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SEMI G78-0699 © SE MI 1999 15 A1-1 .4 Step 2 — Calculate No rmal ize d (by d ie) P ad Of fse t (4) = (2) - Av erage Die Offset (3) loti setj w afk diel padm loti setj wafk d iel padm loti setj wafk diel loti setj wafk di…

SEMI G78-0699 © SEMI 1999 14

APPENDIX 1

CALCULATION OF NORMALIZED DIE OFFSET AND TOTAL PROBER

ERROR RANGE (3σ

σσ

σ)

A1-1 Probe Mark Data Analysis Algorithm:

A1-1.1 Introduction

A1-1.1.1 The Probe Mark Analysis syst em recognizes the edge of the bond pad passivation opening and the probe

mark, draws a best-fit rectangle around the probe mark and passivation opening, and returns the four distances, Left,

Right, Bottom and Top to a text file. The center position of the best-fit rectangle can be used to represent the center

of the scrub mark. An offset of this center of scrub mark from the center of the bond pad can be calculated as

follows:

2/)(

TopBottomPadYoffset

RightLeftPadXoffset

−=

(1)

A1-1.1.2 The variation of this offset fro m pad to pad, die to die, wafer to wafer and setup to setup captures most of

the process variations.

A1-1.2

PMA Data Analysis

A1-1.2.1 We will use a sampling scheme of 9 wafers per lot, (3 setups per lot, 3 wafers per setup), 12 die per wafer

and 24 pads per die. The first step of doing data analysis is to obtain the offsets for all the pads that have been

sampled using Eqn.(1). This means that the offsets

yoff

off

padmdielwafksetjloti

t][PadYoffse

t][PadXoffse

,,,,

(2)

for a pad m on die l, wafer k, under setup j in lot i are known.

A1-1.3 Step 1 — Calculate

Average Die Offset (3)

loti setj wafk diel loti setj wafk diel padm

xoff xoff

yoff yoff

,, , ,, ,,

,, , ,, , ,

(3)

A1-1.3.1 Discussion of Average Die Off set

A1-1.3.1.1 Based on the sample described , there will be an Average Die Offset-X and Average Die Offset Y for

each of the 108 die sampled. This value is probably the most descriptive, especially when graphed (see example

graphs). Both X and Y-graphs will most likely resemble a sine wave. This is due to wafer rotation. As you

serpentine across the wafer there will be a slight offset from die to die. Since the selected sample dice are in the

center and around the edges of the wafer, you can see the progression of the offset as you move farther from the

center of the wafer. The X and Y graphs are usually about 90º out of phase.

A1-1.3.1.2

Other qualitative information can also be gathered by visually looking at the graphs of this data. One

can determine whether the accuracy is varying wafer to wafer (each set of 12 data points is a wafer) or set-up to set-

up (each set of 36 data points is a set-up) or just drifting over time. Drift over time is sometimes caused by

temperature stabilization issues within the prober mechanism. Subsequent steps will quantify how much variability

is caused by each.

SEMI G78-0699 © SEMI 199915

A1-1.4 Step 2 — Calculate

Normalized (by die) Pad Offset (4) = (2) - Average Die Offset (3)

loti setj wafk diel padm

loti setj wafk diel padm loti setj wafk diel

loti setj wafk diel padm loti setj wafk diel padm loti setj wafk diel

xnorm

off

ynorm yoff yoff

,, ,,

,, , , ,, ,

,, , , ,, ,, ,, ,

=−

(4)

A1-1.4.1 Discussion of Normalized (by die) Pad Offset

A1-1.4.1.1 This step helps to quantify how much error is caused by the prober vs. the probe card. The probe card

usually does NOT impact average offset of a die, just the variability within a die. In this equation, we subtract the

average die offset (presumed prober error) from each pad in that die. This data is then used for the next step.

A1-1.5 Step 3 — Calculate

P-P-X or P -P-Y = 3σ of Normalized (by die) Pad Offset (4).

A1-1.5.1 All the normalized pad offsets in the same lot (no matter on which die, on which wafer the pad resides)

are treated on an equal basis. In our example, a total of 2592 pads are sampled in a lot. All 1296 x-direction and

1296 y-direction pads of Normalized (by die) Pad Offset will be used to calculate a 3σ variation which is called

Pad-to-Pad variation

(P-P-X and P-P-Y).

A1-1.5.2 Discussion of P-P-X or P-P-Y (Pad-to-Pad Variation in the X-direction or Pad-to-Pad-Variation in the Y-

direction)

A1-1.5.2.1 These values describe how mu ch variability there is within all the pads in the lot. This value is

frequently attributed to probe tip variation in X, Y, and Z. Although probe tips do change and wear over time, their

unloaded position usually does not change dramatically within one lot. This value does not help tremendously in

describing prober accuracy nor should it be used for any sort of probecard metrology. However, be sure to perform

a mental reality check to verify that it is somewhere near (within an order of magnitude of) your probe card X/Y

probe needle position specification.

A1-1.6

Step 4 — Calculate

Average W afer Offset (5) = average of Average Die Offset (3).

loti setj wafk loti setj wafk diel

xoff xoff

yoff yoff

,, ,, ,

(5)

A1-1.6.1 Discussion of Average Wafer O ffset

A1-1.6.1.1 This equation will result in nine values for Average Wafer Offset-X and nine for Average Wafer Offset-

Y. These numbers could also be graphed to look for trends from wafer to wafer (this is not included on the example

graphs). If there is a consistent trend in one direction possible causes are:

• wafer loading error

• cumulative stepping error, and

• temperature stability errors

SEMI G78-0699 © SEMI 1999 16

A1-1.7 Step 5 — Calculate

Normalize d (by wafer) Die Offset (6) = Average Die Offset (3) - Average Wafer Offset

(5)

loti setj wafk diel

loti setj wafk diel loti setj wafk

loti setj wafk diel loti setj wafk diel loti setj wafk

xnorm

off

ynorm yoff yoff

,, ,

,, , ,,

,, , ,, , ,,

=−

(6)

A1-1.7.1 Discussion of Normalized (by wafer) Die Offset

A1-1.7.1.1 This normalization step is a pr ecursor to calculating a 3σ variation value. To calculate the true Die-to-

Die variation, any wafer-to-wafer induced error is subtracted out from the by-die-data. This data is used in the next

step.

A1-1.8 Step 6 — Calculate

D-D-X or D-D-Y = 3σ of Normalized (by wafer) Die Offset (6)

A1-1.8.1 These normalized die offsets a re again treated on the equal basis. A 3σ value is calculated and becomes

our Die-to-Die Variation

(D-D-X, D-D-Y).

A1-1.8.2 Discussion of D-D-X or D-D-Y (Die-to-Die 3

variation in the X-direction, Die-to-Die 3

variation in

the Y-direction)

A1-1.8.2.1 This equation will result in the 3σ variation of the average die offsets from Die-to-Die in both X- and

Y-directions. If this number is very large, there should be concern about the repeatability of the prober.

A1-1.9 Step 7 — Calculate

Average Setup Offset (7)

loti setj loti setj wafk

xoff xoff

yoff yoff

,,,

(7)

A1-1.9.1 Discussion of Average Setup Offset

A1-1.9.1.1 These equations will produce six values, three for Average- (by Setup) Offset-in-the-X-direction and

three for Average- (by Setup) Offset-in-the-Y-direction. These values describe the average offset of all of the die

“tested” with a particular setup.

A1-1.10

Step 8 — Calculate a

Normali zed (by setup) Wafer Offset (8) = Average Wafer Offset (5) - Average

Setup Offset (7).

loti setj wafk

loti setj wafk loti setj

loti setj wafk loti setj wafk loti setj

xnorm

off

ynorm yoff yoff

,, ,

,, ,, ,

=−

(8)

A1-1.10.1 Discussion of Normalized (by setup) Wafer Offset

A1-1.10.1.1 A normalizing step to help calculate the true wafer-to-wafer variation.