- Email: [email protected]
Si
ARTICLE IN PRESS
Vacuum 82 (2008) 178–181 www.elsevier.com/locate/vacuum
Determination of relative sputtering yield of Cr/Si L. Kotisa,, M. Menyharda, L. Totha, A. Zalarb, P. Panjanb a
Research Institute for Technical Physics and Materials Science, P.B. 49, Budapest H-1525, Hungary b Jozˇef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
Abstract To understand the various effects induced by the ion bombardment one needs to know the sputtering yields for the sputtering conditions applied. Experimental data are rare however, and the reliability of the calculated values should be checked. Thus the measurement of sputtering yield is important. Recently, we have published a work where we have applied AES depth profiling to determine the relative sputtering yield [Barna A, Menyhard M, Kotis L, Kovacs GyJ, Radnoczi G, Zalar A, et al. J Appl Phys 2005; 98:024901–6]. In this communication, we will describe the method in a more detailed way discussing the reliability as well. It will be applied for Si/Cr multilayer structure (similar to those used in devices of integrated electronics) consisting three Si and three Cr layers sputter deposited onto smooth silicon substrates. The ion energy and projectile were 1 keV and Ar+, respectively. The angle of incidence varied in the range 221–871. The reliability of the derived relative sputtering yields will be discussed and will be compared with those provided by the available simulation. r 2007 Elsevier Ltd. All rights reserved. Keywords: Sputtering yield; AES depth profiling
1. Introduction Many technologies and investigation techniques apply low-energy noble gas ion bombardment. To understand or to estimate the possible effect of the ion bombardment one needs basic data like sputtering yields for the sputtering conditions applied. For example, models describing the surface morphology development use sputtering yield data [1–3] as input parameters. Similarly, to find the optimum adjustment for sputtering conditions in destructive depth profiling, one needs the (in many cases relative) sputtering yield data. Improper adjustment of sputtering conditions can result in roughening, which reduces the applicability of the method [4]. On the other hand, we can find only few data for sputtering yield for low ion energy bombardment [5], which do not cover the whole angular range. For the present study we have chosen Si/Cr multilayer, which is widely used in microelectronics, because metal– silicon systems are known to form compound silicides, which have many good properties. For example, in manufacturing Corresponding author. Fax: +36 13922273.
E-mail address: [email protected] (L. Kotis). 0042-207X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2007.07.017
various memory devices, a special type of silicide known as self-aligned silicide is used [6]. In this work we determine relative sputtering yield of Cr to Si in the angular range 221–871 for 1 keV Ar+ ion bombardment, and we compare the experimental results to the calculated ones provided by SRIM 2003 code [7]. The deviation of the two data sets depends on the angle of incidence and is considerably high. The accuracy of the method will also be discussed. 2. Experiment The Si/Cr multilayer was sputter deposited onto silicon (1 1 1) substrates. The thickness of the individual layers was controlled by using a quartz crystal microbalance during sputter deposition. The nominal thicknesses of the Si and Cr layers were 41 and 45 nm, respectively. For TEM measurement, a sample was cross-sectioned and thinned by ion milling [8]. Cross-sectional transmission electron microscopy (XTEM) image was taken by a Philips CM20 200 kV analytical microscope. The actual thickness of the individual layers was determined from XTEM images.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181
The AES depth profiling was carried out in two dedicated systems in Ljubljana and Budapest. In both cases, 1 keV Ar+ was used for ion bombardment. In Ljubljana, depth profiles without sample rotation were measured by using the PHI SAM 545A instrument applying two symmetrically inclined ion beams. The angle of incidence varied between 221 and 711. In Budapest the AES spectra were recorded by a STAIB DESA 100 preretarded CMA. The sample was rotated during sputtering (4 rev/min) and the angle of incidence varied between 821 and 871. In both laboratories, the ion current was kept constant during sputtering. The concentration was calculated by using relative sensitivity factor, which was determined by the pure regions of the sample using internal standards. 3. Evaluation of relative sputtering yield The structure of the sample is known from the XTEM study. Thus if we can measure the removal time, and the absolute value of the ion current is known, the absolute sputtering yield can, in principle, be determined. In practice, we cannot follow this simple routine for various reasons: a. The measurement of the absolute value of the ion current is difficult especially at grazing angle of incidence. The actual ion current density on the analyzed area strongly depends on the relative position of the sample and ion beam, since the ion beam shape is a Gaussian one. Especially in case of grazing angle of incidence, which is used in these studies, the accuracy of the relative position of the beam and sample cannot be maintained with high accuracy, and thus in our case the absolute measurement of the ion current density is not reliable. b. Due to ion bombardment-induced interface roughening and ion mixing, the interface is broader and not necessarily symmetrical; thus the thickness of the layer cannot be easily defined. c. In the ion mixed region, the density is different from that of pure layer.
179
Having these assumptions the number of removed atoms (N) from area A, during a time interval, Dt, can be calculated as N ¼ DtjASXiYi. Similarly, the removed layer thickness (Dd) during a time interval Dt of ion bombardment is given as Dd ¼ Dtj Yr. The ion current and the relative sputtering yield are the fitting parameters. There are five layers (the last Cr layer will be ignored) to be compared with the layer thicknesses determined by the XTEM. Thus we have more equations than unknown, and it is possible to estimate the accuracy of the method. 4. Results and discussion The XTEM image of the sample can be seen in Fig. 1. Based on the image the actual thicknesses of Si and Cr layers could be determined to be 42, 41, 41 and 46, 46, 44 nm, respectively. The structure of the Cr layers is polycrystalline with a typical grain size of 15 nm.
Fig. 1. TEM cross-sectional view of Si/Cr multilayer sample. The darker layers are of polycrystalline Cr, while the light ones are of amorphous Si. The Si/ Cr interfaces are smoother than those of Cr/Si interfaces.
Thus we developed an algorithm to calculate the relative sputtering yield. The main assumptions are as follows: 1. The ion current density (j) is constant during the measurements. 2. The average sputtering yield can be calculated as Y ¼ SXiYi, where Yi is the sputtering yield of pure element i, and Xi is the concentration of element i. The validity of the assumption is supported by SRIM [7] simulations. 3. The average density (r) of the mixture can be calculated as 1/r ¼ S(Xi/ri), where ri is the density of pure component i.
Fig. 2. A typical AES depth profile. Sputtering conditions: Ar+, 1 keV, 821. Concentration was calculated by relative sensitivity method. The depth calculation is described in the text.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181
180
Table 1 The values of the fitting parameters, their average values and the percentage deviations Angle (1)
22 29 36 49 62 71 82 86 87
YCr/YSi
YCr/YSi
Fitted ion current
1 Cr
2Cr
Aver.
Stand. (%)
SRIM
Si1
Si2
Si3
Aver.
Stand. (%)
1.36 1.50 1.24 1.21 1.21 1.08 0.84 0.68 0.73
1.37 1.45 1.32 1.25 1.14 1.01 0.80 0.68 0.68
1.37 1.48 1.28 1.23 1.18 1.05 0.82 0.68 0.70
0.52 2.40 4.42 2.30 4.21 4.74 3.45 0.00 5.54
2.30 2.03 1.72 1.35 1.05 0.91 0.85 0.84 0.84
1.07 1.13 0.90 0.86 0.84 0.97 0.98
1.01 0.97 0.95 1.03 1.07 1.07 1.02 1.09 0.98
0.94 0.97 1.02 0.99 1.14 1.12 1.00 1.04 1.01
0.98 1.01 1.03 0.98 1.02 1.01 1.00 1.03 0.99
4.65 5.80 8.45 6.70 14.50 14.64 2.32 5.40 1.65
The counting of the layers starts from the free surface. The corresponding relative sputtering yields, calculated with the help of SRIM 2003 code, are also given.
According to the XTEM images, the roughness of the two Cr/Si and Si/Cr interfaces are 1–2 and 1 nm, respectively. The difference is due to the polycrystalline and amorphous structure of the Cr and Si layers, respectively [9,10]. Fig. 2 shows a typical depth profile. The depth resolution depends on the removed layer thickness, which is well known for multilayer samples containing polycrystalline layers [9]. Despite the change in the depth resolution along the depth, there is no overlap between the Si and Cr layers. Thus we can easily identify the number of atoms belonging to a given layer. One can perform the fitting procedure for any layer pairs, resulting in a relative sputtering yield. The layers are counted from the free surface. The ion current will be used to fit the thickness of the Si layers, (YSi ¼ 1). Having the ion current value we can look for the relative sputtering yield value giving the best fit for the Cr layers. The last Cr layer will be ignored, since, because of the presence of the thin SiO2 film on the substrate, the transition is different from the previous ones. Table 1 shows all data. Missing numbers mean missing measurements. The relative sputtering yields calculated from the SRIM 2003 code [7] are also shown in Table 1. The values derived from the three Si (fitting ion current) and two Cr layers (relative sputtering yields) are averaged and the percentage deviations (stand) are also shown. The standard deviation of the ion current value and that of the relative sputtering yields calculated from the measurements is generally less than 10%. This is excellent considering that the interface widths are different for the Si/Cr and Cr/Si interfaces and increases with depth. This means that our procedure can be applied if some broadening of the interface occurs. The deviation from the SRIM results is considerable. It supports the need for the experiential determination of the relative sputtering yield. Finally it should be noted, however, that if a serious roughening occurs then the sputtering yield changes [11,12]
and one cannot use this method. The usage of specimen rotation or/and two ion guns is important for such measurements, which minimizes the roughening. For example, if we repeat the same measurement (1 keV/821 Ar+ bombardment) but without specimen rotation, serious roughening occurred. The relative sputtering yield could be determined to be YCr/YSi ¼ 0.38. This is far from the value of 0.82 (see Table 1). This clearly shows that because of the roughening of the Cr layer the sputtering yield strongly decreased. 5. Conclusions A method based on XTEM investigation and AES depth profiling of Si/Cr multilayer structures for determination of the relative sputtering yields YCr/YSi at different ion incidence angles of 1 keV Ar+ ions was described. The experimentally measured sputtering yields qualitatively follow the trend from the SRIM simulation, but deviations are observed. Some of the deviation might be explained by the influence of the ion-induced surface topography. It was shown that the method is applicable in case of ‘moderate’ roughening, but fails if strong roughening occurs. This emphasizes the importance of sample rotation and/or ion sputtering with two ion beams for precise determination of ion sputtering yields. Acknowledgments Part of this work was done in the framework of the bilateral Hungarian Slovenian TeT agreement of SLO 7/05. The help of the NKFP project of 3A/071/2004 is also acknowledged. References [1] Barna A, Menyhard M, Kotis L, Kovacs GyJ, Radnoczi G, Zalar A, et al. J Appl Phys 2005;98:024901–6. [2] Barna A. Mat Res Soc Symp Proc 1992;254:3.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181 [3] Makeev MA, Cuerno R, Barabasi AL. Nucl Instrum Methods B 2002;197:185–227. [4] Barna A, Menyhard M, Zsolt G, Koos A, Zalar A, Panjan P. J Vac Sci Technol A 2003;21:553–7. [5] Kitano Y, Suzuki T, Tsunoyama K. Tetsu-To-Hagane. J Iron Steel Inst Japan 1991;77:1972–9; Sigmund P. Sputtering by ion bombardment: theoretical concepts. In: Behrish R, editor. Sputtering by particle bombardment, Vol. 1. Berlin: Springer; 1981. [6] Chen et al. US Patent No. US 6,939,764 B2 (2005) 4. [7] /http://www.srim.orgS.
181
[8] Barna A, Radnoczi G, Pecz B. Sample preparation techniques for TEM. In: Amelickx S, Van Dyck D, van Tendeloo J, editors. Handbook for microscopy, vol. 3. Weinheim, Germany: VCH Verlaggesellschaft mbH; 1997. p. 751–801 [Applications, II. Special Topics, chapter 3]. [9] Zalar A, Hofmann S, Panjan P. Thin Solid Films 1991;206:327. [10] Zalar A, Barna A, Barna PB, Panjan P, Hofmann S. Vacuum 1991; 42:485–8. [11] Stepanova M, Dew SK, Soshnikov IP. Phys Rev B 2002;66: 125407–18. [12] Kustner M, Eckstein W, Dose V, Roth J. Nucl Instrum Methods B 1998;145:320–31.
Vacuum 82 (2008) 178–181 www.elsevier.com/locate/vacuum
Determination of relative sputtering yield of Cr/Si L. Kotisa,, M. Menyharda, L. Totha, A. Zalarb, P. Panjanb a
Research Institute for Technical Physics and Materials Science, P.B. 49, Budapest H-1525, Hungary b Jozˇef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
Abstract To understand the various effects induced by the ion bombardment one needs to know the sputtering yields for the sputtering conditions applied. Experimental data are rare however, and the reliability of the calculated values should be checked. Thus the measurement of sputtering yield is important. Recently, we have published a work where we have applied AES depth profiling to determine the relative sputtering yield [Barna A, Menyhard M, Kotis L, Kovacs GyJ, Radnoczi G, Zalar A, et al. J Appl Phys 2005; 98:024901–6]. In this communication, we will describe the method in a more detailed way discussing the reliability as well. It will be applied for Si/Cr multilayer structure (similar to those used in devices of integrated electronics) consisting three Si and three Cr layers sputter deposited onto smooth silicon substrates. The ion energy and projectile were 1 keV and Ar+, respectively. The angle of incidence varied in the range 221–871. The reliability of the derived relative sputtering yields will be discussed and will be compared with those provided by the available simulation. r 2007 Elsevier Ltd. All rights reserved. Keywords: Sputtering yield; AES depth profiling
1. Introduction Many technologies and investigation techniques apply low-energy noble gas ion bombardment. To understand or to estimate the possible effect of the ion bombardment one needs basic data like sputtering yields for the sputtering conditions applied. For example, models describing the surface morphology development use sputtering yield data [1–3] as input parameters. Similarly, to find the optimum adjustment for sputtering conditions in destructive depth profiling, one needs the (in many cases relative) sputtering yield data. Improper adjustment of sputtering conditions can result in roughening, which reduces the applicability of the method [4]. On the other hand, we can find only few data for sputtering yield for low ion energy bombardment [5], which do not cover the whole angular range. For the present study we have chosen Si/Cr multilayer, which is widely used in microelectronics, because metal– silicon systems are known to form compound silicides, which have many good properties. For example, in manufacturing Corresponding author. Fax: +36 13922273.
E-mail address: [email protected] (L. Kotis). 0042-207X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2007.07.017
various memory devices, a special type of silicide known as self-aligned silicide is used [6]. In this work we determine relative sputtering yield of Cr to Si in the angular range 221–871 for 1 keV Ar+ ion bombardment, and we compare the experimental results to the calculated ones provided by SRIM 2003 code [7]. The deviation of the two data sets depends on the angle of incidence and is considerably high. The accuracy of the method will also be discussed. 2. Experiment The Si/Cr multilayer was sputter deposited onto silicon (1 1 1) substrates. The thickness of the individual layers was controlled by using a quartz crystal microbalance during sputter deposition. The nominal thicknesses of the Si and Cr layers were 41 and 45 nm, respectively. For TEM measurement, a sample was cross-sectioned and thinned by ion milling [8]. Cross-sectional transmission electron microscopy (XTEM) image was taken by a Philips CM20 200 kV analytical microscope. The actual thickness of the individual layers was determined from XTEM images.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181
The AES depth profiling was carried out in two dedicated systems in Ljubljana and Budapest. In both cases, 1 keV Ar+ was used for ion bombardment. In Ljubljana, depth profiles without sample rotation were measured by using the PHI SAM 545A instrument applying two symmetrically inclined ion beams. The angle of incidence varied between 221 and 711. In Budapest the AES spectra were recorded by a STAIB DESA 100 preretarded CMA. The sample was rotated during sputtering (4 rev/min) and the angle of incidence varied between 821 and 871. In both laboratories, the ion current was kept constant during sputtering. The concentration was calculated by using relative sensitivity factor, which was determined by the pure regions of the sample using internal standards. 3. Evaluation of relative sputtering yield The structure of the sample is known from the XTEM study. Thus if we can measure the removal time, and the absolute value of the ion current is known, the absolute sputtering yield can, in principle, be determined. In practice, we cannot follow this simple routine for various reasons: a. The measurement of the absolute value of the ion current is difficult especially at grazing angle of incidence. The actual ion current density on the analyzed area strongly depends on the relative position of the sample and ion beam, since the ion beam shape is a Gaussian one. Especially in case of grazing angle of incidence, which is used in these studies, the accuracy of the relative position of the beam and sample cannot be maintained with high accuracy, and thus in our case the absolute measurement of the ion current density is not reliable. b. Due to ion bombardment-induced interface roughening and ion mixing, the interface is broader and not necessarily symmetrical; thus the thickness of the layer cannot be easily defined. c. In the ion mixed region, the density is different from that of pure layer.
179
Having these assumptions the number of removed atoms (N) from area A, during a time interval, Dt, can be calculated as N ¼ DtjASXiYi. Similarly, the removed layer thickness (Dd) during a time interval Dt of ion bombardment is given as Dd ¼ Dtj Yr. The ion current and the relative sputtering yield are the fitting parameters. There are five layers (the last Cr layer will be ignored) to be compared with the layer thicknesses determined by the XTEM. Thus we have more equations than unknown, and it is possible to estimate the accuracy of the method. 4. Results and discussion The XTEM image of the sample can be seen in Fig. 1. Based on the image the actual thicknesses of Si and Cr layers could be determined to be 42, 41, 41 and 46, 46, 44 nm, respectively. The structure of the Cr layers is polycrystalline with a typical grain size of 15 nm.
Fig. 1. TEM cross-sectional view of Si/Cr multilayer sample. The darker layers are of polycrystalline Cr, while the light ones are of amorphous Si. The Si/ Cr interfaces are smoother than those of Cr/Si interfaces.
Thus we developed an algorithm to calculate the relative sputtering yield. The main assumptions are as follows: 1. The ion current density (j) is constant during the measurements. 2. The average sputtering yield can be calculated as Y ¼ SXiYi, where Yi is the sputtering yield of pure element i, and Xi is the concentration of element i. The validity of the assumption is supported by SRIM [7] simulations. 3. The average density (r) of the mixture can be calculated as 1/r ¼ S(Xi/ri), where ri is the density of pure component i.
Fig. 2. A typical AES depth profile. Sputtering conditions: Ar+, 1 keV, 821. Concentration was calculated by relative sensitivity method. The depth calculation is described in the text.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181
180
Table 1 The values of the fitting parameters, their average values and the percentage deviations Angle (1)
22 29 36 49 62 71 82 86 87
YCr/YSi
YCr/YSi
Fitted ion current
1 Cr
2Cr
Aver.
Stand. (%)
SRIM
Si1
Si2
Si3
Aver.
Stand. (%)
1.36 1.50 1.24 1.21 1.21 1.08 0.84 0.68 0.73
1.37 1.45 1.32 1.25 1.14 1.01 0.80 0.68 0.68
1.37 1.48 1.28 1.23 1.18 1.05 0.82 0.68 0.70
0.52 2.40 4.42 2.30 4.21 4.74 3.45 0.00 5.54
2.30 2.03 1.72 1.35 1.05 0.91 0.85 0.84 0.84
1.07 1.13 0.90 0.86 0.84 0.97 0.98
1.01 0.97 0.95 1.03 1.07 1.07 1.02 1.09 0.98
0.94 0.97 1.02 0.99 1.14 1.12 1.00 1.04 1.01
0.98 1.01 1.03 0.98 1.02 1.01 1.00 1.03 0.99
4.65 5.80 8.45 6.70 14.50 14.64 2.32 5.40 1.65
The counting of the layers starts from the free surface. The corresponding relative sputtering yields, calculated with the help of SRIM 2003 code, are also given.
According to the XTEM images, the roughness of the two Cr/Si and Si/Cr interfaces are 1–2 and 1 nm, respectively. The difference is due to the polycrystalline and amorphous structure of the Cr and Si layers, respectively [9,10]. Fig. 2 shows a typical depth profile. The depth resolution depends on the removed layer thickness, which is well known for multilayer samples containing polycrystalline layers [9]. Despite the change in the depth resolution along the depth, there is no overlap between the Si and Cr layers. Thus we can easily identify the number of atoms belonging to a given layer. One can perform the fitting procedure for any layer pairs, resulting in a relative sputtering yield. The layers are counted from the free surface. The ion current will be used to fit the thickness of the Si layers, (YSi ¼ 1). Having the ion current value we can look for the relative sputtering yield value giving the best fit for the Cr layers. The last Cr layer will be ignored, since, because of the presence of the thin SiO2 film on the substrate, the transition is different from the previous ones. Table 1 shows all data. Missing numbers mean missing measurements. The relative sputtering yields calculated from the SRIM 2003 code [7] are also shown in Table 1. The values derived from the three Si (fitting ion current) and two Cr layers (relative sputtering yields) are averaged and the percentage deviations (stand) are also shown. The standard deviation of the ion current value and that of the relative sputtering yields calculated from the measurements is generally less than 10%. This is excellent considering that the interface widths are different for the Si/Cr and Cr/Si interfaces and increases with depth. This means that our procedure can be applied if some broadening of the interface occurs. The deviation from the SRIM results is considerable. It supports the need for the experiential determination of the relative sputtering yield. Finally it should be noted, however, that if a serious roughening occurs then the sputtering yield changes [11,12]
and one cannot use this method. The usage of specimen rotation or/and two ion guns is important for such measurements, which minimizes the roughening. For example, if we repeat the same measurement (1 keV/821 Ar+ bombardment) but without specimen rotation, serious roughening occurred. The relative sputtering yield could be determined to be YCr/YSi ¼ 0.38. This is far from the value of 0.82 (see Table 1). This clearly shows that because of the roughening of the Cr layer the sputtering yield strongly decreased. 5. Conclusions A method based on XTEM investigation and AES depth profiling of Si/Cr multilayer structures for determination of the relative sputtering yields YCr/YSi at different ion incidence angles of 1 keV Ar+ ions was described. The experimentally measured sputtering yields qualitatively follow the trend from the SRIM simulation, but deviations are observed. Some of the deviation might be explained by the influence of the ion-induced surface topography. It was shown that the method is applicable in case of ‘moderate’ roughening, but fails if strong roughening occurs. This emphasizes the importance of sample rotation and/or ion sputtering with two ion beams for precise determination of ion sputtering yields. Acknowledgments Part of this work was done in the framework of the bilateral Hungarian Slovenian TeT agreement of SLO 7/05. The help of the NKFP project of 3A/071/2004 is also acknowledged. References [1] Barna A, Menyhard M, Kotis L, Kovacs GyJ, Radnoczi G, Zalar A, et al. J Appl Phys 2005;98:024901–6. [2] Barna A. Mat Res Soc Symp Proc 1992;254:3.
ARTICLE IN PRESS L. Kotis et al. / Vacuum 82 (2008) 178–181 [3] Makeev MA, Cuerno R, Barabasi AL. Nucl Instrum Methods B 2002;197:185–227. [4] Barna A, Menyhard M, Zsolt G, Koos A, Zalar A, Panjan P. J Vac Sci Technol A 2003;21:553–7. [5] Kitano Y, Suzuki T, Tsunoyama K. Tetsu-To-Hagane. J Iron Steel Inst Japan 1991;77:1972–9; Sigmund P. Sputtering by ion bombardment: theoretical concepts. In: Behrish R, editor. Sputtering by particle bombardment, Vol. 1. Berlin: Springer; 1981. [6] Chen et al. US Patent No. US 6,939,764 B2 (2005) 4. [7] /http://www.srim.orgS.
181
[8] Barna A, Radnoczi G, Pecz B. Sample preparation techniques for TEM. In: Amelickx S, Van Dyck D, van Tendeloo J, editors. Handbook for microscopy, vol. 3. Weinheim, Germany: VCH Verlaggesellschaft mbH; 1997. p. 751–801 [Applications, II. Special Topics, chapter 3]. [9] Zalar A, Hofmann S, Panjan P. Thin Solid Films 1991;206:327. [10] Zalar A, Barna A, Barna PB, Panjan P, Hofmann S. Vacuum 1991; 42:485–8. [11] Stepanova M, Dew SK, Soshnikov IP. Phys Rev B 2002;66: 125407–18. [12] Kustner M, Eckstein W, Dose V, Roth J. Nucl Instrum Methods B 1998;145:320–31.