A study of silicon wafers plane lapping process.

Dobrescu, Tiberiu ; Dorin, Alexandru

Abstract: Lapping is a very complicated and random process resulting from the varation of abrasive grains by its size and shapes and from the numerous variables which have an effect on the process quality.Thus it needs to be analyzed by experimental rather than by theory to obtain the relative effectsof variables quantitatively. In this study, the plane lapping was performed and analyzed by ANOVA table. As a result, effective variables and interaction effects were identified and discussed. Also the optimal variable combination to obtain the largest percentage improvement of surface roughness was selected and confirmatory experiments were performed.

Key words: Lapping, silicon wafers, ANOVA, control variable, orthogonal array, roughness, abrasive grain

1. INTRODUCTION

Lapping is a finish method used to obtain good surface quality. Important variables lapping efficiency are abrasive grain size, lapping pressure, lapping speed, quantity of lapping compound supplied and viscosity of the compound, etc. Comparison of the effects of variables on the overall process efficiency is not yet clear owing to the complexity and randomness of the process (Dobrescu, T., 1996)

Using the experimental design method is a typical approach to efficiently and logically identify characteristics of any complex process by experiment. In this method, experiments are generally designed by orthogonal array and the results are analyzed by ANOVA (ANalysis Of Variance). A number of studies related to the experimental design method have been reported in the field of quality control and statistics. In this study, experimental designed by Taguchi's orthogonal array (Taguchi, G., Konishi, S., 1987) were performed. And Taguchi's SN (signal-noise) ratio for percentage improvement of surface roughness in a plane lapping process was used as a performance (or response) variable to evaluate the process efficiency. Yates's (Yates, F, 1988) algorithm and the Lenth (Lenth, R.V., 1989) algorithm were used to analyze the effects of variables on the performance variable.

2. EXPERIMENT

2.1. Experiment design

Two-level fractional design, which is used in this study, is especially efficient in finding out important variables having an effect on the process performance.

Experiments at two levels of each control variable were conduced: grain size, lapping pressure, number of lapping-compound-supply and lapping speed. Control variables and their levels are shown in Table 1. Percentage improvement of surface roughness before and after lapping was taken as an evaluation or response variable. Taguchi's fold-over type orthogonal array is shown in Table 2.

In this study, only four effects (i.e. A, B, C, D) and three two-factor interaction effects (i.e. AB, AC and BC) were considered in the experimental design. All the other effects were considered to be trivial. The first column in Table 2 represents the standard order of experimental treatment combination (tc). The number of combinations is eight, which is the smallest number required to satisfy resolution IV design with four variables. The order columns represents 23--1 (=7) contrasts: four main effects are assigned to the first, second, fourth and seventh columns and interaction effects to the third, fifth and sixth columns. In the Table 2, "+" represents highlevel and "-", low-level. Tough the levels in the experiment are represented as numerical quantitative, they can also be considered to have qualitative meaning, "high" or "low"

2.2. Experimental results

Experiments were performed by a plan-parallel lapping machine MELCHIORRE SP3/600/2PR. All of the silicon wafers have an initial surface roughness of Ra 0.63 [micro]m--Ra 0.8 [micro]m. Four variables were considered as control variables: grain size (A); lapping pressure (B); number of lapping-compoundsupply (C); and lapping speed (D). Experimental levels for each control variable are shown in Table 1. Surface roughness was measured before and after lapping using profilometer HOMMEL-TESTER Typ TR. Experimental results are shown in Table 3, in which yi (i = 1, 2, 3, 4, 5, 6, 7--number of silicon wafers) are percentage improvements of surface roughness any y is the averaged value of the seven. s2 is variance and S/N is response statistic.

In this study, we are interested in the efficiency or percentage improvement of surface roughness, so S/N ratios are calculated for case of "Bigger Is Better" (BIB case)

3. ANALYSIS AND DISCUSSION

3.1. Analysis of experimental results

Table 4 shows the method of Yate's computing algorithm used to obtain mean effect of each variable. Column I is generated using the data (S/N ratio) column by the rule that the first four entries are created by adding adjacent pair-wise sets of data from the response variable column, and the other four entries by subtracting adjacent pair-wise sets. Columns II and III are generated by applying the same rule, column II from column I and column III from column II. The sum of square (SS) is calculated with formula SS= (III) 2/8. Mean effects can compute by subtracting the mean value of four experimental data at low-level from those at high-level. For variable A, for example, high-level appears in rows 2, 4, 6, 8 and low-level 1, 3, 5 and 7 rows in Table 2. So the mean effect for A can be simply computed from Table 3 as follows which is same as that in Table 4.

The optimal combination (not same as optimal lapping condition) required to obtain a larger percentage improvement of surface roughness, that is, A(-)B(+)C(+)D(-): abrasive grain size of #600; lapping pressure of 4.144 N/cm2; number of lapping-compound-supply of 41 and lapping speed of 30 rot/min. It can, thus, be predicted that levels of variables A and D should be taken to minus direction (decreasing the level) and those of B and C to plus direction (increasing the level) to obtain the maximum percentage improvement of surface roughness.

3.2. Discussion

The efficiency of plane lapping of silicon wafers, and the percentage improvement of surface roughness, was increased at coarse grain size. Lapping pressure shows the largest effect of all variables considered in this study and the efficiency of lapping increased dramatically at high-level compared with that at low level. Number of lapping-compound-supply has little effect on the response. But it has significant interaction with lapping pressure and, so, should be treated as an important control variable. Lapping speed has no effect and the efficiency at low speed is a little higher than that at higher-level.

4. CONCLUSIONS

The plane lapping process of silicon wafers with plane parallel lapping machine MELCHIORRE SP3/600/2PR, have been characterized qualitatively by analyzing the effect of four control variables, on the percentage improvement of surface roughness as a measure of efficiency using the experimental design method and the following results were obtained.

* Lapping pressure has a significant effect on the efficiency of plane lapping of silicon wafers;

* Number of lapping-compound-supply should be treated as an important variable even though it has shown no effect on the efficiency because it interacts with lapping pressure;

* This optimal combination has been confirmed by a confirmatory experiment resulting in 9.8% increase in the S/N ratio of efficiency.

5. REFERENCES

Dobrescu, T. (1996), Lapping Process of Silicon Wafers, Research Reports, LAPT, University of Naples "FedericoII", Italy, pp. 31-34

Lenth, R.V. (1989), Quick and easy analysis of unreplicated factorial, Technometrics 31, pp. 469-473

Salje, E., Paulmann, R. (1988), Relations between abrasive processes, Ann. CIRP 37, pp. 641-648

Taguchi, G., Konishi, S. (1987), Taguchi Methods, Orthogonal Arrays and Linear Graphs, American Supplier Institute, Dearborn, Michigan, USA

Yates, F. (1988), Design and analysis of factorial experiments, Technica-1, No. 35, Imperial Bureau of Soil Sciences, London.

Tabel 1. Levels of factors

 Levels

Symbol Factor High (+) Low (-)

A Grain size #280 #600
B Lapping pressure [N/[cm.sup.2]] 4.144 1.657
C Number of lapping-compound-supply 41 20
D Lapping speed [rot/min] 60 30

Tabel 2. Taguchi's orthogonal array (fold-over type)

 Column number and contrast

 1 2 3 4 5 6 7

tc A B AB C AC BC ABC

(1) - - + - + + -
a + - - - - + +
b - + - - + - +
ab + + + - - - -
c - - + + - - +
ac + - - + + - -
bc - + - + - + -
abc + + + + + + +

Tabel 3. Experimental results

 [R.sub.a] improvement [%}

tc [y.sub.1] [y.sub.2] [y.sub.3] [y.sub.4] [y.sub.5]

(1) 47.44 48.63 52.91 49.42 53.68
a 38.41 37.66 38.71 34.38 32.98
b 55.74 54.57 59.48 54.78 55.09
ab 54.29 51.44 50.38 52.98 51.23
c 42.66 42.06 41.57 44.44 43.28
ac 39.44 35.57 37.66 36.98 37.45
bc 80.24 81.69 82.46 83.67 80.94
abc 69.72 69.54 68.42 67.76 67.24

 [R.sub.a] improvement [%}
 y S/N
tc [y.sub.6] [y.sub.7] [%] [dB]

(1) 50.21 51.79 50.58 34.057
a 31.51 36.04 35.67 30.975
b 54.04 54.32 55.43 34.864
ab 52.78 51.97 52.15 34.339
c 42.53 41.91 42.63 32.589
ac 38.27 37.64 37.57 31.486
bc 81.78 80.09 81.55 38.226
abc 68.54 67.98 68.46 36.707

Tabel 4. ANOVA table by computing procedure of Yate's algorithm

 Sum of effects
 S/N
tc [dB] I II III

(1) 34.0570 65.0317 134.2345 273.2433
a 30.9747 69.2028 139.0088 -6.2307
b 34.8642 64.0760 -3.6079 15.0279
ab 34.3386 74.9328 -2.6228 2.1407
c 32.5897 -3.0823 4.1711 4.7743
ac 31.4863 -0.5256 10.8568 0.9851
bc 38.2261 -1.1034 2.5567 6.6857
abc 36.7067 -1.5194 -0.4160 -2.9727

 Mean
tc SS effect Measures

(1) 9332.74 68.311 average
a 4.8527 -1.5576 A
b 28.2297 3.7569 B
ab 0.5728 0.5351 AB
c 2.8492 1.1935 C
ac 0.1213 0.2462 AC
bc 5.5873 1.6714 BC
abc 1.1046 -0.7431 D