X-Ray Diffraction Determination of Stresses in Thin Films
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X-RAY DIFFRACTION DETERMINATION OF STRESSES IN THIN FILMS T VREELAND, JR., A. DOMMANN, C.-J. TSAI, AND M.-A. NICOLET California Institute of Technology, Pasadena, CA 91125 ABSTRACT This paper presents the methodology employed in the determination of the stress tensor for thin crystalline films using x-ray rocking curves. Use of the same equipment for the determination of the average stress in poly- or non-crystalline thin films attached to a crystalline substrate is also discussed. In this case the lattice curvature of the substrate is determined by measurement of the shift In the Bragg peak with lateral position in the substrate. Strains in single crystal layers may be measured using Bragg diffraction from the layers and from the substrate or a reference crystal, with the highest strain sensitivity of any known technique. The difference in Bragg angles for a strained and an unstrained crystal is related to the change in d spacing of the Bragg planes, and the elastic strain is related to'this angular difference. The separation of two peaks on an x-ray rocking curve is generally not equal to the difference in Bragg angles of two diffracting crystals, so diffractometer measurements must be carefully Interpreted in order to obtain x-ray strains in crystalline films (x-ray strains are strains relative to the reference crystal). The unstrained d spacings of the film and the d spacings of the reference crystal must be known to obtain the elastic strains in the film, from which the stress tensor is determined. INTRODUCTION Measurement of the separation of peaks on x-ray rocking curves (curves of
diffracted intensity
vs.
angle)
is
commonly employed
in
the determination
of
strains in a thin single crystal layer on a crystalline substrate. The very high strain sensitivity of x-ray measurements was demonstrated by Bonse and Hartmann in Si [1]. Using a large Bragg angle and sensitive x-ray intensity measurement, a strain sensitivity of lOE-8 was obtained. A strain sensitivity of 2 IOE-5 to 1OE-4 is typical using x-ray rocking curves with Bragg angles z 45 degrees.
We consider here the determination of the stresses in single, uniformly strained layers. The analysis of multilayer structures is briefly discussed The equipment used for obtaining x-ray rocking curves consists of the following components: An x-ray source Typically, a sealed x-ray tube is used with a Cu target. Other targets are sometimes employed to access different Bragg angles. More intensity is needed for a single, very thin layer (less than about 20 nm), and a rotating anode or synchrotron source is used. 1.
2.
An x-ray monochromator
Typically a Ke reflection from one single crystal of high quality is used to reduce the wave
case,
length spread of the Incident beam to the sample.
the Ku2 diffraction
may
be
removed
monochromator crystal and the sample. high angular resolution is to from a sample crystal are monochromator crystal and the monochromator, as suggested by
Mat. Res. Soc. Symp. Proc. Vol. 130.
by
a
placed
In this
between
the
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