Mapping the surface phase diagram of GaAs(001) using droplet epitaxy

C. X. Zheng, K. Hannikainen, Y. R. Niu, J. Tersoff, D. Gomez, J. Pereiro, and D. E. Jesson

Phys. Rev. Materials 3, 124603 – Published 26 December 2019

Abstract

We combine droplet epitaxy with low-energy electron microscopy imaging techniques to map the surface phase diagram of GaAs(001). The phase patterns produced in droplet epitaxy are interpreted using a simple model which links the spatial coordinates of phase boundaries to the free energy. It is thereby possible to gain important information on surface phase stability, based on the observed sequential order of the phases away from the droplet edge. This can be used to augment existing $T = 0 K$ phase diagrams generated by density-functional theory calculations. We establish the existence of a $(3 \times 6)$ phase, and confirm that the controversial $(6 \times 6)$ phase is thermodynamically stable over a narrow range of chemical potential.

Received 2 October 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.124603

Physics Subject Headings (PhySH)

Surface & interfacial phenomena

III-V semiconductors Surfaces

Epitaxy Low-energy electron diffraction Low-energy electron microscopy Molecular beam epitaxy

Condensed Matter, Materials & Applied PhysicsGeneral PhysicsQuantum Information, Science & Technology

Authors & Affiliations

C. X. Zheng^1,2, K. Hannikainen³, Y. R. Niu^3,4, J. Tersoff⁵, D. Gomez³, J. Pereiro ³, and D. E. Jesson^3,*

¹School of Science, Westlake University, Hangzhou 310024, Zhejiang Province, China
²Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang Province, China
³School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom
⁴MAX IV Laboratory, Lund University, Fotongatan 2, 22484 Lund, Sweden
⁵IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA

^*dej.workaddress@gmail.com

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Vol. 3, Iss. 12 — December 2019

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Images

Figure 1
Droplet epitaxy phase pattern (DEPP) of GaAs(001). The bright-field contrast spatially separates surface phases surrounding a central droplet. The scale bar corresponds to $2 μ m$ .
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Figure 2
(a) Ga chemical potential at radial position $r$ away from the droplet edge located at $r_{D}$ . For illustration we have taken $C_{Ga}^{l} / ν_{Ga} = 0.2, C_{Ga}^{L} / ν_{Ga} = 0.01$ , and $r_{D} / L_{Ga} = 1$ (see Appendix pp1). (b) Schematic representation of the free energy $G$ [per $(1 \times 1)$ unit cell] of phases $α$ and $β$ plotted as a function of $μ_{Ga}$ . The phases have the same free energy at $μ_{Ga} (r_{c})$ corresponding to radial position $r_{c}$ in (a).
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Figure 3
Bright-field LEEM image of a Ga droplet and smooth trail region of GaAs(001): (a) at $t = 0 s$ before the As flux is turned on, (b) $30 s$ after the As flux is turned on, and (c) $33 s$ after the As flux is turned off (i.e., $66 s$ after it was first turned on). The black dashed circle in (a) indicates the position of the illumination aperture, and the scale bar corresponds to $2 μ m$ . The sample temperature is $550^{\circ} C$ .
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Figure 4
(a) Time-resolved $μ LEED$ data collected from the illumination aperture shown in Fig. 3 located $8 μ m$ from the droplet. Schematic diffraction patterns are also shown, where large circles indicate the positions of $(1 \times 1)$ spots. (b) Measured $r$ vs $t$ trajectories of phase boundaries I and II, when turning the As flux on and off. The horizontal dotted line marks the position of the aperture in Fig. 3, with the crosses corresponding to the acquisition times of the LEED data contained in (a). The dotted vertical lines represent the times at which the As shutter was opened and closed. (c) Theoretical trajectories of boundaries I and II calculated from Eq. (1) (see Appendix pp2). Time is given in units of reaction time $τ_{Ga} = {(k_{r} F_{As} τ_{As})}^{- 1}$ , and radial coordinate $r$ is given in droplet radii $r_{D}$ . The computational parameters are set to the representative values of $C_{Ga}^{l} / ν_{Ga} = 0.25, C_{Ga}^{L} / ν_{Ga} = 5 \times 10^{- 3}, ρ_{D} = 0.1$ , and $ρ_{L} = 7$ . The chemical potentials defining boundaries I and II give stationary boundary positions at $r_{I} / r_{D} = 2$ and $r_{II} / r_{D} = 3$ , respectively.
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Figure 5
Ga chemical potential profiles $μ_{Ga} (r, t)$ after turning the As flux (a) on, and (b) off. The droplet edge is located at $r = r_{D}$ . The critical chemical potentials $μ_{Ga}^{I}$ and $μ_{Ga}^{II}$ corresponding to boundaries I and II are represented by the upper and lower horizontal dashed lines, respectively. The shaded regions represent the evolving real-space region $Δ r$ corresponding to $Δ μ_{Ga} = μ_{Ga}^{I} - μ_{Ga}^{II}$ [each shaded region relates to one instantaneous $μ_{Ga} (r, t)$ profile, where time is displayed in units of $τ_{Ga} = {(k_{r} F_{As} τ_{As})}^{- 1}$ in both (a) and (b)]. We set the computational parameters to the representative values of $C_{Ga}^{l} / ν_{Ga} = 0.25, C_{Ga}^{L} / ν_{Ga} = 5 \times 10^{- 3}, ρ_{D} = 0.1$ , and $ρ_{L} = 7$ (see Appendix pp1 ). The values of $μ_{Ga}^{I}$ and $μ_{Ga}^{II}$ give stationary boundary positions at $r_{I} / r_{D} = 2$ and $r_{II} / r_{D} = 3$ , respectively.
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Figure 6
(a) SEDF LEEM image where blue, green, orange, and yellow correspond to $β 2 (2 \times 4), (3 \times 6), (6 \times 6)$ , and $c (8 \times 2)$ phases, respectively (see [12]). This map clearly resolves boundary I in more detail, revealing a stable $(6 \times 6)$ region and phase intermixing between the $(6 \times 6)$ and $c (8 \times 2)$ phases. (b) Existing DFT calculation of the GaAs (001) phase diagram (black lines) [13, 23], plotting formation energy with respect to the $α 2 (2 \times 4)$ surface per $(1 \times 1)$ unit cell against relative Ga chemical potential $Δ μ_{Ga}$ with respect to Ga bulk at $0 K$ . From the image in (a) we can schematically superimpose the formation energy lines of the $(3 \times 6)$ and $(6 \times 6)$ phases as shown, to suggest a surface phase diagram at $530^{\circ} C$ . The dashed vertical lines are the chemical potential values defining boundaries I and II. The scale bar in (a) is $2 μ m$ .
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