The flatness of wafers used to manufacture integrated circuits is controlled to tight tolerances to help ensure that all of the wafer is sufficiently flat for lithographic processing. Why is wafer shape such as Thickness, TTV, BOW and Warp important?
The calculated warp value is more useful in this case as it tells the user the wafer does have shape irregularities. The median surface of the wafer shown intersects the reference plane at the wafer center, therefore, bow measurement would be zero. It also illustrates the usefulness of taking both bow and warp readings. RPDmin is – 1.5 and is shown as the maximum distance of the median surface below the reference plane. In this example RPDmax is 1.5 and is shown as the maximum distance of the median surface above the reference plane. RPD min is the largest distance below the reference plane and is a negative number.įigure above is an illustration of the warp calculation. RPD max is defined as the largest distance above the reference plane and is a positive number. Warp is then calculated by finding the maximum deviation from the reference plane (RPD max) and the minimum differentiation from the reference plane (RPD min). The other is by performing a least squares fit calculation of median surface data acquired during the measurement scan. One is the same three point plane around the edge of the wafer. For warp determination, there are two choices for construction of the reference plane. The location of the median surface is calculated exactly as it is for bow and shown above. By looking at the entire wafer, warp provides a more useful measurement of true wafer shape. Warp, however, uses the entire median surface of the wafer instead of just the position at the center point. Like bow, warp is a measurement of the differentiation between the median surface of a wafer and a reference plane. The differences between the maximum and minimum distances of the median surface of a free, unclamped wafer from a reference place. Negative denotes the center point of the median surface is below the three point reference plane. Positive denotes the center point of the median surface is above the three point reference plane. Note that bow can be a positive or negative number. The value of bow is then calculated by measuring the location of the median surface at the center of the wafer and determining it’s distance from the reference plane. Since bow is measured at the center point of the wafer only, a three (3) point reference plane about the edge of the wafer is calculated. Solving both equations for Z, the value can be determined simply by: To determine the value of Z at any location on the wafer, there are two equations: Z = Distance between wafer median surface and the point halfway between the upper and lower probe (D/2).B = Distance from lower probe to bottom wafer surface.A = Distance from upper probe to top wafer surface.D = Distance between upper and lower probe face.By measuring deviations of the median surface, localized thickness variations at the center point of the wafer are removed from the calculation.Ībove shows the relationship of the wafer median surface between the two probe faces where: When measuring and calculating bow, it is important to note that the location median surface of the wafer must be known. The locus of points in the wafer equidistant between the front and back surfaces. The deviation of the center point of the median surface of a free, unclamped wafer from the median surface reference plane established by three points equally spaced on a circle with a diameter a specified amount less than the nominal diameter of the wafer. TTV = T max – T min Non-Contact Bow Measurement Following completion of the scan, TTV is calculated as follows:
#TTV ACRONYM SERIES#
Thickness is calculated as follows:ĭuring an automated scanning of the wafer, a series of point measurements is taken and stored. When the wafer is placed between the probes, a new value of A and B is acquired. With the system calibrated, wafers of unknown thickness can now be measured. The total gap (Gtotal) between the upper and lower probes is then calculated as follows: The area of known thickness is placed between the probes and an upper probe to wafer gap (A) and a lower probe to wafer gap (B) is acquired. First the system must be calibrated with a wafer on known thickness (T w). By monitoring changes between the upper probe face and the upper wafer surface (A) and the bottom probe face and the bottom wafer surface (B), thickness can be calculated. Figure above shows a wafer placed between two non-contact measurement probes.
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