Whether a crack in a brittle material initiates from a damage or not, depends on both, the size of the damage and the extent of the effective load. According to fundamental fracture mechanics relations a crack of the length a initiates, if the

Stress Intensity Factor K| = f о (n a)1/2

exceeds a critical value Kc, which is specific for the given material. о is the applied tensile stress and f is a factor which takes into account the particular geometric conditions. At low stresses о, therefore, large damage sizes a can be tolerated, and at minor damages large stresses can be borne.

Endeavours towards a reduction of loss due to fracturing in a process line, therefore, must aim at both, a reduction of the size of pre-damages in the wafers and a reduction of the effective loads. The manufacturing processes must be optimised under these aspects.

A process which was found to introduce often many pre-damages into a wafer is the wire-sawing from the ingot. An SEM micro-photograph of a
sawing trace is shown in Figure 10.

The influence of such sawing traces on the strength of the wafers is demonstrated in Figure 11. The strength values (arbitrary units) measured in concentric ring tests are plotted for a group of wafers with minor sawing traces (black bars on the left). For comparison the strength values for a group of wafers with distinctly visible traces are given (grey bars on the right). The sawing traces in this example reduce the strength by about 30 percent.

Obviously an analysis and improve­ment of the wire sawing process has a great potential for loss reduction.

One type of manufacturing processes which can implicate mechanical loads to the wafers are high temperature procedures. Due to rapid heating or cooling rates thermally induced stresses can develop. An example is shown in Figure 12. The wafers are etched in a hot bath, and subsequently the hot wafers are immersed into a cool bath (in order to stop the etching process). The quenching process was simulated numerically by means of finite element analysis and the stress field arising in the wafer was calculated. The areas of tensile stresses are represented in Figure 12 by dark zones. The maximum tensile stress occurs at the edges of the wafer on the position of the »waterline« (blackspots marked by arrows). By a numerical variation of the process parameters like temperatures, immersion speed, timing etc. the process can be optimised with respect to the mechanical loading.

Other high temperature processes in cell manu­facturing which can generate thermally induced stresses are tempering procedures like diffusion or fast firing. In Figure 13 the temperature of a wafer is plotted which was measured during its passage through the diffusion furnace (grey curve). The black curve represents the maximum thermal tensile stress induced in the wafer. The stresses were calculated numerically applying finite element analysis. The peak value of the tensile stress in this example is in the order of 40 MPa. Pre-damaged wafers can be destroyed by stresses of this magnitude.

Relatively large stresses can also arise during the tampon printing process for the purpose of metallization, especially with not perfectly planar wafers. Therefore, the deformation of the complete system tampon — wafer — underlay was analysed by means of numerical modelling and simulation and additional verification experi­ments. The resulting stresses in the wafer were calculated. An example is given in Figure 14. A tampon (not drawn in the Figure) is pressed against a non-planar wafer resting on an underlay. The deformation of wafer and underlay can be seen. The stress field in the wafer is represented by the grey colouring (black symbolises high tensile stress). The picture on the top of Figure 14 is valid for a stiff
underlay. The maximum stress (set to 100 percent) occurs inside of the curved segment of the wafer. When the underlay underneath the curvature is made from a soft material, the area of high stresses is spread over a larger region of the wafer (picture in the middle), and the stresses in the elbow become significantly smaller (83 percent). A continuous transition of the stiffness in the underlay leads to a further decay of tensile stresses in the sensitive elbow region (45 percent, picture below).

Applying such numerical simulations it could be shown by variation of the influencing process parameters that the tensile stresses caused by the tampon printing procedure can be reduced by a factor of 3.7