Limits...
Limit of the electrostatic doping in two-dimensional electron gases of LaXO₃(X = Al, Ti)/SrTiO₃.

Biscaras J, Hurand S, Feuillet-Palma C, Rastogi A, Budhani RC, Reyren N, Lesne E, Lesueur J, Bergeal N - Sci Rep (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.


Resistance over time of the LaTiO3/SrTiO3 sample after a ΔVG = +10 V step at t = 0, fitted by equation (6).The escape time tE is 0.8 ± 0.1 s. Inset: Schematic of the situation considered to model the thermal escape of the electrons from the well.
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f6: Resistance over time of the LaTiO3/SrTiO3 sample after a ΔVG = +10 V step at t = 0, fitted by equation (6).The escape time tE is 0.8 ± 0.1 s. Inset: Schematic of the situation considered to model the thermal escape of the electrons from the well.

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.


Limit of the electrostatic doping in two-dimensional electron gases of LaXO₃(X = Al, Ti)/SrTiO₃.

Biscaras J, Hurand S, Feuillet-Palma C, Rastogi A, Budhani RC, Reyren N, Lesne E, Lesueur J, Bergeal N - Sci Rep (2014)

Resistance over time of the LaTiO3/SrTiO3 sample after a ΔVG = +10 V step at t = 0, fitted by equation (6).The escape time tE is 0.8 ± 0.1 s. Inset: Schematic of the situation considered to model the thermal escape of the electrons from the well.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4209450&req=5

f6: Resistance over time of the LaTiO3/SrTiO3 sample after a ΔVG = +10 V step at t = 0, fitted by equation (6).The escape time tE is 0.8 ± 0.1 s. Inset: Schematic of the situation considered to model the thermal escape of the electrons from the well.
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.

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.