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«SMALL QUANTUM DOTS OF DILUTED MAGNETIC III-V SEMICONDACTOR COMPOUNDS Liudmila A. Pozhar PermaNature, Birmingham, AL 35242 Home Address: 149 Essex ...»

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Thus, the InAs-based molecules with one vanadium atom are stronger “magnets”, and thus more suitable for DMS applications. In particular, the pre-designed In10As3V molecule is “ferromagnetic” and possesses the largest magnetic moment among the studied InAs-based molecules. At the same time, the pre-designed In10As3Mn molecule is “antiferromagnetic” singlet with its zero uncompensated magnetic moment. [The latter finding is consistent with experimental observation that with a change in thermodynamic conditions some thin DMS films exhibit magnetic phase transitions; see Sec. 1 for further details and references.] At the same time, much larger and heavier “holes” mediated by Mn atoms in In10As3Mn structures may have their own use for applications.


Interest to GaAs-based DMS is rising, because such systems have some technological advantages over InAs-based DMS systems, and may be simpler to understand than GaAsMntype of DMS. At present, GaAsV DMS systems have not been well investigated, so virtual synthesis and computational studies of basic GaAsV structures may provide guidance to experimentalists and engineers.

Similar to the studied In10As3V molecules, two Ga10As3V molecules have been virtually synthesized using computational procedures discussed in Sec.2 and Chapter 3. Thus, the predesigned Ga10As3V molecule was obtained by the total energy minimization procedure applied to a tetrahedral symmetry element (a pyramid) of the zincblende GaAs lattice described in Chapter 3, where one of As atoms was replaced by a vanadium one. During such conditional energy minimization all positions of the centers of mass of the pyramid atoms were kept fixed. The corresponding vacuum Ga10As3V molecule was virtually synthesized by lifting the special constraints applied to the centers of mass of the atoms in the pre-designed molecule, and minimizing the total energy of the atomic cluster unconditionally (that is, without any constrains applied).

The structure of the obtained molecules is depicted in Fig. 17. To a human eye, these structures seem to be the same, but analysis reveals that many atoms in the vacuum pyramidal molecule moved from their former positions in the pre-designed one. The pre-designed pyramid consists of 4 smaller pyramids built on As and V atoms. All distances between Ga and As atoms in the three As-coordinated pyramids are equal to 2.448 Å, and all Ga-As-Ga angles are 109.5º.

This, of course, corresponds to a separation between an As atom and its 4 closest Ga neighbours, and related angles, respectively, in the GaAs zincblende lattice. The vanadium atom in this molecule simply substitutes an As one, so all dimension of V-driven small pyramid are equal to those of the small As-coordinated pyramids. All closest neighbor distances between As an V atoms are 3,997Å, and the corresponding angles 60º. Thus, geometrically, the pre-designed Ga10As3V molecule is the perfect pyramid.

The vacuum molecule is far from being of perfect pyramidal structure. All As and V atoms in this molecule moved from their original positions corresponding to those in the perfect pre-designed pyramid. Thus, the distances and angles in the small As-topped pyramidal arrangements changed by several tenths of Å and from about 2º to 7º, respectively. In particular, the distances between Ga and V atoms in the V-topped small pyramid have become 2.505Å,

2.998Å, 2.998Å and 2.998Å, and the Ga-V-Ga angles 118.9º, 111.5º, 111.5º and 101.3º, respectively. The Ga-topped small pyramids have changed even more dramatically: the distances between Ga and As atoms in each of the pyramids have become 2.835Å, 2.519Å, 2835Å and

2.487Å. The sets of Ga-As-Ga angles in the As-coordinated small pyramids differ for each of the pyramids. For the pyramid coordinated by the As(13) atom (see the atomic numbering in Figs.

17c and 17f) the set of angles includes 58.5º, 58.5º, 103.7º and 107.9º; for the As(14)coordinated pyramid the set includes 103.7º, 103,7º, 116.6º and 116.6º, and for the As(12)topped pyramid it is 103.7º, 106.7º, 116.6º and 107.9º. This tetrahedral symmetry breaking has developed to stabilize a molecule when spatial constraints were applied to positions of its atoms were lifted.

The dipole moment of the perfect pre-designed pyramid Ga10As3V is 1.387208 D. It is applied directly to the center of the pyramid base farthest from the V atom, and runs strictly along the pyramid heights toward the vertex Ga atom (Fig. 17c). In the case of the vacuum molecule the dipole moment is about 3 times larger: 4.569266 D, and is applied to the pyramid base closest to the V atom running through the V atom itself (Figs. 17e and 17f).

The MEPs of these molecules are pictured in Figs. 18 and 19. Similar to In10As3Mn and In10As3V molecules of Sec. 3 and 4, CDD and MEP surfaces of both Ga10As3V molecules retain appearance of somewhat broken tetrahedral symmetry. Characteristic features of MEP surfaces of the pre-designed Ga10As3V are close to those of In10As3Mn molecules, while such features in the case of the vacuum Ga10As3V molecule remind those of In10As3V molecule. Indeed, the electron charge of the pre-designed molecule is pushed further outside of the molecule’s “surface” (Figs. 18a to 18c), and also deeper inside of the molecule (Figs. 18d to 18f), so the “shell” of electron charge deficit surrounding the “surface” is much thicker than that of the

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Fig. 17. (Color online) Pre-designed [(a) to (c)] and vacuum [(d) to (f)] molecules In10As3V. In (a) and (d) atomic dimensions approximately correspond to the atoms’ covalent radii. In (b) and (e) atomic dimensions are enlarged to reveal the shape of the structures, and in (c) and (f) the atomic dimensions are reduced to show the dipole moment [red arrow in (c), (e) and (f)]. Gallium atoms are blue, As brown, and V yellow.

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Fig. 18. (Color online) The molecular electrostatic potential (MEP) of the pre-designed molecule Ga10As3V for several isosurfaces of the CDD calculated for the following fractions (isovalues) of the CDD maximum value (not shown). (a) and (b): 0.001; (c) 0.01; (d) to (g): 0.1; (h) and (i): 0.3. The color coding scheme for MEP surfaces is shown in each figure. Ga atoms are blue, As brown and V yellow. In (a) to (e) atomic dimensions are slightly smaller than those defined by the atoms’ covalent radii, and in (f) to (i) atomic dimensions are significantly reduced to show the MEP surface structure. In (a) to (f) and (i) MEP surfaces are semi-transparent to reveal the structure.

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Fig. 19. (Color online) The molecular electrostatic potential (MEP) of the pre-designed molecule Ga10As3V for several isosurfaces of the CDD calculated for the following fractions (isovalues) of the CDD maximum value (not shown): (a) 0.02; (b) and (c) 0.05; (d) 0.06; (e) 0.1, and (f) 0.15. The color coding scheme for MEP surfaces is shown in each figure. Ga atoms are blue, As brown and V yellow. In (a) to (e) atomic dimensions are somewhat smaller than those defined by the atom’s covalent radii, and in (f) atomic dimensions are significantly reduced to show the MEP surface structure. In (a), (c), (d) and (e) MEP surfaces are semitransparent to reveal the atoms.

vacuum Ga10As3V molecule. The electron charge of the latter molecule is distributed relatively close to the molecular “surfaces” (Figs. 19a and 19b) on the outer side and inside of the molecular volume creating a relatively thin “shell” of electron charge deficit surrounding the molecular “surface” (Fig. 19a). In the case of this molecule the thickness of the electron charge deficit “shell” is about 2 covalent radii of Ga atom. The major reason for this striking difference in the electron charge distributions of the Ga10As3V molecules is that the pre-designed molecule is strained. Indeed, the covalent radius of a Ga atom is much smaller than that of the In atom (Table I), and is close to that of the As atom. Thus, the partial “volume” occupied by V atom in the pre-designed Ga10As3V molecule is larger than that in the case of the pre-designed In10As3V molecule. As a result, replacement of an As atom by a V one causes much more electron charge imbalance in the pre-designed Ga10As3V molecule as compared to that of the pre-designed In10As3V molecule, and therefore, the former molecule is more strained than the latter one. One can conclude that the CDDs of the pre-designed and vacuum In10As3V molecules should differ less between themselves than the CDDs of the pre-designed and vacuum Ga10As3V molecules.

This is confirmed by the obtained data illustrated in Figs. 18 and 19.

There is yet another fact confirming the above conclusion that the pre-designed Ga10As3V molecule is more strained than the pre-designed In10As3V molecule. Indeed, the total number of electrons (238) contributing to the top 118 doubly occupied MOs of the pre-designed Ga10As3V molecule is the same as that contributing to the top 115 doubly occupied MOs of the predesigned In10As3V molecule. Given that the Ga-based molecule has 180 less electrons than the In-based one, the above fact signifies that much larger number AOs of deeply lying electrons in Ga atoms of the Ga-based molecule have to be re-configured in response to a disturbance caused by the V atom than that in the case of the In-based molecule.

The V atom in the pre-designed Ga10As3V molecule accumulates more of re-distributed electron charge of Ga atoms than As atoms in this molecule (Figs. 18c to 18i). In contrast, in the vacuum Ga10As3V molecule the V atom accumulates less of the electron charge than the As atoms (Figs. 19b to 19f). This is yet another sign that the pre-designed molecule is overly strained, so the V atom has to take more of the Ga electron charge to provide for a stable state (a ROHF triplet; Table II) similar to that of the corresponding vacuum molecule. In the case of much roomier vacuum Ga10As3V molecule there is less need to accumulate charge near the V atom or to push the charge outside the molecule to stabilize the molecule.

The above analysis leads to a conclusion that dimensions and properties of “holes” mediated by a substitution V-atoms in the zincblende GaAs lattice should be more sensitive to the lattice strain than those in the case of the zibcblende InAs lattice. This phenomenon can be used to develop a sensitive device to measure lattice strain by measuring the hole conductivity, or vice versa.

Several MOs from the HOMO-LUMO regions of the studied Ga10As3V molecules, both of which are ROHF triplets (Table II), are shown in Figs. 20 and 21. The electronic level structure of the pre-designed molecule retains significant symmetry in the HOMO-LUMO region exhibiting doubly degenerate MOs, and in particular LUMO. Counting from the proper HOMO 121 (which is non-degenerate) toward the core MOs, ELS is 2A (HOMO 120 and MO 119), E (MOs 118 and 117), A (MO 116), E (MOs 115 and 114), E (MOs 113 and 112), A (MO 111), and so on. In the LUMO region, counting from the proper LUMO 121 and up, ELS is E (LUMO 121 and MO 122), E (MOs 123 and 124), A (MO 125), E (MOs 126 and 127), E (MOs 128 and 129), 2A (MO 130 and 131), T (MOs 132, 133 and 134), etc. This is a result of constraining all

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Fig. 20. (Color online) The pre-designed Ga10As3V molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to several isovalues. (a) and (b): HOMOs 117 and 118, isovalue 0.003, respectively; (c) HOMO 119, isovalue 0.001; (d) HOMO 119, isovalue 0.007; (e) and (f): HOMO 120, isovalue 0.007; (g) LUMO 121, isovalue 0.01; (h): LUMO 122, isovalue 0.007, and (i) LUMO 123, isovalue

0.01. Ga atoms are blue, As brown and V yellow. Atomic dimensions are reduced and isosurfaces made transparent to show the structure.

centers of mass of atoms to their tetrahedral positions in the tetrahedral (pyramidal) symmetry element of the zincblende GaAs lattice. The reduction in symmetry of the electronic charge distribution of this molecule is caused only by replacement of one of Ga atoms by the V atom.

In the pre-designed Ga10As3V molecule 3d AOs of tetra-coordinated vanadium atom always bond it directly to 4 Ga atoms. The arsenic atoms bond the 6 other Ga atoms, and the first 4 Ga atoms bonded to V also bond to 3 Ga atoms from the “arsenic bonding triangle”, thus completing an MO (one of the 4 Ga atoms bonded to V is in a pyramid vertex, and does not contribute much to Ga-As π-type bonding). Ga atoms bond both to V and As ones via their 4p AOs. In contrast to the case of InAs-based molecules where there were some contributions to bonding from 4d AOs of In atoms, there are no contributions to bonding from 3d AOs of Ga atoms in the GaAs-based molecules. Arsenic atoms bond through their 4p AOs only to Ga atoms, and do not bond to the vanadium atom directly. This arrangement is typical for all MOs in Fig.

20. The (4 + 3) Ga atom 4p-bonding brings about a strong π-type ligand bonding MOs of this molecule (see Ref. 122 for further discussion of “aromatic” π-type ligand bonding) in the HOMO region. The π-type ligand bonding MOs are responsible for the molecule being a stable ROHF triplet whose OTE (over 1.26 eV) is larger than that of the vacuum Ga10As3V molecule (about

1.058 eV), and whose minimum of the total energy is almost as deep as that of the vacuum molecule (see Table II).

ELS of the vacuum Ga10As3V molecule does not exhibit any charge symmetry, being composed only of A-type orbits and showing only a very few spontaneously degenerate MOs of E-type in the higher LUMO region. Several MOs in the near HOMO-LUMO region are depicted in Fig. 21. The type of bonding in this molecule is very similar to that of the pre-designed

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Fig. 21. (Color online) The vacuum Ga10As3V molecule. Isosurfaces of the positive (green) and negative (orange) parts of the highest occupied and lowest unoccupied molecular orbits (HOMOs and LUMOs, respectively) corresponding to several isovalues. (a) and (b): HOMO 118, isovalues 0.01 and 0.005, respectively; (c) HOMO 119, isovalue 0.01; (d) and (e): HOMO 120, isovalue 0.005; (f): LUMO 121, isovalue 0.015; (g) and (h): LUMO 122, isovalues 0.01 and 0.01, respectively, and (i) LUMO 123, isovalue

0.01. Ga atoms are blue, As brown and V yellow. Atomic dimensions are reduced and isosurfaces made transparent to show the structure.

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