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SEMI MF1535-1104 © SEMI 2004 16 Figure R3-3 Low-Injection Recombination Lifetime (solid curve) as a Functi on of Resis tivity for Iron-Bor on Pairs in p -Type Silicon at Room Temperature Figure R3-2 Low-In j ection Recom…

SEMI MF1535-1104 © SEMI 2004 15

RELATED INFORMATION 3

MINORITY-CARRIER RECOMBINATION LIFETIME

NOTICE: This related information is not an official part of SEMI MF1535. It was derived from

information developed during the original preparation of the standard in ASTM Committee F-1 in 1994.

This related information was approved for publication by full letter ballot procedures.

R3-1 The recombination of an excess electron-hole

pair at a defect center is a two-step process. It involves

either (a) the capture of an electron in an empty defect

center followed by the capture of a hole or (b) the

capture of a hole on a filled defect center followed by

the capture of an electron. Thus, the recombination

time depends on the number of filled or empty defect

centers as well as the capture time constants.

R3-2 The occupancy of the defect centres is controlled

by the position of the Fermi energy as discussed by

Blakemore.

If all of the defect centers are empty, the

electron recombination time is governed by the electron

capture time constant,



; this occurs when the Fermi

energy is well below the defect center energy. If all of

the defect centers are filled, the hole recombination

time is governed by the hole capture time constant,



;

this occurs when the Fermi energy is well above the

defect energy. Since the position of the Fermi energy is

governed primarily by the dopant density, the

occupancy of the defect centers may be different for

different resistivity wafers.

R3-3 There are two sets of equivalent cases. The

defect center may be in the same half of the forbidden

gap as the Fermi energy or it may be in the other half.

Thus, the case for the defect center in the lower half of

the gap of a

p-type semiconductor is the same as for the

defect center in the upper half of the gap in an n-type

semiconductor with the roles of electrons and holes

interchanged. Similarly, the case for the defect center

in the upper half of the gap in a p-type semiconductor is

the same as for the defect center in the lower half of the

gap in an n-type semiconductor.

R3-4 As examples, consider the three cases of

elemental iron in both n- and p-type silicon and iron-

boron pairs in p-type silicon at room temperature (300

K). In each case the iron density is assumed to be

5 × 10

atoms/cm

. Note that at for very low resistivity

wafers, the nondegeneracy requirement of the S-R-H

model may be violated.

R3-4.1 Elemental Iron in p-Type Silicon (see Figure

R3-1) — For all practical values of resistivity, the

Fermi energy lies many kT below the near mid-gap

energy of the elemental iron center. Consequently, the

defect centers are empty and the limiting process is

capture of excess minority electrons, there being ample

numbers of holes present to recombine with the electron

immediately upon its capture by the defect center.

Therefore, the small-signal carrier recombination

lifetime is equal to the electron (minority-carrier)

capture time constant:



R3-4.2 Elemental Iron in n-type Silicon (see Figure

R3-2) — In this case, for all values of resistivity, the

Fermi energy is very far above the defect center energy

and all the defect centers are filled, and hole capture is

governed by the hole capture time constant,



Because the Fermi energy is close to the conduction

band edge, there are large numbers of electrons present

so that as soon as a hole is captured, the defect center is

filled again. Therefore, hole capture is the limiting

process, and the small-signal carrier recombination

lifetime is equal to the hole (minority-carrier) capture

time constant:



R3-4.3 Iron-Boron Pairs in p-Type (Boron-Doped)

Silicon (see Figure R3-3) — This defect center is

located quite close to the valence band edge. For all but

very low resistivity wafers, the Fermi energy lies above

the defect center energy so that some of the defect

centers are filled. In this case, the capture of minority

electrons is still the limiting process, but since only a

fraction of the sites can capture an electron, the small-

signal recombination lifetime is larger than the electron

capture time constant. Quantitatively, because

<< p

the small-signal carrier recombination lifetime is given



R3-4.4 The fourth possible case is one in which the

defect center is located near valence band edge in n-

type material. The iron-boron pair, of course, cannot

exist in n-type material; however, for the case of a

hypothetical defect center with energy near the valence

band in n-type material,



for all but the

most heavily doped material so this term dominates the

small-signal lifetime and the minority-carrier properties

do not influence the recombination process.

R3-5 Thus, for deep lying defect centers, the low-

injection (small-signal) carrier recombination lifetime is

equal to the minority-carrier capture time constant (or

minority-carrier lifetime), while for centers close to the

band edge, the small-signal carrier recombination

lifetime can be much larger than the minority-carrier

capture time constant.

SEMI MF1535-1104 © SEMI 2004 16

Figure R3-3

Low-Injection Recombination Lifetime (solid curve)

as a Function of Resistivity for Iron-Boron Pairs in

p-Type Silicon at Room Temperature

Figure R3-2

Low-In

ection Recombination Lifetime (solid

curve) as a Function of Resistivity for

Elemental Iron in n-Type Silicon at Room

Temperature

Figure R3-1

Low-In

ection Recombination Lifetime (solid

curve) as a Function of Resistivity for

Elemental Iron in p-Type Silicon at Room

Temperature

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SEMI MF1569-0705

GUIDE FOR GENERATION OF CONSENSUS REFERENCE MATERIALS

FOR SEMICONDUCTOR TECHNOLOGY

This guide was technically approved by the global Silicon Wafer Committee. This edition was approved for

publication by the global Audits and Reviews Subcommittee on April 7, 2005. It was available at

www.semi.org in June 2005 and on CD-ROM in July 2005. Original edition published by ASTM

International as ASTM F 1569-94. Last previous edition SEMI MF1569-94 (Reapproved 1999).

1 Purpose

1.1 This guide covers the procedures for producing a single set of consensus reference materials (ConRefs) in the

absence of suitable certified reference materials from an established source.

1.2 Such reference materials are frequently required for calibration of measurement systems to reduce bias

differences between different organizations.

1.3 The generated ConRefs can be used by a single laboratory for internal use or for interlaboratory comparison of

related equipment and materials.

1.4 Most often, however, they are used for replicating multiple sets of reference materials. In such a case, the

property values of these reference materials are traceable to the values of the property value of the ConRefs.

Depending on the nature of the preparing organization, these multiple sets may be certified reference materials or

working reference materials. For this purpose, a guide for generation of reference materials specific to the materials

and property may be required; Appendix 1 outlines the requirements for preparing a guide for generation of multiple

sets of reference materials.

2 Scope

2.1 This guide covers the steps to be taken to generate a set of ConRefs for a specific property or family of related

properties required in semiconductor technology.

2.2 The procedure for generating the set of ConRefs is based on interlaboratory testing in accordance with ASTM

Practice E 691. It is assumed for the purposes of this guide that the test method evaluated by the interlaboratory

study (ILS) is appropriate for determining the property values of the ConRef.

2.3 This guide does not cover the selection of one of several possible test methods nor does it cover the case for

which other reference materials must be used in the measurement of the properties of the ConRef.

2.4 This guide also describes procedures that may be used to generate consensus property values that may form the

basis for the generation of multiple sets of CRMs or reference materials (RMs).

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 guides and determine the

applicability of regulatory or other limitations prior to use.

3 Referenced Standards and Documents

3.1 ASTM Standards

E 456 — Terminology Relating to Quality and Statistics

E 691 — Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method

3.2 ISO Standards

ISO Guide 30:1981 — Terms and Definitions Used in Connection with Reference Materials

1 Annual Book of ASTM Standards, Vol 14.02, ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. Telephone: 610-

832-9500, Fax: 610-832-9555, Website: