Interaction of Mn with GaAs and InSb: incorporation, surface reconstruction and nano-cluster formation

Three InSb crystal faces were investigated, with the starting reconstructions: c(8 × 2) and c(4 × 4) on InSb(0 0 1); (2 × 2) and $(2\sqrt{3}\times2\sqrt{3})$R30° on InSb(1 1 1)A; (3 × 3) and (2 × 2) on InSb(1 1 1)B. These reconstructions can be separated into two distinct categories, namely In-rich and Sb-rich, as shown in table 1. The In-rich (0 0 1)-c(8 × 2), (1 1 1)A-(2 × 2) and (1 1 1)B-(3 × 3) surfaces are typically obtained by MBE growth under Sb-poor conditions or by IBA. They terminate at In atomic layers or elementally mixed layers. In contrast, the Sb-rich (0 0 1)-c(4 × 4), (1 1 1)A- $(2\sqrt{3}\times 2 \sqrt{3})$R30° and (1 1 1)B-(2 × 2) surfaces are obtained by growth under Sb-rich growth conditions or by annealing with incident Sb flux. These surfaces are terminated by Sb layers. These reconstructions could all be obtained with sharp and streaky RHEED patterns in the Warwick MBE system and examples of the Sb-rich RHEED patterns are shown in the upper panels of figures 1–3.

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Table 1. Reconstructions and reported models for InSb and GaAs surfaces. The ideal elemental content is given in ML for the top layer(s) of the reconstruction.

	Surface	Reconstruction	Group III content (ML)	Group V content (ML)	Reference
InSb	(0 0 1)	c(8 × 2)	0.84 In	—	[45]
		a(1 × 3)	—	1.66 Sb	[57]
		c(4 × 4)	—	1.75 Sb	[58]
	(1 1 1)A	(2 × 2)	0.75 In	—	[59]
		$({2}{\sqrt{3}}{\times}{2}{\sqrt{3}})$R30°	0.50 In	0.25 Sb	[60]
	(1 1 1)B	(3 × 3)	0.44 In	0.22 Sb	[61]
		(2 × 2)	—	1.75 Sb	[59]
GaAs	(0 0 1)	(4 × 6)	1.00 Ga	0.08 As	[40]
		β2(2 × 4)	—	0.75 As	[43]
		c(4 × 4)	—	1.75 As	[39]

For all In-rich surfaces studied, deposition of Mn up to 1 ML coverage had no effect on the RHEED pattern, beyond slight degradation in the streak sharpness consistent with surface roughening, and sometimes very weak transmission diffraction features. In contrast, the Sb-rich surfaces were seen by RHEED to go through reconstruction changes at well defined and reproducible Mn coverages (θ_Mn, in ML).

The RHEED patterns observed during Mn deposition on Sb-rich (0 0 1), (1 1 1)A and (1 1 1)B InSb surfaces are shown in figures 1–3 respectively. The (0 0 1) samples demonstrated two reconstruction changes. In the first, at low Mn coverage (θ_Mn = 0.10 ML), the Sb rich (4 × 4) changed to a fainter a(1 × 3). This reconstruction persisted during subsequent Mn deposition up to θ_Mn = 0.35 ML, where it transformed into a slightly spotty c(8 × 2). On the (1 1 1)A substrate the Sb-rich $(2\sqrt{{3}}\times2\sqrt{{3}})$R30° surface changed to a sharp (2 × 2) reconstruction at a Mn coverage of θ_Mn = 0.05. The InSb(1 1 1)B surface changed from the Sb-rich (2 × 2) to a (3 × 3) surface reconstruction at θ_Mn = 0.10 ML. The transitions were all simultaneous with deposition, and not seen to change in the pauses between 'burst' doses of Mn. A brief period of mixed domains of the initial and subsequent reconstructions was observed close to the transition.

The relationship between the change of Sb content in the reconstruction Δ_Sb and the Mn coverage, θ_Mn, is shown in figure 4 for the three InSb surfaces. The Δ_Sb values are taken from table 2, based on the layer-by-layer atomic contents in table 1. These values are not precisely defined since real surface reconstructions are not perfectly stoichiometric, e.g. the c(4 × 4) can accommodate top layer heterodimers, reducing its Sb content and increasing its In content [39]. Despite this, and the experimental uncertainty in the Mn coverage, there is a clear linear relationship between Δ_Sb and θ_Mn. Furthermore, there is no indication of any surface reconstruction not characteristic of clean InSb, and all the transitions occur in the direction Sb-rich to In-rich.

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Table 2. Details of the transitions observed on the Sb terminated surfaces of InSb. Δ_Sb is defined as the Sb content in the reconstruction layers of the Sb rich reconstruction and the resulting reconstruction, whilst Δ_In is the corresponding change of In content in the reconstruction layers. The transitions correspond to the labels shown in figure 4.

Transition	Surface	Transition	ΔSb	ΔIn
A	InSb(0 0 1)	c(4 × 4) → a(1 × 3)	−0.09 ML	−0.16 ML
B	InSb(1 1 1)A	$(2{\sqrt{3}}\times2{\sqrt{3}})$R30° → (2 × 2)	−0.25 ML	+0.25 ML
C	InSb(1 1 1)B	(2 × 2) → (3 × 3)	−0.53 ML	+0.44 ML
D	InSb(0 0 1)	c(4 × 4) → c(8 × 2)	−1.75 ML	0 ML

Figure 5 shows the surface morphology of the Sb-rich c(4 × 4) and the In-rich c(8 × 2) surfaces using in-situ STM and ex-situ AFM. The STM images clearly show ML-height terraces and steps. While the c(4 × 4) has typically meandering terraces (figure 5(a)), c(8 × 2) surfaces have squarer terraces, higher step density and higher anisotropy (figure 5(b)). The surface morphology of the c(4 × 4) surface after 0.4 ML Mn deposition is shown in figure 5(c) and strongly resembles that of the clean c(8 × 2) surface, in agreement with the observed c(8 × 2) RHEED pattern. Typical AFM images for 1.00 ML of Mn on the c(4 × 4) and c(8 × 2) InSb(0 0 1) surfaces are shown in figures 5(d) and (e) respectively, together with height profiles across typical islands. Irregularly shaped islands with heights of approximately 30 nm and basal diameters ranging from 150 nm to 300 nm are found for Mn deposition on to the Sb-rich c(4 × 4), together with a much higher density of small 3D islands with heights (2–5) nm. In contrast to this bimodal island size distribution, Mn deposition on to the In-rich c(8 × 2) produces a lower density of quite uniformly sized islands, with heights around 50 nm and base diameters of 200 nm. It is straightforward to integrate the total volume in the island arrays and convert to ML equivalents. This yields island volume densities (total volume per unit area) of (1.92 ± 0.18) ML for the c(4 × 4) surface and (1.10 ± 0.06) ML for the c(8 × 2) surface respectively.

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The GaAs(0 0 1) surface has been studied with three different starting reconstructions: (4 × 6), β2(2 × 4) and c(4 × 4). From table 1 it can be seen that, analogously to InSb, distinct Ga- and As-rich reconstructions can be obtained by direct substrate surface cleaning or epitaxial growth. The broadly Ga-rich (4 × 6) reconstruction occurs following ion sputtering and UHV annealing without As flux (Warwick MBE), and is thought to have a complex sub-surface structure with surface heterodimers [40]. The As-rich surfaces are obtained through growth under As rich conditions and/or annealing under As flux (Sheffield MBE). The β2(2 × 4) reconstruction is the normal reconstruction during MBE growth, while the c(4 × 4) is an As-rich surface similar to that found on InSb(0 0 1) which may be present during low temperature MBE growth of Ga_1−xMn_xAs DMS materials.

The evolution of the RHEED patterns (not shown) for Mn deposition on the As-rich (2 × 4) and c(4 × 4) surfaces was more complicated than that seen on InSb surfaces. Unlike InSb, no simple trend from V-rich to III-rich reconstruction was observed with increased Mn deposition. On c(4 × 4), the fractional order streaks faded during Mn deposition leaving a (1 × 1) pattern, while on (2 × 4) starting surfaces a similar loss of fractional order streaks was observed along with increasing spotty transmission diffraction features. In both cases, half-order streaks were most persistent. On the Ga-rich (0 0 1)-(4 × 6) surface, the RHEED evolution was clearer (figure 6). The (4 × 6) periodicity clearly changes at θ_Mn = 0.23 ML to (2 × 2), although hints of coexisting (4 × 6) remain. The transition is complete by θ_Mn = 0.30 ML, at which the (2 × 2) pattern is sharpest. At larger Mn coverages the pattern begins to degrade and incommensurate transmission features are subsequently observed. As with the InSb surfaces, these transitions were simultaneous with deposition and persist between doses, i.e. the time dependence is weak.

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AFM images of the surface morphology for the GaAs(0 0 1)-(4 × 6) surface after Mn deposition (θ_Mn = 1.25 ML) are shown in figure 7. At larger scan sizes (figure 7(a), 5 µm × 5 µm), the surface appears rather flat, with a low density of 3D islands present on the surface. At higher magnification (figures 7(b) and (c)) the presence of smaller 3D islands at high density is revealed. The islands are approximately 2 nm in height and 25 nm in base diameter. The volume density of material in these nano-islands is (0.82 ± 0.16) ML, although the volume integration for this surface is hampered because thresholding to obtain the background height of the substrate is more difficult.

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The As-rich (2 × 4) and c(4 × 4) surfaces were studied using STM and the images obtained for them are shown in figures 8 and 9, respectively. Figure 8(a) shows the clean (2 × 4) surface, with As dimer rows orientated along the [1  $\overline{1}$ 0] direction visible. Following deposition of 0.8 ML of Mn, figure 8(b), the original (2 × 4) structure has been disrupted and a co-existing (2 × n) structure develops. Some small islands are also visible on the surface. With increasing θ_Mn (1.2 ML, figure 8(c)), the ordering of the (2 × n) improves and rod-like features form on the surface. The orientation of the rods is perpendicular to the As dimer row direction on the (2 × 4) surface. On this basis, and noting that Group III-rich domains of similar appearance in STM have been observed during InAs-GaAs growth in As-deficient conditions [41], these rods are attributed to Ga-rich reconstruction domains. However, we cannot rule out the formation of an alternative Mn-induced reconstruction. Finally, at high coverages of Mn (1.8 ML in figure 8(d) and 2.4 ML in figure 8(e)) the density and size of the islands increases. The number of Ga-rich domains also increases with periodicities ranging from (2×) to (6×) while the observed heights range from 0.2 nm to 0.6 nm. The height of the 3D islands is approximately 2 nm at θ_Mn = 2.4 ML and they exhibit lateral extensions of greater than 40 nm. The formation of irregularly shaped islands and the presence of Ga-rich surface reconstructions indicates that As removal is taking place, analogously to Sb removal on InSb.

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The c(4 × 4) surface follows the same general trends as those seen on the (2 × 4). STM of the clean surface is shown in figure 9(a), with the characteristic brickwork pattern of surface dimers clearly visible (an expanded view with atomic positions overlain is inset). The asymmetric nature of the dimers and the preparation conditions used suggest that this is the α variant of the c(4 × 4) surface and so consists of heterodimers [42]. At θ_Mn = 0.8 ML, figure 9(b), the (2 × n) periodicity appears, although it is more disordered than for the equivalent Mn coverage on the (2 × 4) surface. At θ_Mn = 1.2 ML, figure 9(c), the surface island density has increased in addition to a greater number of rods visible on the surface. Finally, at θ_Mn = 1.8 ML (figure 9(d)), the surface has degraded substantially and features a large number of irregularly shaped islands. The size of the islands ranges between 1.5 and 2 nm at θ_Mn = 0.8 ML, to between 2.5 and 4 nm at θ_Mn = 1.2 ML. The behaviour of the islands and rod features on this surface is identical to those on the (2 × 4) surface, although a greater level of disruption is observed due to the higher As content of this surface.

One clear difference in morphology persists between the initial (2 × 4) or c(4 × 4) surfaces. Starting with the c(4 × 4), the surface morphology beneath the islands and rods is a rather isotropic patchwork of few-nm-sized islands by around 1 ML Mn coverage (figure 9(c)). Conversely, the (2 × 4) starting surface leads to a distinct pattern of meandering dark trenches elongated along the [1  $\overline{1}$ 0] direction (figure 8(d)). The average spacing along [1 1 0] between these trenches is about 3 nm (roughly an 8× spacing), indicating that about half the original (2 × 4) trenches have been preserved in some sense (originally the trenches comprised two absent As dimers and a pair of absent second layer Ga atoms [43]). One implication is that the Mn-induced surface structures can either fill the trench or leave it at least partly unfilled. Finally, it appears that the corrugation of the top layer of the more Mn-rich surfaces (beneath the Ga-stable domains) becomes lower, and is less than that of the starting (2 × 4) dimer-pair rows (figures 8(b) and (c)). This suggests less well defined covalent bonds and a more metallic character to the surface.

All the reconstruction periodicities induced by Mn on InSb are characteristic of clean InSb and the observed transitions are all consistent with a reduction in Sb content in the surface layers. It is exceedingly unlikely that a sequence of reconstruction periodicities matching those of clean InSb would occur as a result of Mn surface alloy formation on all three faces studied. Therefore, the simplest explanation is that the main action of the Mn on the Sb-rich surfaces is removal of Sb from the reconstruction, in the process forming a new surface with a lower Sb content. The first transition on InSb(0 0 1) is from the c(4 × 4) structure to the a(1 × 3), a reconstruction associated with the c(4 × 4) but with a slight reduction in surface Sb, resulting in disordered top layer Sb dimers [44]. The second transition is to the c(8 × 2) surface, which is the In rich reconstruction and is terminated by 0.84 ML of In [45]. The process appears to be quite generic since similar transitions occur on the (1 1 1)A and (1 1 1)B surfaces. Indeed, the linear relationship between Δ_Sb and θ_Mn (figure 4) suggests that the efficiency of Mn-induced Sb removal is similar on the three low index faces studied. The gradient of the line is 0.16, suggesting that one Mn adatom removes around 6 Sb atoms from the reconstructions at the substrate temperature of 280 °C. It is plausible that some Sb will desorb into UHV during the Mn deposition process but Mn atoms cannot desorb at such low substrate temperatures. Since the underlying reconstructions after Mn deposition are characteristic of clean In-rich InSb, we conclude that Mn is not incorporated into a two-dimensional (2D) surface reconstruction, and instead it forms 3D islands, as confirmed by AFM (figure 5). The post-Mn deposition RHEED patterns (figures 1–3) show faint transmission features on the InSb integer streaks, which is consistent with transmission diffraction through small 3D surface features. The volume density in the islands is significantly greater for the c(4 × 4) surface [(1.92 ± 0.18) ML] compared to the c(8 × 2) surface [(1.10 ± 0.06) ML], at 1 ML Mn coverage. This suggests that the 3D islands are nearly pure Mn for deposition on the c(8 × 2) surface, but during growth and Sb removal on the c(4 × 4) surface, Sb is incorporated into the 3D islands to give a composition close to stoichiometric MnSb. During MnAs growth on GaAs(0 0 1), Braun et al found RHEED evidence (powder-like diffraction rings) for randomly oriented clusters with MnAs-like bond length during nucleation at sub-ML coverage [22]. Since the film becomes epitaxial, these clusters must be mobile. It is plausible that similar mobile clusters develop during Mn deposition on Sb(As)-rich surfaces without Sb(As) incident flux, such that MnSb(As) nano-clusters can form and reconstruction domain changes can be mediated.

Models based on standard thermodynamic quantities have been successful in predicting interface reactivity and phase equilibria for various metal-semiconductor systems [46–48]. Some simple thermodynamic considerations can illuminate basic differences between Mn behaviour on Group III and Group V rich surfaces, especially for InSb where the difference is stark. The enthalpies of formation for relevant binary compounds are shown in table 3. The reaction enthalpy for conversion from an Sb terminated surface to an In terminated surface, $\it{\Delta}{H}_{R}^{\rm ({Sb}\rightarrow{In})}$, can be expressed as:

$$\begin{eqnarray} \it{\Delta}{{{H}_{R}}^{\rm ({Sb}{\rightarrow}{In})}} &=& \it{\Delta}{{H}_{f}} {\rm (MnSb)} + \it{\Delta}{H}_{f}{\rm (In)} - \it{\Delta}{{H}_{f}}{\rm (InSb)} \nonumber\\ &&\! - \it{\Delta}{{H}_{f}} {\rm (Mn)} + \it{\Delta}H_{\rm SR}. {} \end{eqnarray} \tag{ 1 }$$

Here ΔH_SR is the energy difference between the In terminated and the Sb terminated crystal. Such surface reconstruction energies can be calculated from density functional theory (DFT), incorporating the allowed range of chemical potentials for one of the species of a binary material. Such DFT calculations have been performed over many years for a wide range of III-V materials (e.g. [49]). Typically, surface energy differences between reconstructions are up to 10 meV Å⁻², or approximately (5–10) kJ mol⁻¹. The ΔH_SR term tends to drive III-V surfaces annealed in UHV towards Group III termination due to the higher volatility of the Group V component, i.e. we would expect a negative value for the Sb-to-In (or As-to-Ga) reaction.

Equation (2) shows $\it{\Delta}{H}_{R}^{\rm ({In}\rightarrow{Sb})}$ for the formation of an Sb terminated surface from an In terminated surface:

$$\begin{eqnarray} \fl \it{\Delta}{{{H}_{R}}^{\rm ({In}{\rightarrow}{Sb})}} &=& \it{\Delta}{{H}_{f}} {\rm (MnIn)} + \it{\Delta}{H}_{f}{\rm (Sb)} - \it{\Delta}{{H}_{f}}{\rm (InSb)} \nonumber\\ &&\! - \it{\Delta}{{H}_{f}}{\rm (Mn)} - \it{\Delta}H_{\rm SR}. {} \end{eqnarray} \tag{ 2 }$$

Using the enthalpy values given in table 3, $\it{\Delta}{H}_{R}^{\rm ({Sb}\rightarrow{In})}\,{=}-14.5\,{\rm kJ}\,{\rm mol}^{-1}$ and $\it{\Delta}{H}_{R}^{\rm ({In}\rightarrow{Sb})}\,{=}\,{+}29.5\,{\rm kJ}\,{\rm mol}^{-1}$. The reaction of Mn with an Sb terminated surface is exothermic and can occur spontaneously, while the reaction of Mn with an In terminated surface will not occur for any reasonable value of ΔH_SR. This is consistent with the observed formation of hexagonal MnSb nano-particles in dilute In_1−xMn_xSb thin films without post-growth annealing [50, 51]. Note that the opposite process has been reported for Au deposited on to the InSb(0 0 1) surface, in which the In termination is changed to the Sb termination surface by addition of Au [52]. This difference in behaviour is also explained by equation (2) due to the higher stability of AuIn compared to AuSb (table 3).

The simple picture of the Sb-terminated surface being reactive with incoming Mn while the In-terminated surface is rather inert can also explain the difference in 3D island morphology for Mn-InSb (figure 5). The nearest-neighbour distance is larger on the starting c(8 × 2) surface as Mn adatoms are free to migrate a long distance to find a 3D island. On c(4 × 4), it is plausible that the bimodal size distribution arises due to an initially short migration length of Mn adatoms and/or or MnSb clusters on the Sb-rich surface (producing a large density of small, more Sb-rich islands) which increases as more Sb is stripped from the surface (allowing larger, more Mn-rich islands to form with longer nearest-neighbour distances).

The observed behaviour on GaAs is more complex due to the combination of As removal (island formation) and Mn incorporation (new surface periodicity). If one neglects Mn incorporation, the resulting enthalpy changes would be $\it{\Delta}{H}_{R}^{\rm ({As}\rightarrow{Ga})}\,{=}\,-4.0\,{\rm kJ}\,{\rm mol}^{-1}$ and $\it{\Delta}{H}_{R}^{\rm ({Ga}\rightarrow{As})}\,{=}+47.0\,{\rm kJ}\,{\rm mol}^{-1}$. Therefore, the formation of MnAs on an As-rich GaAs surface is marginally favourable but the absolute value of the enthalpy change is well within the likely range of variation of ΔH_SR. Conversely, Mn will not react with a Ga-rich surface to form MnGa, although Mn₂As and MnGa are known to form by annealing thick films of Mn in contact with GaAs [53]. Of course, the incorporation of Mn into new (2 × 2) reconstruction domains cannot be described in a simple binary alloy model and so we now discuss reconstruction formation on GaAs and InSb.

Various adsorption sites can be considered for Mn at III-V surfaces [30, 31, 38]. Perhaps the most crucial distinction is between interstitial and substitutional sites, since substitutional sites should favour Mn incorporation for the growth of DMS thin films. Ohtake, Hagiwara and Nakamura [31] studied the influence of initial surface reconstruction on Mn incorporation into GaAs and found that substitutional sites are favoured in group V-rich conditions since the surface stress from As dimers in the c(4 × 4) reconstruction can be partly compensated by bulk bond length strain of around 5% due to substitutional Mn. This contrasts with the less group V-rich (2 × 4) surface, on which interstitial Mn is preferred leading to a (2 × 2) reconstruction [31]. The local strain due to the incorporation of Mn on to a substitutional site is related to the preferred bond lengths of cubic (zincblende B3 structure) MnSb or MnAs, compared to the host semiconductor. Experimental as well as DFT-derived values for the lattice parameter of cubic MnSb are available [5], giving a bond length of 2.815 Å. This is much closer to the bond length of InSb (2.806 Å) than is the case for Mn in GaAs, resulting in a bond length mismatch of only 0.3% (InSb) compared to 4.7% (GaAs) [31]. Since the surface stress due to Sb dimers in InSb(0 0 1)-c(4 × 4) is also small [54] reconstruction-dependent tendencies for Mn to adopt either substitutional or interstitial sites are weak. Rather, the thermodynamic driving force towards MnSb formation dominates, as borne out by the repeatable behaviour found here on (0 0 1), (1 1 1)A and (1 1 1)B reconstructed surfaces.

Concentrating on GaAs(0 0 1), where the surface reconstruction does play a strong role, we note that Mn-induced (2 × n) reconstructions have been observed by several groups (n = 1 or 2). It has been suggested that the fundamental unit is (2 × 2) and that one-dimensional disorder in the [1 1 0] direction leads to the observation of (2 × 1) diffraction patterns [30]. Our results (figure 8) are consistent with this idea. The Mn-induced (2 × 2) reconstruction on an initially (4 × 6)-reconstructed surface has not previously been reported, and our results in concert with previous studies suggest that this (2 × 2) periodicity is quite ubiquitous on GaAs(0 0 1) under a wide range of deposition conditions and initial surface reconstructions. However, it appears that the initially (4 × 6)-reconstructed surface, in the absence of As flux, cannot accommodate more than about 0.5 ML Mn in the (2 × 2) phase, since 3D nano-islands begin to appear for coverages above about 0.4 ML (figure 7). The volume density of these islands is consistent with their composition being Mn, not MnAs. The structural motifs considered in previous work for Mn-induced reconstructions on GaAs(0 0 1) have principally involved As-terminated structures but Yang et al [38] report higher total energies (less stable) for the Ga-rich γ₁₄₀ and β₄₀₋₁ structures shown in their paper. For As-free Mn deposition on a Ga-rich GaAs substrate, either no alloyed reconstructions above about 0.5 ML Mn are sufficiently stable or the formation of stable reconstructions with high Mn content is kinetically hindered, hence Mn nanocluster formation occurs.

In the following discussion we focus on behaviour of the (2 × 4) and c(4 × 4) under Mn deposition. The GECR [38] has been proposed as a heuristic for narrowing the range of possible reconstructions in metal/III-V systems. Consideration of the relevant Pauling electronegativities suggests that Mn will act as a donor on both GaAs and InSb. The surface then reconstructs according to standard ECR principles with interstitial Mn providing two valence electrons to the structure without forming covalent bonds. Conversely, substitutional Mn is assumed to form tetrahedral covalent bonds but to still only contribute two electrons. As mentioned above, interstitial versus substitutional incorporation can depend on the initial surface reconstruction [31]. Substitutional Mn on Ga sites results in a deficit of 1 electron per Mn, while interstitial Mn adds 2 electrons per Mn. Compliance with GECR does not guarantee stability, which may be compromised by local strain, for example. Some extra considerations must be borne in mind. Strict GECR-compliance will likely become less important as the Mn content of the surface layer increases beyond 1 ML where MnAs-like metallic structures arise. Indeed, the c(4 × 4)-Mn surface identified in [31] is not GECR-compliant, and Yang et al calculated non-GECR-compliant (2 × 2) structures at 0.75 ML and 1 ML Mn coverages [38]. This is consistent with the reduced atomic corrugation observed in STM at higher Mn coverages. Additionally, the formation of new structures clearly may be kinetically limited as observed by Colonna et al [30]. In the absence of incident As or Sb flux in our experiments, and given strong evidence for As removal by incident Mn, the formation of new As-rich reconstructions is likely to be hindered. However, structural rearrangements may be mediated both by mobile MnAs clusters (for which diffraction evidence was found by Braun et al [22]) and by mobile Ga atoms liberated by erosion of the As-rich reconstructions [55].

For the c(4 × 4) starting surface, Mn can adopt third layer Ga substitutional sites [31]. However, in the absence of incoming As flux this appears to disrupt the As-on-As dimer structure of the initial reconstruction and by 0.8 ML coverage the c(4 × 4) has been replaced by a (2 × n) (figure 9(b)). The formation of large islands and Ga-rich reconstruction domains confirms that atoms are displaced from within the reconstructed surface. It is worth noting that the c(4 × 4)-(2 × 4) transition on GaAs(0 0 1) can be triggered by deposition of Ga at fixed temperature in static conditions, and that mobile Ga atoms are required to effect the transition under As flux [55, 56]. Clearly, migrating Mn atoms are able to break up the As-on-As dimer structure in a similar way. The degree of disorder on this surface makes it difficult to speculate further about the incorporation pathways of the Mn. Nonetheless the results highlight the significant structural rearrangement induced by incident Mn in the absence of coincident As.

For the β2(2 × 4) surface the initial absence of As-on-As dimers suggests that interstitial Mn will be favoured [31]. Direct formation of both Ga-As heterodimers on an As atomic plane [31] and As dimers on As atomic plane [30] is likely suppressed by the lack of incident As flux in our experiment. This is supported by the observation of residual β2(2 × 4) domains co-existing with the same atomic plane terminating most structures (figure 8(b)). Hence the low coverage (0.25 ML Mn) dimer-on-As (2 × 2) reconstructions [31, 38] may not occur under the present conditions. Figure 10 shows plausible pathways to increasing Mn incorporation in an initially β2(2 × 4) GaAs surface which evolves towards a nominal (2 × 8) periodicity consistent with the observed (albeit highly disordered) structures. The (2 × 8) unit meshes shown are divided up into left (L) and right (R) (2 × 4) sub-units, with trench-filling occurring in the L sub-unit and a trench structure preserved in the R sub-unit. All the structures shown are compliant with GECR. For example, in structure (e), there are 28 As atoms (140 electrons), 14 Ga atoms (42 electrons) and 5 interstitial Mn atoms (10 electrons) giving a total of 192 electrons to distribute. Counting the different types of bonds, we have 44 Ga-to-As covalent bonds (taking 88 electrons), 10 As-to-As covalent bonds (20 electrons), 24 As dangling bonds (48 electrons), 24 As back-bonds (30 electrons) and 8 Ga back-bonds (6 electrons). Ga dangling bonds remain empty, hence the total number of electrons required is 192, providing charge neutrality.

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Initially, Mn can break As dimers in the top layer (a) or in the trench (b). Strain is induced by Mn in these planar interstitial sites [31, 38] so it is possible that local regions with high Mn density such as (c) with ${\sim}\frac{3}{8}\,{\rm ML}$ are destabilised. This induces the Mn atoms and As dimers to become a mobile MnAs-like cluster [22] and leads to the As removal observed here. The Ga-terminated structures remaining are not stable under GECR and form a source of free Ga atoms which can fill trenches in the β2(2 × 4). This allows the substantial structural rearrangement needed to form new structures with longer period along [1  $\overline{1}$ 0], observed in figures 8(b)–(d), along with Ga-rich reconstruction domains and larger 3D clusters. Such large-scale migration at these temperatures is consistent with the behaviour of GaAs during the (2 × 4)–c(4 × 4) reconstruction transition [55, 56]. It is very difficult to speculate about transient structures present during the local destabilization of the starting reconstructions and so we present the Mn-induced strain argument as a plausible mechanism which could be tested further by detailed DFT calculations. Such calculations have favoured planar interstitial Mn incorporation in the growing Mn-induced reconstructions in the absence of As-on-As dimers [31] and hence we use only this motif in figure 10, which does not attempt to explain the destabilization but rather the development of Mn-induced (2 × n) structures. The structures illustrated in figures 10(d)–(g) correspond to local Mn coverages from $\frac{5}{16}\,{\rm ML}{\hbox{--}}\frac{9}{16}\,{\rm ML}$. The left sub-unit labelled L undergoes trench-filling while the right sub-unit R maintains a trench-like structure. Filling could proceed by first the bonding of Ga in the empty trench sites [(d) L] using Ga liberated from erosion of destabilised dimer rows on which As-on-As 'split dimer structures' are formed [(d) R] akin to the γ₂₀₂ structures of Yang et al [38]. Arsenic dimer adsorption on the filled trench can occur at the same Mn coverage [(e) L]. At higher local Mn coverage a continuous row of mixed As dimers and split dimers can form with a missing-Ga trench remaining ((f) and (g)). These illustrative structures are all GECR-compliant. Above $\frac{9}{16}\,{\rm ML}$ the metallicity of the surface is likely to render strict charge neutrality less important. The wide range of structural motifs involved in these long-period structures clearly allows for the observed deviations from ideal (2 × 8) periodicity and meandering of the residual trench structure.