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Precision measurement of axial channel angles
Nuclear Instruments 4% Methods in Physics Research Secllon B
Nuclear Instruments and Methods in Physics Research B63 (1992) 56-58 North-Holland
Precision measurement
of axial channel angles
S. Blunier a, V. Meyer b, R.E. Pixley b, H. Stiissi b, S. Teodoropol b and H. Zogg a *AFIF (Arbeltsgemeinschaft fiir rndustrielle Forschung) at the Swiss Federal Institute of Technology, ETH-Hdnggerberg,
CH-8093
Zurich, Switzerland ’ Physrcs Institute, Umversity of Zurich, CH-8001 Zurich, Switzerland
RBS axial channeling is used to determine channel-angle differences with an accuracy approaching a few mdeg. Measurements in bulk Si and in a strained
BaF,
are described.
1. Introduction RBS axial channeling is one means of measuring the tetragonal distortion of epitaxial layers [I]. The method is illustrated in fig. 1 in which the channels of the layer are displaced relative to the same channels of the undistorted substrate. The displacement is small, typically less than OS”, so that measurements of high accuracy are required in order to obtain meaningful results. Most experiments are designed to measure the positions of the layer channel and the corresponding substrate channel in the same angular scan. This method works well when the particles scattered from the nuclei in the layer can be resolved from those of the substrate and when the steering effect of the beam in the layer is negligible [1,2]. One can avoid these limitations by making measurements of two channel directions in the layer [3]; however, the goniometer accuracy over the large angular
Fig.
1. Channel
0168-583X/92/$05.00
directions in a strained strained substrate.
0 1992 - Elsevier
layer
and
range normally limits the accuracy of such measurements to something greater than 0.01”. We have recently installed a DARD #’ (digital angle-readout device) on the e-axis of our two-axis goniometer which allows measurements of the large channel-angle difference with an accuracy approaching 1 mdeg. In order to learn what the ultimate accuracy of such measurements could be under very favorable conditions, we have made a series of measurements on bulk Si. As a practical example illustrating the usefulness of this method, we give the results for a strained BaF, layer. All measurements described in this report have been obtained with 2 MeV He+ ions.
2. Setup and analysis method In most respects, our setup is typical of those used at Van de Graaff accelerators; however, for the precision channeling measurements an improved beam guidance system was required in order to obtain a directional stability of the beam of the order of 1 mdeg. A two slit stabilizer controlling the deflection of the beam in the horizontal plane before and just following the first slit gave the desired stability. It should be pointed out that this stability was obtained with a beam divergence of + 0.01’. The goniometer is a simple 2-axis device driven by computer controlled step motors. The mechanical accuracy of either drive is about k 0.02 O. The DARD is mounted on the &axis. In order to make use of the mdeg accuracy of the DARD, one must measure axial channels having large 13 and small 4 differences. The expression for the spherical angle difference contains the 0 values of both channels as well as the 4 differ-
an un#’ Manufactured
Science
Publishers
B.V. All rights reserved
by Dr. Johannes
Heidenhain
GmbH.
S. Blunier et al. / Preclslon measurement of axial channel angles
3. Measurements
ence. The zero of 0 can be determined by measuring a channel minimum in 4 and 4 + 180 o geometry. The step motor of the 4 drive is accurate enough for 4 differences less than 3”. Our goniometer has a slight nonorthogonality ( N 0.07 ” > of the t9 and 4 axes: however, its effect on the determination of spherical angles is less than 1 mdeg. For determining the lattice distortion it is convenient to use axial channels which are symmetrical about the surface normal and which lie in the same crystal plane. For (111) oriented material we normally measure the [210] channels (78.4630 deg no-strain difference). For (100) material we use the [211] channels (70.5288 deg no-strain difference). Angular scans are made along the planar direction about each axial channel. Pulse-height spectra of particles scattered through 175” (annular detector 6 cm from the target) are measured at some 40 goniometer angles over a f3 o range about each channel. The angle steps are approximately 10% of the FWHA (full width at half amplitude) near the scan minimum and several times larger in the outer regions of the scan. The spectra are stored in the computer so that energy windows can be selected upon completion of the measurement. In order to analyze the scan data, we first make a linear correction for the nonchannel slope of the yield with target angle (approximately l%/deg) as determined by the outer points of the scan. A least squares fit to the corrected data over a range of angles somewhat greater than the FWHA is then made using a power series as fit function. The number of terms is incremented until an acceptable x2 is obtained. Both odd and even terms are employed. The minimum of the fit function in the region of the fit is determined from the best values of the parameters. The error in the minimum is calculated from the full error matrix. Experience with this procedure has shown it to be reliable even when the fit range is displaced by one angle step. Analysis of two channels is always possible with a fit range shifted by less than 0.5 angle steps.
Table 1 Angle differences given in mdeg.
minus no-strain
value for the [210] channels
57
In order to test the accuracy of this method and the reproducibility of the equipment we have made a series of measurements on each of two samples of bulk Si, one with (111) and the other with (100) orientation. Four channel-angle differences (8 scans) were measured for each sample employing 100 nA and 100 ~.LC per scan. The data were analyzed in four equal width energy windows extending from 44 to 96% of the maximum scattered energy. The angle differences of the four windows were consistent with one another in each run with the exception of the high energy window of the (111) sample which was consistently several standard deviations smaller than the others. In table I, we therefore list a 3-window mean for the (111)‘sample along with the 4-window mean for both samples. The cause of this discrepancy is not known: however, it might have to do with oscillations of the particle in the channel which tend to be less prominent at greater depths. The accuracy of the (100) measurement was not sufficient to detect an effect of this size. In general the mean values of all measurements for each sample agree reasonably well with one another; however, the values are not the expected no-strain values. The [210] channel differences are roughly 5 mdeg too small while the [211] differences are about the same amount too large. It is tempting to suggest that the differences are due to tension in the bulk samples; however, for the present, we prefer to treat this difference as the limiting accuracy of the method. As an example of a measurement on a strained epitaxy layer we describe the results obtained for a 3100 A layer of BaF, with a 100 A CaF, buffer layer on Si (111). The fluoride layers were produced by MBE at 800 K. The scan data about one channel representing a total charge accumulation of 15 PC are shown in fig. 2. The value obtained for the angle difference is larger than the no-strain value for the [210] channels by + 0.113 + 0.004 deg (tensile strain). Repeated mea-
of (111) SI and the [211] channels
of (100) Si. The angle valies
Run number
[210] channels Mean of 3 Mean of 4
1
2
3
4
- 4.2 + 0.7 - 6.5 k 0.5
- 0.7 + 0.7 - 2.7 + 0.5
- 4.2 * 0.7 -6.1 kO.5
- 4.5 + 0.7 - 5.5 &-0.5
8.2k2.1
4.7k2.1
[211] channels Mean of 4
3.5 + 2.1
3.2k2.1
are
S. Blunier et al. / Precision measurement of axial channel angles
58
0.0’.
I
-3
’
-2
-1
0
1
2
3
A8,Cdeg) Fig. 2. Angular scan near a [210] channel of a BaF, layer. x2 for the fit is 5.5 for six degrees of freedom.
surements resulted in progressively smaller values of the difference indicating that the strain was being relaxed by radiation damage. Extrapolating a series of measurements on the same target spot to zero charge gave + 0.121 o corresponding to a tetragonal distortion of 2.15 * 0.15%0. Analysis of the Si [210] channels in the same measurements gave an angle difference relative to the no-strain value of +0.13 k 0.03 deg. Since the Si is essentially strain free, the difference indicates that the beam was fully steered by the channels of the layer. It
should be mentioned that the effect of steering is much less severe for BaF, layers of less than 1500 A. From the above example it can be seen that this procedure can be extremely useful for thick layers in which the steering effect is important. It is also apparent that the relaxation of strain with increasing bombardment will limit the accuracy of the distortion determined by any RBS measurement. The effect is material dependent and should be investigated prior to any final determination of the distortion. Averaging a series of low charge measurements made at different sample positions obviously will reduce the effect; in addition, extrapolation to zero charge of measurements at the same sample position can be made if required.
Acknowledgement This work has been supported by the Swiss National Science Foundation.
References [l] W.K. Chu, C.K. Pan and C.-A. Chang, Phys. Rev. B28 (1983) 4033. [2] S. Hashimoto, Y.-Q. Peng, W.M. Gibson, L.J. Schowalter and B.D. Hunt, Nucl. Instr. and Meth. B13 (1986) 45. [3] A. Carnera and A.V. Drigo, Nucl. Instr. and Meth. B44 (1990) 357.
Nuclear Instruments and Methods in Physics Research B63 (1992) 56-58 North-Holland
Precision measurement
of axial channel angles
S. Blunier a, V. Meyer b, R.E. Pixley b, H. Stiissi b, S. Teodoropol b and H. Zogg a *AFIF (Arbeltsgemeinschaft fiir rndustrielle Forschung) at the Swiss Federal Institute of Technology, ETH-Hdnggerberg,
CH-8093
Zurich, Switzerland ’ Physrcs Institute, Umversity of Zurich, CH-8001 Zurich, Switzerland
RBS axial channeling is used to determine channel-angle differences with an accuracy approaching a few mdeg. Measurements in bulk Si and in a strained
BaF,
are described.
1. Introduction RBS axial channeling is one means of measuring the tetragonal distortion of epitaxial layers [I]. The method is illustrated in fig. 1 in which the channels of the layer are displaced relative to the same channels of the undistorted substrate. The displacement is small, typically less than OS”, so that measurements of high accuracy are required in order to obtain meaningful results. Most experiments are designed to measure the positions of the layer channel and the corresponding substrate channel in the same angular scan. This method works well when the particles scattered from the nuclei in the layer can be resolved from those of the substrate and when the steering effect of the beam in the layer is negligible [1,2]. One can avoid these limitations by making measurements of two channel directions in the layer [3]; however, the goniometer accuracy over the large angular
Fig.
1. Channel
0168-583X/92/$05.00
directions in a strained strained substrate.
0 1992 - Elsevier
layer
and
range normally limits the accuracy of such measurements to something greater than 0.01”. We have recently installed a DARD #’ (digital angle-readout device) on the e-axis of our two-axis goniometer which allows measurements of the large channel-angle difference with an accuracy approaching 1 mdeg. In order to learn what the ultimate accuracy of such measurements could be under very favorable conditions, we have made a series of measurements on bulk Si. As a practical example illustrating the usefulness of this method, we give the results for a strained BaF, layer. All measurements described in this report have been obtained with 2 MeV He+ ions.
2. Setup and analysis method In most respects, our setup is typical of those used at Van de Graaff accelerators; however, for the precision channeling measurements an improved beam guidance system was required in order to obtain a directional stability of the beam of the order of 1 mdeg. A two slit stabilizer controlling the deflection of the beam in the horizontal plane before and just following the first slit gave the desired stability. It should be pointed out that this stability was obtained with a beam divergence of + 0.01’. The goniometer is a simple 2-axis device driven by computer controlled step motors. The mechanical accuracy of either drive is about k 0.02 O. The DARD is mounted on the &axis. In order to make use of the mdeg accuracy of the DARD, one must measure axial channels having large 13 and small 4 differences. The expression for the spherical angle difference contains the 0 values of both channels as well as the 4 differ-
an un#’ Manufactured
Science
Publishers
B.V. All rights reserved
by Dr. Johannes
Heidenhain
GmbH.
S. Blunier et al. / Preclslon measurement of axial channel angles
3. Measurements
ence. The zero of 0 can be determined by measuring a channel minimum in 4 and 4 + 180 o geometry. The step motor of the 4 drive is accurate enough for 4 differences less than 3”. Our goniometer has a slight nonorthogonality ( N 0.07 ” > of the t9 and 4 axes: however, its effect on the determination of spherical angles is less than 1 mdeg. For determining the lattice distortion it is convenient to use axial channels which are symmetrical about the surface normal and which lie in the same crystal plane. For (111) oriented material we normally measure the [210] channels (78.4630 deg no-strain difference). For (100) material we use the [211] channels (70.5288 deg no-strain difference). Angular scans are made along the planar direction about each axial channel. Pulse-height spectra of particles scattered through 175” (annular detector 6 cm from the target) are measured at some 40 goniometer angles over a f3 o range about each channel. The angle steps are approximately 10% of the FWHA (full width at half amplitude) near the scan minimum and several times larger in the outer regions of the scan. The spectra are stored in the computer so that energy windows can be selected upon completion of the measurement. In order to analyze the scan data, we first make a linear correction for the nonchannel slope of the yield with target angle (approximately l%/deg) as determined by the outer points of the scan. A least squares fit to the corrected data over a range of angles somewhat greater than the FWHA is then made using a power series as fit function. The number of terms is incremented until an acceptable x2 is obtained. Both odd and even terms are employed. The minimum of the fit function in the region of the fit is determined from the best values of the parameters. The error in the minimum is calculated from the full error matrix. Experience with this procedure has shown it to be reliable even when the fit range is displaced by one angle step. Analysis of two channels is always possible with a fit range shifted by less than 0.5 angle steps.
Table 1 Angle differences given in mdeg.
minus no-strain
value for the [210] channels
57
In order to test the accuracy of this method and the reproducibility of the equipment we have made a series of measurements on each of two samples of bulk Si, one with (111) and the other with (100) orientation. Four channel-angle differences (8 scans) were measured for each sample employing 100 nA and 100 ~.LC per scan. The data were analyzed in four equal width energy windows extending from 44 to 96% of the maximum scattered energy. The angle differences of the four windows were consistent with one another in each run with the exception of the high energy window of the (111) sample which was consistently several standard deviations smaller than the others. In table I, we therefore list a 3-window mean for the (111)‘sample along with the 4-window mean for both samples. The cause of this discrepancy is not known: however, it might have to do with oscillations of the particle in the channel which tend to be less prominent at greater depths. The accuracy of the (100) measurement was not sufficient to detect an effect of this size. In general the mean values of all measurements for each sample agree reasonably well with one another; however, the values are not the expected no-strain values. The [210] channel differences are roughly 5 mdeg too small while the [211] differences are about the same amount too large. It is tempting to suggest that the differences are due to tension in the bulk samples; however, for the present, we prefer to treat this difference as the limiting accuracy of the method. As an example of a measurement on a strained epitaxy layer we describe the results obtained for a 3100 A layer of BaF, with a 100 A CaF, buffer layer on Si (111). The fluoride layers were produced by MBE at 800 K. The scan data about one channel representing a total charge accumulation of 15 PC are shown in fig. 2. The value obtained for the angle difference is larger than the no-strain value for the [210] channels by + 0.113 + 0.004 deg (tensile strain). Repeated mea-
of (111) SI and the [211] channels
of (100) Si. The angle valies
Run number
[210] channels Mean of 3 Mean of 4
1
2
3
4
- 4.2 + 0.7 - 6.5 k 0.5
- 0.7 + 0.7 - 2.7 + 0.5
- 4.2 * 0.7 -6.1 kO.5
- 4.5 + 0.7 - 5.5 &-0.5
8.2k2.1
4.7k2.1
[211] channels Mean of 4
3.5 + 2.1
3.2k2.1
are
S. Blunier et al. / Precision measurement of axial channel angles
58
0.0’.
I
-3
’
-2
-1
0
1
2
3
A8,Cdeg) Fig. 2. Angular scan near a [210] channel of a BaF, layer. x2 for the fit is 5.5 for six degrees of freedom.
surements resulted in progressively smaller values of the difference indicating that the strain was being relaxed by radiation damage. Extrapolating a series of measurements on the same target spot to zero charge gave + 0.121 o corresponding to a tetragonal distortion of 2.15 * 0.15%0. Analysis of the Si [210] channels in the same measurements gave an angle difference relative to the no-strain value of +0.13 k 0.03 deg. Since the Si is essentially strain free, the difference indicates that the beam was fully steered by the channels of the layer. It
should be mentioned that the effect of steering is much less severe for BaF, layers of less than 1500 A. From the above example it can be seen that this procedure can be extremely useful for thick layers in which the steering effect is important. It is also apparent that the relaxation of strain with increasing bombardment will limit the accuracy of the distortion determined by any RBS measurement. The effect is material dependent and should be investigated prior to any final determination of the distortion. Averaging a series of low charge measurements made at different sample positions obviously will reduce the effect; in addition, extrapolation to zero charge of measurements at the same sample position can be made if required.
Acknowledgement This work has been supported by the Swiss National Science Foundation.
References [l] W.K. Chu, C.K. Pan and C.-A. Chang, Phys. Rev. B28 (1983) 4033. [2] S. Hashimoto, Y.-Q. Peng, W.M. Gibson, L.J. Schowalter and B.D. Hunt, Nucl. Instr. and Meth. B13 (1986) 45. [3] A. Carnera and A.V. Drigo, Nucl. Instr. and Meth. B44 (1990) 357.