Wafer thickness profile

FIGURE 11.13 Prepolished (solid) and Postpolished (dotted) wafer thickness profiles with end-point control (from Ref. 27). 

For these conditions, Armaou and Christofides [4] determine the thickness profile, in Fig. 10.4-3, for the amorphous silicon film after 60 s, when the average thickness reaches 500 A. When characterizing the non-uniformity of the film, the sharp increase in thickness calculated near the outer edge of the wafer is assumed to be due to the boundary conditions, which assume step changes to zero concentrations at the edge. Brass and Lee (2003) disregard the profile from r = 3.6 to 4 cm, and compute the non-uniformity as ... 

Unlike W plasma etch back process, the typical W CMP process usually removes the adhesion layer such as Ti/TiN or TiN during the primary polish. As a result, during the over polish step there is some oxide loss. Since the oxide deposition, planarization CMP (oxide CMP), and tungsten CMP steps are subsequent to each other, the oxide thickness profile could become worse further into the process flow. Therefore, the across-wafer non-uniformity of the oxide loss during W CMP process is one of the very important process parameters needs to be optimized. To determine the effect of the process and hardware parameters on the polish rate and the across-wafer uniformity, designed experiments were run and trends were determined using analysis of variance techniques. Table speed, wafer carrier speed, down force, back pressure, blocked hole pattern, and carrier types were examined for their effects on polish rate and across-wafer uniformity. The variable ranges encompassed by the experiments used in this study are summarized in Table I. 

In addition to the possibility of a nommiform wafer thickness in the radical direction, the thickness of the wafers can vary down the length of the boat reactor. We want to obtain an analytical solution of the silicon deposition rate and reactant concentration profile for the simplified version of the LPCVD reactor just discussed. Analytical solutions of this type are important in that an engineer can rapidly gain an imderstanding of the important parameters and their sensitivities without making a number of runs on the computer. 

In this paper we describe a model of a cup plater with a peripheral continuous contact and passive elements that shape the potential field. The model takes into account the ohmic drop in the electrolyte, the charge-transfer overpotential at the electrode surface, the ohmic drop within the seed layer, and the transient effect of the growing metal film as it plates up (treated as a series of pseudo-steady time steps). Comparison of experimental plated thickness profiles with thickness profile evolution predicted by the model is shown. Tool scale-up for 300 mm wafers was also simulated and compared with results from a dimensionless analysis. 

Figure 10. Relative a of the thickness profiles as a function of plated thickness for 200 mm wafers both simulated and experimental and model prediction for 300 mm wafers...

Draw the dimensionless molar density profile of reactant A within a porous wafer catalyst for the following values of the intrapeUet Damkohler number. The reaction kinetics are zeroth-order and the characteristic length L is one-half of the wafer thickness, measured in the thinnest dimension. Put all five curves on the same set of axes and be as quantitative as possible on both axes. Dimensionless molar density I a is on the vertical axis and dimensional spatial coordinate rj is on the horizontal axis. 

FIGURE 5.11 Examples of the correlation between the nanotopography and inverse fflm thickness profiles before and after CMP for (a) A1 wafer and (b) C2 wafer. 

From a process control point of view, a within-fihn stop CMP process like a conventional oxide ILD CMP process may face difficulties in maintaining good within-wafer uniformity. The final thickness can be missed because of the inaccuracy of endpoint technology and the variable oxide removal rate. In addition, within-wafer oxide profile can be degraded because of noncahbrated pressure zone control at the polishing head, or bad quality of the polishing pad. 

The thickness profiles of microdroplets of polydimethylsiloxane (PDMS) oligomers deposited on oxidized silicon wafers exhibit equal thickness steps, each 0.7 nm thick (Fig. 5.4). The number of visible steps, their lengths, and their growth d3mamics depend on the surface chemistry of the wafers. The common step thickness is the transverse size of the PDMS chain, which means that each step corresponds to a compact flat monolayer of chains, that is, a 2D nonvolatile liquid. Information on the disjoining pressure, and on the friction coefficients between successive layers, can be extracted. " The d3mamics of adsorption of silanol ends when silanol-terminated PDMS (PDMS-OH) is deposited on the wafer can also be monitored in real time. ... 

Thickness profiles of microdroplets of the very common 5CB liquid crystal on bare, oxidized silicon wafers appear on Fig. 5.6. The nematic-isotropic (Nl) transition temperature Tni is close to 35°C. The scenario is complex, both at the molecular and at mesoscopic scale. 

FIG. 13 Top-. SPFM image of the spreading front of a smectic drop of 8CB liquid crystal on a Si wafer, showing a layered structure. Each layer is 32 A thick. The layers advance in the direction of the arrow at the rate of 20-30 A/s at room temperature. Middle-. Profile of the droplet front showing the steps. Bottom-. Drop and surrounding smectic layers. Vertical scale is greatly exaggerated. (From Ref. 62.)... 

Zink et al. used a blend of polystyrene (hPS) and its deuterated counterpart (dPS), both of molecular weight 1.95 x 106 (abbreviated 1.95 M). The average volume fraction (4>dPS) of deuterated polystyrene was 30%. The polymers were dissolved in toluene and spin cast on thin silicon wafers (about 10 x 10 mm), the resulting film thickness being about 300 nm. The samples were annealed at 245°C for 8 days, and the measurement of the resulting depth profiles was conducted by NRA using a monoenergetic 700 keV 3He beam. The nuclear reaction employed can be written ... 

For a one-material case, analytic solutions exist for both the deformation profile of the elastic material as well as the pressure and stress distributions for the indenter (approximating wafer features). Consider a single-layer pad that is thick relative to the vertical deformation and has a deformation force applied over a circular region of radius a. The deformation is given by a set of two equations that represent deformations within and outside the circular radius over which the force is applied. The deformation at any radius r less than a is given by [59] ... 

If a single grain of thin wafer of thickness I is used and total mass loss or gain is measured instead of the concentration profile, the diffusion coefficient may be obtained by fitting the data to Equation 3-52d ... 

---