# Role Of Process-induced Wafer Geometry Changes In Advanced Semiconductor Manufacturing

^{1}and Jaydeep Sinha

^{2}

^{1}Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania

^{2}Surfscan-ADE Division, KLA-Tencor Corporation discuss.

*Figure 1: Range of wafer geometry features commonly encountered in semiconductor processing. Different types of wafer geometry features are classified based on spatial wavelength (horizontal axis). Typical heights of these features are indicated on the vertical axis.*

*Figure 2: Examples of changes in wafer geometry that occur as a result of wafer processing. The top two rows show wafer shape while the bottom rows show geometry maps that have been filtered to remove long wavelength (>10 mm) variations.*

**Process-induced wafer geometry changes**

**Wafer geometry effects in chucking during lithography processes**

*Figure 3: (a) Schematic of simple model used to understand effect of PIWG on wafer chucking. (b) Amplitude of wafer geometry feature that can be chucked as a function of spatial wavelength for vacuum chuck with a clamping pressure of 80 kPa. Figure reproduced from [13].*

*Figure 4: Two examples of wafers with PIWG across a range of spatial wavelengths. (a), (b) and (c) show the wafer shape, local curvature map of a section of the wafer, and the predicted wafer-chuck gap for the first wafer. (d), (e) and (f) show the wafer shape, local curvature map of a section of the wafer, and the predicted wafer- chuck gap for the second wafer. Note the strong correlation between local curvature and wafer-chuck gap for both wafers. Figure adapted from [13].*

*Figure 5: Schematic of out-of-plane and in-plane distortion due to the deposition of a residually stressed film and the effect of distortion on lithography processes. Figure adapted from [4].*

**Relationship between PIWG and overlay**

*EQUATION IS MISSING*_{2}, are the biaxial modulus and thickness of the wafer, σR and h are residual stress and thickness of the film, and r is the radial coordinate. In exposure tools, corrections are applied to compensate for such distortions of the wafer. The deformation field given in the above equation can be fully compensated through a magnification correction, which is standard in the simplest linear correction schemes available in lithography tools. Thus, for residually stressed films to cause overlay errors, more complex deformation fields must be introduced via the processing.

*Figure 6: Results of a finite element simulation of a wafer with a film with a non-uniform radial stress distribution. In the top row, the predicted overlay (left) and shape-slope-residual, which is termed PWG-IPD, (right) are shown. The lower plots show the correlation between overlay and PWG-IPD. Figure reproduced from [15].*

**Conclusions**