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SEMI MF1527-1104 © SEMI 2003, 2004 4 control chart s (see Section 7.1. 1), (3) retur n measured resistivity values of app ropriate CRMs to within desired limits through measurement of resistivity CRMs at regular interval…

SEMI MF1527-1104 © SEMI 2003, 2004 3

which is issued by a certifying body (ISO

Guide 30:1981).

4.1.2 Discussion — ISO 8402 states that in a

calibration sense, traceability relates measuring

equipment to national or international standards,

primary standards, or basic physical constants or

properties. In the present guide, as in ISO 10012-1, the

term “measuring equipment” is extended to include

both measuring instruments and measurement standards

(including reference wafers).

4.1.3 reference material (RM) — a material or

substance one or more properties of which are

sufficiently well established to be used for the

calibration of an apparatus, (for) the assessment of a

measurement method, or for assigning values to

materials (ISO Guide 30:1981; ISO 10012-1).

4.1.4 resistivity reference wafer — a CRM or RM in

the form of a silicon wafer or chip used for routine

calibration or control of resistivity measuring

equipment.

4.1.5 Standard Reference Material (SRM

®) — a

certified reference material issued by the U.S. National

Institute of Standards and Technology.

4.1.6 traceability — the ability to trace the history,

application, or location of an item or activity, or similar

items or activities, by means of recorded identification

(ISO 8402).

4.2 Definitions of Terms Related to Four-point Probes

4.2.1 four-point probe — an electrical probe

arrangement for determining the resistivity of a material

in which separate pairs of contacts are used (1) for

passing current through the specimen, and (2)

measuring the potential drop caused by the current.

4.2.2 probe head, of a four-point probe — the

mounting that (1) fixes the positions of the four pins of

the probe in a specific pattern such as an in-line

(collinear) or square array, and (2) contains the pin

bearings and springs or other means for applying a load

to the probe pins.

4.2.3 probe pin, of a four-point probe — one of the

four needles supporting the probe tips; mounted in a

bearing contained in the probe head and loaded by a

spring or dead weight.

4.2.4 probe tip, of a four-point probe — the part of the

pin that contacts the wafer.

4.2.5 probe-tip spacing, of a four-point probe — the

distance between adjacent probe tips.

SRM

is a registered trademark of the U.S. National Institute of

Standards and Technology and the U.S. Government.

4.3 For definitions of other terms used in silicon wafer

technology refer to SEMI M1 and SEMI MF1241.

5 Reagents

5.1 Purity of Reagents — All chemicals for which such

specifications exist shall conform to Grade 1 SEMI

specifications for those specific chemicals. Other

grades may be used, provided it is first determined that

the chemical is of sufficiently high purity to permit its

use without lessening the accuracy of the test.

5.2 Purity of Water — Reference to water shall be

understood to mean water meeting the requirements of

Type E-3 water or better as described in ASTM Guide

D 5127.

5.3 The recommended chemicals shall have the

following nominal assays:

5.3.1 Nitric Acid, HNO

, concentrated, 70 to 71%,

Grade 1 in accordance with SEMI C35,

5.3.2 Hydrofluoric Acid, HF, concentrated, 49.00 ±

0.25%, Grade 1 in accordance with SEMI C28, and

5.3.3 Potassium Hydroxide, KOH, pellets, 85% min,

Grade 1 in accordance with SEMI C39.

5.4 KOH Etching Solution — Dissolve potassium

hydroxide (KOH) in water to make a 50 weight % KOH

solution in sufficient volume to allow complete

immersion of the largest wafers to be prepared for test.

This solution is to be used at a temperature of 65 to

75°C.

5.5 Etching Solution (15 + 1) — Mix 15 parts of nitric

acid (HNO

) with one part of hydrofluoric acid (HF) in

sufficient volume to allow complete immersion of the

largest wafers to be prepared for test.

6 Resistivity CRMs

6.1 Resistivity CRMs are available from several

sources in a variety of configurations, orientations,

conductivity types, and resistivity. Choose the

configuration to match the desired application as

closely as possible. For example, choose whole wafers

for applications involving whole wafer measurements

and chip sets with relatively closely spaced resistivity

values and appropriate orientation and conductivity

type for applications involving spreading resistance.

7 Control of Primary Resistivity Measuring

Instruments

7.1 “Primary” resistivity measuring instruments are

four-point probes used for calibrating resistivity

reference wafers. Such instruments must (1) meet the

requirements of SEMI MF84, (2) be maintained in a

state of control through the use of

and s instrument

SEMI MF1527-1104 © SEMI 2003, 2004 4

control charts (see Section 7.1.1), (3) return measured

resistivity values of appropriate CRMs to within desired

limits through measurement of resistivity CRMs at

regular intervals (see Section 7.1.2), and (4) be operated

within the temperature range specified in SEMI MF84

(see Section R2-4 of this guide).

7.1.1 Instrument Control Charts —

and s control

charts should be maintained to establish the stability of

the instrument over the range of resistivity that the

instrument is expected to measure. A separate control

chart should be maintained for each reference wafer

used. Initially, resistivity CRMs or other wafers with

adequate radial resistivity uniformity (see Section 8.5.1)

should be used for this purpose. As resistivity reference

wafers are prepared, these should be used for

maintaining the control charts. After in-house

resistivity reference wafers become available, it is

recommended that three wafers at each resistivity level

be set aside for control charting. Two of these should

be used for maintaining the

and s charts on a regular

basis. The third is retained as a reference to ensure that

any apparently out-of-control conditions are due to the

instrument and not to changes in sample surface

conditions, as might occur after prolonged use of a

particular sample. Each resistivity determination

should consist of six to ten measurements made in

accordance with SEMI MF84. Established procedures

for generating and maintaining the control charts and

for determining the existence of out-of-control

conditions and the need for corrective action should be

used. A suggested procedure for these determinations

is given in Section R1-2 for use in organizations

without previously established procedures.

7.1.2

Comparison with CRMs — To provide

traceability, measurements of the resistivity of available

CRMs that encompass the range of resistivity expected

to be encountered should be made on a periodic, but

less frequent, basis. In addition to being in control, the

instruments should return measured values of the

resistivity of the CRMs that do not deviate from their

certified value by more than the root mean square of the

two-sigma (95 % confidence level estimate) uncertainty

of the CRM (Note 1) and the two-sigma instrument

variability determined by control charting procedures

(Note 2). A suggested procedure for control charting of

CRMs is given in Section R1-3 for use in organizations

without previously established procedures.

NOTE 1: A laboratory issuing a CRM should provide a

comprehensive statement of its uncertainty associated with

the measurement and reporting of the CRM value. This

should include evaluations, or estimates, of both random and

systematic “errors” following ISO procedures for Type A and

Type B evaluations of components of uncertainty. The result

would be expressed as a Combined Standard Uncertainty

(standard deviation, or square-root of a sum of variances of

uncertainty components), or as an “Expanded Uncertainty” (2

times the Combined Standard Uncertainty). If based on

sufficient statistical degrees of freedom, the Combined

Standard Uncertainty is a one-sigma estimate, and the

Expanded Uncertainty is a two-sigma, or 95% confidence-

level, estimate. If there are insufficient statistical degrees of

freedom, the effective number of degrees of freedom should

be reported by the CRM-issuing laboratory. It is then

necessary to multiply the uncertainty value provided by the

student-t factor appropriate to that number of degrees of

freedom in order to obtain values for the one-sigma or two-

sigma (95% confidence-level) measurement uncertainty.

NOTE 2: A laboratory following this procedure to establish

traceability to resistivity CRMs incorporates a value of its

measurement uncertainty based on its control chart

measurements, which evaluate random components of

uncertainty only. If the laboratory then measures a value for

the CRM within the total uncertainty interval, calculated

following the root-mean-square procedure, above, about the

certified value, its instrument is validated for use. If it

measures a value outside the prescribed interval, this is an

indication that its measurement bias with respect to true value

is statistically significant at the 95% level, and instrument

repair, or “calibration” is necessary before proceeding.

7.1.3 Probe Assembly and Electrical Equipment Tests

— Should an out-of-control or out-of-specification

condition be encountered, the probe assembly and

electrical equipment can be tested in accordance with

the section on Suitability of Test Equipment in SEMI

MF84. These tests may serve to isolate the cause of the

problem encountered. Either or both of these

components should be repaired or replaced if they fail

to meet the requirements specified in this section of

SEMI MF84.

NOTE 3: The stringent requirements on control of probe-tip

spacing as well as the need for off-center diameter correction

factors required for determination of radial resistivity

uniformity (see Section 8.5) are a consequence of the single-

configuration method of using the four-point probe in

accordance with SEMI MF84. Errors resulting from

uncertainty in probe-tip spacing when using the single-

configuration method are considered in Related Information

2. The probe-tip spacing requirements can be relaxed

significantly if the dual-configuration method

of measuring

resistivity with a four-point probe is used. Use of this method

is recommended for determination of the radial resistivity

uniformity (see Section 8.5). However, the dual-

configuration method has not yet been standardized for bulk

resistivity measurements because appropriate thickness

correction factors have not yet been published. Such

corrections are required for thickness to probe spacing ratios

greater than 0.36. Nevertheless, it is noted that the most

5 Perloff, D. S., “Four-point Probe Correction Factors for Use in

Measuring Large Diameter Doped Semiconductor Wafers,” J.

Electrochem. Soc. 123, 1745–1750 (1976).

SEMI MF1527-1104 © SEMI 2003, 2004 5

recently issued CRMs are calibrated and certified by this

technique.

8 Selection and Qualification of Materials for

Resistivity Reference Wafers

8.1 Factors that must be considered in selecting

materials for resistivity reference wafers are nominal

resistivity (see Section 8.2), wafer diameter (see

Section 8.3), axial and radial uniformity of the

resistivity (see Sections 8.4 and 8.5, respectively),

wafer thickness (see 8.6), wafer conductivity type and

surface orientation (see Section 8.7), and surface finish

(see Section 9.1.2). It is generally desirable to qualify a

crystal section for the desired parameters and then

verify that individual wafers meet the requirements

during the calibration procedure. The uniformity

requirements, in particular, depend on the specific

application of the reference wafers because different

resistivity measuring instruments are sensitive to

different volumes of material.

8.1.1

Four-point Probes — The most straightforward

application of resistivity reference wafers is for control

of four-point probes used for measurement of resistivity

and resistivity variation. If the wafer under test has the

same geometry and surface characteristics as the

reference wafer and if the same probe geometry is used

for the measurement of both the reference wafer and the

wafer under test, the transfer is direct and no special

precautions need be observed. If the wafer under test

has different thickness or diameter from the resistivity

reference wafer or if four-point probes with different

probe-tip spacings are used to measure the test and

reference wafers, attention must be paid to the use of

the appropriate correction factors. In particular, if the

ratio of thickness to probe-tip spacing becomes too

large, (Note 3) while the ratio of diameter to probe-tip

spacing becomes too small, second order errors due to

the use of two two-dimensional corrections for a three-

dimensional geometry may become significant. Also, if

different probe-tip spacings are used, differences in

sampling volume must be recognized; in this case,

resistivity uniformity of both the reference wafer and

the wafer under test limits the transfer accuracy. If the

wafer under test has a different surface condition from

that of the reference wafer, it is necessary to

demonstrate the equivalence of the resulting

measurement value with that which would have been

obtained had the same surface condition been employed

for both. These considerations apply to single-

6 See, for example, Ehrstein, J. R., and Croarkin, M. C., “Standard

Reference Materials: The Certification of 100 mm Diameter Silicon

Resistivity SRMs 2541 through 2547 Using Dual-Configuration

Four-point Probe Measurements, NIST Special Publication 260–131,

1999 edition, 106 pp. Available from the National Technical

Information Service, Springfield, VA 22161, as PB 98-113731.

configuration four-point probes. Because the standard

test method for use of dual-configuration four-point

probes is intended for sheet resistance, rather than bulk-

resistivity measurement, these concerns with thickness

and diameter issues can be ignored. However, if the

thickness is too great, an unknown thickness correction

factor must be used if bulk resistivity values are to be

compared.

8.1.2 Eddy-current Gages — The eddy-current

detector is sensitive to the integrated sheet resistance

across the thickness of the wafer; in this respect it is

similar to the four-point probe. However, the eddy-

current probe may weight various elements of the

volume sampled differently than that of a four-point

probe. Therefore, the weighted average resistivity seen

in nonuniform wafers by the eddy current gage may not

be the same as the center-point average resistivity value

determined by the four-point probe. As a result, the

accuracy of transfer between these types of instruments

depends strongly on the macro-scale uniformity of the

resistivity over the central area of the reference wafer.

Because the eddy-current gage is a bulk measurement

device, the thickness uniformity over the area sampled

by the eddy-current probe is also important. The upper

limit of the expected reduction of transfer accuracy is

given as follows:

1001

TTV

reductionpercent maximum





































































(1)

where:



= average center-

oint resistivity of resistivity

reference wafer, corrected to 23°C, in ·cm,



= radial resistivity variation of resistivity reference

wafer, corrected to 23°C, in ·cm, over the area

sampled by the eddy-current probe,

TTV = total thickness variation of resistivity reference

wafer, in m, over the area sampled by the

eddy-current probe, and

w = average thickness of resistivity reference wafer,

in m.

8.1.3

Spreading Resistance Probes — Because the

spreading resistance probe samples a volume that is

exceedingly small compared with the volume sampled

by the four-point probe, the most critical reference

wafer parameter for accurate transfer of resistivity

value is the micro-variation of the resistivity both

axially and radially. Very complex and time-

consuming procedures are required to determine the

micro-scale depth and lateral variations of resistivity in

a reference wafer (see Sections 8.4.3 and 8.5.2,