Interplay between quantum confinement and dielectric mismatch for ultrashallow dopants

J. A. Mol, J. Salfi, J. A. Miwa, M. Y. Simmons, and S. Rogge

Phys. Rev. B 87, 245417 – Published 13 June 2013

Abstract

Understanding the electronic properties of dopants near an interface is a critical challenge for nanoscale devices. We have determined the effect of dielectric mismatch and quantum confinement on the ionization energy of individual acceptors beneath a hydrogen passivated silicon (100) surface. While dielectric mismatch between the vacuum and the silicon at the interface results in an image charge which enhances the binding energy of subsurface acceptors, quantum confinement is shown to reduce the binding energy. Using scanning tunneling spectroscopy we measure resonant transport through the localized states of individual acceptors. Thermal broadening of the conductance peaks provides a direct measure for the absolute energy scale. Our data unambiguously demonstrates that these two independent effects compete with the result that the ionization energy is less than 5 meV lower than the bulk value for acceptors less than a Bohr radius from the interface.

Received 19 August 2012

DOI:https://doi.org/10.1103/PhysRevB.87.245417

Authors & Affiliations

J. A. Mol^1,2, J. Salfi¹, J. A. Miwa¹, M. Y. Simmons¹, and S. Rogge^1,2

¹Centre for Quantum Computation and Communication Technology, University of New South Wales, Sydney NSW 2052, Australia
²Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

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Vol. 87, Iss. 24 — 15 June 2013

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Figure 1
Schematic energy diagram of the tip-vacuum-sample tunnel junction. (a) When $e V < E_{V} < e V_{F B}$ electrons tunnel from the valence band to the tip and the presence of a subsurface acceptor is observed as a protrusion in the STM topography. (b) In case $e V_{F B} < e V \sim E_{C}$ direct tunneling via the localized acceptor state leads to a protrusion in the topography. (c) Suppression of the local density of states by the acceptor potential reduces the tunnel current when $E_{C} < e V$ , resulting in a depression in the topography.Reuse & Permissions
Figure 2
(a) Normalized conductance $G_{N}$ measured on a hydrogen terminated Si(100):H surface away from (solid line) and above (dashed line) an acceptor. The top of the valence band $V_{V}$ and bottom of the conduction band $V_{C}$ are determined by the slopes of $G_{N}$ away from the acceptor (dotted lines). (b) Surface potential $ϕ_{S}$ assuming linear TIBB (dotted line) and nonlinear TIBB (solid line) calculated using the code developed by Feenstra.[23] The relevant parameters chosen for these calculations to match the change in band gap are the tip-sample separation 0.8 nm, the tip radius 8 nm, and the doping concentration $1 \times 10^{18}$ cm $^{- 3}$ . Note that the doping concentration is lower than the substrate doping, which is expected from acceptor out-diffusion during the flash anneal.Reuse & Permissions
Figure 3
(a) $d I / d V$ map recorded simultaneously with empty-state topography ( $+$ 2.2 V, 300 pA). Tunneling from the valence band to the tip is indicated by VB, tunneling from the tip to the conduction band is indicated by CB. The $d I / d V$ map is cut at the acceptor site to show the upward shift of the valence band states. (b) Schematic potential landscape due to a negatively charged nucleus below the sample surface and its image charge in the vacuum. The solid line indicates the potential along the vacuum-semiconductor interface. (c) Shift in the valence band maximum $E_{V}$ as a function of lateral tip position. (d) Azimuthal averaged shift in the valence band maximum $E_{V}$ (filled squares) as a function lateral tip separation $s$ from the acceptor as indicated in (c). The dopant depth is determined by fitting $E_{V}$ to a bare Coulomb potential (solid line), taking into account the image charge due to dielectric mismatch as illustrated in (b).Reuse & Permissions
Figure 4
(a) Schematic energy diagram. Local tip induced band bending brings the acceptor level $E_{A}$ into resonance with the Fermi energy. The voltage $V_{onset}$ at which this occurs depends on the acceptor depth, ionization energy, and the screening length. (b) The lever arm $α$ and the onset voltage $V_{onset}$ are determined fitting the two conductance peaks in the band gap to the sum of two thermally broadened Lorentzian line shapes (relevant fitting parameters are listed in Appendix ). (c) Measured (squares) and calculated (line) onset voltage for resonant tunneling as a function of acceptor depth. (d) Measured (squares) and calculated (line) lever arm as a function of acceptor depth. (e) The shift in ionization energy $Δ E$ with respect to the bulk ionization energy inferred from the measured onset voltage and the lever arm (squares). The onset voltage and lever arm are calculated for $Δ E = - 2.5$ meV, line in (c), and an overlap between the acceptor wave function and the tip induced band bending $Δ E = - 0.06 \times TIBB$ , where TIBB is the tip induced band bending at the acceptor site as illustrated in (a).Reuse & Permissions
Figure 5
(a) Measured barrier height as a function of voltage and relative tip position $Δ z$ . The imaging condition $Δ z = 0$ corresponds to a tunnel current $I = 300$ pA and bias voltage $V = - 0.6$ V. (b) Extracted effective barrier height at $V = 0$ .Reuse & Permissions

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