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1、 1 SEMI MF723-0307 SEMI 2005, 2007 SEMI MF723-0307 PRACTICE FOR CONVERSION BETWEEN RESISTIVITY AND DOPANT OR CARRIER DENSITY FOR BORON-DOPED, PHOSPHORUS-DOPED, AND ARSENIC-DOPED SILICON This standard was technically approved by the global Silicon Wafer Committee. This edition was approved for public
2、ation by the global Audits and Reviews Subcommittee on November 21, 2006. It was available at www.semi.org in February 2007 and on CD-ROM in March 2007. Original edition published by ASTM International as ASTM F 723-81; previously published July 2006. 1 Purpose 1.1 Dopant density and resistivity of
3、silicon are two important acceptance parameters used in the interchange of material by consumers and producers in the semiconductor industry. Therefore, a particular method of converting from dopant density to resistivity and vice versa must be available since some test methods measure resistivity w
4、hile others measure dopant density. 1.2 In addition, there are occasions when conversion from resistivity to carrier density is required. 1.3 These conversions are useful in mathematical modeling of semiconductor processing and devices. 1.4 This practice describes conversions between dopant density
5、and resistivity for arsenic-, boron- and phosphorus- doped single crystal silicon and conversions from resistivity to carrier density for boron- and phosphorus doped single crystal silicon at 23C. NOTE 1: Except that it does not include dopant density conversions for arsenic-doped silicon or any car
6、rier density conversions, DIN 50444 is an equivalent practice. 1.5 Despite some experimental limitations, the conversions are more readily established from an empirical database than from theoretical calculations. 1.5.1 The conversions for boron- and phosphorus- doped silicon in this practice are ba
7、sed 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 1013 cm3 to 1 1020 cm3 for phosphorus-doped silicon and in the range from 1014 cm3 to 1 1020 cm3 for boron-doped silicon. The phosphorus data base was supplemented i
8、n the following manner: two bulk specimen data points of Esaki and Miyahara4 and one diffused specimen data point of Fair and Tsai5 were used to extend the data base above 1020 cm3, and an imaginary point was added at 1012 cm3 to improve the quality of the conversion for low dopant density values. 1
9、.6 A limited additional conversion is given for arsenic-doped silicon, for the doping range 1019 to 6 1020 cm3, where it is shown to differ from the conversion for phosphorus-doped silicon, but it is only available in the direction from dopant density to resistivity. This conversion from Fair and Ts
10、ai 6 was generated using Hall effect measurements covering the this dopant density range. Below this dopant density range, the conversion for phosphorus-doped silicon can be applied to arsenic-doped silicon. NOTE 2: Resistivity may be unambiguously determined throughout the desired resistivity range
11、 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 supporting these conversions, capacitance-
12、voltage measurements were used to determine the dopant density of both boron- and phosphorous- doped specimens with dopant densities less than about 1018 cm3. The specimens were assumed to be negligibly compensated; hence, the data given by the capacitance-voltage measurements were taken to be a dir
13、ect measure of the dopant density in the 1 Thurber, W. R., Mattis, R. L., Liu, Y. M., and Filliben, J. J., “Resistivity-Dopant Density Relationship for Phosphorus-Doped Silicon,” J. Electrochem. Soc. 127, 18071812 (1980) 2 Thurber, W. R., Mattis, R. L., Liu, Y. M., and Filliben, J. J., “Resistivity-
14、Dopant Density Relationship for Boron-Doped Silicon,” J. Electrochem. Soc. 127, 22912294 (1980) 3 Thurber, W. R., Mattis, R. L., Liu, Y. M., and Filliben, J. J., Semiconductor Measurement Technology,“Relationship Between Resistivity and Dopant Density for Phosphorus- and Boron-Doped Silicon,” NBS Sp
15、ecial Publication 400-64 (April 1981) 4 Esaki, L., and Miyahara, Y., “A New Device Using the Tunneling Process in Narrow p-n Junction,” Solid-State Electron. 1, 1321 (1960) 5 Fair, R. B., and Tsai, J. C. C., “A Quantitative Model for the Diffusing of Phosphorus in Silicon and the Emitter Dip Effect,
16、” J. Electrochem. Soc. 124, 11071118 (1977) 6 Fair, R. B., and Tsai, J. C. C., “The Diffusion of Ion-Implanted Arsenic in Silicon,” J. Electrochem. Soc. 122, 1689 (1975) SEMI MF723-0307 SEMI 2005, 2007 2 specimen. Hall effect measurements were used to obtain dopant density values greater than 1018 c
17、m3. 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
18、to the Hall effect results. 2 Scope 2.1 These conversions are based upon data from boron- and phosphorus-doped silicon. 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 expec
19、ted that the phosphorus data would be satisfactory for use with arsenic and antimony, except when approaching solid solubility (see 3.3). 2.2 Conversions between resistivity and dopant density should not be confused with conversions between resistivity and carrier density (see 3.1). Depending on the
20、 desired application, the correct conversion relationship should be applied. NOTE 3: The conversion between resistivity and dopant density compiled by Irvin7 is compared with this conversion (see Related Information 1). In this compilation, Irvin used the term “impurity concentration” instead of the
21、 term “dopant density.” 2.3 The self-consistency of the dopant density conversions (resistivity to dopant density and dopant density to resistivity) (see 7.3.1) is within 3% for boron from 0.0001 to 10,000 cm, (1012 to 1021 cm3) and within 4.5% for phosphorus from 0.00024000 cm (1012 to 5 1020 cm3).
22、 This error increases rapidly if the phosphorus conversions are used for densities above 5 1020 cm3. 2.4 The self-consistency of the carrier density conversions (resistivity to carrier density and carrier density to resistivity) is of similar magnitude.3 NOTICE: This standard does not purport to add
23、ress safety issues, if any, associated with its use. It is the responsibility of the users of this standard to establish appropriate safety and health practices and determine the applicability of regulatory or other limitations prior to use. 3 Limitations 3.1 Carrier Density Attempts to derive carri
24、er density values from resistivity values by using conversions for dopant density are subject to error. While dopant density and carrier density values are expected to be nearly the same at 23 K at low densities (up to about 1017 cm3), the two quantities generally do not have the same value in a giv
25、en specimen at moderate densities. At such moderate densities, (about 1017 cm3 to 1019 cm3), dopant densities are larger than carrier densities due to incomplete ionization. At densities above 1019 cm3, the population statistics become degenerate, and carrier densities would normally be equal to dop
26、ant 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 pho
27、sphorus- or arsenic-doped silicon. Precipitation occurs at dopant densities greater than solid solubility. For derivation of carrier density from resistivity, use the appropriate relationship from 7.4. 3.2 Heavily Phosphorus-Doped Silicon These conversions are given as functions of resistivity and o
28、f 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 these heavily doped specimens that all atoms were electrically active; th
29、at 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 base or the resulting conv
30、ersions. The existence of such phosphorus-vacancy pairs would cause the Hall measurements to understate the total dopant density for the heavily phosphorus-doped specimens. 3.3 Other Dopant Species The applicability of these conversions to silicon doped with other than arsenic, boron, or phosphorus
31、has not yet been established. However, in the lightly doped range (1019 cm3), the formation of complexes involving dopant atoms, lattice defects, and other impurities may lead to a modification in 7 Irvin, J. C., “Resistivity of Bulk Silicon and of Diffused Layers in Silicon,” Bell System Tech. J. 4
32、1, 387410 (1962) -,-,- 3 SEMI MF723-0307 SEMI 2005, 2007 the number of charge carriers. The extent of this effect depends on the particular dopant species and is not well detailed in the literature for the various common dopants. Its onset is expected to be related to the density of the dopant compa
33、red to the solid solubility of that dopant in silicon. Therefore, in this upper dopant density range, the applicability of these conversions to dopants other than boron and phosphorus is unclear. 3.4 Compensation The specimens used to obtain the data base for these conversions were assumed to be unc
34、ompensated. 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, these conversions may not apply. NOTE 4: Compensation occurs when both donor and acceptor dopant impurities are present in
35、a semiconductor. In this case, the net dopant density (which 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
36、-level impurities or defects are present in quantities comparable with the dopant impurities. In this case, 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.8 A semiconductor that e
37、xhibits compensation is said to be “compensated.” 3.5 Temperature The conversions in this practice hold for a temperature of 23C. Resistivity varies with temperature, but dopant density does not. NOTE 5: It is possible to obtain dopant density values from resistivity values that were not measured at
38、 23C by using SEMI MF84 to correct the resistivity values to 23C. Also, the conversion from dopant density to resistivity may be made directly and the temperature correction for resistivity then made following SEMI MF84 to obtain the resistivity at a temperature other than 23C. 3.6 Other Electricall
39、y 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 these mechanisms are (1) lattice damage due to radiation (neutron
40、 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
41、. When any of these effects is known or expected to be present, the conversions given here may not apply. 3.7 Heavily Arsenic-Doped Silicon The relation given for heavily arsenic-doped silicon must not be used for densities outside the stated range because the equation diverges rapidly from realisti
42、c values of calculated resistivity. This is in contrast to the equations for boron and phosphorus, for which extrapolations are shown, although with unknown accuracy. This relation is stated for dopant density and resistivity but the density scale was obtained from Hall effect measurements, and thus
43、 has the same limitation as the conversion for heavily phosphorus-doped silicon (see 3.1 and 3.3). Unlike the samples used for the boron and phosphorus data base, which were Czochralski doped bulk silicon wafers, the samples used by Fair and Tsai6 were arsenic diffusions into bulk silicon. However,
44、the Fair and Tsai conversion for arsenic is supported by other studies on arsenic-diffused and arsenic-implanted specimens.9,10,11,12 For the slightly reduced density range 2 1019 cm3 to 1020 cm3, Fair and Tsai show that their arsenic conversion relation agrees with Irvins conversion relation for n-
45、type samples, which is discussed in Related Information 1. NOTE 6: A study of the relation between dopant density for arsenic-doped Czochralski grown wafers in a slightly lower range of doping, 1 1018 cm3 to 1.1 1019 cm-3 was published by Newman, et al. 13 Newman used neutron activation to measure d
46、oping density rather than Hall effect to measure carrier density. The range above 6 1020 cm3 is discussed only by Masetti, et al.12 4 Referenced Standards and Documents 4.1 SEMI Standards SEMI M59 Terminology for Silicon Technology SEMI MF84 Test Method for Measuring Resistivity of Silicon Wafers wi
47、th an In-Line Four-Point Probe 8 Blakemore, J. S., Semiconductor Statistics (Dover Publications, New York, 1987) 3.3 9 Furukawa, Y., “Impurity Effect Upon Mobility in Heavily Doped Silicon,” J. Phys. Soc., Japan 16, 577 (l961) 10 Murota, J., Arai, E., Kobayashi, K., and Kudo, K., “Relationship Betwe
48、en Total Arsenic and Electrically Active Arsenic Concentrations in Silicon Produced by the Diffusion Process,” J. Appl. Phys. 50, 804 (l979) 11 Matsumoto, S., Niimi, T., Murota, J., and Arai, E., “Carrier Concentration and Hall Mobility in Heavily Arsenic-Diffused Silicon,” J. Electrochem. Soc. 127,
49、 1650 (l980) 12 Masetti, G., Severi, M., and Solmi, S., “Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron- Doped Silicon,” IEEE Trans. Elec. Dev. ED-30, 764 (l983) 13 Newman, P. F., Hirsch, M. J., and Holcomb, D. F., “A Calibration Curve for Room-Temperature Resistivity versus Donor Atom Concentration in Si:As,” J. Appl. Phys. 58, 3779 (l985) -,-,- SEMI MF723-0307