Structure of AlSb(001) and GaSb(001) Surfaces Under Extreme Sb-rich Conditions
Jeffery Houze, Sungho Kim, Seong-Gon Kim, S. C. Erwin, L. J. Whitman
aa r X i v : . [ c ond - m a t . m t r l - s c i ] S e p Structure of AlSb(001) and GaSb(001) Surfaces Under Extreme Sb-rich Conditions
Jeffery Houze, Sungho Kim, and Seong-Gon Kim ∗ Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS 39762, USA andCenter for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762, USA
S. C. Erwin and L. J. Whitman
Naval Research Laboratory, Washington, DC 20375, USA (Dated: June 15, 2007)We use density-functional theory to study the structure of AlSb(001) and GaSb(001) surfaces.Based on a variety of reconstruction models, we construct surface stability diagrams for AlSb andGaSb under different growth conditions. For AlSb(001), the predictions are in excellent agreementwith experimentally observed reconstructions. For GaSb(001), we show that previously proposedmodel accounts for the experimentally observed reconstructions under Ga-rich growth conditions,but fails to explain the experimental observations under Sb-rich conditions. We propose a newmodel that has a substantially lower surface energy than all ( n × × ×
5) and (2 ×
5) structures on GaSb(001) are kinetically limitedrather than at the ground state.
PACS numbers: 68.35.Bs, 68.35.Md, 68.37.Ef, 68.47.Fg
I. INTRODUCTION
The surfaces and interfaces of III-V semiconductorsconstitute some of the most important components of thesemiconductor industry. For example, III-V heterostruc-ture quantum wells are key components in a wide range ofoptical and high-frequency electronic devices, includingfield-effect transistors , resonant tunneling structures ,infrared lasers , and infrared detectors . Many of thesedevices require extremely sharp and clean interfaces. Forthis reason, an understanding of the atomic-scale mor-phology of III-V semiconductor surfaces is critical to con-trolling the growth and formation of their interfaces .It is generally accepted that the surfaces of III-V semi-conductors should reconstruct in such a way that thenumber of electrons is exactly enough to doubly occupyall orbitals on electronegative (V) atoms, leaving all or-bitals on electropositive (III) atoms unoccupied. Thisguiding principle, known as the electron-counting model(ECM), has been used to screen candidate structuralmodels of many observed reconstructions on the surfacesof III-V semiconductors . In practice, however,not all experimentally realized reconstructions follow thisprinciple. For example, under Sb-rich growth conditions,GaSb(001) forms surface reconstructions that are weaklymetallic and hence violate the ECM , even though theclosely related AlSb(001) surface forms insulating recon-structions that satisfy it . The nature of reconstruc-tions that violate the ECM, and the underlying reasonsfor their stability, are thus important for understandingIII-V surfaces in general.In this article we explore theoretically a large num-ber of judiciously chosen candidate reconstructions onGaSb(001) and AlSb(001). We find that as the growth conditions are varied between Sb-poor and Sb-rich,the predicted sequence of stable reconstructions forGaSb(001) is exactly analogous to those of AlSb(001).Experimentally, however, the picture is more compli-cated. In the Sb-poor limit, the observed GaSb(001) re-construction is indeed analogous to that of AlSb(001).On the other hand, in the Sb-rich limit, the exper-imentally observed reconstructions for GaSb(001) andAlSb(001) are different. Moreover, in this limit the pre-dicted and observed reconstructions are in good agree-ment only for AlSb(001), while for GaSb(001) there re-mains an unresolved discrepancy between theory and ex-periment.Experimentally, the Sb-terminated AlSb(001) surfaceevolves through the sequence α (4 × → β (4 × → γ (4 × → c(4 ×
4) as the growth condition is changedfrom low Sb flux (or high substrate temperature) to highSb flux (or low temperature) . All of these reconstruc-tions are insulating, and are well accounted for by struc-tural models proposed in the literature that satisfy theECM.Of particular interest here is the Sb-rich AlSb(001)- c (4 ×
4) reconstruction, analogous to the As-richGaAs(001)- c (4 ×
4) reconstruction, which is observed onAlSb but not GaSb. In contrast to both AlSb andGaAs, the GaSb(001) surface does not exhibit a sta-ble, insulating c (4 ×
4) reconstruction under similar—orany other—growth conditions. Instead, it forms ( n × . Structural models pro-posed in the literature for these ( n × . Simulated scanning tunneling mi-croscopy (STM) images based on (2 ×
10) and c (2 × . Asa result, these models have been generally accepted asdescribing the GaSb(001) surface under Sb-rich growthconditions. Nevertheless, we show below on energeticgrounds that these models are unlikely to be correct.Specifically, we find their calculated surface energy tobe significantly higher than GaSb(001)- c (4 ×
4) for anyplausible value of Sb chemical potential. However, sincethe experimentally observed reconstruction of GaSb(001)does not have c (4 ×
4) periodicity, this model cannot becorrect either. Thus a definitive structural model remainsto be found.
II. METHODS
The basic structural models we considered are takenfrom the literature and are shown in Figs. 1 and 2. Sur-faces that satisfy the ECM are generally semiconducting,while those that do not may be metallic. The degree towhich a given surface satisfies the ECM can be measuredby the excess electron count, ∆ ν , which we define here asthe difference between the number of available electronsand the number required to satisfy the ECM, per (1 × γ = E surf /A = ( E tot − n III µ ′ III − n V µ ′ V ) /A, (1)where E tot is the total energy of a reconstructed sur-face, of area A , containing n III group-III and n V group-V adatoms in excess with respect to the bulk-truncated,Sb-terminated AlSb(001) or GaSb(001). The atomicchemical potentials µ ′ are more conveniently expressedin terms of excess chemical potentials µ , relative to theenergy per atom in the ground-state elemental phases: µ ′ = µ bulk + µ . Assuming the surface to be in thermo-dynamic equilibrium with the bulk, the III and V chem-ical potentials are related by µ III + µ V = ∆ H f , where∆ H f = µ bulkIII-V − ( µ bulkIII + µ bulkV ) is the formation enthalpyof the bulk III-V crystalline phase (note that ∆ H f isintrinsically negative). Eq. (1) can then be rewritten toshow more clearly the dependence of γ on the surfacestoichiometry and chemical potential: γ = γ + µ V ∆Θ . (2)Here γ = ( E t − E sub ) − µ bulkIII-V Θ III + µ bulkV ∆Θ is indepen-dent of the chemical potentials, and ∆Θ = Θ III − Θ V =( n III − n V ) /A is the deviation of the surface stoichiome-try from its bulk value. The dependence of γ on chemi-cal potential is given entirely by the second term. Notethat µ V is intrinsically negative, and can take values inthe range ∆ H f ≤ µ V ≤
0. Hence, Eq. (2) reflects in asimple way that III-rich reconstructions (Θ
III > Θ V ) arefavored under III-rich conditions ( µ V → ∆ H f ), V-rich re-constructions (Θ V > Θ III ) are favored under V-rich con- (4x3) γ (4x3) α (4x3) β h0(4x3) [110] [110][001] c(4x4) FIG. 1: (color online) Reconstruction models proposed for theAlSb(001) or GaSb(001) surfaces with (4 ×
3) and (4 ×
4) peri-odicities. The first two upper layers are shown in a top view.Smaller white circles represent Sb atoms in the top layer ofthe underlying Sb-terminated AlSb(001) or GaSb(001) sur-face. Larger circles represent Al or Ga (black) and Sb (white)adatoms. The unit cells are shown in light blue. ditions ( µ V → V = Θ III ) γ does not depend on chemical potential.To compute the total-energy contribution, γ , to thesurface energy we performed first-principles calculationsusing density-functional theory (DFT). The calculationswere performed within the local-density approximation(LDA) using ultrasoft pseudopotentials . Weused a standard supercell technique, modeling the (001)surface with a slab consisting of four bilayers and 10 ˚Aof vacuum. Atoms in the bottom bilayer were fixed attheir bulk positions, while all other atoms are allowedto relax until the rms force was less than 0.005 eV/˚A.The bottom layer (either Ga or Al) was passivated withpseudohydrogens. A plane-wave cutoff of 300 eV wasused, and reciprocal space was sampled with a densityequivalent to at least 192 k -points in the (1 ×
1) surfaceBrillouin zone. To define the III-V formation enthalpy∆ H f from the bulk chemical potentials µ bulk , separateDFT calculations were performed for the elements intheir ground-state phases: Ga in the α -Ga structure, Alin the face-centered cubic structure, Sb in the rhombo-hedral structure, and both AlSb and GaSb in the zincblende structure. TABLE I: Electron count for different reconstructions of GaSb(001) surface. The excess electron count per (1 ×
1) surface unitcell is defined as ∆ ν = (˜ n − ˜ m ) /A where ˜ n is the number of available electrons and ˜ m is the number of required electrons tosatisfy the ECM in the excess of Sb-terminated GaSb(001). A is the area of the surface unit cell in terms of the (1 ×
1) surfaceunit cell. n i is number of adatoms of species i in excess with respect to the Sb-terminated GaSb(001) and Θ i = n i /A is thecoverage of adatoms of species i . The relative γ values, in eV per (1 ×
1) surface unit cell, are given with respect to that of α (4 × A n
III n V Θ III Θ V ∆Θ ˜ n ˜ m ∆ ν γ (Ga-rich) γ (Sb-rich) α (4 ×
3) 12 4 4 0.333 0.333 0.0 62 62 0 0.000 0.000 β (4 ×
3) 12 1 7 0.083 0.583 -0.5 68 68 0 0.076 -0.074 γ (4 ×
3) 12 0 8 0.0 0.667 -0.667 70 70 0 0.114 -0.087 h ×
3) 12 0 8 0.0 0.667 -0.667 70 70 0 0.118 -0.083 c (4 ×
4) 8 0 6 0.0 0.750 -0.750 50 50 0 0.142 -0.084 c (2 ×
10) 10 0 8 0.0 0.800 -0.800 65 62 0.3 0.255 0.014(2 ×
10) 20 0 24 0.0 1.200 -1.200 170 164 0.3 0.528 0.166s1a- c (2 ×
10) 10 1 7 0.1 0.700 -0.600 63 62 0.1 0.143 -0.038 s1b- c (2 ×
10) 10 1 7 0.1 0.700 -0.600 63 62 0.1 0.181 0.000s1c- c (2 ×
10) 10 1 7 0.1 0.700 -0.600 63 62 0.1 0.280 0.099s2a- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.137 0.016s2b- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.124 0.003s2c- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.143 0.023s2d- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.141 0.020s2e- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.167 0.046s2f- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.144 0.023s2g- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.182 0.062s2h- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.164 0.043s2i- c (2 ×
10) 10 2 6 0.2 0.600 -0.400 61 62 -0.1 0.166 0.045 c(2x10)[110] [110][001] (2x10)
FIG. 2: (color online) Reconstruction models proposed forthe GaSb(001)-(1 × III. RESULTS AND DISCUSSIONS
The resulting relative surface energies for AlSb(001)and GaSb(001) are shown in Figs. 5(a) and 5(b), respec-tively, for the eight models considered here. For eachmodel, the surface energy is linear in µ V , with the slope s1b−c(2x10)[110] [110][001] s1c−c(2x10)s1a−c(2x10) FIG. 3: (color online) Reconstruction models with a singlesubstitution of Sb atoms by Ga atoms. See Fig. 1 for colorschemes. given by ∆Θ.For AlSb(001) the predicted stable reconstructions,and their energetic ordering, are in excellent agreement s2g−c(2x10) s2h−c(2x10)s2e−c(2x10) s2f−c(2x10)s2c−c(2x10) s2d−c(2x10)s2a−c(2x10) s2b−c(2x10)[110] [110][001]s2i−c(2x10)
FIG. 4: (color online) Reconstruction models with a double substitution of Sb atoms by Ga atoms. See Fig. 1 for color schemes. with experiment. Proceeding from Sb-poor to Sb-richconditions, the predicted sequence is α (4 × → β (4 × → γ (4 × → c (4 × . This isthe same sequence observed experimentally . Moreover, γ (4 ×
3) is predicted to exist only over a very narrow rangeof µ Sb , in agreement with experiment .For GaSb(001) the predicted sequence is qualitativelythe same as for AlSb(001), although the c (4 ×
4) is onlypredicted to be stable for values of µ Sb above the ther-modynamically allowed limit of zero. Experimentally,however, the situation is quite different. As reportedpreviously, neither the γ (4 ×
3) nor the c (4 ×
4) phase isobserved for any growth condition . Instead, under Sb-rich conditions, only the (1 ×
5) and (2 ×
5) periodicitieshave been observed . Righi et al. suggested h × .Our calculation indeed shows that it is energetically asfavorable as γ (4 × h ×
3) must be rejected as it has a wrongperiodicity.In order to explain the experimentally observed (1 × ×
5) structures on GaSb(001) surface, we studied alarge number of structures based on variations of c (2 × × c (2 ×
10) violates the ECMsubstantially (∆ ν = 0 .
3) and substitution of Sb atoms inthe top layer of the underlying Sb-terminated GaSb(001)surface by Ga atoms can lower the excess electron count.Fig. 3 shows the possible reconstructions when a singleSb atom is replaced by a Ga atom. We use the naming -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 µ Sb /|H f (AlSb)| -0.100.1 γ ( e V ) Al-rich Sb-rich α (4x3) β (4x3) γ (4x3) c ( x ) h0(4x3)c(4x4) (a) -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 µ Sb /|H f (GaSb)| -0.100.1 γ ( e V ) Ga-rich Sb-rich α (4x3) β (4x3) γ (4x3) c ( x ) s - c ( x ) c(4x4) (2x10) (b) h0(4x3) FIG. 5: (color online) (a) Surface stability phase diagram forAlSb(001) surface. The relative surface energy [Eq. (2)] isplotted as a function of the Sb chemical potential relative toits corresponding bulk value. Dotted vertical lines mark thethermodynamically allowed range of µ Sb . ∆ H f is the heat offormation for AlSb. (b) Surface stability phase diagram forGaSb(001) surface; ∆ H f is the heat of formation for GaSb. convention of s x to denote a “single substitution”. Asshown in Table I, all s x reconstruction indeed have lowerexcess electron counts.For completeness, we also considered reconstructionsresulting from double substitution of Sb atoms by Gaatoms as shown in Fig. 4. More substitutions, however,were not found to be energetically favorable: Table Ishows that the surface energy of these structures arehigher than that of s x reconstructions. We note thatfor these double substitutions the excess electron counts∆ ν are negative, indicating a deficit of electrons relativeto the ECM.One of the most energetically favorable structureshaving the correct periodicity is s1a- c (2 × c (2 ×
10) has two clear advantages over c (2 × c (2 ×
10) is
FIG. 6: Filled-state STM images of GaSb(001) with (1 ×
5) pe-riodicity. (a) Experimental STM image; a c (2 ×
10) unit cellis indicated. (b) Simulated STM image of s1a- c (2 × c (2 × lower than that of c (2 ×
10) by more than 50 meV per(1 ×
1) unit cell. Second, as shown in Fig. 6, the simu-lated STM image for s1a- c (2 ×
10) is in a better agree-ment with the experiment image, in that it reproducesthe left-right asymmetry within the surface Sb dimers .Furthermore, as shown in Table I, this model violatesthe ECM and thus is predicted to be weakly metallic,as observed in tunneling spectroscopy . Therefore, thepreviously proposed model c (2 ×
10) is unlikely to be theexperimentally realized structure.However, the calculated surface energy of s1a- c (2 × higher than that of γ (4 × × ×
5) periodicity,is the least energetically favorable structure among theeight structures of Table I. On the other hand, γ (4 × ∼ ◦ C, to room temperatureand no flux while trying to stabilize the surface. Thisprocess typically involved simultaneously lowering thetemperature while turning off the Ga and then lower-ing the Sb flux. The surface cannot be annealed, be-cause that would drive off Sb and create ( n ×
3) recon-structions. These considerations lead us to propose thatthe s1a- c (2 ×
10) structure is the most likely model forthe observed GaSb(001) surface as created under Sb-richgrowth conditions and subsequently stabilized under vac-uum.
IV. SUMMARY AND CONCLUSIONS
We have performed ab initio calculations on the surfaceenergy and atomic structure of AlSb(001) and GaSb(001)surfaces with various reconstructions. Surface stabilitydiagrams for a large number of reconstruction modelsare constructed under different growth conditions. ForAlSb(001), we confirmed that the predictions of the cur-rently accepted models are in good agreement with ex-perimentally observed reconstructions. For GaSb(001),we showed that previously proposed model accounts forthe experimentally observed reconstructions under Ga-rich growth conditions, but fails to explain the experi-mental observations under Sb-rich conditions. Therefore, we propose s1a- c (2 ×
10) as a better alternative to exist-ing models for GaSb(001) under extreme Sb-rich growthconditions. Our calculations show that s1a- c (2 ×
10) hasa substantially lower surface energy than all ( n × c (2 × γ (4 × ×
5) and (2 ×
5) struc-tures on GaSb(001) are not the ground-state structure,but kinetically limited ones.
V. ACKNOWLEDGMENT
This work was in part supported by the US Depart-ment of Defense under the CHSSI MBD-04 (MolecularPacking Software for ab initio
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