Error-Free Matthiessen's Rule in the MOSFET Universal Mobility Region

Through the experimentally validated inversion-layer mobility simulation, we devise an error-free version of Matthiessen's rule for a single-gate n-channel bulk MOSFET in the universal mobility region. The core of the new rule lies in a semi-empirical model, which explicitly expresses the errors due to the conventional use of Matthiessen's rule as a function of both the lowest subband population and the relative strength of individual mobility components. The model holds under practical conditions (with temperatures up to 400 K) and in a broad range of substrate doping concentrations (10¹⁴ to 10¹⁸ cm^-3). To make the error-free proposal more general, we elaborate on several issues, including strain, impurity Coulomb scattering, and remote scattering. The thin-film case can be treated accordingly.

I. Introduction

To probe individual scattering mechanisms in the inversion layers of MOSFETs, Matthiessen's rule may be favored because of its additive property of reciprocal mobility components. As pointed out earlier by Stern [1], however, there will be errors of more than 15% due to the use of Matthiessen's rule for temperatures over 40 K. Since then, there have been four fundamentally different methods published in the literature concerning the validity and applicability of Matthiessen's rule [2]–[7]. First, Matthiessen's rule must be carried out under extreme or impractical conditions such as very low temperatures (near absolute zero) [2]. Second, sophisticated numerical simulations on individual mobility components were instead used, with no need to account for Matthiessen's rule [3]. Third, for the engineering purpose, the errors caused by Matthiessen's rule were overlooked while assessing mobility components individually [4], [5]. Fourth, mobility simulations were performed to deliver the errors of the mobility components extracted using the rule, with [6] and without [3], [7] the inclusion of ionized impurity Coulomb scattering.