Screened shallow impurity properties of quantum well heterosystems with high-κ dielectric barrier environment

The effect of high-κ dielectric mismatch on the impurity states screened by free electron gas is investigated theoretically in high-κ dielectric barrier/quantum well/high-κ dielectric barrier (hh-κ) and low-κ dielectric barrier/quantum well/high-κ dielectric barrier (lh-κ) types of quasi two-dimensional (Q2D) heterostructures. A restriction of the characteristic long-range nature of the impurity Q2D screened interaction due to the high-κ dielectric mismatch has been revealed here - atypical of the Q2D dielectrically homogeneous systems. Accordingly, for the hh-κ type heterostructure, an impurity screened interaction potential at moderately large (relative to the quantum well width values) in-plane distances behaves as the Q2D Debye-Hückel potential, while at rather large distances falls off on the background of the high-κ dielectric constant of the barrier medium. The screened impurity ground state energy in the framework of the Q2D Debye-Hückel potential has been investigated variationally for the first time. A role of high-κ dielectric mismatch is exposed when comparing the results for the discussed heterostructures based on the realistic InSb/HfO2 interface. The characteristic ranges where the quantum confinement effect, enhancing the Coulomb interaction, balances the joint weakening influence of the impurity screening and high-κ dielectric mismatch effects are revealed. The received admissible values of the in-plane density/temperature ratio parameter for the hh-κ type heterostructure typically refer to non-degenerate electron gas while for the lh-κ type both electron gas statistics are significant. Due to the high-κ dielectric mismatch a binding energy sufficient decline with reducing of the quantum well width has been established. In the hh-κ type heterostructure an impurity binding is quite sizable at the wide quantum wells (d ∼8 ÷ 10 nm). Meanwhile, for the lh-κ-type heterostructure, an impurity binding energy is enough large (∼10 meV) in both wide and narrow quantum well cases. •The effect of high-κ dielectric mismatch on the quantum well screened impurity states is studied.•A restriction of the long-range nature of the impurity Q2D screened interaction has been revealed.•The Q2D Debye-Hückel type of screened potential at moderately large distances has been received.•The impurity binding energy explicit expression at moderately large distances is derived at the first time.•The binding energy sufficient decline with reducing of the quantum well wid