Direct experimental determination of the spontaneous polarization of GaN

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Direct experimental determination of the spontaneous polarization of GaN

Jonas Lähnemann, Oliver Brandt, Uwe Jahn, Carsten Pfüller, Claudia Roder, Pinar Dogan, Frank Grosse, Abderrezak Belabbes, Friedhelm Bechstedt, Achim Trampert, and Lutz Geelhaar

Phys. Rev. B 86, 081302(R) – Published 9 August 2012

Abstract

We present a universal approach for determining the spontaneous polarization $P_{sp}$ of a wurtzite semiconductor from the emission energies of excitons bound to the different types of stacking faults in these crystals. Employing microphotoluminescence and cathodoluminescence spectroscopy, we observe emission lines from the intrinsic and extrinsic stacking faults in strain-free GaN microcrystals. By treating the polarization sheet charges associated with these stacking faults as a plate capacitor, $P_{sp}$ can be obtained from the observed transition energies with no additional assumptions. Self-consistent Poisson-Schrödinger calculations, aided by the microscopic electrostatic potential computed using density-functional theory, lead to nearly identical values for $P_{sp}$ . Our recommended value for $P_{sp}$ of GaN is $- 0.022 \pm 0.007$ C/m $^{2}$ .

Received 20 October 2011

DOI:https://doi.org/10.1103/PhysRevB.86.081302

Authors & Affiliations

Jonas Lähnemann^1,*, Oliver Brandt¹, Uwe Jahn¹, Carsten Pfüller¹, Claudia Roder¹, Pinar Dogan¹, Frank Grosse¹, Abderrezak Belabbes², Friedhelm Bechstedt², Achim Trampert¹, and Lutz Geelhaar¹

¹Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5–7, 10117 Berlin, Germany
²Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany

^*laehnemann@pdi-berlin.de

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Issue

Vol. 86, Iss. 8 — 15 August 2012

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Images

Figure 1
(a) $μ$ PL spectrum of an individual microcrystal at low excitation density. (D $^{0}$ ,X) and FX are at the position of strain-free material, while individual SFs and SF bundles emerge as sharp lines right below the energies of the three SF types. The inset shows a top-view scanning electron micrograph of such microcrystals. (b), (c) False-color monochromatic CL maps superimposed on the corresponding cross-sectional scanning electron micrograph of a GaN microcrystal with the detected energies denoted in the respective colors. The CL related to SFs shows a characteristic elongation along the basal plane.Reuse & Permissions
Figure 2
High-resolution transmission electron micrographs revealing SFs of all three types and the bundling of such SFs with only thin WZ interlayers. The micrographs (a) and (b) were taken on two crystals from the same sample used for the spectroscopic analysis. Both micrographs contain I $_{1}$ SFs. In addition, micrograph (a) contains the I $_{2}$ and micrograph (b) the E SF. The overlaid ball-and-stick model (note that bright spots correspond to tunneling positions) illustrates the stacking sequence as also indicated explicitly for each SF type.Reuse & Permissions
Figure 3
CL spectral image acquired on the cross section of a microcrystal along the arrow indicated in the scanning electron micrograph in the inset. For each position along this line, a spectrum is recorded which is displayed in the spectral image with its intensity color coded on a logarithmic scale. Note that the energy is blueshifted by $Δ E$ (26 meV for the marked case) due to a screening of the polarization field when the electron beam approaches the SFs.Reuse & Permissions
Figure 4
Histogram compiled of peak energies from low-excitation $μ$ PL and of the lowest (unscreened) energies in CL (excluding phonon replicas). The Gaussian fit further illustrates the energies around which the peaks assigned to the different SF types are grouped.Reuse & Permissions
Figure 5
(a) Microscopic electrostatic potential $V_{es}$ for the E SF calculated by DFT. From the envelope of the potential, we estimate the thickness (3.7 bilayers) and $Δ V = 0.21$ eV resulting from the polarization field. (b) Band profile for the E SF from a selfconsistent Poisson-Schrödinger calculation for a type-I band alignment. The horizontal lines denote the single-particle energy levels, the arrow the resulting transition. (c) Transition energies for all three SF types from the Poisson-Schrödinger calculations with varied $P_{sp}$ and for two different conduction band offsets $Δ E_{C}$ corresponding to a type-I and a type-II alignment. The vertical lines denote the values of $P_{sp}$ for which the spectroscopically observed differences in the transition energy between the SF types are reproduced best; the absolute emission energies from experiment (including error bars) are shaded in gray for comparison.Reuse & Permissions

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