## Wafer Bow & Warp

## Thickness Measurement for Metrology Systems

**ASTM F657:**

The distance through a wafer between corresponding points on the front and back surface. Thickness is expressed in microns or mils (thousandths of an inch).

## Total Thickness Variation (TTV)

**ASTM F657:**

The difference between the maximum and minimum values of thickness encountered during a scan pattern or series of point measurements. TTV is expressed in microns or mils (thousandths of an inch).

Figure above shows a wafer placed between two non-contact measurement probes. 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. First the system must be calibrated with a wafer on known thickness (T*w*). 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. The total gap (Gtotal) between the upper and lower probes is then calculated as follows:

**G total = A + B + Tw**

With the system calibrated, wafers of unknown thickness can now be measured. When the wafer is placed between the probes, a new value of A and B is acquired. Thickness is calculated as follows:

**T w = Gtotal – (A + B)**

During an automated scanning of the wafer, a series of point measurements is taken and stored. Following completion of the scan, TTV is calculated as follows:

**TTV = T max – Tmin**

## Non-Contact Bow Measurement

**ASTM F534 3.1.2:**

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.

**Median Surface:**

The locus of points in the wafer equidistant between the front and back surfaces. When measuring and calculating bow, it is important to note that the location median surface of the wafer must be known. By measuring deviations of the median surface, localized thickness variations at the center point of the wafer are removed from the calculation.

Above shows the relationship of the wafer median surface between the two probe faces where:

**D = Distance between upper and lower probe face****A = Distance from upper probe to top wafer surface****B = Distance from lower probe to bottom wafer surface****Z = Distance between wafer median surface and the point halfway between the upper and lower probe (D/2)**

To determine the value of Z at any location on the wafer, there are two equations:

**Z = D/2 – A – T/2 and Z= -D/2 + B + T/2**

Solving both equations for Z, the value can be determined simply by:

**Z = (B – A)/2**

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. 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. Note that bow can be a positive or negative number. Positive denotes the center point of the median surface is above the three point reference plane. Negative denotes the center point of the median surface is below the three point reference plane.

## WARP MEASUREMENT FOR THE SOLAR INDUSTRY

**ASTM F1390:**

The differences between the maximum and minimum distances of the median surface of a free, unclamped wafer from a reference place. Like bow, warp is a measurement of the differentiation between the median surface of a wafer and a reference plane. Warp, however, uses the entire median surface of the wafer instead of just the position at the center point. By looking at the entire wafer, warp provides a more useful measurement of true wafer shape. The location of the median surface is calculated exactly as it is for bow and shown above. For warp determination, there are two choices for construction of the reference plane. One is the same three point plane around the edge of the wafer. The other is by performing a least squares fit calculation of median surface data acquired during the measurement scan. 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*). RPD*max* is defined as the largest distance above the reference plane and is a positive number. RPD*min* is the largest distance below the reference plane and is a negative number.

Figure above is an illustration of the warp calculation. In this example RPDmax is 1.5 and is shown as the maximum distance of the median surface above the reference plane. RPDmin is – 1.5 and is shown as the maximum distance of the median surface below the reference plane. Note warp is always a positive value.

**Warp = 1.5 – (-1.5) = 3**

It also illustrates the usefulness of taking both bow and warp readings. The median surface of the wafer shown intersects the reference plane at the wafer center, therefore, bow measurement would be zero. The calculated warp value is more useful in this case as it tells the user the wafer does have shape irregularities.

## Why is wafer shape such as Thickness, TTV, BOW and Warp important?

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. Optical lithography methods will continue to be used past the 100 nm technology generation for patterning of larger feature sizes. The variations in wafer flatness must be smaller than the depth of focus of optical lithography exposure tools over the illuminated region of the top surface of the wafer+films. To ensure the wafers remain in the depth of focus of the lithography process being used it is necessary to measure the **Thickness,** **TTV, BOW** and **WARP** of the wafers to ensure the wafer’s top physical surface is planar and within the specification of the lithography system being used otherwise there could be defective IC patterns which raise costs through scrap and wasted time.

Rather than discard out of spec wafers it is also possible to sort the wafers by **Thickness**, **TTV**, **BOW** and **WARP** so that they may still be used with longer wavelength lithography systems or eventually reclaimed by being melted back down and turned into new ingots if they are too far out of spec.

Measuring the wafers **thickness** and **TTV** also allows for process control of the CMP (Chemical Mechanical Planarization or Polishing) /Lapping processes and allows these processes to be adjusted to meet customer needs.

Wafers for **MEMS** applications are commonly double-side polished. This can be done either by polishing first one side, then flipping the wafer over and polishing the second side, or polishing both sides simultaneously between two rotating polishing pads. The challenge is to retain the good wafer flatness achieved in previous process steps. This is where monitoring the wafer **Thickness **and **TTV** can become very important in controlling the polishing process.

Post processing of wafers with resists and films can cause **BOW** and **WARP** due to stress on the wafer caused by these post process films. MTI’s 300iSA can be used to check for **BOW** and **WARP** after these post processing film operations. Even though there is a film on the wafer the 300iSA can still make the measurement.

Lithography tools use vacuum chucks. It is assumed that the wafer is pulled down on the chuck so that the backside is perfectly flat, nominally removing wafer **warp** (Diebold and Goodall 1999). The surface topography of a chucked wafer results from wafer thickness variations (**TTV)**, chuck nonplanarity, and surface structures. Effective metrology requires standard measurement procedures and definitions of the quantity of interest. SEMI and ASTM definitions for surface flatness criteria have been developed for silicon wafers (Diebold and Goodall 1999 and Huff *et al*. 1993). The relevant definitions must be selected based on the lithography tool type.

- SFSR/SFSD (Site (or field) flatness–Frontside–Scanner slit leveling/focus–Range/Deviation) should be used for scanning lithography tools.
- SFQR/SFQD (Site flatness–Frontside–least squares field leveling/focus–Range/Deviation) should be used for full-field steppers (Diebold and Goodall 1999 and Huff
*et al*. 1993).

MTI’s 300iSA is capable of all these measurements. Note that range (for full depth of focus) and deviation (for maximum excursion) are relative to a plane recalculated for every exposed site (or for many sites in the scanner case).The metrology concepts for whole-wafer geometry measurement are also well developed in the standards community. Global flatness (variations relative to a whole-wafer plane) can be an issue in CMP process development and control since these processes often thin the edge of a wafer more than the center. Global flatness metrics defined for silicon wafers include:

- GFLR (Global flatness–Front surface–Least squares reference plane–Range)
- GBIR (Global flatness–Back surface–Ideal reference plane–Range) (Diebold and Goodall 1999 and Huff
*et al*. 1993)

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