Simultaneous Conduction and Valence Band Quantization in Ultrashallow High-Density Doping Profiles in Semiconductors

F. Mazzola, J. W. Wells, A. C. Pakpour-Tabrizi, R. B. Jackman, B. Thiagarajan, Ph. Hofmann, and J. A. Miwa

Phys. Rev. Lett. 120, 046403 – Published 26 January 2018

Abstract

We demonstrate simultaneous quantization of conduction band (CB) and valence band (VB) states in silicon using ultrashallow, high-density, phosphorus doping profiles (so-called Si:P $δ$ layers). We show that, in addition to the well-known quantization of CB states within the dopant plane, the confinement of VB-derived states between the subsurface P dopant layer and the Si surface gives rise to a simultaneous quantization of VB states in this narrow region. We also show that the VB quantization can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantized VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantized CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantized CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.

Received 22 November 2016
Revised 8 December 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.046403

Physics Subject Headings (PhySH)

Electronic structure Growth Valleytronics

2-dimensional systems Doped semiconductors Interfaces Surfaces Two-dimensional electron gas

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. Mazzola¹, J. W. Wells^1,*, A. C. Pakpour-Tabrizi², R. B. Jackman², B. Thiagarajan³, Ph. Hofmann⁴, and J. A. Miwa⁴

¹Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
²London Centre for Nanotechnology and Department of Electronic and Electrical Engineering, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
³MAX-lab, P.O. Box 118, S-22100 Lund, Sweden
⁴Department of Physics and Astronomy and Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Ny Munkegade 120, DK-8000 Aarhus, Denmark

^*quantum.wells@gmail.com

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Issue

Vol. 120, Iss. 4 — 26 January 2018

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Images

Figure 1
Simultaneous quantization for CB and VB states in silicon. (a) ARPES data for the control sample, (b) corresponding ARPES data of a Si:P $δ$ -layer sample with a 4 nm encapsulation thickness, CB and VB states indicated. (c) Momentum integrated EDCs to emphasize the differences between the two samples. (d) Band bending schematic of a Si:P $δ$ layer. The resulting potential, $V (z)$ , is shown by the black line and confines the CB band electrons to give rise to the states labeled $1 Γ$ and $2 Γ$ . Recovery of the potential well to the surface leads to quantized states confined to the Si encapsulation layer: $q w_{1}$ , $q w_{2}$ , and $q w_{3}$ . The blue and green shaded areas represent the continuum of CB and VB bulk states where these quantized states cannot form.
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Figure 2
Evolution of the quantized VB states with encapsulation thickness. (a) ARPES data for the control Si sample. (b)–(e) Si:P $δ$ -layer ARPES spectra acquired for different Si encapsulation thicknesses ranging from 1 to 4 nm. The CB state at the Fermi level ( $1 Γ$ ) becomes gradually weaker with increasing Si encapsulation thickness while the states within the VB region become more intense. For panels (c)–(e), the ARPES spectra are shown twice with salient features marked and labeled on the spectra displayed in the lower panels. To enhance the visibility of the quantized VB states, the curvature method [28] was applied and the results are presented on right-hand sides of the lower panels of (d) and (e). The spectra for the 1–4 nm encapsulation thicknesses have been left-right symmetrized, while the control sample has not. An even sixth-order polynomial was used to fit the quantized VB states, $q w_{1}$ (orange) and $q w_{2}$ (yellow), for the data shown in (c)–(e) [29]. (f) Momentum integrated EDCs for Si:P $δ$ layers with different encapsulation thicknesses. The positions of the CB ( $1 Γ$ ) and SS are indicated. The inset shows an enlarged region of the 4-nm-thick Si encapsulation data where the $q w_{2}$ state is readily visible. Adjacent to the $q w_{2}$ state, an unlabeled arrow marks the location of small peak which may be due to a third quantized valence band state. (g) The intensity ratio of CB to VB states for each of the Si:P $δ$ -layer samples. (h), (i) Numerically obtained solutions to the Schrödinger equation for a linear potential well [ $V (z)$ , black line] for 3 and 4 nm Si encapsulation layers, respectively. The calculated eigenstates are marked by the green curves and the separation energies (in eV) marked by the double-headed arrows.
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