Computer Algorithm for Determining Precipitate Location From Optical Cross-Section Image

Computer Algorithm for Determining Precipitate Location From Optical
Cross-Section Image

      The determination of the defect-free zone depth
(precipitate-free zone) is important in integrated circuit processing
to assure that precipitates do not cause defects in the devices.  The
Optical Precipitate Profiler (OPP) uses a Nomarski-based optical
system at infrared wavelength to produce a two-dimensional
cross-sectional image of a silicon wafer, showing the location of
oxygen precipitates.  This image is taken through the wafer without
cleaving or damaging the wafer.  In this article a computer algorithm
is presented, which analyzes the images produced, to determine the
defect-free zone depth.

      A number of factors make the analysis of the image somewhat
complicated.  First, the images produced by the OPP are a convolution
of the rather small precipitates (0.1 mm) with the much larger
optical beam (2 by 10 mm).  Thus, a single precipitate can be
detected, but not resolved, and, in fact, appears highly elongated.
When the density of precipitates is large, their images overlap.
Secondly the focal spot is aberrated due to the transition from the
low refractive index, air, to the high refractive index, silicon.
Thus, non-ideal waveshapes are produced.  Thirdly, birefringence of
the precipitates can also contribute to the non-ideality of the wave
shape.

      The problem is to determine: 1) the start of the precipitate
"wall", the point at which the high density of precipitates begins,
and 2) the depth of precipitate "stragglers", lone precipitates at
shallower depth than the majority. Algorithm

      Prior to applying algorithms below the data is smoothed in the
z-direction, since this cannot be done during scanning (only
x-direction).

      Problem 1 is addressed by considering that the presence of a
precipitate will cause a signal roughly proportional to the
precipitate size (volume).  By calculating the standard deviation of
an image row (constant z), a curve indicating RMS volume density as a
function of depth can be produced. Before this is done a threshold is
applied such that all signals less than the threshold are set equal
to zero, to reduce RMS accumulation from noise.  Comparison to human
determination indicates that the wall of precipitates starts at about
3/4 of the height of the curve.

      Problem 2 is more difficult.  One may consider that each
precipitate image should reach a peak in the z-direction at the
location of the precipitate, even though the image itself is highly
elongated...