SEMI MF723-99
Practice for Conversion Between Resistivity and Dopant Density for Boron-Doped, Phosphorus-Doped, and Arnic-Doped Silicon
This standard was originally published by ASTM International as ASTM F 723-81. It was formally approved by ASTM
balloting procedures and adhered to ASTM patent requirements. Though ownership of this standard has been transferred
to SEMI, it has not been formally approved by SEMI balloting procedures and does not adhere either to SEMI
Regulations dealing with patents or to SEMI Editorial Guidelines. Available at October 2003, to be
published November 2003. Last published by ASTM International as ASTM F 723-99.
INTRODUCTION
The ability to convert between resistivity and dopant density in a miconductor 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 ba than from theoretical calculations.
Resistivity may be unambiguously determined throughout the desired resistivity range regardless of the dopant
impurity. However, it was necessary to u a variety of techniques to establish the complete dopant density scale of
cmwapinterest; the techniques do not all respond to the same parameter of the miconductor.
In the experimental work (1), (2), (3)1 supporting the conversions, capacitance-voltage measurements were ud to
determine the dopant density of both boron- and phosphorous-doped specimens with dopant densities less than about
1018 cm−3. 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
ud to obtain dopant density values greater than 1018 cm−3. In addition, in this range neutron activation analysis and
spectrophotometric analysis were ud to determine phosphorus density, and the nuclear track technique was ud 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 the specimens were assumed equal to the carrier densities obtained from the Hall
effect measurements with the u of an estimate for the Hall proportionality factor bad on the best availableonepiece是什么
experimental and theoretical information. In the ca of specimens heavily doped with phosphorus, the Hall
proportionality factor is unity, but there is considerable evidence that at densities above about 5 × 1019 cm−3 not all of
the phosphorus is electrically active becau of the formation of complexes. In the abnce 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. Conquently, the
conversions bad on the data may understate the total phosphorus density for stated values above about
5 × 1019 cm−3.
1. Scope
1.1 This practice 2 describes a conversion between dopant density and resistivity for arnic-, boron- and phosphorus-doped single crystal silicon at 23°C. The conversions are bad primarily on the data of Thurber et al (1), (2), (3)2 taken on bulk single crystal silicon having dopant density values in the range from 3 × 1013 cm−3 to 1 × 1020 cm−3 for phosphorus-doped silicon and in the range from 1014 cm−3 to 1 × 1020 cm−3 for boron-doped silicon. The phosphorus data ba was supplemented in the following manner: two bulk specimen data points of Esaki and Miyahara (4) an
d one diffud specimen data point of Fair and Tsai (5) were ud to extend the data ba above 1020cm−3, and an imaginary point was added at 1012 cm−3 to improve the quality of the conversion for low dopant density values. A conversion for arnic, distint from that of phosphorus, is prented for the range 1019 to 6 by 1020cm−3.
1.2 The lf consistency of the conversion (resistivity to dopant density and dopant density to resistivity) (e Appendix X1) is within 3 % for boron from 0.0001 to 10 000 Ω·cm, (10 12 to 1021 cm−3) and within 4.5 % for phosphorus from 0.0002 to 4000 Ω·cm (1012 to 5 × 10 20cm−3). This error increas rapidly if the phosphorus conversions are ud for densities above 5 × 1020 cm−3 .
1.3 The conversions are bad 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 u with arnic and antimony, except when approaching solid solubility (e 6.3).
1 Boldface numbers in parenthes refer to the list of references at the end of this practice.
2 DIN 50434 is an equivalent method. It is the responsibility of DIN Committee NMP 221, with which Comittee F-1 maintains clo technical liaison. DIN 50444, Testing of Materials for Semiconductor T
echnology: Conversion Between Resistivity and Dopant Density of Silicon, is available from Beuth Verlag GmbH Burggrafenstras 4-10, D-1000 Berlin 30, Federal Republic of Germany.slideunlock
1.4 The conversions are between resistivity and dopant density and should not be confud with conversions between resistivity and carrier density or with mobility relations.
N OTE 1—The commonly ud conversion between resistivity and dopant density compiled by Irvin (6) is compared with this conversion in Appendix X2. In this compilation, Irvin ud 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 u. It is the responsibility of the ur of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to u.
托福是什么2. Referenced Documents
2.1 ASTM Standards:
F 84 Test Method for Measuring Resistivity of Silicon Wafers with an In-Line Four-Point Probe 3
2.2 Adjuncts:
Large Wall Chart 4
3. Terminology
3.1 Definitions:
3.1.1 carrier density, n (electrons);p (holes)—the number of majority carriers per unit volume in an extrinsic miconductor, usually given in number/cm 3 although the SI unit is number/m3.
3.1.2 compensation—reduction in number of free carriers resulting from the prence of impurities other than the majority dopant density impurity. Compensation occurs when both donor and acceptor dopant impurities are prent in a miconductor; in this ca the net dopant density (whi
ch is equal to the carrier density provided that all the dopant impurities are ionized) is given by the absolute magnitude of the difference between the acceptor dopant density and the donor dopant density. Compensation may also occur if deep-level impurities or defects are prent in quantities comparable with the dopant impurities; in this ca the relationship between the carrier density and the dopant density (under the assumption of full ionization of the dopant impurity) depends on a variety of parameters (7). A miconductor that exhibits compensation is said to be “compensated.”
3.1.3 concentration—relative amount of a minority constituent of a mixture to the majority constituent (for example, parts per million, parts per billion, or percent) by either volume or weight. In the miconductor literature, often ud interchangeably with number density (for example, number per unit volume).
圣诞节英文怎么说3.1.4 deep-level impurity—a chemical element that when introduced into a miconductor has an energy level (or levels) that lies in the mid-range of the forbidden energy gap, between tho of the dopant impurity species.
3.1.
4.1 Discussion-Certain crystal defects and complexes may also introduce electrically active deep lev
els in the miconductor.
3.1.5 dopant density—in an uncompensated extrinsic miconductor, the number of dopant impurity atoms per unit volume, usually given in atoms/cm3 although the SI unit is atoms/m3. Symbols: N D for donor impurities and N A for acceptor impurities.
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4. Summary of Practices
4.1 The conversions between resistivity and dopant density are made using equations, tables, or graphs.
5. Significance and U
5.1 Dopant density and resistivity of silicon are two important acceptance parameters ud in the interchange of material by consumers and producers in the miconductor industry. Therefore, a particular method of converting from dopant density to resistivity and vice versa must be available since some test methods measure resistivity while others measure dopant density.
5.2 The conversions are uful in mathematical modeling of miconductor processing and devices.
3 Annual Book of ASTM Standards, Vol 10.05, ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. Telephone: 610-832-9500, Fax: 610-832-9555, Website:
4 A large wall chart, “Conversion Between Resistivity and Dopant Density” is available from ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428. Order Adjunct ADJF0723.
6. Interferences
6.1 Carrier Density— Attempts to derive carrier density values from resistivity values by using the conversions are subject to error. While dopant density and carrier density values are expected to be the same at low densities (up to about 1017 cm−3), the two quantities generally do not have the same value in a given specimen at moderate densities. At such moderate densities, (about 1017 cm−3 to 1019 cm−3), dopant densities are larger than carrier densities due to incomplete ionization.
汽车玻璃划痕 At densities above 10 19 cm−3, the population statistics become degenerate, and carrier densities would normally be equal to dopant densities. However, in this upper range of densities, the possibility of formation of compounds or complexes involving dopant atoms is more pronounced and would prevent some of the dopant atoms from being electrically active. Such formation of compounds or complexes is particularly likely in phosphorus- or arnic-doped silicon. Precipitation occurs at dopant densities greater than solid solubility.
6.2 Heavily Phosphorus-Doped Silicon—The conversions are given as functions of resistivity and of dopant density. For heavily phosphorus-doped specimens, primary emphasis was placed on Hall effect measurements for establishing the density values. However, since the Hall effect measures carrier density, it was assumed for the heavily doped specimens that all atoms were electrically active; that is, the dopant density was equal to the carrier density as measured by the Hall effect. The possible formation of phosphorus-vacancy pairs which are known to reduce the electrically active phosphorus atoms at high densities (5) was not tested or accounted for in the data ba or the resulting conversions. The existence of such phosphorus-vacancy pairs would cau the Hall measurements to understate the total dopant density for the heavily phosphorus-doped specimens.
6.3 Other Dopant Species—The applicability of the conversions to silicon doped with other than ar
nic, boron or phosphorus has not yet been established. However, in the lightly doped range (<1017 cm−3) the conversions are expected to be reasonably accurate for other dopants. Between 10 17 and 1019 cm −3, the difference in activation energy of different dopant species will cau different resistivities to be measured for the same dopant density. In this range the differences in resistivities will be larger among the p-type dopants than among the n-type dopants due to larger differences in the activation energies among the p-type dopants. At high dopant densities (>1019 cm−3), the formation of complexes involving dopant atoms, lattice defects, and other impurities will lead to a modification in the number of charge carriers. The extent of this effect will depend upon the particular dopant species and is not well detailed in the literature for the various common dopants. Its ont is expected to be related to the density of the dopant compared to the solid solubility of that dopant in silicon. Therefore, in this upper dopant density range, the applicability of the conversions to dopants other than boron and phosphorus is unclear.
6.4 Compensation— The specimens ud to obtain the data ba for the conversions were assumed to be uncompensated. The measured net dopant density was taken to be the total density of the intentional dopant in the specimen. For specimens in which significant compensation occurs, the conversions may not apply.
6.5 Temperature— The conversions in this practice hold for a temperature of 23°C. Resistivity varies with temperature, but dopant density does not.
N OTE 2—It is possible to obtain dopant density values from resistivity values that were not measured at 23°C by using Test Method F 84 to correct the resistivity values to 23°C. Also, the conversion from dopant density to resistivity may be made directly and the temperature correction for resistivity then made following Test Method F 84 to obtain the resistivity at other than 23°C.
N OTE 3—References 1, 2, and 3 give values for the coefficients in the conversion equations at both 23°C and 300 K.
6.6 Other Electrically Active Centers—Numerous other mechanisms exist that may modify the number of free carriers or noticeably alter carrier mobility, either of which will change the resistivity from the value given here for a given dopant density. Among the mechanisms are (1) lattice damage due to radiation (neutron transmutation doping or ion implantation), (2) formation of deep level centers due to chemical impurities (typically heavy metals, either unwanted or sometimes intentionally added for minority carrier lifetime control), and (3) unintentional doping due, for example, to electrically activated oxygen. When any of the effects is known or expected to be prent, the conversions given here may not apply.
6.7 Range of Arnic-Doped Silicon Data—The conversion given for arnic-doped silicon is from Fair and Tsai (8), covering the doping range of 1019 to 6 by 1020. This conversion was generated using Hall effect measurements. The principal reference for neutron activation data is that of Newman et al.(9). Neutron activation data give higher resistivity values for a given dopant density than do Hall data becau of the assumption that the Hall coefficient R H = 1/ne. A more complicated relationship between R H and n is given in Ref (9). Care must be taken in using any conversion not to extrapolate beyond the range of the data fitted, as the formulas will diverge beyond that range. Other studies support the u of the conversion given here Refs (10, 11, 12, and 13), which means that the conversion to resistivity for phosphorus can be ud for arnic in this range. In the range 2 by 1019 to 1020, the Fair and Tsai fit matches the Irvin formula. The range beyond 6 by 1020 is discusd only in Ref (13).
7. Procedure
7.1 Convert Resistivity Values to Dopant Density Values— Follow 7.1.1 (graphical method), 7.1.2 (tabular method), or 7.1.3 (computation method). 5
7.1.1 Graphical Method:
7.1.1.1 For boron-doped silicon, u the curve labeled “boron” in Fig. 1.
7.1.1.2 For phosphorus-doped silicon, u the curve labeled “phosphorus” in Fig. 1.
7.1.2 Tabular Method:
7.1.2.1 For boron-doped silicon u Table 1.
TABLE 1 Dopant Density as a Function of Resistivity for Boron-Doped Silicon
N OTE 1—Entries in two significant digits are for regions of extrapolated data.
TABLE 1 Continued
7.1.2.2 For phosphorus-doped silicon u Table 2.
7.1.3 Computational Method :
vision7.1.3.1 For boron-doped silicon, calculate the dopant density value from the resistivity value as follows:
N = 1.330 × 10 16ρ + 1.082 × 10 17
ρ []1 + ()54.56ρ 1.105 (1)
where:
ρ
= resistivity and N = dopant density.
7.1.3.2 For phosphorus-doped silicon, calculate the dopant density from the resistivity as follows:
N = 6.242 × 10 18
ρ × 10 Z (2)
where:
Z = A 0 + A 1x + A 2x 2 + A 3x 3
1 + B 1x + B 2x
2 + B 3x
3 (3)
where:
英语春节作文x = log 10ρ,
饰品拍摄
A 0 = −3.1083,
