[Paper Review] Two distinct methods to evaluate graphene relaxation time and mobility in Boltzmann diffusive transport, considering ionized impurity scattering and Thomas-Fermi screening

Yi Zhan|arXiv (Cornell University)|Dec 24, 2017

Graphene research and applications2 references3 citations

TL;DR

This paper presents two equivalent methods—Boltzmann transport equation with scattering matrix and scattering cross-section approach—to calculate graphene's relaxation time and mobility under ionized impurity scattering, incorporating Thomas-Fermi screening. Both methods yield identical results, confirming graphene’s high mobility potential for ultrafast electronic devices at reasonable carrier densities.

ABSTRACT

Boltzmann diffusive transport including relaxation time and mobility in graphene limited by ionized impurity scattering is investigated. The relaxation time is evaluated with two different methods, first one directly use Boltzmann transport equation via scattering matrix, second one is based on scattering cross-section. Two methods yield the same relaxation time results for graphene. Assume linear Thomas-Fermi screening and a reasonable electron carrier density, relaxation time and mobility can be calculated and plotted, which demonstrates graphene is a very promising high mobility material for ultra fast electronic device applications.

Motivation & Objective

• To evaluate graphene’s relaxation time and mobility in Boltzmann diffusive transport limited by ionized impurity scattering.
• To compare two distinct theoretical approaches for calculating relaxation time: one using the Boltzmann transport equation with scattering matrix, and another based on scattering cross-section.
• To incorporate Thomas-Fermi screening effects into the transport model for accurate relaxation time and mobility estimation.
• To demonstrate that graphene exhibits high mobility suitable for ultrafast electronic device applications.
• To validate consistency between the two calculation methods under linear Thomas-Fermi screening and realistic carrier densities.

Proposed method

• The first method applies the Boltzmann transport equation using the scattering matrix to compute relaxation time directly from scattering processes.
• The second method derives relaxation time from the scattering cross-section, providing an alternative route to the same physical quantity.
• Ionized impurity scattering is modeled as the dominant scattering mechanism in graphene’s diffusive transport regime.
• Thomas-Fermi screening is implemented linearly to account for electron-electron screening effects in the presence of ionized impurities.
• The electron carrier density is assumed to be within a reasonable range to enable quantitative evaluation of mobility and relaxation time.
• Both methods are analytically and numerically compared to confirm consistency in results under identical physical assumptions.

Experimental results

Research questions

• RQ1 Do the two distinct theoretical approaches—scattering matrix and scattering cross-section—yield consistent relaxation time values in graphene under ionized impurity scattering?
• RQ2 How does Thomas-Fermi screening influence the calculated relaxation time and mobility in graphene?
• RQ3 What is the predicted mobility of graphene when ionized impurity scattering and screening are accounted for?
• RQ4 Can the two methods be used interchangeably for mobility and relaxation time estimation in graphene transport models?
• RQ5 To what extent does graphene’s high mobility potential persist under realistic carrier density conditions?

Key findings

• Both the scattering matrix and scattering cross-section methods produce identical relaxation time values, confirming their theoretical equivalence in the context of graphene transport.
• The inclusion of linear Thomas-Fermi screening significantly affects the screening of ionized impurities, reducing scattering strength and enhancing mobility.
• At reasonable electron carrier densities, the calculated mobility remains high, indicating strong potential for ultrafast electronic applications.
• The relaxation time is found to be inversely proportional to the ionized impurity concentration and screening strength, as expected from transport theory.
• The consistency between the two methods validates the reliability of the theoretical framework for modeling graphene transport.
• The results support graphene as a promising material for high-speed nanoelectronic devices due to its intrinsic high mobility under realistic scattering conditions.