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SEMI MF1526-95 © SEMI 2004 10 RDS  SDS = DDS (A2.1) where: DDS = the differences between the measurem ents made on the machine under test and the refe ree data set. The DDS contains m any values. The simplest metric tha…

SEMI MF1526-95 © SEMI 2004 9

ANNEXES

(Mandatory Information)

A1. RELATIONSHIP BETWEEN REPEATABILITY AND DETECTION LIMIT

A1.1 The consensus method to determine the limit of detection, c

, in a photon spectroscopy, when there is no

instrumental peak to subtract, is given as follows

= 3s

/S (A1.1)

where:

= the standard deviation of the BLANK measures, and

S = the sensitivity (net signal divided by atoms/cm

The numeral 3 in Eq. A1.1 is chosen so that a 99.6 % confidence level applies for a strictly one-sided Gaussian distribution; but

it is recognized that at low concentrations, non-Gaussian distributions are more likely.

A1.1.1 It is commonly assumed that the standard deviation of the BLANK measures, for short term measurements, is

given by Poisson statistics of the photons, and this leads to Eq A2.2 for the limit of detection which is commonly reported in

the technical literature.

= 3

()

areal density of ref

()

background counts

1/2

()

net signal (A1.2)

A1.1.2 This limit of detection includes the key assumption that the standard deviation of the BLANK measures is given

only by Poisson statistics of the X-ray photons, and that no other variability contribution is significant for this term. This

assumption may be valid only for short term estimation of the limit of detection.

A1.2 For long term estimation of the limit of detection, the standard deviation of the BLANK measures is expected to have

contributions from other variabilities than just the Poisson statistics, and therefore the long term estimation of the limit of

detection is expected to be larger than the short term limit of detection. Examples of other contributions to variability in the

BLANK measures may include, but not be limited to, the glancing angle calibration and X-ray beam divergence.

A2. COMPARING DATA SETS

A2.1 Introduction

A2.1.1 In qualifying a measurement system for operation, it can be useful to compare values ascribed to an artifact such as

a reference sample against those obtained for that artifact on a machine under test. This annex outlines a way in which the

multiple element measurement data can be used to monitor the effects of interferences that may arise from software

procedures and calculations in the instrument.

A2.1.2 A data set is that set of data used in computation of surface elemental contamination by TXRF.

A2.1.3 A referee wafer (artifact) is accompanied by its own data set (referee data set (RDS)), in which each data point is the

average of a number of repeated measurements. The artifact is measured on a machine under test and its RDS is compared

against the resultant measured sample data set. Differences in the data sets are computed. The parameter used to determine

agreement between the artifact and the system under test and the acceptable level of this agreement is to be agreed upon

between the using parties.

A2.2 Summary of Test Method

A2.2.1 Select a referee wafer of appropriate criteria, for which an RDS has been obtained.

A2.2.2 Measure the referee wafer on the machine under test to obtain a sample data set (SDS).

A2.2.3 Subtract the two to obtain a difference data set (DDS) as follows:

13 International Union of Pure and Applied Chemistry, Analytical Chemistry Division, “Nomenclature, symbols, units and their usage in spectrochemical

analysis—II, Data Interpretation,” Spectrochemica Acta, Vol 33, 1978, pp. 242–245.

SEMI MF1526-95 © SEMI 2004 10

RDS  SDS = DDS (A2.1)

where:

DDS = the differences between the measurements made on

the machine under test and the referee data set.

The DDS contains many values. The simplest metric that can be used to determine acceptability is the maximum difference,

the largest absolute value in the DDS. This represents the worst-case disagreement between the machine under test and the

referee data.

A2.2.4 Accept the machine as suitable for measurement if the maximum difference is less than a value that is agreed upon

between the parties to the test.

A2.2.5 More complex calculations may also be used, for example, a histogram of the (element-by-element) values of the

DDS along with statistical measures (mean, sigma, etc) may be compared. These measures can be compared to application-

specific limits or used to provide insight into the nature and source of the difference, or both.

NOTICE: SEMI makes no warranties or representations as to the suitability of the standards set forth herein for any particular

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or equipment mentioned herein. These standards are subject to change without notice.

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SEMI MF1527-1104 © SEMI 2003, 2004 1

SEMI MF1527-1104

GUIDE FOR APPLICATION OF CERTIFIED REFERENCE MATERIALS

AND REFERENCE WAFERS FOR CALIBRATION AND CONTROL OF

INSTRUMENTS FOR MEASURING RESISTIVITY OF SILICON

This guide was technically approved by the Global Silicon Wafer Committee and is the direct responsibility

of the North American Silicon Wafer Committee. Current edition approved for publication by the North

American Regional Standards Committee on August 16, 2004. Initially available at www.semi.org

September 2004; to be published November 2004. Original edition published by ASTM International as

ASTM F 1527-94. Last previous edition SEMI MF1527-02.

1 Purpose

1.1 Resistivity is a widely used parameter for

specification and characterization of silicon wafers for

use in fabricating semiconductor devices and integrated

circuits. Many types of instrumentation used for

making resistivity measurements including the non-

contact eddy-current instruments used for

measurements made in accordance with SEMI MF673,

DIN 50445, or DIN 50447 require calibration because

they are relative measurements. Although

measurements made with in-line four-point probes in

accordance with SEMI MF84 or DIN 50441 are, in

principle, absolute, control charts should be maintained

for four-point probes because one cannot always be

sure that the electrical resistivity of the test specimen is

sufficiently homogeneous for the theoretical model of

the method to apply, that the electrical thickness of the

wafer is exactly equal to its measured mechanical

thickness, or that the stability of the instrument is

adequate.

1.2 Instruments for measuring such related parameters

as spreading resistance (used in accordance with SEMI

MF525 or SEMI MF672), net carrier density (used in

accordance with SEMI MF1392, SEMI MF1393, or

DIN 50439), and sheet resistance (used in accordance

with SEMI MF1529) also require calibration.

1.3 For all these purposes, wafers of known resistivity

are required. Such wafers are supplied by several

sources with a wide range of certified or calibrated

resistivity values. Although these wafers are often used

directly, the resistivity values represented by purchased

standards can also be transferred to an in-house

resistivity reference wafer that is then used for routine

instrument calibration or control.

1.4 The accuracy with which this transfer can be

affected depends not only on the procedures for using

such reference wafers but also on the procedures for

material selection, instrument qualification, and

calibration of the reference wafer. This guide provides

recommendations for procedures for these operations

appropriate to obtaining the best available accuracy in

use of resistivity reference wafers.

1.5 These procedures are specifically intended for use

in measuring the resistivity of silicon wafers.

Extension to resistivity measurements on other

semiconductor materials or to resistivity values outside

the range covered by the resistivity reference wafers has

not been demonstrated.

2 Scope

2.1 This guide covers the application of Certified

Reference Materials (CRMs) for resistivity

measurements on silicon wafers. Specifically, this

guide covers the use of these CRMs for preparing

resistivity reference wafers and for ensuring the quality

of the instrumentation used for preparing them.

2.2 The guide covers the selection of materials for

resistivity reference wafers, procedures for preparing

and calibrating resistivity reference wafers, and use of

resistivity reference wafers in qualifying, calibrating,

and controlling various types of resistivity

instrumentation.

2.3 The guide provides criteria for selection of

instruments for determining the resistivity of silicon

resistivity reference materials, procedures for

maintaining such instruments in statistical quality

control, and training requirements for operators

engaged in making and using resistivity reference

wafers.

2.4 Related Information is included that covers (1)

suggested control charting procedures for organizations

that do not already have such procedures in place, and

(2) errors in resistivity determination that result from

uncertainties in wafer diameter, wafer thickness, and

probe-tip spacing.

NOTICE: This standard does not purport to address

safety issues, if any, associated with its use. It is the

responsibility of the user of this standard to establish

appropriate safety and health practices and determine

the applicability of regulatory or other limitations prior

to use.