Field-effect conductivity scaling for two-dimensional materials with tunable impurity density

Chulin Wang, Lintao Peng, Spencer A. Wells, Jeffrey D. Cain, Yi Kai Huang, Lawrence A. Rhoads, Vinayak P. Dravid, Mark C. Hersam, Matthew A. Grayson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A scaling law is demonstrated in the conductivity of gated two-dimensional (2D) materials with tunable concentrations of ionized impurity scatterers. Experimental data is shown to collapse onto a single 2D conductivity scaling (2DCS) curve when the mobility is scaled by r, the relative impurity-induced scattering, and the gate voltage is shifted by Vs, a consequence of impurity-induced doping. This 2DCS analysis is demonstrated first in an encapsulated 2D black phosphorus multilayer at T=100K with charge trap densities programmed by a gate bias upon cooldown, and next in a Bi2Se3 2D monolayer at room temperature exposed to varying concentrations of gas adsorbates. The observed scaling can be explained using a conductivity model with screened ionized impurity scatterers. The slope of the r vs. Vs plot defines a disorder-charge specific scattering rate "q=dr/dVs equivalent to a scattering strength per unit impurity charge density: "q>0 indicates a preponderance of positively charged impurities with "q<0 for negatively charged. This 2DCS analysis is expected to be applicable in arbitrary 2D materials systems with tunable impurity density, which will advance 2D materials characterization and improve performance of 2D sensors and transistors.

Original languageEnglish (US)
Article number031002
Journal2D Materials
Issue number3
StatePublished - Jul 2022


  • 2D electronics
  • bismuth selenide
  • black phosphorous
  • deep-level transient spectroscopy
  • electronic transport
  • ionized impurities
  • negative bias instability

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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