Limit of the electrostatic doping in two-dimensional electron gases of LaXO₃(X = Al, Ti)/SrTiO₃.
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Beyond a filling threshold, electrons added by electrostatic gating escape from the well, hence limiting the possibility to reach a highly-doped regime.This leads to an irreversible doping regime where all the electronic properties of the 2-DEG, such as its resistivity and its superconducting transition temperature, saturate.The escape mechanism can be described by the simple analytical model we propose.
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Affiliation: LPEM- UMR8213/CNRS - ESPCI ParisTech - UPMC, 10 rue Vauquelin - 75005 Paris, France.
ABSTRACT
In LaTiO₃/SrTiO₃ and LaAlO₃/SrTiO₃ heterostructures, the bending of the SrTiO₃ conduction band at the interface forms a quantum well that contains a superconducting two-dimensional electron gas (2-DEG). Its carrier density and electronic properties, such as superconductivity and Rashba spin-orbit coupling can be controlled by electrostatic gating. In this article we show that the Fermi energy lies intrinsically near the top of the quantum well. Beyond a filling threshold, electrons added by electrostatic gating escape from the well, hence limiting the possibility to reach a highly-doped regime. This leads to an irreversible doping regime where all the electronic properties of the 2-DEG, such as its resistivity and its superconducting transition temperature, saturate. The escape mechanism can be described by the simple analytical model we propose. No MeSH data available. Related in: MedlinePlus |
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Mentions: To analyze the relaxation in the irreversible regime we propose a model that describes the dynamics of electrons escaping from the well. We consider a 2D quantum well at the interface with an infinite barrier on the LaXO3(X = Al, Ti) side and a barrier of finite height EB on the SrTiO3 side (Inset of Fig. 6). A number nL of 2D parabolic sub-bands with energy Ei (i = 1,…,nL) and density of states are filled. We assume that at a temperature T, electrons at the Fermi level EF can jump over the barrier with first order kinetics: where n is the carrier density of the 2-DEG and k is the kinetic factor. This latter follows an Arrhenius law: where the activation energy is Δ = EB − EF, and ν is a characteristic frequency factor. In two dimensions, the electron density is given by where NF = nLN is the total density of states at the Fermi energy and . This situation is formally equivalent to the one with a single band of energy EL and a density of state NF. For a small variation of n, the temporal evolution of the Fermi energy is At low temperature (kBT ≪ EF − EL), a good approximate solution to equation (3) is where is the Fermi level at t = 0+ (immediately after the voltage step, neglecting the short charging time RGCaA) and tE is the characteristic escape time given by where is the carrier density at t = 0+. Therefore, the Fermi level is constant for t < tE, after which it decreases logarithmically. From (2) and (4) we can obtain the temporal dynamics of the 2-DEG Drude resistivity as where is the resistivity at t = 0+. In Figure 6 we show the resistance relaxation after a ΔVG = +10 V step; this relaxation agrees very well with equation (6) over more than six decades of time (10 ms to 14 hours). A direct consequence of the logarithmic relaxation is the absence of an asymptotic value. However, on a linear scale the resistance changes very slowly after a few minutes, which can give a false impression of saturation. We emphasise here that the peculiar form of relaxation given by Eq. 6 is specific to the case of a well that empties itself and cannot describe other thermally activated mechanisms. |
View Article: PubMed Central - PubMed
Affiliation: LPEM- UMR8213/CNRS - ESPCI ParisTech - UPMC, 10 rue Vauquelin - 75005 Paris, France.
No MeSH data available.