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Accurate evaluation of subband structure in a carrier accumulation layer at an n-type InAs surface: LDF calculation combined with high-resolution photoelectron spectroscopy
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Figures

Image of FIG. 1.

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FIG. 1.

Nonparabolic (NP) energy dispersion E c(k) of the bulk conduction band of InAs at T = 300 K (full curve), in comparison with the parabolic (P) dispersion for the band-edge effective mass m 0 * (dotted curve). The horizontal full bar marked μNP and the horizontal dotted one designated as μP locate the Fermi level for the NP dispersion E c(k) and that for the P dispersion, respectively, both at T = 300 K and the doping level n 0 = 4.5×1017 cm−3.

Image of FIG. 2.

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FIG. 2.

Subband-edge energies E j (j = 1, 2, 3) as a function of the areal density of accumulated carriers, N s, for (a) the NP conduction band E c(k) and (b) the P one. In each panel, the three full curves show the theoretical results, and the circles, squares, and diamonds exhibit the experimental ones for K adsorption, Cs adsorption, and the clean surface in Ref. 4, respectively. In analyzing the experimental results, the N s value is adjusted so that the observed E j values (j = 1, 2, 3) at each stage of the accumulation-layer formation process accord with the calculated curves as well as possible.

Image of FIG. 3.

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FIG. 3.

Relation of N s (NP) and N s (P) at various stages of the accumulation-layer formation process. Here, N s (NP) on the abscissa denotes the N s value obtained by fitting the observed E j values (j = 1, 2, 3) to the theoretical curves using the NP conduction band, and N s (P) on the ordinate signifies the N s value determined by fitting the observed E j values (j = 1, 2, 3) to the theoretical curves using the P conduction band. The circles, squares, and the diamond are the experimental results for K adsorption, Cs adsorption, and the clean surface, respectively,4 as in Fig. 2. The N s (NP) value and the N s (P) value of each point correspond to an adjusted N s value in Fig. 2(a) and that in Fig. 2(b), respectively. The dotted line is the one of N s (NP) = N s (P).

Image of FIG. 4.

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FIG. 4.

Depth dependence of (a) the effective one-electron potential V(z) and (b) the carrier-density distribution n(z) for the NP conduction band and N s = 6×1012 cm−2 (full curve), for the P conduction band and N s = 4×1012 cm−2 (broken curve), and for the P conduction band and N s = 6×1012 cm−2 (dotted curve). In (a), the horizontal bar (full, broken or dotted) connected with one of the three potential curves indicates the edge energy E 1 of the lowest subband corresponding to the potential curve.

Image of FIG. 5.

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FIG. 5.

Energy dispersions of the lowest subband E 1(K) at N s = 1, 2, 4, and 6×1012 cm−2 (full curves), in comparison with the NP dispersion of the bulk conduction band E c(k) (dotted curve) and the P dispersion using the band-edge effective mass (broken curve). Each horizontal bar combined with one of the full curves locates the Fermi level μ for the corresponding N s value. For example, the bar numbered ‘6’ is for N s = 6×1012 cm−2.

Image of FIG. 6.

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FIG. 6.

Dependence of the effective-mass ratio m*/m 0 on the areal electron density of the lowest subband N 1. The circles connected by dotted lines and the full curve can be obtained from Eq. (13) by using the NP subband dispersion and the projected bulk-band dispersion for E 1(K) in this equation, respectively. The broken line represents the band-edge effective mass ratio.

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/content/aip/journal/adva/2/4/10.1063/1.4768671
2012-11-20
2014-04-20

Abstract

Adsorption on an n-type InAssurface often induces a gradual formation of a carrier-accumulation layer at the surface. By means of high-resolution photoelectron spectroscopy (PES), Betti et al. made a systematic observation of subbands in the accumulation layer in the formation process. Incorporating a highly nonparabolic (NP) dispersion of the conduction band into the local-density-functional (LDF) formalism, we examine the subband structure in the accumulation-layer formation process. Combining the LDF calculation with the PES experiment, we make an accurate evaluation of the accumulated-carrier density, the subband-edge energies, and the subband energy dispersion at each formation stage. Our theoretical calculation can reproduce the three observed subbands quantitatively. The subband dispersion, which deviates downward from that of the projected bulk conduction band with an increase in wave number, becomes significantly weaker in the formation process. Accurate evaluation of the NP subband dispersion at each formation stage is indispensable in making a quantitative analysis of collective electronic excitations and transport properties in the subbands.

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Scitation: Accurate evaluation of subband structure in a carrier accumulation layer at an n-type InAs surface: LDF calculation combined with high-resolution photoelectron spectroscopy
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4768671
10.1063/1.4768671
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