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Mapping the wavefunction of transition metal acceptor states in the GaAs surface

We utilize a single atom substitution technique with spectroscopic imaging in a scanning tunneling microscope (STM) to visualize the anisotropic spatial structure of magnetic and non-magnetic transition metal acceptor states in the GaAs (110) surface. The character of the defect states play a critical role in the properties of the semiconductor, the localization of the states influencing such things as the onset of the metal-insulator transition, and in dilute magnetic semiconductors the mechanism and strength of magnetic interactions that lead to the emergence of ferromagnetism. We study these states in the GaAs surface finding remarkable similarities between the shape of the acceptor state wavefunction for Mn, Fe, Co and Zn dopants, which is determined by the GaAs host and is generally reproduced by tight binding calculations of Mn in bulk GaAs [Tang, J.M.&Flatte, M.E., Phys. Rev. Lett. 92, 047201 (2004)]. The similarities originate from the antibonding nature of the acceptor states that arise from the hybridization of the impurity d-levels with the host. A second deeper in-gap state is also observed for Fe and Co that can be explained by the symmetry breaking of the surface.


I. Introduction
A dilute magnetic semiconductor (DMS) is a semiconductor doped with a random distribution of magnetic, usually transition metal, atoms whose local moments can couple, giving rise to a collective ferromagnetic state. 1 In the prototypical DMS, Ga 1-x Mn x As, Mn dopants are acceptors providing holes that are believed to be responsible for mediating the ferromagnetic interaction between Mn 3d 5 core spins. The nature of the interaction between the hole and the core spin is then a central question whose answer hinges on the character of the hole state. Transition metals substitute the trivalent cation in III-V materials. In GaAs, Zn forms a shallow acceptor whose valence band-like hole state is well described by effective mass theory. Fe and Co are deep acceptors that are expected to have a localized state that is largely determined by their atomic central cell potential. Mn sits between these cases as a fairly deep acceptor that binds a hole in an Mn 2+ 3d 5 +hole configuration. 2 In this sense it is like Zn, but its binding energy is larger because there is hybridization between the d levels and the host which, importantly, provides a means of coupling to the spin of the core state. The strength and influence of this hybridization on the nature of the hole state has been a source of debate. In the effective mass limit, when the doping crosses the metal-insulator transition, the holes reside in the valence band and their interaction mediating ferromagnetism between Mn sites can be understood within the RKKY model. 3,4 Others have questioned this, finding the hybridization to be large enough to give the hole significant impurity-like d character and the magnetic order to arise from exchange interactions between localized Mn impurity states 5, 6 . The two limits will in general predict different anisotropies in both the defect state wavefunctions and the magnetic interaction and it will be necessary to understand these to both to raise T c and to effectively make devices that utilize these materials. 7 Thus the question of the nature and character of the acceptor states in III-V materials is an important one and one that can be probed by comparing the acceptor states of various substitutional transition metal impurities. To do this we have used a scanning tunneling microscope (STM) and an atomic scale manipulation technique to substitute transition metal atoms into a GaAs host.

II. Experiment
The DMSs are complex materials to study experimentally due to a number of factors such as the high doping concentrations, compensating defects due to non-equilibrium growth conditions, and disorder. This challenges the ability of macroscopic scale measurements that average over large areas to provide insights into the microscopic scale interactions that give rise to ferromagnetic order.
Alternatively, microscopic visualization of Mn in the surface of GaAs has been used to probe ferromagnetic interactions in these materials. 8 Using an STM, various species of isolated acceptor defects can be created and probed in an identical layer, allowing spectroscopic resonances, unambiguously associated with the defect wavefunctions, to be directly compared.
The experiments were performed using a home-built cryogenic STM that operates near 4 K in ultra- direction, while Co atoms move oppositely. Using higher current and voltages, the transition metal atoms could be made to substitute into Ga sites in the first layer of the (110) surface, ejecting the Ga atom to the surface. The energetics of the substitution process varied between species but were generally similar. Using a setup condition of 200pA at -1.5V, the tunnel current would drop to zero as the bias voltage was swept through the gap, begin to rise sharply near +1V and then drop suddenly a few hundred mV later when the substitution occurred, providing a rough qualitative measure of the activation barrier required to be overcome to occupy the cation site. Only Co could be induced to swap with a Ga adatom and return to the Co adatom configuration again, as shown in Fig. 1. After substitution, the displaced Ga atom often remained loosely bound to the newly created defect site, proving more difficult to remove for Co than for Fe or Mn. The substitution process is likely similar to the ejection of cation atoms to the surface that can occur during the initial growth of transition metal overlayers on III-V surfaces at room temperature, suggesting this technique may work on a variety of substrates. 13,14 Recent work on the deposition of Fe films on GaAs that found that the intermixing of species and formation of compounds at the interface can be significantly reduced by low temperature deposition 15,16 is potentially consistent with our observation that the adatoms at low temperature sit on the surface as adatoms and do not substitute with atoms of the substrate until we manipulate them.
Topography of Mn, Zn, Co, and Fe in the surface layer are displayed in Fig. 2. The topography maps the acceptor states by applying the bias voltage near the conduction band edge so that the image is the sum of all states in the gap above the Fermi energy. An anisotropic star-shaped structure is apparent for each with C s symmetry similar to that observed for subsurface acceptors in GaAs. [17][18][19] The wavefunction of Mn in bulk GaAs predicted by tight-binding calculations viewed in the plane of the Mn site resembles our data well. 8,20 It is known that the depth of the dopant beneath the surface affects the symmetry of the acceptor wavefunction observed by STM, with Mn going from C 2v to C s symmetry the nearer to the surface it is, possibly as a result of surface related strain. 21 The wavefunctions in Fig. 2 can be viewed as the extreme limit of that trend. Recent tight-binding work that attempted to take the surface into account is consistent with this trend but doesn't include the case of Mn at the surface. 22 The  Fig. 3(b) and Fig. 3(c). Spatial maps of the energy-resolved density of states in Fig. 4 show that the shape of the lower energy state is similar to that of Mn. The higher energy state is responsible for the greatly enhanced arm-like features. The low contrast at the location of the dopant in the maps of the higher energy states in Fig. 4 is somewhat exaggerated due to the lower energy state causing the STM tip to move out, decreasing the sensitivity. Nevertheless, the maps clearly show that spatial dependence is quite different for the two states.
The filled state topography of the defects (insets Fig. 2) shows an enhancement on the two in-row

III. Discussion
While the similarity of the ground state of all four species of acceptor may at first be surprising, it follows from the well known effect of symmetry on the hybridization of a substitutional impurity with the host. The defect states can be seen as arising from the interaction of the atomic states of the isolated impurity with the dangling bond states of an ideal vacancy in the lattice (Fig. 6). Clearly, if the vacancy is filled with the host atom the hybridization forms a bonding state in the valence band and an antibonding one in the conduction band. It is the difference in the hybridization that occurs with an impurity that gives rise to the defect states. 31 The case of Zn is the easiest to understand: the Zn d levels are deeply bound below the valence band edge and non-interacting and the Zn valence orbitals are comparable to but higher than those of Ga. This gives rise to a state with primarily host-like bonding character that isn't pushed all the way down into the valence band and an antibonding state with impurity character above the conduction band edge.
As shown in Fig. 6, the case when the d levels are interacting is more involved and is well summarized by Mahadevan and Zunger. 5 The s and p levels that make up the sp 3  This is the origin of the Mn 2+ 3d 5 + hole configuration, the hole is host-like and, though antibonding instead of bonding, it shares the same t 2 (p-like) symmetry as the valence band. The core spin in preserved in the deep impurity-like e and bonding t 2 states that fill in a high spin configuration according to Hund's rules.
With this in mind, a few conclusions can be draw. First, the anisotropy of the ground state for all four acceptors is similar, implying they are all states of the same (t 2 ) symmetry. It should be noted that the character of acceptor state will depend sensitively on the order of levels in energy and be determined by the lowest unoccupied state. The similarity between them is most simply explained if the bonding d levels fill according to their atomic configuration. Second, the spatial extent of the Mn, Fe and Co ground state is the same and that of Zn is smaller. This is a result of the antibonding nature of the Mn, Fe and Co states causing the wavefunction to be more delocalized onto the As dangling bonds than the bonding nature of the Zn state. This result is somewhat counterintuitive, because as the shallowest acceptor the Zn wavefunction is expected to be the most delocalized. It arises from the fact that STM doesn't sample the wavefunction within the material but rather the part that is exponentially decaying into the vacuum at the location of the tip. Since the acceptors at the surface have no layers above them for the wavefunction to spread out in, instead the STM only images the core of the wavefunction at the impurity site. Third, a partially filled triply degenerate t 2 level could be expected to be susceptible to Jahn-Teller distortions as are observed for some configuration terms of Fe and Co in III-V materials, potentially explaining Fig. 5. 32,33 In our analysis thus far, however, we have ignored the effect of the surface and surface reconstruction which lowers the symmetry from T d all the way to C s ((1⥘0) mirror plane). This will split the t 2 states into functions of parity, creating two a' (even) levels and one a'' (odd) level (Fig. 6). While it is hard to estimate the resulting energies of these levels, ab-initio calculations of the unrelaxed surface Ga vacancy in GaP found the t 2 level to split into one a' level in the valence band and the remaining a' and a'' levels to be nearly degenerate above the valence band maximum. 34 This implies the possibility of two states in the gap, one having even symmetry and other odd. The comparison to the spatial structure of the two states of Fe and Co is immediately obvious: the lower energy state being symmetric with respect to the (1⥘0) plane and the higher energy state being consistent with the wavefunction squared of an odd state with respect to the mirror plane. For the higher state, it is unlikely that the doubly ionized state is being observed, but rather that the electron is tunneling into an unoccupied excited state. In Fig. 6(c) one possible level order that allows for two unoccupied states of different symmetry is shown.
Finally, we attempt to address the energies of the states. The order of the acceptors in bulk is Zn (31 meV), Mn (113 meV), Co (160 meV) and Fe(~0.5 eV). 35 At the surface we observe the same trend with the exception that the ground state of Fe is below Co. The shift to higher energy is likely due both to tip induced band-bending and the energy of the acceptor states being affected by being at the surface. If the Ga vacancy dangling bond levels are higher at the surface than in bulk this would lead directly to a deeper acceptor state. It is worth noting also that charge transfer from cation to anion sites due to the surface reconstruction is known to increase the binding energy of the surface Ga 3d levels by ~0.3 eV. 36,37 If this applies to the transition metal impurities, it would be expected to push the d-states deeper into the valence band lessening the p-d hybridization, and pinning the acceptor energies closer to the Ga vacancy dangling bond energy, resulting in the confluence of similar energies for the first states of Mn, Fe and Co. The energy splitting of the states may also be correlated with the amount of lattice distortion observed for each impurity, with Co having no observable distortion and the smallest energy splitting and Fe having more distortion and splitting. As Mn had the most distortion, the upper energy level would be pushed into the valence band. This would explain the lack of an observation of a second level for Mn which would be expected from the preceding analysis of the origin of the acceptor states.

IV. Conclusion
We have demonstrated an atomic scale technique to study single transition metal impurities in the surface of a III-V semiconductor, successfully substituting single Mn, Fe, and Co atoms into the GaAs (110) surface, as well as identifying native Zn dopants in the same layer. The similarity of the anisotropic wavefunctions measured for all these acceptors shows the importance of the host in determining the shape of these states even for deep non-effective mass acceptors. The character of these states can be seen to follow directly from simple symmetry arguments and the hybridization of the impurity and host states.