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SEMI MF1527-1104 © SEMI 2003, 2004 8 point pro bes 5 or square-arr ay four-poi nt probes 7 are available. These instrument s provide for collection of sufficient data to enab le determination of the macro- scale variatio…

SEMI MF1527-1104 © SEMI 2003, 2004 7

correction factor for such geometries varies rapidly

with thickness (see Section 8.6).

8.3.1 Because of the relative insensitivity of the

calculated center-point resistivity to the exact value of

diameter for large diameter wafers, it is usually

adequate to assume the nominal diameter of standard

commercially available wafers specified in accordance

with SEMI M1. However, diameter correction factors

are usually required for off-center resistivity

measurements made in accordance with SEMI MF81.

When required, diameter measurements should be made

at the positions outlined in SEMI MF2074.

8.4 Axial Resistivity Uniformity — The uniformity of

the resistivity along the crystal axis is important for all

applications in which the sampling volume of the

measuring instrument in the direction perpendicular to

the wafer surface is different from that of the certifying

or calibrating instrument. In addition, gross axial

uniformity along a crystal section may be ascertained in

order to qualify the section as a source of resistivity

reference wafers of a particular resistivity prior to

slicing the section.

8.4.1 Very crude indications of the range of center-

point resistivity within a crystal section may be

obtained from measurements made on the ends of the

section in accordance with the Four-probe Method of

SEMI MF43. While these measurements provide a

useful preliminary screen for the crystal section, they

cannot be relied upon to give accurate values of

resistivity.

8.4.2 Somewhat more accurate but still gross

indications of axial resistivity uniformity may be

obtained from measurements of the resistivity at the

center of wafers in accordance with SEMI MF84 as a

function of position along the crystal section. However,

because of local fluctuations in dopant incorporation as

the crystal was grown, this procedure does not yield

reliable information about the center-point resistivity of

any wafer that is not measured. In addition, it does not

yield information about the local variation in resistivity

as a function of depth from the wafer surface, even if

center-point resistivity measurements are made on each

wafer in the section.

8.4.3 For use in connection with measurements in

which the sampling volume differs from the sampling

volume of an in-line four-point probe with 1.59

[10/(2)] mm spacing as specified in SEMI MF84,

transfer accuracy is affected by local resistivity

uniformity. In particular, the resistivity in the near-

surface region sampled by spreading resistance or

mercury probes may differ significantly from the

average resistivity of the resistivity reference wafer.

Depth profiles of resistivity near the wafer surface may

be obtained from spreading resistance measurements on

beveled sections in accordance with SEMI MF672. To

obtain depth profiles across the entire wafer, spreading

resistance measurements can be made on a cleaved or

polished perpendicular section; special fixtures are

required for these measurements, which do not provide

the depth resolution of an angle beveled section. Since

relative measurements only are required, accurate

calibration of the spreading resistance probe is not

necessary; however, linearity is important. Two

difficulties with this approach must be recognized.

First, if beveled specimens are employed, the

possibility of mixing the vertical and horizontal

resistivity variations must be considered. Second,

because the method is destructive, the resistivity

variation of the actual material being used for the

resistivity reference wafer cannot be determined

directly at the center of a resistivity reference wafer; it

can only be inferred from measurements on nearby

sections or adjacent wafers.

8.5

Radial Resistivity Uniformity — The uniformity of

the resistivity along the surface of the resistivity

reference wafer is important for all applications in

which the measuring instrument samples a different

area than the certifying or calibrating instrument. Since

all resistivity measurements other than those conducted

in accordance with SEMI MF84, including four-point

probe measurements made with probes with different

probe-tip spacing, sample different areas, this factor is

one of the most significant limitations in transfer of

resistivity values from one instrument to another.

8.5.1 Large scale (macro) variations in resistivity

across the surface of a wafer can be measured with a

four-point probe.

8.5.1.1 Coarse indications can be obtained using an in-

line four-point probe in accordance with SEMI MF81

modified to yield a nine-site map of resistivity variation

over the central 38-mm diameter region of the wafer.

In addition to four-point probes, eddy current

instruments are frequently used for these

measurements. Although the procedures for using eddy

current instruments for measuring resistivity variation

are not standardized, they provide an adequate measure

of radial resistivity variation, especially in the central

region of the wafer where edge effects are not

significant. Although more dense patterns may be

measured, they are very inconvenient to obtain

manually using either a four-point probe or an eddy

current instrument.

8.5.1.2 Several commercial automated mapping

instruments that utilize dual-configuration, in-line, four-

SEMI MF1527-1104 © SEMI 2003, 2004 8

point probes

or square-array four-point probes

are

available. These instruments provide for collection of

sufficient data to enable determination of the macro-

scale variation of the sheet resistance in detail adequate

for the application. Measurements should be taken in a

49-site pattern consisting of the center point and sites

on three equally spaced, concentric circles as specified

in SEMI MF1618. In this pattern the inner, middle, and

outer circles have 8, 16, and 24 sites, respectively. The

nominal diameter of the outer circle should be 38 mm

(Note 5). Procedures for measurements with square-

array four-point probes have not been standardized.

Dual-configuration sheet resistance measurements

using in-line four-point probes should be made in

accordance with SEMI MF1529. Since the thickness

correction factor is not established for dual-

configuration probes, the resistivity at each

measurement site cannot be calculated accurately.

However, provided that the wafer thickness is

sufficiently uniform, determination of the sheet

resistance is adequate for this application because

relative values are all that are required to establish the

variation.

8.5.2 Micro-scale variations in resistivity across the

surface of a wafer can be established by means of

spreading resistance measurements made in accordance

with SEMI MF525. It is especially important to

minimize such variations in material to be used as

resistivity reference wafers for spreading resistance

calibrations. Because of the high density of data points

required to obtain information on micro-scale variations

over a meaningful area, long times are required for

making these measurements.

NOTE 5: If it is desired to qualify a larger area of a wafer for

use in preparing chip sets for spreading resistance calibration,

the uniformity of both resistivity and thickness should be

determined over the larger area of the wafer. For

determinations of macro-scale radial resistivity uniformity, it

is recommended that, as a minimum, the site density used in

evaluating the central region of the wafer (see Section 8.5.1.2)

be maintained. Table 1 lists the minimum number of sites

required for areas of various diameters. Micro-scale

variations should also be determined over the larger area, but

because it is impractical to make detailed micro-scale

variation measurements on each wafer, each chip should be

evaluated for micro-scale resistivity variations prior to use.

7 Swartzendruber, L. J.,“Correction Factor Tables for Four-point

Probe Resistivity Measurements on Thin, Circular Semiconductor

Samples,” NBS Technical Note 199, April 1964, 42 pp. Available

from the National Technical Information Service, Springfield, VA

22161, as AD 683 408.

8 Ehrstein, J. R., “Standard Reference Materials: Preparation and

Certification of SRM's for Calibration of Spreading Resistance

Probes,” NBS Special Publication 260-93, January 1985, 30 pp.

Available from the National Technical Information Service,

Springfield, VA 22161, as PB 85-177921.

8.6 Wafer Thickness — Resistivity reference wafers

should be thick enough to avoid extreme fragility and to

allow determination of the center-point thickness to

±0.25% but not too thick to require large corrections to

the thin wafer equation for resistivity (see Section R2-

3.2). A thickness of 625 to 875 m is recommended for

resistivity reference wafers. Wafers with thickness as

small as 500 m may be used, but particular attention

must be given to control of the total thickness variation

(see Section 9.1.1).

Table 1 Minimum Number of Sites for Evaluating

Macro-Scale Resistivity Variation

Diameter of Area to be

Evaluated, mm

Minimum Number of Sites in

Map

51 81

63 121

76 169

89 225

101 289

8.6.1 For four-point probes with 1.59-mm probe-tip

spacing as specified in SEMI MF84, the thickness

correction factor is within 0.5% of unity for test

specimens up to 875-m thick. For probes with 1.016-

mm (40-mil) spacing, the thickness correction is about

1% for a test specimen thickness of 625 m, increasing

to about 5% at 875 m. For probes with 0.635-mm

(25-mil) spacing, the thickness correction is about 7.5%

at a thickness of 625 m, increasing to nearly 20% at

875 m.

8.6.2 The thickness enters into the determination of the

resistivity of the reference wafer directly as an

independent factor. Therefore determination of

thickness should be made as accurately as possible. If

manual methods are used for determining radial

resistivity uniformity (see Section 8.5.1.1), the average

thickness and total thickness variation should be

determined in accordance with the contactless method

of Test Methods SEMI MF533 using the same sites for

the thickness and resistivity measurements. This

method, however, has only marginal precision for this

application. If automated methods are used for

determining radial resistivity uniformity (see Section

8.5.1.2), the average thickness and total thickness

variation should be determined over the central 38-mm

diameter circle (Note 5) in accordance with SEMI

MF1530.

8.6.3 The various errors in resistivity determination

that result from uncertainties in thickness are discussed

in Section R2-3.2.

SEMI MF1527-1104 © SEMI 2003, 2004 9

8.7 Wafer Conductivity Type and Surface Orientation

— For control of four-point probes or for calibrating

eddy current probes, conductivity type and surface

orientation do not influence the result. In this case

these parameters should be chosen so as to provide the

most uniform specimens available. For low resistivity

reference wafers, p-type (100) or (111) wafers are most

appropriate, while for high resistivity reference wafers,

n-type (neutron transmutation doped) wafers of either

orientation are preferred. For use in calibrating

mercury probes, the conductivity type of the reference

wafers must match that of the specimens to be tested.

For use in calibrating spreading resistance instruments,

the type and surface orientation of the reference wafers

must match those of the specimens to be tested.

NOTE 6: When uniformity considerations are the dominant

issue, the following should be kept in mind. At low

resistivity, wafers cut from Cz crystal are not only more

readily available but probably have better uniformity than

wafers cut from FZ crystals. Wafers cut from MCz crystals,

if available, may be an acceptable alternative to NTD wafers

for the higher resistivity ranges. In general, (100) crystals

have better radial resistivity uniformity than (111) crystals.

Also p-type crystals have generally better radial resistivity

uniformity than n-type crystals.

9 Preparation and Calibration of Resistivity

Reference Wafers

9.1 Wafer Preparation — Wafers should be sliced

from a qualified crystal section of the desired

resistivity, diameter, conductivity type, and orientation.

The thickness of the as-cut wafers should be at least

100 m larger than the desired finished thickness to

allow for removal of 25 m from each surface during

both etching and lapping. Etching immediately after

slicing in either KOH etching solution (see Section 5.4)

or etching solution (15 + 1) (see Section 5.5) is

recommended to remove damage introduced during

slicing. Subsequent lapping with 5 to 9-m aluminum

oxide abrasive is intended to provide both control of

thickness variation and a uniform matte surface.

9.1.1 The total thickness variation (TTV) of resistivity

reference wafers should be as small as possible. As a

minimum, the reference wafers should meet the TTV

requirement of ±1 % of the center-point thickness as

specified in SEMI MF84. For 625-m thick wafers,

this would require TTV  12.5 m. In most cases, it

should be possible to obtain lapped wafers with TTV 

6 m over the entire wafer and TTV  3 m (± 0.25%

of the center-point thickness) over the region of the

wafer where the resistivity uniformity is determined

(see Section 8.5.1.2). Etched or single-side polished

wafers may have somewhat larger TTV.

9.1.2 The preferred surface finish is that obtained by

lapping with 5-m alumina powder as specified in

SEMI MF84; generally similar results can be obtained

by lapping with alumina powders up to 9 m. This

surface finish was originally chosen to provide good

probe-tip and specimen-surface wear together with

sufficient smoothness to reduce probe wander.

However, resistivity reference wafers intended for

calibration of mercury probe and spreading resistance

instruments must be polished. On the other hand, if

polished wafers are used for four-point probe

measurements, difficulties may be encountered with

accumulated probe damage and the resultant contact

quality degradation or surface charge, or both.

However, use of instruments calibrated with lapped

resistivity reference wafers for measuring polished

wafers could result in errors because the electrical

thickness may be different for lapped and polished

wafers of the same mechanical thickness.

NOTE 7: An unpublished roughness-thickness correlation

study has shown that the electrical thickness of lapped wafers

with root-mean-square (rms) surface roughness < 0.58 m on

both sides does not differ from the mechanical thickness by

more than 2.5 m.

9.2 Calibration

9.2.1 Determine that the candidate resistivity reference

wafer meets the resistivity uniformity requirements

appropriate to the intended application or applications

(see Sections 8.1, 8.4, and 8.5).

9.2.2 Determine the resistivity of the candidate

reference wafer at its center in accordance with SEMI

MF84 except that (1) thickness should be measured in

accordance with Section 8.6.2, (2) each determination

should consist of m measurements, where 6  m  10,

taken with the wafer rotated about (360/m) deg between

each measurement, and (3) wafers with a surface finish

that results in stable, reproducible measurements may

be used. If the measurement is made on an etched or

polished surface, equivalence with the result that would

have been obtained using a lapped surface must be

demonstrated.

9.2.3 Calculate the average resistivity corrected to

23°C in accordance with SEMI MF84 and the sample

standard deviation of the six to ten individual resistivity

measurements (corrected to 23°C).

9.2.4 If the resistivity reference wafer is to be used for

calibrating a mercury probe system, convert the

temperature-corrected average resistivity value to net

carrier density using the computational method given in

9 Hargreaves, J. K., and Millard, D., “The Accuracy of Four-probe

Resistivity Measurements on Silicon,” Brit. J. Appl. Phys. 13, 231–

234 (1962).