Tailored profile pedestal for thermo-elastically stable cooling or heating of substrates

Abstract

A shaped pedestal having a substantially convex profile for cooling a substrate or a substantially concave profile for heating a substrate. The tailored pedestal is formed of at least one continuous curvature segment that is generally elliptical, parabolic, or spherical in shape. The pedestal may be formed from more than one piecewise linear segments that are angled adjacent one another or stepped in a substantially convex or concave manner.

1 - 18 . (canceled) 
     
     
         19 . A method for cooling a substrate having a lower surface, a center area, and an edge area, the method comprising:
 introducing a pedestal having a center, an edge, and a substantially convex shaped top surface underneath said substrate lower surface such that for a substantially flat substrate said pedestal center is initially located at a closer distance to said substrate lower surface than said pedestal edge;   inserting a thermally conductive gas between said substrate lower surface and said pedestal top surface through the gap between the pedestal edge and the substrate lower surface at such process conditions that the thermally conductive gas initiates heat transfer from; and   said substrate lower surface to said pedestal top surface causing faster contraction of the center area than the edge area of the substrate causing substrate flattening during cooling.   
     
     
         20 . The method of  claim 19 , wherein said substantially convex shape top surface comprises AT least one continuous curvature segment, substantially convex in shape. 
     
     
         21 . The method of  claim 20  wherein said at least one continuous curvature segment comprises a portion of an elliptical, parabolic, or spherical shape. 
     
     
         22 . The method of  claim 19 , wherein said substantially convex shape top surface comprises more than one piecewise linear segments. 
     
     
         23 . The method of  claim 22  wherein said piecewise linear segments are angled relative to one another to form said substantially convex shape. 
     
     
         24 . The method of  claim 22  wherein said piecewise linear segments are stepped relative to one another to form said substantially convex shape. 
     
     
         25 . A method for heating a substrate having a lower surface, a center area, and an edge area, the method comprising:
 introducing a pedestal having a center, an edge, and a substantially concave shaped top surface underneath said substrate lower surface such that for a substantially flat substrate said pedestal center is initially located at a further distance to said substrate lower surface than said pedestal edge;   inserting a thermally conductive gas between said substrate lower surface and said pedestal top surface through the gap between the pedestal edge and the substrate lower surface at such process conditions that the thermally conductive gas initiates heat transfer from;   said pedestal top surface to said substrate lower surface causing slower expansion of the center area than the edge area of the substrate causing substrate flattening during heating.   
     
     
         26 . The method of  claim 25 , wherein said substantially concave shape top surface at least one continuous curvature segment, substantially concave in shape. 
     
     
         27 . The method of  claim 26  wherein said at least one continuous curvature segment comprises a portion of an elliptical, parabolic, or spherical shape. 
     
     
         28 . The method of  claim 25 , wherein said substantially concave shape top surface comprises more than one piecewise linear segments. 
     
     
         29 . The method of  claim 28  wherein said piecewise linear segments are angled relative to one another to form said substantially concave shape. 
     
     
         30 . The method of  claim 28  wherein said piecewise linear segments are stepped relative to one another to form said substantially concave shape. 
     
     
         31 . The method of  claim 19 , wherein the substrate is flatter after cooling than before cooling. 
     
     
         32 . The method of  claim 19 , wherein the substrate comprises a 300-millimeter wafer distorting less than about  0 . 5  millimeters during cooling. 
     
     
         33 . The method of  claim 32 , wherein the 300-millimeter wafer has a dome deviation of at least about 0.1 millimeter before cooling. 
     
     
         34 . The method of  claim 19 , wherein the substrate comprises a 300-millimeter wafer and wherein said substrate lower surface is initially located closed to said pedestal center than to said pedestal edge by about 0.020 inches. 
     
     
         35 . The method of  claim 19 , wherein the temperature of the substrate center area is within less than about 50° C. from the temperature of the substrate edge area during cooling.