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9.2.5 More complex calculations may al so be used to determine acceptability. For exam ple, a histogram of the parameter values of the DDS along with statistical measures (mean, sample stan dar d deviation, etc.) may be …

Table 1 Acronyms for Wafer Flatness Parameters

Reference Plane

Acronym

Measurement

Method

Reference Surface

Construction Area

Measurement

Parameter

GBIR Global Back Ideal back surface Entire FQA Range (TIR)

GF3R Global Front Three-point Range (TIR)

GF3D Global Front Three-point Deviation (FPD)

GFLR Global Front Least squares Entire FQA Range (TIR)

GFLD Global Front Least squares Entire FQA Deviation (FPD)

SBIR Site Back Ideal back surface Entire FQA Range (TIR)

SBID Site Back Ideal back surface Entire FQA Deviation (FPD)

SF3R Site Front Three-point Range (TIR)

SF3D Site Front Three-point Deviation (FPD)

SFLR Site Front Least squares Entire FQA Range (TIR)

SFLD Site Front Least squares Entire FQA Deviation (FPD)

SFQR Site Front Least squares Site Range (TIR)

SFQD Site Front Least squares Site Deviation (FPD)

SFSR Site Front Least squares Sub-site Range (TIR)

SFSD Site Front Least squares Sub-site Deviation (FPD)

8 Materials

8.1 Set-up Masters — suitable to accomplish

calibration and standardization as recommended by the

equipment manufacturer.

8.2 Reference Wafer — with total thickness variation

(TTV) value and flatness value similar to the product or

process to be monitored and with a data set that is used

to determine the level of agreement between the data

set obtained by the measuring equipment under test and

the reference wafer data set (see Section 9 ).

9 Suitability of Measuring Equipment

9.1 Determine the suitability of the measuring

equipment with the use of a reference wafer and its

associated data set in accordance with the procedures of

Sub-section 9.2 , or by performance of a statistically-

based instrument repeatability study to ascertain

whether the equipment is operating within the

manufacturer's stated specification for repeatability.

9.1.1 The reference wafer data set is a set of thickness

or flatness parameters based on corrected data in that all

possible interferences have been removed and the data

has been replanarized in accordance with this method.

9.1.2 Each reference wafer (artifact) is accompanied by

its own data set, the reference data set (RDS), in which

each parameter value is the average of a number of

values obtained for that parameter over a number of

“passes” (repeat measurements). The artifact is

measured on a measurement equipment under test and

its RDS is compared against the resultant-measured

sample data set. Delta-parameter and other values are

computed from the differences. The parameter used to

determine agreement between the artifact and the

measuring equipment under test and the acceptable

level of this agreement is to be agreed upon between the

parties to the test.

9.2 Procedure

9.2.1 Select a reference wafer of appropriate criteria

together with its associated reference data set (RDS).

9.2.2 Measure the reference wafer on the measurement

equipment under test to obtain a sample data set (SDS).

9.2.3 Subtract the two data sets on a parameter basis to

obtain a difference data set (DDS):

DDSSDSRDS 



(1)

9.2.3.1 The DDS represents the differences between

the measurements made on the measuring equipment

under test and the reference data set. The DDS contains

many values.

9.2.4 The simplest metric that can be used to determine

acceptability is maximum difference, the largest

absolute value in the DDS. This represents the worst-

case disagreement between the results obtained from

the measurement equipment under test and the

reference data. Accept the measurement equipment as

suitable for measurement if the maximum difference is

less than a value that is agreed upon between the parties

to the test.

SEMI MF1530-1104 © SEMI 2003, 2004 3

9.2.5 More complex calculations may also be used to

determine acceptability. For example, a histogram of

the parameter values of the DDS along with statistical

measures (mean, sample standard deviation, etc.) may

be used. These measures may be compared to

application-specific limits or used to provide insight

into the nature and source of the difference, or both, as

arranged by agreement of the parties to the test.

10 Sampling

10.1 This test method is nondestructive and may be

used on either 100% of the wafers in a lot or on a

sampling basis.

10.1.1 If samples are to be taken, procedures for

selecting the sample from each lot of wafers to be tested

shall be agreed upon between the parties to the test, as

shall the definition of what constitutes a lot.

11 Calibration and Standardization

11.1 Calibrate the measuring equipment in accordance

with the manufacturer's instructions.

12 Procedure

12.1 Prepare the apparatus for measurement of wafers,

including selection of data display/output functions.

12.2 Select the fixed quality area (FQA) by specifying

the nominal edge exclusion EE.

12.3 Select the flatness parameter(s) to be determined

as follows:

12.3.1 Select the measurement method — global

flatness (G) or site flatness (S):

12.3.1.1 If S is chosen, then also specify site array

details:

12.3.1.1.1 site size,

12.3.1.1.2 location of sites relative to FQA center,

12.3.1.1.3 location of sites relative to each other,

rectilinear or tiled pattern, and

12.3.1.1.4 partial sites, included or excluded.

12.3.2 Select the reference surface — front (F) or back

(B).

12.3.3 Select the reference plane construction and area

as follows:

12.3.3.1 For global flatness measurements, select one

of the following global reference planes using all points

within the FQA to construct the reference plane:

12.3.3.1.1 Ideal back surface plane (I),

12.3.3.1.2 Three-point front surface plane (3), or

12.3.3.1.3 Least-squares front surface plane (L).

12.3.3.2 For site flatness measurements with a global

reference plane, select one of the following global

reference planes using all points within the FQA to

construct the reference plane:

12.3.3.2.1 Ideal back surface plane (I),

12.3.3.2.2

Three-point front surface plane (3), or

12.3.3.2.3 Least-squares front surface plane(L).

12.3.3.3 For site flatness measurements with a site

reference plane, select the following reference plane

using all points within the site that lie within the FQA

to construct the reference plane:

12.3.3.3.1 Site least-squares front surface plane (Q).

12.3.3.4 For scanner site flatness measurements with a

sub-site reference plane, select the following reference

plane using all points within the sub-site that lie within

the FQA to construct the reference plane:

12.3.3.4.1 Sub-site least squares front surface plane

(S).

12.3.4 Select the measurement parameter:

12.3.4.1 Global Flatness:

12.3.4.1.1 Range (Total indicator reading, TIR) (R), or

12.3.4.1.2 Deviation (Focal plane deviation, FPD) (D).

12.3.4.2 Site Flatness:

12.3.4.2.1 Range (TIR) — each site or maximum value

for all sites, or both, or

12.3.4.2.2 Deviation (FPD) — each site or maximum

value for all sites, or both, or

12.3.4.2.3 A map or histogram showing the

distribution of either or both of these values.

12.4 Introduce the test specimen into the measurement

mechanism and initiate the measurement sequence.

12.5 Use the resulting data set, whose elements are the

thicknesses [t(x,y)] as the basis to make thickness and

flatness calculations.

13 Calculations

13.1 The calculations of wafer thickness, total

thickness variation and the desired flatness parameter(s)

are performed automatically within the instrument. An

outline of the calculation structures is provided here to

indicate the nature of the procedure.

13.2 Thickness Determination

13.2.1 Determine the displacements (distances)

between each probe and the nearest surface of the wafer

SEMI MF1530-1104 © SEMI 2003, 2004 4

(in pairs) at intervals along the scan pattern. At each

measurement location, the sum of the displacements is

subtracted from D, yielding the thickness at each

measurement location as follows:

(2)

)],(),([),(),( yxbyxayxDyxt 

where:

D = distance between Probes A and B,

a = distance between Probe A and the nearest

wafer surface,

b = distance between Probe B and the nearest

wafer surface, and

t = wafer thickness (see Figure 1).

13.2.2 Take the wafer thickness as the thickness at the

center point of the wafer.

13.2.3 Determine the total thickness variation, TTV, as

the largest thickness value, t

max

minus the smallest

thickness value, t

min

(3)

minmax

ttTTV 

13.3 Flatness Determination

13.3.1 Construct the reference plane from the data set

t(x,y). The reference plane is of the following form (see

Notes 2 and 3):

(4)

RRRref

cybxaZ 

where a

, b

, and c

are constants chosen as follows:

13.3.1.1 For ideal back surface reference plane,

(5) 0

RRR

cba

13.3.1.2 For the least squares reference plane, select

, b

, and c

so that (see Note 4):

(6)





RRR

cybxayxt

)](),([

is minimized over the FQA for global determination,

over the portion of the site within the FQA for site

determination, or over the portion of the sub-site within

the FQA for sub-site determination.

13.3.1.3 For the three-point reference plane, construct

a plane so that

(7)

RRR

cybxayxt



3333

2222

1111

),(

and,),(

,),(

where x

, y

; x

; and x

, y

are equally spaced points

located on a circle whose perimeter is located 3 mm

from the edge of a wafer of nominal diameter (see Note

4).

13.3.2 Construct a focal plane to calculate deviation

parameters from the data set t(x,y). The focal plane is

of the following form:

FFFfocal

cybxaZ 





(8)

The focal plane is parallel with the reference plane so

that in all cases

 a

= a

, and

 b

= b

13.3.2.1 A global focal plane is the same as the

corresponding reference plane so that

 c

= c

13.3.2.2 A site or sub-site focal plane is displaced from

the corresponding reference plane as follows:

 c

= t(x

)  (a

+ b

)

where x

and y

are the coordinates of the site or sub-

site center, respectively.

NOTE 2: Use of the thickness data set, t(x,y), in this regard is

equivalent to setting the origin of the z-axis, as defined in

SEMI M20, at the back surface of the wafer at each point of

the data set. Then the value of z at each point is equal to the

thickness t at that point. This is equivalent to constraining the

wafer so that the back surface is pulled down uniformly onto

an ideal chuck.

NOTE 3: The constants a

and a

provide the slopes of the

reference and focal planes, respectively, in the x direction, the

constants b

and b

provide the slopes of the reference and

focal planes, respectively, in the y direction, and the constants

and c

provide the distances of the center point of the

reference and focal planes, respectively, from the back surface

at that point.

NOTE 4: The values t(x,y) at any point represent z

(x,y),

where z

is the height of the front surface from the z-axis

origin at each point. It is use of this data set that causes the

reference surface to be the front surface for both the least

squares and three-point reference planes.

13.3.3 Determine the point-by-point differences

between the thickness and the reference or focal plane

)(),(),(

iii

cxbxayxtyxf 





(9)

where the subscript i is either R or F depending on

whether a reference or focal plane is being used and x

and y range over the FQA, the site, or the sub-site, for

global, site, or sub-site determinations.

13.3.4 Determine range (also called TIR) as follows:

minmax

),(),( yxfyxfTIR 



(10)

where:

(x,y)

max

= largest (most positive) algebraic value of