Measurement of Residual Stress in Thin Films Using the Optical Microprobe
- PDF / 1,824,658 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 75 Downloads / 195 Views
mapped laterally by measuring the optical shift as the optical probe is scanned over the sample surface. The depth distribution can be studied by measuring the shift as the probe is focused at different depths below the specimen surface, provided that the material is sufficiently transparent at both incident and scattered wavelengths. If, on the other hand, the stress varies significantly within the volume excited by the probe then the spectrum of scattered light is a convolution of all the stresses in that volume. There is then no way in which the observed shift can be assigned to a single characteristic stress parameter. In such a case it is necessary to calculate the scattered spectrum from a trial stress distribution and compare the calculated spectrum with that observed experimentally. In this paper we present two examples of the use of these techniques; one to illustrate each of the two situations mentioned above. RAMAN SPECTROSCOPY OF QUANTUM WIRES Experiment Raman spectroscopy has been used extensively to study stress distributions in semiconductor device structures, especially those in which stress and strain are crucial for successful device performance, such as strained GexSil.x alloys. Recently Dietrich et al. [1] reported Raman microprobe measurements on Geo.11 Si0 .89 quantum wire arrays comprising 9 stripes of width 150 nm and spacing 150 nm as illustrated in Figure 1. Each stripe on the silicon substrate had 100 nm Si, followed by 50 nm of Geo.i I Si0 .89 and capped by a further 30 nm of Si. The incident light was from an argon ion laser (514.5 nm) and the beam width was 513
Mat. Res. Soc. Symp. Proc. Vol. 505 © 1998 Materials Research Society
approximately 2 micron. The incident beam was focused on the top of the central stripe and therefore sampled all the stripes simultaneously. Thus the stress distribution in this structure varies on a much finer scale than the diameter of the optical microprobe. Theoy The effective intensity of light scattered from the point (x, y, z) when the incident beam is focused on the point (xo, yo, zo) is given by [2] Is
exp-2(x-
)2 + (y _ y° )exp(-2az) B2
p2 + (Z _-Zo)2 + p
In this expression 2B is the beam width, a is the absorption coefficient of the light and p is the "beam response parameter", which is determined by the focusing optics [3]. To obtain the observable Raman spectrum the individual spectra originating from each point in the sample (and shifted corresponding to the local stress distribution at that point) must be convoluted with the effective intensity of light scattered from that point. The Raman spectrum from each point is assumed to be Lorentzian with peak frequency Dwp A2 I(Aw) =(A
_
+ A2
(2)
Dw varies with position and depends on the stress field at that position. It can be calculated ?rom the stress field by solving the secular equation relating Raman shift to strain [4]. In the structure shown in Figure 1 there is no variation in the y direction and so only the x and z variations need be considered. The convolution to give the observed
Data Loading...
