Background Statement for SEMI Draft Document 5732
Revision of SEMI M63-0306 with Title Change To
TEST METHOD FOR MEASURING THE Al FRACTION IN AlGaAs ON
GaAs SUBSTRATES BY HIGH RESOLUTION X-RAY DIFFRACTION
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Background
The document is due for five year review. The EU Compound Semiconductor Materials TC Chapter
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Review and Adjudication Information
Task Force Review
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Date:
Committee Adjudication
Task Force for Reapproval of SEMI M63-0306, EU Compound Semiconductor Materials
M46-1101E (reapproved 0309), and M64-0306 TC Chapter
April 15, 2015
April 15, 2015
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SEMI Draft Document #5732
Revision of SEMI M63-0306 with Title Change To:
TEST METHOD FOR MEASURING THE Al FRACTION IN AlGaAs ON
GaAs SUBSTRATES BY HIGH RESOLUTION X-RAY DIFFRACTION
This standard was technically approved by the global Compound Semiconductor Materials Committee. This
edition was approved for publication by the global Audits and Reviews Subcommittee on November 29, 2005.
It was available at www.semi.org in January 2006 and on CD-ROM in March 2006.
1 Purpose
1.1 The purpose of this test method is to describe the use of High Resolution X-Ray Diffraction as a means of
measuring the Al fraction in an AlGaAs epilayer on GaAs substrates, by defining the experimental method and
explaining the analysis.
2 Scope
2.1 This test method addresses measurement of the composition of unrelaxed, undoped AlGaAs epilayers on
<001>-oriented GaAs substrates.
2.2 Principles are given for a standardized measurement method.
2.3 There are differing parameters for analysis already widely in use, either for historical reasons or from local
values (e.g. of GaAs lattice parameter) which are appropriate to that user. As such, examples of analysis are given
but a single standardized analysis is avoided.
2.4 With the standardized measurement method and a guide for standardized reporting of results, it should be
possible to reproduce measurements at different sites, using suitable equipment.
NOTICE: SEMI Standards and Safety Guidelines do not purport to address all safety issues associated with their
use. It is the responsibility of the users of the Documents to establish appropriate safety and health practices, and
determine the applicability of regulatory or other limitations prior to use.
3 Limitations
3.1 This test method does not apply to substrates which are cut to crystallographic planes other than (001).
3.2 The substrates shall have an off-orientation of no more than 15 to the (001) crystallographic planes.
3.3 For determination of Al fraction using direct calculation from peak separation, the layer(s) shall be more than
300 nm thick.
3.4 While thickness of the epilayer can be obtained from high resolution diffraction data, such analysis is not
covered in this test method.
4 Referenced Standards and Documents
4.1 None
5 Terminology
5.1 [Refer to SEMI’s Compilation of Terms (COT) for a list of the most current terms and their definitions.]
5.2 Abbreviations and Acronyms
5.2.1 FWHM — Full Width at Half Maximum (maximum = peak of the curve).
5.2.2 HRXRD — High Resolution X-Ray Diffraction.
5.3 Definitions
5.3.1 2Theta (2) — the axis which alters the angle of the detector to the incident beam direction.
5.3.2 -2 — a scanning axis where the detector angle (2) is scanned at twice the rate of the sample axis ()
5.3.3 Arc second — there are 3600 arc seconds in 1 angle.
5.3.4 Bragg angle — the angle for diffraction of X-rays from a set of crystallographic planes, as defined by Bragg’s
Law:
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=2dsin
(1)
where  is the wavelength of X-rays, d is the spacing between adjacent crystallographic lattice planes and  is the
angle between the planes and the X-ray beam when diffraction occurs.
5.3.5 Chi — the axis which tilts the sample about an axis in the plane of the sample and in the diffraction plane.
5.3.6 Omega () — the axis which alters the angle between the incident beam direction and the sample surface.
5.3.7 Phi — the axis which rotates the sample about the normal to the surface.
5.3.8 Poisson ratio,  — an elasticity parameter which describes how a material expands or contracts in one
direction if compressed or extended in the orthogonal direction. It is composition-dependent.
5.3.9 rocking curve — scan of diffracted intensity measured as the angle between the incident beam and the sample
diffracting planes is changed, going through a diffraction peak. The peak may be only a few arc seconds wide in a
HRXRD measurement.
5.3.10 scattering plane — the plane containing the incident and diffracted X-ray beams.
5.3.11 Vegard’s Law — this law states that the lattice parameter of a ternary alloy epilayer AxB1-xC varies linearly
with composition, x, between the lattice parameters of the two component binary alloys AB and AC, i.e. between
0  x  1.
6 Summary of Method
 Instrument alignment
 Sample alignment
 Sample optimization
 Measurement
 Analysis
7 Apparatus
7.1 High Resolution X-ray Diffractometer
7.1.1 The incident beam divergence should be comparable with the intrinsic FWHM from a GaAs substrate under a
plane wave. For Cu radiation and the 004 reflection from a <001>-oriented sample, this should be ~12 arc seconds.
A true double crystal system has a larger beam divergence but will measure the intrinsic FWHM of the sample,
which would be <~12 arc seconds with Cu radiation.
7.1.2 There must be a means of mounting the sample stress-free. Vacuum methods must not be used.
8 Safety Precautions
8.1 X-rays are ionizing radiation and, as such, are hazardous to health. National and local regulations and rules must
be adhered to, and good practice followed.
9 Test Specimen
9.1 The sample is an epilayer of AlxGa1-xAs on a GaAs substrate; specifically, an unrelaxed, undoped AlGaAs
epilayer on a <001>-oriented GaAs substrate.
10 Preparation of Apparatus
10.1 The diffractometer should be aligned with the beam incident within 1 mm of the center of rotation of the
sample axis.
10.2 The sample axis, Omega, must be capable of angular steps of 2 arc seconds or less.
10.3 The 2Theta axis need not be movable, provided that the detector can be placed at twice the Bragg angle for
diffraction and collect the diffracted beam over the whole range of the scan.
11 Calibration and Standardization
11.1 The measurement relies on the wavelength of the radiation used, which is usually very well known, and the
accurate measurement of angle. Angle has a natural calibration in a full circle, if the X-ray instrument used has a full
circle on Omega.
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11.2 There is no need for standard samples in order to calibrate the measurement or analysis. However, users may
wish to have “golden” samples available to check repeatability of the measurement on a given X-ray tool.
12 Procedure
12.1 The sample shall be mounted such that any off-orientation is directed perpendicular to the direction of the
incident beam.
12.2 If the sample is off-orientation, adjust Chi by the nominal size of the off-orientation, in the direction which
will bring the diffracting crystallographic planes perpendicular to the scattering plane.
12.3 If there is no off-orientation, place the major flat or notch 90 counter-clockwise from the incident beam
direction (Figure 1).
Incident beam
direction
Position of
flat or notch
Figure 1
Orientation of Wafer Relative to Incident X-ray Beam, in the Absence of Off-Orientation
12.4 The surface of the sample shall be within 1 mm of the center of rotation of the sample axis, which shall
coincide with the incident X-ray beam.
12.5 Adjust the detector position to 2 = 66.046 and the sample position to  = 33.023
12.6 Mount the sample in a stress-free manner. The success of this can be assessed by measuring the FWHM of the
rocking curve of the substrate, after optimization (see ¶12.10). The FWHM should be less than 30 arc seconds.
12.7 If the FWHM is too large:
12.7.1 Try remounting the sample, in case the mounting caused stress;
12.7.2 Try reducing the beam size, in case there is an issue of sample curvature; and
12.7.3 Try rotating the sample 45 about its surface normal, in case there is an off-orientation issue.
12.8 If the FWHM remains large, there is an issue with the sample, e.g. poor quality.
12.9 Locate the Bragg diffraction peak from the substrate by rocking Omega about the Bragg angle until strong
diffracted intensity is observed.
12.10 Optimize Chi with Omega until the highest substrate intensity is observed. This should be done to within 0.1
step size on Chi, and to less than 3 arc seconds step size in Omega. The procedure can be carried out either manually
or automatically using a software routine. For each Chi position investigated, the Omega position must be checked
for the highest intensity. NB the substrate peak is always on the high angle side of the layer peak for samples treated
in this document.
12.11 Perform a rocking curve scan, either by rocking  or scanning -2:
12.11.1 Relative to the substrate peak, scan from –750 arc seconds to +100 arc seconds. If the epilayer is thin or of
poor quality, then a lower starting angle may be needed in order to see the layer peak clearly. To define the peak
requires that the intensity drop at the side of the peak to less than half the peak intensity. For low Al fractions, a
narrower scan range will suffice.
12.11.2 The step size shall be no more than one fifth of the substrate FWHM. Thus the Omega step size is typically
2 to 3 arc seconds (~0.0005 to 0.0008) but may be as high as 8 arc seconds (~0.0022).
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12.11.3 The count time per point depends on the observed intensity in the layer peak. It should be set so that the
dynamic range of intensities in the scan covers at least 3 orders of magnitude. In practice, the count time can then be
as little as 0.001 s per point and is often 0.1 to 0.2 s in a Quality Assurance environment.
12.11.4 This first scan shall be referred to as the “Phi = 0 scan”.
12.12 Rotate the sample 180 about the normal to the surface, compensating nominal off-orientation by Chi as
before (¶12.2).
12.13 Repeat ¶12.9 to ¶12.11.
12.13.1 This second scan shall be referred to as the “Phi = 180 scan”.
13 Calculations or Interpretation of Results: Calculation From Peak Separations
13.1 From the two scans collected above, measure the separation of the epilayer peak from the substrate peak. Use
peak fitting over at least the upper half of each peak in order to obtain a precise measure. To obtain repeatable
results, it is necessary to have a repeatable selection of the range for peak fitting.
13.2 From the “Phi = 0 scan”, let the peak separation be 0. From the “Phi = 180 scan”, let the peak separation be
180.
13.3 Find the average peak separation, :
 
 0  180
2
(2)
13.4 From , the Al fraction in the AlGaAs layer may be found from the equation(s) below; note the slight
differences when different lattice parameters are used (see Appendix):
Al fraction = −1.994  10−7 ()2 − 0.002740()
(3)
(Using a0GaAs = 5.65361 Å, a0AlAs = 5.6617 Å, (GaAs) = 0.311; (AlAs) = 0.325; Vegard’s Law assumed).
or
Al fraction = −1.908  10−7 ()2 − 0.002758()
(4)
(Using a0GaAs = 5.65338 Å, a0AlAs = 5.6614 Å, (GaAs) = 0.311; (AlAs) = 0.325, Vegard’s Law assumed)
where  is the peak separation in arc seconds, for the 004 reflection, collected using Cu K1 radiation (wavelength
1.54056 Å).
13.5 See also Table 1 below. It gives a “ready reckoner” for specific peak separations, and clearly shows the
influence of using different lattice parameters in the calculation, as well as comparing Vegard’s law with a nonlinear variation of lattice parameter with composition.
Table 1 Al fractions calculated from 004 HRXRD peak
separations. Cu K1 radiation.
Al fraction (nonAl fraction
linear relation
(Vegard’s Law,
GaAs
a0GaAs = 5.65338 from [17.3]; a0
AlAs
= 5.66171 Å, a0AlAs = 5.6614 = 5.65359 Å, a0
=
5.66171
Å)
Å)
Å)
Average peak
Al fraction
separation,  (Vegard’s Law,
GaAs
(arc seconds) a0 AlAs= 5.65361
Å, a0
−375
0.999
1.008
1.000
−350
0.934
0.942
0.925
−325
0.869
0.876
0.852
−300
0.804
0.810
0.781
−275
0.738
0.744
0.710
−250
0.672
0.678
0.641
−225
0.606
0.611
0.573
−200
0.540
0.544
0.506
−175
0.473
0.477
0.440
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Al fraction (nonAl fraction
linear relation
(Vegard’s Law,
GaAs
a0GaAs = 5.65338 from [17.3]; a0
AlAs
= 5.66171 Å, a0AlAs = 5.6614 = 5.65359 Å, a0
= 5.66171 Å)
Å)
Å)
Average peak
Al fraction
separation,  (Vegard’s Law,
GaAs
(arc seconds) a0 AlAs= 5.65361
Å, a0
−150
0.406
0.410
0.374
−125
0.339
0.342
0.310
−100
0.272
0.274
0.246
−75
0.204
0.206
0.184
−50
0.136
0.138
0.122
−25
0.068
0.069
0.061
0
0
0
0
NOTE 1: Vegard’s Law (a linear relationship between the measured lattice parameter and the Al fraction) has been used for the
middle two columns. The Poisson ratio for the epilayer was calculated assuming a linear variation between the Poisson ratios of
AlAs and GaAs, iterated with the composition calculation until consistent results were obtained. (GaAs) = 0.311; (AlAs) =
0.325 for all cases.
14 Calculations or Interpretation of Results: Data Fitting
14.1 More accurate results may be obtained by fitting the data using dynamical theory. It is still necessary to
consider what the lattice parameters, Poisson ratio and relationship between composition and lattice parameter are,
however – see §16.
14.2 Fitting data where thickness fringes are observed enables epitaxial layer thickness to be determined.
14.3 Where structures are more complex (multiple layers) or peaks or fringes overlap or interfere, data fitting is
necessary for accurate interpretation of results.
14.4 Simulation software using dynamical theory, including auto-fitting software, are available commercially from
several vendors.
15 Reporting Results
15.1 The supplier and customer may agree to report results in terms of average peak separation in the diffraction
scans.
15.2 The supplier and customer may agree to report results in terms of Al fraction, having agreed on lattice
parameters, Poisson ratios and the relationship between lattice parameter and composition (e.g. Vegard’s Law). In
this case, the lattice parameters, Poisson ratios and the relationship between lattice parameter and composition
should be stated in the report of results.
16 Precision and Accuracy
16.1 There are several considerations which affect the precision and accuracy of the measurement and analysis.
16.2 The count time is chosen to give sufficient dynamic range to make peaks clear. The positions of noisy peaks
are less well defined than clean peaks.
16.3 The scan step size has been recommended above to give enough points over a peak to identify its position.
Step size affects the precision of the measurement.
16.4 Curve fitting gives the center position more precisely than is defined by the step size.
16.5 Analysis depends on the lattice constants used for GaAs and AlAs. These affect the absolute accuracy of the
analysis.
16.6 There is variation in the actual lattice constant of different SI GaAs wafers grown by different methods. See
[¶17.1] and [¶17.2] for an overview, and [¶17.3] – in these references, a0GaAs varies between 5.6524 Å and 5.6538 Å,
a difference of nearly 250 ppm. Values used by different vendors of analytical software differ less (~50 ppm).
16.7 Lattice constants for AlAs are generally determined to less precision than for GaAs. See [¶17.1] to [¶17.4].
Values reported for a0AlAs vary from 5.6605 Å to 5.66291 Å, a difference of 426 ppm (one outlier skews this
analysis). Values used by different vendors of analytical software differ less (~75 ppm).
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16.8 However, provided the same lattice constant values are always used in calculations, consistent analysis results
will be obtained.
16.9 Some of the analysis given in this Guideline assumes that Vegard’s Law holds [¶17.5], i.e. that the variation of
lattice parameter of AlxGa1-xAs is linear with x. Some workers have shown that this is not strictly the case – see, for
example, [¶17.3] and [¶17.4]. The effect is shown below; see also Table 1.
1.2
Al fraction
1
0.8
Table 1, Column 2
0.6
Table 1, Column 3
Table 1, Column 4
0.4
0.2
0
-400
-300
-200
-100
0
AlGaAs-GaAs peak separation / arc seconds
Figure 2
Al Fraction Deduced From Peak Separation Using the Results in Table 1
16.10 The Poisson ratios of the materials are also used in the analysis. There is less variation of this parameter
reported in the literature, and general agreement among suppliers of analysis software, on the values given in this
guideline. For other values, see [¶17.1] to [¶17.3] and references therein; also [¶17.6] and [¶17.7].
16.11 The analysis also makes the common assumption that the Poisson ratio varies linearly with x and that any
deviation is negligible. This may also not be strictly the case, but the variation follows a different form from that of
the lattice parameter with x. See [¶17.3].
16.12 Although uncertainties in parameters used in the calculations affect the absolute accuracy of the result, they
do not affect the precision of the measurement or the repeatability.
17 Related Documents
17.1 I. C. Bassignana, D. A Macquistan, R. W. Streater, G. C. Hiller, R. Packwood and V. Moore, “Setting limits
on the accuracy of X-ray determination of Al concentration in AlGaAs/GaAs epitaxial layers”, Journal of Crystal
Growth 172 (1997) 25-36; and references therein.
17.2 N. Herres, A. Dommann, M. Krieger, H. Sigg, K. Bachem and K.; Kohler, “Precision determination of lattice
constants and Poisson ratios in the system AlAs-GaAs”, 2nd European Symposium on X-ray topography and high
resolution diffraction, Berlin, 1994.
17.3 S. Gehrsitz, H. Sigg, N. Herres, K. Bachem, K. Köhler and F. K. Reinhart, “Compositional dependence of the
elastic contstants and the lattice parameter of AlxGa1-xAs”, Physical Review B 60 (16) (1999) 11601-11610.
17.4 Z. R. Wasilewski, M. M. Dion, D. J. Lockwood, P. Pole, R. W. Streater and A. J. Spring Thorpe, Journal of
Applied Physics 81 (1997) 1683.
17.5 L. Vegard, Zeitschrift für Physik 5 (1921) 17.
17.6 H. M. Kagaya, phys. stat. sol. 127B (1985) 89
17.7 Landolt-Bornstein, “Numerical Data and Functional Relationships in Science and Technology”, ed. K. H.
Hellwege (Springer, New York, 1979) vol. 2, pp. 242 and 479.
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APPENDIX 1
SOURCES OF UNCERTAINTY
NOTICE: This appendix offers information related to test calculations and example forms. It was approved as an official part of
SEMI M63 by full letter ballot procedures on November 29, 2006.
A1-1 Lattice parameters
A1-1.1 The lattice parameter of GaAs depends on the growth method. Values in the literature vary by ~250 ppm.
Doping of the substrate or layer also affects the lattice parameter, which in turn affects the Al fraction calculated.
See §16.
A1-1.2 Literature values for the lattice parameter of AlAs vary by ~450 ppm.
A1-1.3 For example, a 50 ppm difference in a0GaAs or a0AlAs with a –100 arc seconds peak separation gives a
change of ~0.016 in the Al fraction for Al ~0.27 (Vegard’s law applied).
A1-2 Poisson ratio
A1-2.1 Poisson ratios, , for AlAs and GaAs are known and generally used to three (3) significant figures.
A1-2.2 Using a0GaAs = 5.65361 Å, a0AlAs = 5.66171 Å, GaAs = 0.311 and AlAs = 0.325, a peak separation of –100 arc
seconds gives an Al fraction of 0.272 (Vegard’s law). Changing one or other Poisson ratio by 0.005 changes the Al
fraction between 0.269 and 0.274. However, note that Poisson ratios of GaAs = 0.311 and AlAs = 0.325 are widely
accepted and used, and there is little cause to use different values.
A1-3 Angular accuracy, precision and repeatability of the equipment
A1-3.1 The HRXRD technique relies on measurement of small angular differences. A 2 arc seconds difference in
a peak separation of −100 arc seconds affects the calculated Al fraction by 0.005.
A1-4 Sample homogeneity
A1-4.1 HRXRD measures the average composition of the volume of the sample interrogated by the incident X-ray
beam. With epitaxial layers, it is usual for the incident beam to penetrate through to the substrate, so the whole layer
structure is examined. The area of the beam on the sample depends on the equipment being used.
A1-5 Temperature
A1-5.1 The lattice parameters of semiconductors change by a few ppm/C. A 5 ppm expansion in both a0GaAs and
a0AlAs with 0.270 Al does not change the peak separation from –99.4 arc seconds. However, differential thermal
expansion of +5 ppm in the GaAs lattice parameter only would change the peak separation to –98.8 arc seconds,
giving an apparent Al fraction change of 0.002.
NOTICE: SEMI makes no warranties or representations as to the suitability of the Standards and Safety Guidelines
set forth herein for any particular application. The determination of the suitability of the Standard or Safety
Guideline is solely the responsibility of the user. Users are cautioned to refer to manufacturer’s instructions, product
labels, product data sheets, and other relevant literature, respecting any materials or equipment mentioned herein.
Standards and Safety Guidelines are subject to change without notice.
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