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SEMI MF1527-1104 © SEMI 2003, 2004 7 correction factor for such g eometries vari es rapidly with thickness (see Section 8.6). 8.3.1 Because of the relative insensitivity of the calculated center-point resistivity to th e…

SEMI MF1527-1104 © SEMI 2003, 2004 6

respectively). Further, the procedures for determining

micro-scale depth profiles are destructive and cannot be

carried out on the reference wafer itself. Consequently,

for this application crystals should be grown by

procedures that result in the best possible uniformity.

These include neutron transmutation doping of very

high purity FZ crystals to obtain high resistivity

(neutron transmutation doped (NTD)) n-type wafers

and magnetic Czochralski (MCz) growth of crystals for

both n- and p-type wafers.

8.1.4 Mercury Probes — Similar conditions exist for

reference wafers intended for calibration and control of

mercury probe systems that are primarily used for

determining the net carrier density of epitaxial layers

from capacitance measurements. Such probes sample a

lateral area much smaller than the four-point probe and

a depth that is only a very tiny fraction of the wafer

thickness. To ensure that the resistivity in the region

sampled by the mercury probe can be taken as the

resistivity measured by the four-point probe, it is

necessary to establish that both the macro- and micro-

scale variations in resistivity of the reference wafer are

within tolerable limits. Thus, it is desirable to use

highly uniform crystal such as NTD FZ or MCz crystal

for resistivity reference wafers for this application (see

Section 8.1.3). It is further required in this case to

establish the net carrier density of the reference wafer

from the resistivity measurement (see Section 9.2.4).

8.2

Resistivity — The center-point resistivity of the

reference wafer should be chosen to meet the

requirements of the measuring instrument to be

calibrated or controlled. Most of the test methods cited

in Section 1.2 specify the resistivity range of the

required resistivity reference wafers.

8.2.1 Four-point Probes — For control of

instrumentation for making four-point probe resistivity

measurements in accordance with SEMI MF84, it is

recommended that a minimum of three resistivity

reference wafers, with resistivity values in the upper,

middle, and lower portions of the resistivity range of

interest be used (Note 4). It is preferable to use more

closely spaced resistivity reference wafers to ensure

instrument linearity over the entire measurement range.

If only a narrow resistivity range (less than ±25% of the

nominal value) needs to be measured, it is sufficient to

use two resistivity reference wafers at the extremes of

this range. Similar considerations apply for control of

instrumentation for making sheet resistance

measurements in accordance with SEMI MF1529,

except that, in this case, of course, the parameter of

interest is the sheet resistance rather than the resistivity.

NOTE 4: For control of instrumentation for making four-

point probe measurements over a narrow resistivity range, it

may be appropriate to use only one or two resistivity

reference wafers.

8.2.2 Eddy–Current Gages — For calibration of eddy

current resistivity measuring instruments, SEMI MF673

specifies that for calibration by Method I, five reference

wafers that span the full resistivity range of the

instrument are required. However, many organizations

prefer to use many more reference wafers for the

Method I calibration. Two resistivity reference wafers

at the extremes of a narrow resistivity range (typically

less than about ±25 % of the nominal value) are

required for Method II calibration.

8.2.3 Spreading Resistance Probes — For calibration

of spreading resistance equipment, SEMI MF672

recommends use of at least three resistivity reference

wafers per decade over the range of resistivity to be

measured. Regular spacing is desirable, but it may not

be possible to secure samples with adequate uniformity

with arbitrary nominal resistivity values. Selection of

samples for micro-scale uniformity should take

precedence over regular spacing.

8.2.4 Mercury Probes — The resistivity of a resistivity

reference wafer intended for use in calibrating mercury

probe systems for making net carrier density

measurements in accordance with SEMI MF1392 or

SEMI MF1393 is specified to be between one-half and

two times the resistivity of the specimens to be

measured. However, there is some benefit to employ

several resistivity reference wafers with a range of

resistivity from very high (net carrier density less than

about 1 × 10

3

) to the lowest value to be

measured.

8.3 Wafer Diameter — Resistivity reference wafers do

not need to be the same diameter as the wafers to be

measured by the system; any diameter that fits the

instrumentation and its associated wafer handling is, in

principle, acceptable. However, advances in crystal

growing design and control together with certain aspect

ratio considerations make it likely that superior radial

resistivity uniformity in the central region of the wafer

can be obtained with larger diameter (100 mm) wafers

as compared to that of smaller diameter wafers. In

addition, the diameter correction factor for wafers 100

mm in diameter and larger measured with a four-point

probe with probe-tip spacing of 1.59 mm is within 0.2%

of its limiting value of /ln2 ( = 4.5324).

Consequently, errors due to small variations in diameter

or probe placement at the wafer center are negligibly

small (see Section R2-3.1), and the second order errors

associated with the combination of the thickness and

diameter correction factors can also be neglected. The

latter point is particularly significant when four-point

probes with small probe-tip spacings are employed on

standard thickness wafers because the thickness

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.