Thickness-dependent conductivity of nanometric semiconductor thin films

The miniaturization of electronic devices has led to the prominence, in technological applications, of semiconductor thin films that are only a few nanometers thick. In spite of intense research, the thickness-dependent resistivity or conductivity of semiconductor thin films is not understood at a fundamental physical level. We develop a theory based on quantum confinement which yields the dependence of the concentration of intrinsic carriers on the film thickness. The theory predicts that the resistivity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>ρ</a:mi></a:math>, in the 1–10 nm thickness range, increases exponentially as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ρ</b:mi><b:mo>∼</b:mo><b:mo form="prefix">exp</b:mo><b:mo>(</b:mo><b:mi>const</b:mi><b:mo>/</b:mo><b:msup><b:mi>L</b:mi><b:mrow><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:msup><b:mo>)</b:mo></b:mrow></b:math> upon decreasing the film thickness <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>L</d:mi></d:math>. This law is able to reproduce the remarkable increase in resistivity observed experimentally in Si thin films, whereas the effect of surface scattering (Fuchs-Sondheimer theory) alone cannot explain the data when the film thickness is lower than 10 nm.