Wafer Curvature

The residual thermal stress was investigated with a Plexus stress analyzer. The residual stress, was calculated from the radii of wafer curvatures before and after polyimide film deposition by the following equation ... 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

While the resulting model is not quantitatively predictive, important observations can be made based on parametric simulation studies. It is proposed that changes in viscosity due to wafer temperature may be as large as 30%, and that such viscosity dependencies can have significant impact on fluid film thickness and transitively on removal rate. The importance of other process parameters, such as wafer curvature, is also indicated by the model. 

Bending beam method — The principles of the bending beam ( bending cantilever , laser beam deflection wafer curvature ) method were first stated by Stoney [i], who derived an equation relating the stress in the film to the radius of curvature of the beam. The bending beam method can be effectively used in electrochemical experiments, since the changes of the surface stress... 

Wafer Curvature Wafer curvature affects the distribution the applied load across the wafer. If a wafer is bowed up in the... 

Wafer Mounting The wafer should be mounted parallel to the pad surface. Proper wafer mounting design may account for wafer curvature or wafer thickness variations. Wafer mounting may also affect slurry transport. 

Considering a baseline CMP process. Runnels and Eyman determine fluid layer thickness as a function of velocity, wafer curvature, and slurry viscosity. The baseline process is as follows velocity = 20 rpm (63 cm/sec), pressure = 50 kPa (7 psi), slurry viscosity = 0.0214 kg m/sec, and wafer diameter = 20 cm. The wafer curvature (assumed to have a negative radius) is given in terms of the difference in height between the center and the edge of the wafer (dome height) and is assumed to be 10 pm. For the baseline process,model results yield h=63 pm and 0=0.01°. Figures... 

Fluid layer thickness as a function of wafer curvature. (From Ref. (7)). 

Figure S shows a schenutic of a long stylus profilometer trace. It is based on actual profilometry. The wafer has been polished so that the steps have been removed. Lower pattern density at the periphery of the dies has led to the formation of doming. The smaller humps are periodic with the same period as the die length. This periodic doming is superimposed on an overall wafer curvature. The wafer is not completely polished additional oxide could be removed.

A 0.614/xm thick tetraethylorthosilane (TEOS) film is deposited on a relatively thick Si wafer. The biaxial stress in the TEOS film, say is estimated from wafer curvature measurements to be — 114 MPa. A 0.6 pm thick silicon nitride film is then deposited on the TEOS film. The average stress in the bilayer film (composite TEOS and silicon nitride layers) is estimated from curvature measurements to be — 190 MPa. (a) If a 0.6 pm thick silicon nitride film is then deposited on a Si wafer, estimate the mismatch stress (Tsin in this film, (b) Suggest an experimental strategy for determining the stress in each film for a two-film stack deposited on a substrate, without relying on the superposition formula given in (2.74). 

The data shown in Figure 2.25 were obtained by means of the wafer curvature scan, the grid reflection method, or the coherent gradient sensor method. The last of these will be discussed further in Section 2.6.2 in the context of a visualization of deformation via Mohr s circle for curvature. The grid reflection method was described in Section 2.3.3, and a typical set of images obtained with this method is shown in Figure 2.26. 

To provide a measure of residual stress (Tm, which is necessary to estimate pull-in voltage, the fabrication process usually involves deposition of a film of the device plate material, commonly polysilicon, onto a solid Si substrate. This structure can then be observed by means of wafer curvature techniques, for example, to infer a value of residual stress in the film layer. Among the system parameters that influence functional characteristics, the residual stress is the most difiicult to assess properly. On the other hand, control of its value provides an additional means for controlling device characteristics. 

Wafer curvature in the two in-plane directions [0001] and [1-100] the thickness of a-plane GaN films. The dashed lines are guides to the eye. 

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