0 Es s ¼ s0 exp ; ð1Þ R kBT where R0 = 0.1 nm/s. R is the deposition rate in nm/s. s and Es are the 1/e decay length and the
o
T ( C) 600
500
400
300 Nutzel et al. Our results Fit: Es=0.66eV
1000
Decay length (nm)
200
Fit: Es=0.43eV
100
10
1
1.2
1.4
1.6
1.8
segregation barrier energy, respectively. s0 is a constant, and kB is the Boltzmann constant. Their experimental results gave Es of 0.66 eV. From Fig. 6 it can be clearly seen that values of decay length we obtained are about one order lower than theirs and give a smaller Es of 0.43 eV. The differences in s and Es obtained may be attributed to two factors as follows. First, the total amounts of deposited P atoms are different. In Ref. [2] the total P amount is <0.2 ML, while in our case the total amount is 0.45 ML, more than doubled compared with theirs. A larger surface coverage of P atoms may reduce the segregation barrier energy via changing the surface atom configurations [5]. Second, their samples were prepared by codeposition of P and Si, and the Si growth rate 0.06 nm/s is lower than 0.1 nm/s used in our case. A higher growth rate results in a weaker segregation, and thus a smaller segregation decay length s. In addition, we also did small angle XRR measurements on these samples. However, it is hard to observe intensity oscillation resulted from the existence of d doping layer on XRR curve. This fact is ascribed to a much lower detection sensitivity of small angle XRR technique compared with X-ray CTR scattering technique due to the small change in average electron density induced by the substitution of P atoms for Si atoms, which is confirmed by theoretical simulations.
2.0
3
1/T (10 / K) Fig. 6. The 1/e decay length s (dots) of P segregation obtained by simulating X-ray CTR curves and the results of Nu¨tzel et al. (squares). The dashed and solid lines fits to formula (1) in text to obtain the segregation barrier energy (see text).
4. Summary In conclusion, we have studied P surface segregation in Si MBE at low temperatures by synchrotron radiation X-ray CTR scattering measurement.
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J. Qin et al. / Surface Science 580 (2005) 51–56
X-ray CTR data were analyzed by fitting the experimental curves within kinematical approximation. The results show that P surface segregation can be negligible at temperatures below 350 C with a segregation decay length not larger than 4 nm. At temperature of 450 C strong surface segregation of P atoms is observed with a decay length as large as 14 nm. The segregation barrier energy is determined to be 0.43 eV.
Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC) project numbers 60425411 and 10321003, and partially supported by the special funds for Major State Basic Research Project No. G2001CB3095 of China, and the special funds for the National Advanced Technology Research and Development, and also supported by Shanghai Science and Technology Commission.
References [1] International technology roadmap for semiconductors, Front end processes, Semiconductor Industry Association, 2001, available online at http://public.itrs.net/Files/ 2001ITRS/Home.htm. [2] J.F. Nu¨tzel, G. Abstreiter, J. Appl. Phys. 78 (1995) 937. [3] H. Jorke, H. Kibbel, Appl. Phys. Lett. 57 (1990) 1763. [4] H. Jorke, Surf. Sci. 193 (1988) 569. [5] Z.M. Jiang, C.W. Pei, L.S. Liao, X.F. Zhou, X.J. Zhang, Xun Wang, Q.J. Jia, X.M. Jiang, Z.H. Ma, Terry Smith, I.K. Sou, Thin Solid Films 336 (1998) 236. [6] J. Falta, D. Bahr, A. Hille, G. Materlik, M. Kammler, M. Horn-von Hoegen, Appl. Phys. Lett. 69 (1996) 2906. [7] G. Lippert, H.J. Osten, D. Kru¨ger, J. Cryst. Growth 157 (1995) 304. [8] L. Oberbeck, N.J. Curson, M.Y. Simmons, R. Brenner, A. Hamilton, S.R. Schofield, R.G. Clark, Appl. Phys. Lett. 81 (2002) 3197. [9] I.K. Robinson, Phys. Rev. B 33 (1986) 3830. [10] J. Falta, D. Bahr, A. Hille, G. Materlik, H.J. Osten, Appl. Phys. Lett. 71 (1997) 3525. [11] T. Shitara, K. Eberl, Appl. Phys. Lett. 65 (1994) 356. [12] I.K. Robinson, R.T. Tung, R. FeidenhansÕl, Phys. Rev. B 38 (1988) 3632. [13] C. Celotti, D. Nobili, P. Ostoja, J. Mater. Sci. 9 (1974) 821.
Investigation of phosphorus surface segregation by X-ray scattering measurements J. Qin a, F. Xue a, L. Huang a, Y.L. Fan a, X.J. Yang a, Z.M. Jiang Q.J. Jia b, X.M. Jiang b b
a,*
,
a Surface Physics Laboratory (National Key Laboratory), Fudan University, Shanghai 200433, China Synchrotron Radiation Laboratory, Institute of High Energy Physics, Chinese Academy of Science, Beijing 100039, China
Received 5 November 2004; accepted for publication 1 February 2005
Abstract The surface segregation of phosphorus in silicon at low temperatures is studied by using d doping structures grown by molecular beam epitaxy. The samples are characterized by X-ray crystal truncation rod (CTR) scattering using synchrotron radiation as the light source. The 1/e decay length of P segregation and segregation barrier energy are obtained by fitting the CTR curves within kinematical approximation of X-ray diffraction theory. The surface segregation of P is strong at a growth temperature of 450 C, with a 1/e decay length of 14 nm, while for growth temperatures below 350 C, P segregation is negligible with a 1/e decay length not larger than 4 nm. The segregation barrier energy is determined to be 0.43 eV. 2005 Elsevier B.V. All rights reserved. Keywords: Molecular beam epitaxy (MBE); Surface segregation; Phosphorus; Silicon; X-ray scattering, diffraction, and reflection
1. Introduction With the further reduction of device dimensions to deep-submicron and nanometer scale, precise control of dopant profiles and diminishing unintentional doping are essential for the electronic perfor-
*
Corresponding author. Tel.: +86 21 65643827; fax: +86 21 65104949. E-mail address: [email protected] (Z.M. Jiang).
mance of devices [1]. Compared with p-type B doping in Si, n-type doping suffers severe donor segregation at typical Si molecular beam epitaxy (MBE) temperatures (P500 C) [2–6]. Most studies in this field have been concentrated on Sb [2,4–6] doping in Si, P doping and P segregation behavior were much less studied. In general, dopant segregation behavior can be divided into two regimes: equilibrium segregation at higher temperatures (>550 C) and kinetically limited segregation at lower temperatures. Nu¨tzel and Abstreiter
0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.02.002
52
J. Qin et al. / Surface Science 580 (2005) 51–56
[2] studied both P and Sb segregation in Si MBE by secondary-ion mass spectroscopy (SIMS) and electrochemical capacitance/voltage profiling. They found that P segregates in Si much less noticeably than Sb does: the decay length of P segregation in Si is about 2–3 orders lower than that of Sb at higher temperatures and more than a half order lower than that of Sb at lower temperatures. According to their results, however, the decay length of P segregation in Si is still as large as 10 nm even at a low temperature of 300 C. Whereas Lippert et al. [7] showed that above 450 C P segregation becomes crucial and at 350 C P segregation seems not significant by SIMS measurement. Further understanding of the segregation behavior of P in Si MBE is required. Moreover, the recent proposal of quantum computers based on the encapsulation of P dopant atoms in Si [8] leads to an increasing importance of controlling P doping profile in Si. For studying dopant segregation, d doping structures are often used and usually characterized by SIMS, Rutherford backscattering spectrometry (RBS), small angle X-ray reflectivity (XRR) and X-ray crystal truncation rod (CTR) scattering. X-ray crystal truncation rod is a line-like distribution of the diffracted intensity around a Bragg point in reciprocal space and is caused by abrupt truncation of a crystal lattice at the surface [9]. X-ray CTR scattering is very sensitive to the difference in average lattice constant across the interface, while XRR is sensitive to the difference in average electron density across the interface [10]. Moreover, with the help of intensive and highly collimated synchrotron X-ray beam, reflected or diffracted intensities as low as 107 (normalized by the intensity of incident X-ray beam) could be detected, resulting in a high depth resolution (1 nm) in characterizing the dopant depth distribution [5]. In this paper, the surface segregation of P atoms in Si in temperature range of 250–450 C is studied by synchrotron radiation X-ray CTR scattering measurement on d doping structures grown by MBE. The 1/e decay length and the barrier energy of P segregation in this temperature range are determined through fitting the CTR curves within the kinematical theory of X-ray diffraction.
2. Experimental The samples were grown by Si MBE in a Riber EVA-32 system with an electron beam evaporator for Si. A GaP decomposition cell was used as P source, which has a specially designed Ga-capture cap to separate the parasitic Ga atoms from P2 beams [11]. The flux density of the P source on sample surface was calibrated by SIMS and verified by the four-point-probe method. The base pressure of the system is better than 5 · 1010 Torr. The growth procedure is as follows: a 50 nm thick Si buffer layer was first deposited on a p-type Si(0 0 1) wafer (1–10 X cm) at 650 C, then a nominal amount of 0.41 ML (1 ML = 6.78 · 1014 atoms/cm2) P was deposited at a substrate temperature of 500 C. Finally a thin Si cap layer was grown at temperatures of 250, 350 and 450 C, respectively. The same growth procedure and parameters are used in the first two steps to keep the surface status as same as possible before Si capping for three samples. X-ray CTR scattering measurements were carried out at the beam line 17C of the Photon Factory in Japan using h 2h scan mode. The wavelength of the X-ray was set at 0.1118 nm. Sample morphology was measured by atomic force microscopy (AFM) in contact mode in air.
3. Results and discussion Fig. 1 shows the measured CTRs around the Si(0 0 4) reflection of the samples grown at different temperatures and the corresponding best simulations (solid lines). The abscissa in Fig. 1 is the scattering vector normalized by the reciprocal lattice vector of Si(0 0 1) reflection. In general, intensity oscillations appear on CTR curve due to the presence of a d doping layer which results in a phase shift between the X-rays reflected from top Si cap layers and those from substrate layers [6]. The oscillation period depends on the thickness of Si top layer [6]. The oscillation amplitudes are mainly determined by the difference of average lattice constant across the Si/P interface (Dd) caused by the incorporation of P atoms, and reduced in logarithmic scale by the surface and interface
J. Qin et al. / Surface Science 580 (2005) 51–56
53
12
P concentration
10
θ
θ
0
Intensity (arb. units)
Si cap 8
10
P
o
450 C
Si buffer
4
10
z
o
350 C Fig. 2. Schematic diagram of the sample structure and distribution of P atoms as a function of depth.
0
10
o
250 C -4
10
3.7
3.8
3.9
4.0
4.1
4.2
Q [G001(Si)] Fig. 1. Measured X-ray CTRs (scatters) of samples grown at different temperatures and the corresponding best fittings (solid curves).
roughness [6,10]. The reduction due to the surface and interface roughness become more and more significant with increasing diffraction vector deviation q = jQ QBraggj. Therefore, oscillation amplitudes in logarithmic scale at smaller q values on CTR curves directly reflect the amount of P atom at the interface, whereas the reduction of these amplitudes in logarithmic scale with increasing q is mainly determined by surface and interface roughness. For samples grown at 250 and 350 C, oscillation of CTR intensity is clearly seen between Q values of 3.7 and 4.2 as shown in Fig. 1. The oscillation amplitudes for the sample grown at 250 C are larger than those for the sample grown at 350 C, indicating a larger amount of P atoms at the interface for the former sample. In contrast, for the sample grown at 450 C the intensity oscillation is significantly reduced and only observed within a much smaller Q range, indicating much less P atoms remaining at the Si/P interface after Si capping at 450 C. This means that the depth distribution profile of P atoms is seriously broadened by P surface segregation at this temperature. In order to obtain quantitative information such as 1/e decay length and the barrier energy of P segregation, numerical simulations for X-ray CTR curves were carried out using kinematical approximation of X-ray diffraction theory as described in literatures [6,10,12]. The structural model
adopted here is schematically illustrated in Fig. 2. In simulation we include the decay length s of P segregation and the lattice constant change induced by P atoms substituting for Si atoms. The P distribution towards the sample surface is assumed to have an exponential decay profile with a decay length of s (we also tried other functions such as Gaussian function however the best fittings which can be obtained are inferior to that using the exponential functions). As we know, P incorporation in Si causes lattice contraction near the dopant atoms [13]. This lattice contraction is taken into account in our fitting model. The lattice constant change is obtained by the first-principles calculations using a supercell consisting of a 20-atomic-layer slab. We also calculated lattice constant changes induced by ddoped Sb and Ge in Si to check the correctness of our calculations. For ideal d doping in Si, 1 ML P, 1 ML Sb and 3 ML Ge are inserted in Si respectively and have the same in-plan lattice constant with Si. The corresponding lattice constant changes perpendicular to the plane are calculated to be 6.6%, 23.6% (for the atomic plane spacing nearest to the dopant layer), and 7.2% (for the atomic plane spacing of two adjacent Ge layers). The lattice constant change of 7.2% for strained coherent Ge layers in Si coincides quite well with the value of 7.3% calculated by using PoissonÕs ratio and elastic coefficients, confirming the correctness of our calculation. We then further assume a linear relationship between the lattice constant change and the P amount, and do the interpolation to obtain the lattice constant change induced by less than 1 ML d-doped P atoms. Table 1 summarizes the growth parameters and the fitting parameters for the best fittings shown in
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J. Qin et al. / Surface Science 580 (2005) 51–56
Table 1 Sample growth parameters and fitting parameters obtained by the best fittings to X-ray CTRs D1 (nm)
N (ML)
N1 (ML)
s (nm)
r (nm)
250 350 450
18.0 22.0 22.0
16.0 19.8 19.8
0.41 0.41 0.41
0.45 0.45 0.45
1.0 4.0 14.0
0.32 [0.233] 0.23 [0.175] 0.60 [0.254]
T is Si capping temperature. D and N are the thickness of the Si cap layer and the expected value of the total amount of P atoms in unit of monolayer, respectively; D1 and N1 are the corresponding values obtained by the best fittings. s is the 1/e decay length of P segregation towards the sample surface. r is the rms roughness of sample surface. The rms roughness data obtained by AFM (2 · 2 lm2) are shown in square brackets.
measured τ =0.01nm, N1=0.35 ML τ =0.3 nm, N1=0.6 ML
2
10
0
10
-2
10
3.7
3.8
3.9
4.0
4.1
4.2
Q [G001(Si)] Fig. 3. Measured X-ray CTRs (scatters) of samples grown at 250 C and the ‘‘best’’ fittings (solid curves) obtained with either N1 or s being fixed and much deviated from the optimal value, showing the uniqueness of N1 and s values for the best fitting.
0.10 20
o
250 C
0.08
o
350 C 15
o
450 C
0.06
10
0.04
5
0.02 0.00
P (%)
Fig. 1. The thickness of Si cap layer and the incorporated amount of P atoms obtained by fitting are very close to those expected for each sample, showing the reliability of our fitting. The rootmean-square (rms) roughness values given by AFM measurement (for 2 · 2 lm2 area) are also listed in square brackets in Table 1. They are quite smaller than those obtained by fitting CTR curves but the trend is consistent. This difference may be due to both different measurement techniques and correspondingly different detected surface sizes. AFM measures external roughness, CTR would likely include internal interface roughness. So the rms value obtained by fitting CTR data may be larger than that obtained by AFM. As mentioned earlier, although both Dd (which is determined by the incorporation of P atoms, i.e., N1, the amount of P and the decay length s) and surface roughness (r) affect the oscillation amplitudes, the fine features located just next to the Si substrate peak are most sensitive to Dd, while the surface roughness reduces the oscillation amplitudes in logarithm scale significantly at larger q values. Moreover, the fine features have different sensitivities to the variation of N1 and s. It is found that N1 and s values which give the best fitting are unique with certain errors. When either parameter (N1 or s) is much deviated from the optimal value, the ‘‘best’’ fitting obtained by changing all the other parameters is still far from satisfying as shown in Fig. 3. Fig. 4 shows the depth distribution profiles of P atoms in Si cap layer obtained from fitting CTR
Intensity (arb. units)
D (nm)
P (ML)
T (C)
4
10
0
5
10
152
0
0
Distance from the interface (nm) Fig. 4. Depth distribution profiles of P atoms obtained by fitting X-ray CTR curves.
curves. It can be seen that at 450 C most P atoms distribute in the whole Si cap layer, with about 19% of the total amount of P atoms having moved to the sample surface via segregation, while only 1% remain at the interface. The amount of P atoms at the interface is so small that only a very limited modification to the atomic plane spacing at the interface is induced, resulting in a very weak intensity oscillation on CTR curve as shown in Fig. 1. The segregation of many P atoms to the surface may have a great influence on surface morphology, which is confirmed by AFM observation as shown
J. Qin et al. / Surface Science 580 (2005) 51–56
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Fig. 5. AFM images (2 · 2 lm2) of the samples grown at different temperatures.
in Fig. 5. It can be found from Fig. 5 that the surface of the sample grown at 450 C is obviously rougher than that of the other two samples. Fig. 6 gives the dependence of 1/e decay length (s) on Si capping temperature as determined by fitting CTR curves. For comparison, the results of Nu¨tzel and Abstreiter [2] are also plotted. They studied P segregation and concluded that in the kinetically limited region P segregation obeys the following formula [2]: rffiffiffiffiffi R0 Es s ¼ s0 exp ; ð1Þ R kBT where R0 = 0.1 nm/s. R is the deposition rate in nm/s. s and Es are the 1/e decay length and the
o
T ( C) 600
500
400
300 Nutzel et al. Our results Fit: Es=0.66eV
1000
Decay length (nm)
200
Fit: Es=0.43eV
100
10
1
1.2
1.4
1.6
1.8
segregation barrier energy, respectively. s0 is a constant, and kB is the Boltzmann constant. Their experimental results gave Es of 0.66 eV. From Fig. 6 it can be clearly seen that values of decay length we obtained are about one order lower than theirs and give a smaller Es of 0.43 eV. The differences in s and Es obtained may be attributed to two factors as follows. First, the total amounts of deposited P atoms are different. In Ref. [2] the total P amount is <0.2 ML, while in our case the total amount is 0.45 ML, more than doubled compared with theirs. A larger surface coverage of P atoms may reduce the segregation barrier energy via changing the surface atom configurations [5]. Second, their samples were prepared by codeposition of P and Si, and the Si growth rate 0.06 nm/s is lower than 0.1 nm/s used in our case. A higher growth rate results in a weaker segregation, and thus a smaller segregation decay length s. In addition, we also did small angle XRR measurements on these samples. However, it is hard to observe intensity oscillation resulted from the existence of d doping layer on XRR curve. This fact is ascribed to a much lower detection sensitivity of small angle XRR technique compared with X-ray CTR scattering technique due to the small change in average electron density induced by the substitution of P atoms for Si atoms, which is confirmed by theoretical simulations.
2.0
3
1/T (10 / K) Fig. 6. The 1/e decay length s (dots) of P segregation obtained by simulating X-ray CTR curves and the results of Nu¨tzel et al. (squares). The dashed and solid lines fits to formula (1) in text to obtain the segregation barrier energy (see text).
4. Summary In conclusion, we have studied P surface segregation in Si MBE at low temperatures by synchrotron radiation X-ray CTR scattering measurement.
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X-ray CTR data were analyzed by fitting the experimental curves within kinematical approximation. The results show that P surface segregation can be negligible at temperatures below 350 C with a segregation decay length not larger than 4 nm. At temperature of 450 C strong surface segregation of P atoms is observed with a decay length as large as 14 nm. The segregation barrier energy is determined to be 0.43 eV.
Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC) project numbers 60425411 and 10321003, and partially supported by the special funds for Major State Basic Research Project No. G2001CB3095 of China, and the special funds for the National Advanced Technology Research and Development, and also supported by Shanghai Science and Technology Commission.
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