Gate-driven transition temperatures of electron hopping behaviors in Hubbard bands formed by dopant-induced QD array in silicon nanowire

Abstract

Abstract Dopant atoms confined in silicon nanoscale channel can be ionized to form quantum dots (QDs). Several dopant atoms couple with each other forming energy bands, where the electron hopping behavior can be described by the Hubbard model. This characteristic renders dopant-induced quantum dots particularly appealing for applications in nanoelectronic and quantum devices. Herein we study the gate-driven transition temperatures of electron hopping behavior in upper and lower Hubbard bands formed by dopant-induced QD array in junctionless silicon nanowire transistors. The gate-dependent transition temperatures are calculated for three stages of electron hopping behaviors including Efros-Shklovskii Variable Range Hopping (ES-VRH), Mott Variable Range Hopping (Mott-VRH) and Nearest Neighbor Hopping (NNH). Our experimental results indicate that the ES-VRH in arrays of dopant atoms occurs in the domination of a long-range Coulomb interaction, in which the hopping distance relies on the Coulomb gap. Furthermore, the localization length of ES-VRH can be modulated by gate voltages.Those factors lead to the significant difference of transition temperatures between the upper and lower Hubbard bands. In addition, we find that the source-drain bias voltage can effectively modulate the transition temperatures between VRH and NNH by thermal activation energies under different bias voltages Vds.