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SEMI M40-0200 © SE MI 2000 13 RELATED INFORM A TI ON 1 EXPERIMENTS A N D MODELS RELA TING TO ROUGHNESS DISTRIBUTI ON OF SILICON WAFERS NOTE: This re lated inf o rmation is n o t an of ficial part of SEMI M40 b ut was app…

SEMI M40-0200 © SEMI 2000 12

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SEMI M40-0200 © SEMI 200013

RELATED INFORMATION 1

EXPERIMENTS AND MODELS RELATING TO ROUGHNESS

DISTRIBUTION OF SILICON WAFERS

NOTE: This related information is not an official part of

SEMI M40 but was approved for publication by full letter

ballot procedures.

R1-1 Executive Summary

R1-1.1 Roughness is measured traditionally only on

selected spots on a surface and only a few methods,

such as light scattering, are practical for a complete

surface scan. Therefore a systematic, standardized

approach is required for defining the roughness of the

entire surface of a silicon wafer. This can be done by

defining one or several patterns of measurement spots

which represent the entire surface so that the deviation

of the average roughness and its standard deviation

from the “true” values are small. The task of finding

such patterns and verifying that they represent the entire

surface was approached in two steps: 1. by

investigating various patterns on various wafer surfaces

experimentally, and 2. by simulating the roughness map

of surfaces and by applying the selected patterns to

them.

R1-1.2 Five different site patterns were used for the

experimental investigation of silicon wafer surfaces

which were final polished, stock removal polished and

acid etched. The patterns consist of one, five, nine, ten

and thirteen points (thirteen being the sum of a five and

nine point pattern), respectively, and the measurements

were performed with 10, 30, 80 and 250 µm filter

lengths. Therefore 20 average roughness values and

corresponding standard deviations were obtained for

every wafer investigated, five for any filter length.

R1-1.3 Haze maps of these surfaces either displayed no

variation, variations with an approximately rotational

symmetry or a gradient across the surface, respectively.

The average roughness of the surfaces measured with

the various site patterns varied over four and a half

orders of magnitude for the set of wafers used and the

filter settings selected. The corresponding standard

deviations were found to be <10% of the average

roughness with the exception of four 200 mm final

polished wafers where standard deviations up to 50-

60% occurred. The 5-, 9- and 10-point site patterns

were compared with respect to the average roughness

and the corresponding standard deviation for every

wafer. The variation (standard deviation) of the

average roughness and the standard deviations as

measured were found to be smaller than or

approximately 10% in any case when normalized to the

total average roughness of the corresponding wafer

(average over all points of all patterns for a wafer).

R1-1.4 Roughness maps were generated for the

simulation according to three different models: maps

with a roughness pattern with rotational symmetry, with

a linear gradient and with mirror symmetry. Two maps

with a pixel size of 1 mm

were generated for each

surface to take into account any anisotropy of the

roughness, and center roughness and edge roughness,

respectively, were used as free parameters for both

maps. These parameters were varied between two level

(0.1 and 0.2) for both maps resulting in a 2

factorial

design of “experiment” where the symmetry was

considered as 5

parameter. The 1-, 5- and 9-point site

patterns were applied to the various maps and the

average roughness and standard deviation of roughness

were calculated as well as the true values using all

points of a map. Strong effects were observed for the

1-point pattern. As expected one point in the wafer

center does in general not represent the average

roughness of the entire surface reasonably well. The 5-

point measurement provides the correct average ± 6%,

the 9-point measurement is ± 2.5%. Similarly, the 5-

point standard deviation is correct ± 1.6% and the 9-

point one is ± 1%. Second order effects were found to

be smaller than the main effects. Therefore it is

concluded that the suggested five and nine point

measurement patterns provide a good estimate of the

roughness of an entire surface and its variations for

reasonably homogeneous Si wafer surfaces.

R1-2 Introduction

R1-2.1 Roughness measurement of surfaces is

performed with a variety of techniques, the most

common ones being mechanical or optical profiling in

real space or light scattering in reciprocal space (1,2,3).

The numerical result of a roughness measurement

process depends significantly on several parameters

such as spatial bandwidth of the response function of

the tool used including filtering, scan length, probe

diameter, scanning speed etc. These parameters are not

independent of each other and have been standardized

only for mechanical profilers (e.g.4,5). The roughness

values reported by different types of tools usually do

not agree but they correlate provided their parameters

were set up not too differently (6). The standardized

roughness metrics such as average roughness R

root-mean-square roughness R

refer mainly to line

scans as performed by profiling techniques (e.g. 7).

Area scans performed by profiling tools by aligning a

series of line scans are usually very slow. Scanning the

entire surface of a Si wafer with a profiler therefore

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would consume many hours, in the case of AFM

(Atomic Force Microscope) many years.

R1-2.2 Techniques based on light scattering are

capable of scanning the entire wafer surface quite

rapidly, in about 1-2 min. Their response function,

however, has a limited spatial bandwidth ranging

approximately from 0.5 to 40 µm. Standards for light

scattering measurements are now emerging (8,9).

R1-2.3 The obvious solution for obtaining a

standardized roughness value of an entire surface is a)

to define a pattern of sites where one- or two-

dimensional scans are performed and b) to report the

significant parameters along with the measurement

(roughness) result. The second task can be solved

theoretically by collecting the important parameters and

by designing an appropriate abbreviation code. The

first task requires experiments to collect data about the

variation of roughness across a typical, real wafer

surface and numerical simulations to find a set of sites

the roughness of which agrees sufficiently well with the

roughness of the entire surface.

R1-2.4 This appendix reports the results of

corresponding roughness measurements as well as of a

numerical simulation using a virtual design-of-

experiment (DOX).

R1-3 Roughness Definitions

R1-3.1 A variety of definitions for roughness have

been standardized by national and international

institutions in the US, Japan and Europe.

Corresponding standards are listed in section 5 of the

main document and some selected ones again in

reference 7. Most widely used are average roughness

and root-mean-square roughness R

. Both refer to

the average deviation of a profile from a reference line.

R1-4 Roughness Measurements

R1-4.1 Experimental Details

R1-4.1.1 Four groups of four wafers each were

investigated to collect data about the variation of

roughness across the wafer surface. The wafers were

selected to represent different process steps and

polishing techniques:

final polished wafers, 150 mm, #1-4

b) final polished wafers, 200 mm, #4-8

c) pre-polished wafers, 200 mm, #9-12

d) acid-etched wafers, 200 mm, #13-16.

R1-4.1.2 The wafers were characterized for haze with

an SSIS (Censor ANS-100) and the roughness

measurements were performed with an optical non-

contact profiler (Chapman MP-2000+). The roughness

data were taken by performing scans of length 3 mm

and were evaluated using filters of 19, 30, 80 and 250

µm, respectively. The scans were performed at a

variety of sites according to four different site patterns

as displayed in Figure R1-1 where also the directions of

the various scans are indicated:

i) center of wafer, one scan

ii) five points, center of wafer plus four points at 2/3

of radius

iii) nine points, center of wafer plus four points at 2/5

of radius plus four points at 4/5 of radius

iv) ten points, two in the center of wafer plus four

points at ½ of radius and four points at radius

minus 10 mm.

v) thirteen points, combination of pattern ii and iii.

Figure R1-1

Site Patterns