ASTM F723-99

Standard Practice for Conversion Between Resistivity and Dopant Density for Boron-Doped, Phosphorus-Doped, and Arsenic-Doped Silicon (Withdrawn 2003)

SCOPE
This standard was transferred to SEMI (www.semi.org) May 2003
1.1 This practice  describes a conversion between dopant density and resistivity for boron- and phosphorus-doped single crystal silicon at 23°C. The conversions are based primarily on the data of Thurber et al (1,2,3)  taken on bulk single crystal silicon having dopant density values in the range from 3 X 10   cm   to 1 X 10   cm   for phosphorus-doped silicon and in the range from 10   cm   to 1 X 10   cm   for boron-doped silicon. The phosphorus data base was supplemented in the following manner:two bulk specimen data points of Esaki and Miyahara (4) and one diffused specimen data point of Fair and Tsai (5) were used to extend the data base above 10   cm  , and an imaginary point was added at 10   cm   to improve the quality of the conversion for low dopant density values.  
1.2 The self consistency of the conversion (resistivity to dopant density and dopant density to resistivity) (see Appendix X1) is within 3% for boron from 0.0001 to 10 000 [omega][dot]cm, (10   to 10   cm  ) and within 4.5% for phosphorus from 0.0002 to 4000 [omega][dot]cm (10   to 5 X 10   cm  ). This error increases rapidly if the phosphorus conversions are used for densities above 5 X 10   cm  .  
1.3 These conversions are based upon boron and phosphorus data. They may be extended to other dopants in silicon that have similar activation energies; although the accuracy of conversions for other dopants has not been established, it is expected that the phosphorus data would be satisfactory for use with arsenic and antimony, except when approaching solid solubility. See 5.3.  
1.4 These conversions are between resistivity and dopant density and should not be confused with conversions between resistivity and carrier density or with mobility relations.  Note 1-The commonly used conversion between resistivity and dopant density compiled by Irvin (6) is compared with this conversion in Appendix X2. In this compilation, Irvin used the term "impurity concentration" instead of the term "dopant density."
1.5 This standard does not purport to address all of the safety concerns, 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 limitations prior to use.

General Information

• Status: Withdrawn
• Publication Date: 09-Jun-1999
• Withdrawal Date: 11-Aug-2003
• ICS: 29.045 - Semiconducting materials
• Technical Committee: F01 - Electronics

Standards Content (Sample)

NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: F 723 – 99
Standard Practice for
Conversion Between Resistivity and Dopant Density for
Boron-Doped, Phosphorus-Doped, and Arsenic-Doped
Silicon
This standard is issued under the fixed designation F 723; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The ability to convert between resistivity and dopant density in a semiconductor is important for a
variety of applications ranging from material inspection and acceptance to process and device
modeling. Despite some experimental limitations, the conversion is more readily established from an
empirical data base than from theoretical calculations. Resistivity may be unambiguously determined
throughout the desired resistivity range regardless of the dopant impurity. However, it was necessary
to use a variety of techniques to establish the complete dopant density scale of interest; these
techniques do not all respond to the same parameter of the semiconductor.
In the experimental work (1), (2), (3) supporting these conversions, capacitance-voltage measure-
ments were used to determine the dopant density of both boron- and phosphorous-doped specimens
18 −3
with dopant densities less than about 10 cm . The specimens were assumed to be negligibly
compensated; hence, the data given by the capacitance-voltage measurements were taken to be a direct
measure of the dopant density in the specimen. Hall effect measurements were used to obtain dopant
18 −3
density values greater than 10 cm . In addition, in this range neutron activation analysis and
spectrophotometric analysis were used to determine phosphorus density, and the nuclear track
technique was used to determine boron density. Where there were discrepancies in the data from the
analytical techniques, more weight was given to the Hall effect results. Up to the highest densities
measured, boron is expected to be fully electrically active. Therefore, the boron densities of these
specimens were assumed equal to the carrier densities obtained from the Hall effect measurements
with the use of an estimate for the Hall proportionality factor based on the best available experimental
and theoretical information. In the case of specimens heavily doped with phosphorus, the Hall
proportionality factor is unity, but there is considerable evidence that at densities above about
19 −3
5 3 10 cm not all of the phosphorus is electrically active because of the formation of complexes.
In the absence of data regarding the fraction of phosphorus atoms withdrawn from electrically active
states due to complexing, the values of carrier density taken from the Hall effect measurements were
assumed to be equal to the phosphorus density values. Consequently, the conversions based on these
19 −3
data may understate the total phosphorus density for stated values above about 5 3 10 cm .
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NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
F 723
1. Scope Wafers with an In-Line Four-Point Probe
3 2.2 ASTM Adjuncts:
1.1 This practice describes a conversion between dopant
Large Wall Chart
density and resistivity for arsenic-, boron- and phosphorus-
doped single crystal silicon at 23°C. The conversions are based
3. Terminology
primarily on the data of Thurber et al (1), (2), (3) taken on
3.1 Definitions:
bulk single crystal silicon having dopant density values in the
13 −3 20 −3
3.1.1 carrier density, n (electrons); p (holes)—the number
range from 3 3 10 cm to 1 3 10 cm for phosphorus-
14 −3 20
of majority carriers per unit volume in an extrinsic semicon-
doped silicon and in the range from 10 cm to 1 3 10 cm
ductor, usually given in number/cm although the SI unit is
−3 for boron-doped silicon. The phosphorus data base was
number/m .
supplemented in the following manner: two bulk specimen data
3.1.2 compensation—reduction in number of free carriers
points of Esaki and Miyahara (4) and one diffused specimen
resulting from the presence of impurities other than the
data point of Fair and Tsai (5) were used to extend the data base
20 −3
majority dopant density impurity. Compensation occurs when
above 10 cm , and an imaginary point was added at
12 −3
both donor and acceptor dopant impurities are present in a
10 cm to improve the quality of the conversion for low
semiconductor; in this case the net dopant density (which is
dopant density values. A conversion for arsenic, distint from
19 20
equal to the carrier density provided that all the dopant
that of phosphorus, is presented for the range 10 to6by10
−3
impurities are ionized) is given by the absolute magnitude of
cm .
the difference between the acceptor dopant density and the
1.2 The self consistency of the conversion (resistivity to
donor dopant density. Compensation may also occur if deep-
dopant density and dopant density to resistivity) (see Appendix
level impurities or defects are present in quantities comparable
X1) is within 3 % for boron from 0.0001 to 10 000 V·cm, (10
21 −3
with the dopant impurities; in this case the relationship
12 to 10 cm ) and within 4.5 % for phosphorus from 0.0002
12 20 −3
between the carrier density and the dopant density (under the
to 4000 V·cm (10 to 5 3 10 cm ). This error increases
assumption of full ionization of the dopant impurity) depends
rapidly if the phosphorus conversions are used for densities
20 −3
on a variety of parameters (7). A semiconductor that exhibits
above 5 3 10 cm .
compensation is said to be “compensated.”
1.3 These conversions are based upon boron and phospho-
3.1.3 concentration—relative amount of a minority con-
rus data. They may be extended to other dopants in silicon that
stituent of a mixture to the majority constituent (for example,
have similar activation energies; although the accuracy of
parts per million, parts per billion, or percent) by either volume
conversions for other dopants has not been established, it is
or weight. In the semiconductor literature, often used inter-
expected that the phosphorus data would be satisfactory for use
changeably with number density (for example, number per unit
with arsenic and antimony, except when approaching solid
volume).
solubility (see 6.3).
3.1.4 deep-level impurity—a chemical element that when
1.4 These conversions are between resistivity and dopant
introduced into a semiconductor has an energy level (or levels)
density and should not be confused with conversions between
that lies in the mid-range of the forbidden energy gap, between
resistivity and carrier density or with mobility relations.
those of the dopant impurity species.
NOTE 1—The commonly used conversion between resistivity and
3.1.4.1 Discussion—Certain crystal defects and complexes
dopant density compiled by Irvin (6) is compared with this conversion in
may also introduce electrically active deep levels in the
Appendix X2. In this compilation, Irvin used the term “impurity concen-
semiconductor.
tration” instead of the term “dopant density.”
3.1.5 dopant density—in an uncompensated extrinsic semi-
1.5 This standard does not purport to address all of the
conductor, the number of dopant impurity atoms per unit
safety concerns, if any, associated with its use. It is the
volume, usually given in atoms/cm although the SI unit is
responsibility of the user of this standard to establish appro-
atoms/m . Symbols: N for donor impurities and N for
D A
priate safety and health practices and determine the applica-
acceptor impurities.
bility of regulatory limitations prior to use.
4. Summary of Practice
2. Referenced Documents
4.1 The conversions between resistivity and dopant density
2.1 ASTM Standards:
are made using equations, tables, or graphs.
F 84 Test Method for Measuring Resistivity of Silicon
5. Significance and Use
This practice is under the jurisdiction of ASTM Committee F-1 on Electronics
5.1 Dopant density and resistivity of silicon are two impor-
and is the direct responsibility of Subcommittee F01.06 on Silicon Materials and
tant acceptance parameters used in the interchange of material
Process Control.
by consumers and producers in the semiconductor industry.
Current edition approved June 10, 1999. Published August 1999. Originally
published as F 723 – 81. Last previous edition F 723 – 97. Therefore, a particular method of converting from dopant
Boldface numbers in parentheses refer to the list of references at the end of this
practice.
DIN 50434 is an equivalent method. It is the responsibility of DIN Committee
NMP 221, with which Comittee F-1 maintains close technical liaison. DIN 50444, Annual Book of ASTM Standards, Vol 10.05.
Testing of Materials for Semiconductor Technology: Conversion Between Resistiv- A large wall chart, “Conversion Between Resistivity and Dopant Density” is
ity and Dopant Density of Silicon, is available from Beuth Verlag GmbH available from ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428.
Burggrafenstrasse 4-10, D-1000 Berlin 30, Federal Republic of Germany. Order Adjunct ADJF0723.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
F 723
density to resistivity and vice versa must be available since values from resistivity values by using these conversions are
some test methods measure resistivity while others measure
subject to error. While dopant density and carrier density
dopant density.
values are expected to be the same at low densities (up to about
17 −3
5.2 These conversions are useful in mathematical modeling
10 cm ), the two quantities generally do not have the same
of semiconductor processing and devices.
value in a given specimen at moderate densities. At such
17 −3 19 −3
moderate densities, (about 10 cm to 10 cm ), dopant
6. Interferences
densities are larger than carrier densities due to incomplete
6.1 Carrier Density— Attempts to derive carrier density
NOTE 1—The solid line shows the resistivity to dopant density conversion for the range of actual data. The chain dot line shows the dopant density
to resistivity conversion for the range of actual data. Dashed lines show regions of extrapolation from data.
NOTE 2—On the scale of the figure as reproduced in this book, the solid and chaindot lines cannot be distinguished visually. They are distinguishable,
however, on the wall chart available as Adjunct PCN 12-607230-46, wherever the self-consistency error (see Appendix X1) becomes appreciable.
FIG. 1 Preferred Conversion Between Resistivity and Total Dopant Density Values for Boron- and Phosphorus-Doped Silicon
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
F 723
19 −3
ionization. At densities above 10 cm , the population 6.5 Temperature— The conversions in this practice hold for
statistics become degenerate, and carrier densities would nor- a temperature of 23°C. Resistivity varies with temperature, but
mally be equal to dopant densities. However, in this upper dopant density does not.
range of densities, the possibility of formation of compounds
NOTE 2—It is possible to obtain dopant density values from resistivity
or complexes involving dopant atoms is more pronounced and
values that were not measured at 23°C by using Test Method F 84 to
would prevent some of the dopant atoms from being electri-
correct the resistivity values to 23°C. Also, the conversion from dopant
cally active. Such formation of compounds or complexes is density to resistivity may be made directly and the temperature correction
for resistivity then made following Test Method F 84 to obtain the
particularly likely in phosphorus- or arsenic-doped silicon.
resistivity at other than 23°C.
Precipitation occurs at dopant densities greater than solid
NOTE 3—References 1, 2, and 3 give values for the coefficients in the
solubility.
conversion equations at both 23°C and 300 K.
6.2 Heavily Phosphorus-Doped Silicon—These conversions
6.6 Other Electrically Active Centers—Numerous other
are given as functions of resistivity and of dopant density. For
mechanisms exist that may modify the number of free carriers
heavily phosphorus-doped specimens, primary emphasis was
or noticeably alter carrier mobility, either of which will change
placed on Hall effect measurements for establishing the density
the resistivity from the value given here for a given dopant
values. However, since the Hall effect measures carrier density,
density. Among these mechanisms are (1) lattice damage due to
it was assumed for these heavily doped specimens that all
radiation (neutron transmutation doping or ion implantation), (
atoms were electrically active; that is, the dopant density was
2) formation of deep level centers due to chemical impurities
equal to the carrier density as measured by the Hall effect. The
(typically heavy metals, either unwanted or sometimes inten-
possible formation of phosphorus-vacancy pairs which are
tionally added for minority carrier lifetime control), and (3)
known to reduce the electrically active phosphorus atoms at
unintentional doping due, for example, to electrically activated
high densities (5) was not tested or accounted for in the data
oxygen. When any of these effects is known or expected to be
base or the resulting conversions. The existence of such
present, the conversions given here may not apply.
phosphorus-vacancy pairs would cause the Hall measurements
6.7 Range of Arsenic-Doped Silicon Data—The conversion
to understate the total dopant density for the heavily
given for arsenic-doped silicon is from Fair and Tsai (8),
phosphorus-doped specimens.
19 20
covering the doping range of 10 to6by10 . This conversion
6.3 Other Dopant Species—The applicability of these con-
was generated using Hall effect measurements. The principal
versions to silicon doped with other than arsenic, boron or
reference for neutron activation data is that of Newman et
phosphorus has not yet been established. However, in the
17 −3
al.(9). Neutron activation data give higher resistivity values for
lightly doped range (<10 cm ) the conversions are expected
a given dopant density than do Hall data because of the
to be reasonably a
...