- SEMI MF723 - Practice for Conversion Between Resistivity and Dopant or Carrier Density for Boron-Doped, Phosphorous-Doped, and Arsenic-Doped Silicon
This Standard was technically approved by the global Silicon Wafer Technical Committee. This edition was approved for publication by the global Audits and Reviews Subcommittee on December 24, 2011. Available at www.semiviews.org and www.semi.org in April 2012; originally published by ASTM International as ASTM F723-81; previously published July 2009.
E This Standard was editorially modified in November 2016 to correct a publication error during the 0412 reapproval. Changes were made to Equation 2.
Dopant density and resistivity of 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 while others measure dopant density.
In addition, there are occasions when conversion from resistivity to carrier density is required.
These conversions are useful in mathematical modeling of semiconductor processing and devices.
This Practice describes conversions between dopant density 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 23°C.
Despite some experimental limitations, the conversions are more readily established from an empirical database than from theoretical calculations.
The conversions for boron- and phosphorus-doped silicon in this Practice are based primarily on the data of Thurber et al. 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 base was supplemented in the following manner: two bulk specimen data points of Esaki and Miyahara and one diffused specimen data point of Fair and Tsai were used to extend the data base above 1020 cm- 3, and an imaginary point was added at 1012 cm- 3 to improve the quality of the conversion for low dopant density values.
A limited additional conversion is given for arsenic-doped silicon, for the doping range 1019 to 6 × 1020 cm- 3, 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 Tsai was generated using Hall effect measurements covering the dopant density range. Below this dopant density range, the conversion for phosphorus-doped silicon can be applied to arsenic-doped silicon.
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 expected that the phosphorus data would be satisfactory for use with arsenic and antimony, except when approaching solid solubility (see ¶ 3.3).
Conversions between resistivity and dopant density should not be confused with conversions between resistivity and carrier density (see ¶ 3.1). Depending on the desired application, the correct conversion relationship should be applied.
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 W ·cm, (1012 to 1021 cm- 3) and within 4.5% for phosphorus from 0.0002–4000 W ·cm (1012 to 5 × 1020 cm- 3). This error increases rapidly if the phosphorus conversions are used for densities above 5 × 1020 cm- 3.
The self-consistency of the carrier density conversions (resistivity to carrier density and carrier density to resistivity) is of similar magnitude.
Referenced SEMI Standards
SEMI M59 — Terminology for Silicon Technology
SEMI MF84 — Test Method for Measuring Resistivity of Silicon Wafers with an In-Line Four-Point Probe