pubs.acs.org/NanoLett
Band Alignment Tuning in Twin-Plane Superlattices of Semiconductor Nanowires Toru Akiyama,* Tomoki Yamashita, Kohji Nakamura, and Tomonori Ito Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan ABSTRACT The band alignments of twin-plane superlattices in semiconductor nanowires are systematically investigated on the basis of density functional calculations. Our calculations demonstrate that for nanowires with small diameters the quantum-confinement effect is prominent within wurtzite structure regions and the energy gap in wurtzite-structured nanowires is remarkably larger than that including zinc-blende structure. This results in the straddling band alignment, in which both electrons and holes are confined in zinc-blende structure region. The analysis using a simple tight-binding methods also clarifies that the straddling band alignments can be realized when the diameters of nanowires are less than 4-8 nm, leading to full control of band alignments by varying the nanowire diameter. Our results provide the ability of band-alignment tuning and open new possibilities for band engineering. KEYWORDS Nanowire, twin-plane superlattices, band alingment, density functional calculations
S
Because of the formation of {111}A and {111}B side facets in nanowires grown by the VLS growth,6,15,16 the nanowire cross-section in ZB structure varies between triangular and hexagonal shapes with inclusion of twin planes. On the other hand, the cross-section in WZ structure is either hexagon or triangular shape because {11¯00} side facets always emerge. This structural difference effectively induces the difference in nanowire diameter between ZB and WZ structures and is expected to be crucial to the band alignments of nanowire twin-plane superlattices for small diameters. In this letter, we theoretically demonstrate the band alignments of twin-plane superlattices in which both electrons and holes are confined in zinc-blende structure region. We clarify that for nanowires with small diameters the quantum-confinement effect is prominent within wurtzite structure region, leading to their remarkably larger band gap compared to zinc-blende structure region. This structuredependent quantum-confinement effect results in the formation of quantum wells whose band alignments are quite different from those in conventional zinc-blende/wurtzite interface. The density functional calculations have been performed within plane-wave pseudopotential approach using the generalized gradient approximation.20 We use norm-conserving pseudopotentials21 and 3d (4d) electrons of Ga and Zn (In) atoms are treated by partial core corrections.22 The conjugategradient technique is utilized both for the electronic structure calculations and for geometry optimization.23 The valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 25 Ry. For the k-point sampling for integration over the one-dimensional Brillouin zone, we use k-point mesh correponding to the six k-points sampling in WZ structure. Dangling bonds of nanowire facets are terminated by artificial hydrogen atoms.24 This treatment could be one of mimic models for actual nanowires whose side facets are passivated by taking core-shell structure.25 Pe-
emiconductor nanowires offer the possibility to assemble nanodevices under the bottom-up approach, which allows for new device concepts. To explore various nanoscale applications in nanowires, such as singleelectron memories1 and nanowire lasers,2 the ability to control and modulate crystal structure of nanowires is one of essential parameters. Nanowires made from group III-V (GaAs,3-5 GaP,6 InP,7 and InAs3,8) and II-VI (ZnS9 and ZnSe10) semiconductor materials form zinc-blende (ZB) structure as seen the bulk phase but often include randomly distributed rotational twin planes and stacking faults perpendicular to the growth 〈111〉 direction. Since a twin plane in ZB structure in the 〈111〉 direction can be considered as a monolayer of wurtzite (WZ) structure, a mixture of ZB and WZ segments has an impact on the optical and electrical properties. This has led to intensive experimental and theoretical efforts3,6,11-14 to clarify the formation mechanisms of these imperfections in nanowires. By varying nanowire diameter and growth temperature during the vapor-liquid-solid (VLS) growth, twin-plane superlattices (i.e., twin planes forming a constant spacing) have been recently fabricated in InP15 and InAs16 nanowires, leading to the band gap engineering and novel electronic behavior. Furtheremore, the photoluminescence measurements in twined InP17 and GaAs18 nanowires for large diameters (50-80 nm) have suggested that the quantum confinement effect can be neglected and the heterojunction in twin-plane superlattices forms a staggered band alignment.19 These accomplishments pose a challenging issue to clarify the role of quantum confinement on the heterojunction in nanowire twin-plane superlattices for small diameters.
* To whom correspondence should be addressed. E-mail: akiyama@ phen.mie-u.ac.jp. Received for review: 08/2/2010 Published on Web: 10/08/2010 © 2010 American Chemical Society
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FIGURE 1. Structures of nanowires with {111} and {11¯00} side facets. Nanowire models to obtain the valence band position of (a) WZ and (b) 6H structures, and (c) the lineup in electrostatic potential across 6H/WZ interface, along with (d) perspective image of nanowire with 6H/WZ interface shown in (c) as seen from one of the 〈1¯10〉 directions. Gray and yellow circles represent cations and anions, respectively. Small circles are artificial hydrogen atoms that terminate dangling bonds of nanowire facets. The periodic supercell used to simulate a single nanowire is enclosed by a rectangle.
FIGURE 2. Schematic diagram of the band alignments at (a) ZB-{111}/WZ-{0001} and 6H-{0001}/WZ-{0001} interfaces and (b) InP nanowire 6H/WZ interface with diameter of 1.3 nm. The calculated gap energies in bulk InP and those in NWs are also shown. Values in parentheses in (a) correspond to data for 6H-{0001}/WZ-{0001} interfaces. Note that density functional calculations underestimate the gap energies of semiconductors in the bulk phase.
riodic boundary conditions are employed along the growth direction with supercells large enough to eliminate the interraction between adjacent nanowires. The separation of 8 Å between the closest artificial H atoms on adjacent nanowires is found be sufficient to avoid such ineraction. Our analysis of the band alignments at ZB/WZ nanowire interfaces using density functional calculations reveals a consequence of the quantum confinement effect. The calculated gap energy of nanowires including ZB structure (Figure 1a) and for WZ structured nanowires (Figure 1b) becomes larger than those in the bulk phase by 1.0-1.6 eV, consistent with previous calculations.26-29 More importantly, the gap energies of WZ structured nanowires with triangular shape shown in Figure 1a increase more significantly than those including ZB structure shown Figure 1b (see Table S1 of Supporting Information). Here, we note that pure ZB structured nanowires consisting of {111} side facets cannot be constructed due to its crystal symmetry and twin planes are inevitably incorporated along the 〈111〉 direction (see Figure 1 of Supporting Information). The structure shown in Figure 1b, 6H structure, has the largest ZB structure © 2010 American Chemical Society
content. When the cross-section of WZ structured nanowire takes the triangular shape, (see Tables S1 and S2 of Supporting Information) the band alignments at 6H/WZ nanowire interfaces estimated from the lineup of electrostatic potentials30 of a nanowire superlattice (Figure 1c,d) are different from those at conventional ZB-{111}/WZ-{0001} and 6H-{0001}/WZ-{0001} interfaces,19 as shown in Figure 2. The gap energy of InP nanowire with WZ structure is found to be larger than that including ZB structure by 0.14 eV, indicating that the quantum confinement effect is prominent in WZ structure region. Furthermore, the valence band maximum (VBM) of WZ-structured nanowire is lower than that including ZB structure by 0.02 eV (Figure 2b) whereas the VBM in WZ structure region in ZB-{111}/WZ-{0001} and 6H-{0001}/WZ-{0001} interfaces (Figure 2a) is higher than those in ZB and 6H structure regions, respectively. Using the valence band offset and the gap energy, the offset in conduction band minimum (CBM) of 0.11 eV is obtained in InP nanowire. As a consequence, the heterojunction in twin-plane superlattices of InP nanowire has a straddling 4615
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Table S1 of Supporting Information) clearly shows that the VBM of WZ structure is lower than that including ZB structure depending on fi; the valence band offset tends to increase with decreasing fi. This ionicity dependence can be explained in terms of the modification of VBM due to the quantum confinement using a simple tight-biding approach.32 In the bulk phase with WZ structure, the VBM (Ev) varies from the average of cation and anion energies written as
Ev )
εpc + εpa 2
[(
εpc - εpa 2
)
2
+
(
)]
2 4 8 V + Vppπ + Wppπ 3 ppσ 3
1/2
(1)
where εcp and εap are the energy of cation and anion p-orbitals, respectively, Vppσ and Vppπ are transfer energies between nearest neighbors, and Wppπ is transfer energy for firstneighbor interlayer interaction that is applied only in WZ structure. This formula indicates that the entity of Wppπ taking negative value is the origin of staggered band alignment at ZB-{111}/WZ-{0001} interface. If we consider a simple polar bond as an ultimate limit of the quantum confinement, Ev is replaced by the energy of bonding state Eb expressed as FIGURE 3. Distributions of squared wave functions of (a) the highest occupied and (b) lowest unoccupied electronic states of InP nanowires with 6H and WZ structures. The isosurfaces are at 0.02 electrons Å-3. The notation of circles is the same as in Figure 1. The periodic supercell of WZ structure is multiplied along the 〈0001〉 direction.
Eb )
[(
εpc - εpa 2
)
2 2 + Vppσ
]
1/2
(2)
indicating that the VBM of nanowires approaches Eb with decreasing the diameter. By comparing eq 1 with eq 2, we furthermore derive that (i) the relationship Vppσ > (4/3)Vppσ + (8/3)Vppπ + Wppπ leading to Eb < Ev is usually satisfied, and (ii) the deviation from the bulk value, Ev - Eb, is large when the ionicity and nanowire diameter is small (see Figure S2 of Supporting Information). These characteristics imply that for small fi the variation in gap energy is marked for effectively small WZ structured nanowires (see Figure S3 of Supporting Information), resulting in large negative valence band offsets. The structure-dependent quantum confinement effect can also be seen in the conduction band offset shown in Figure 4b (see Table 1 of Supporting Information). The conduction band offset in nanowires is higher than those in ZB-{111}/WZ-{0001} and 6H-{0001}/WZ-{0001} interfaces. However, the monotonic band offset modification depending on fi is not recognized explicitly due to a variety of conduction band character depending on the chemical composition. In particular, the CBM in GaP nanowire with WZ structure is located at about 70% along Γ to X points, so that its gap energy is much smaller than that including ZB structure (see Figure S4 of Supporting Information). This leads to the negative value in the conduction band offset and
band alignment forming type I quantum well in which both electrons and holes are confined in the region including ZB structure. Figure 3 shows the distribution of squared wave function of the highest occupied and lowest unoccupied electronic states of InP nanowires, which provide a evidence for the prominence of the quantum confinement in WZ-structured nanowires in comparison with that including ZB structure. The distribution of the highest occupied state shown in Figure 3a manifests that the VBM consists of 3p-orbitals of phosphorus atoms for both 6H and WZ structures. However, the wavefuction for 6H structure spreads over spatially wide regions within the nanowire. The spatial wavefuncion width of the highest occupied state in 6H structure is about ∼13 Å taking a sawtoothlike distribution along {111}A and {111}B facets while that in WZ structure is at most 9 Å due to its smooth triangular shape distribution. Similarly, in Figure 3b, the difference between 6H and WZ structures can be seen in the lowest unoccupied state. The calculated band offsets for various materials unequivocally reveal the nature of structure-dependent quantum-confinement effect. The valence band offset as a function ionicity of semiconductors fi31 shown in Figure 4a (see © 2010 American Chemical Society
εpc + εpa 2
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FIGURE 4. Calculated (a) valence band and (b) conduction band offsets as a function of ionicity fi. Empty and filled squares represent the band offsets at ZB-{111}/WZ-{0001} and 6H-{0001}/WZ-{0001} interfaces, respectively. Circles mark the band offsets at 6H/WZ interface in nanowires.
higher than that including ZB structure, the heterojunction of nanowires whose diameters are larger than 4-8 nm has a staggered band alignment, qualitatively consistent with recent photoluminescence measurements.17,18 In addition, it seems that the largest diameter tends to increase with fi. This is because for small fi the VBM of nanowire rapidly converges into that in the bulk phase. Although this result should be checked by using accurate ab initio calculations, the relationship between the largest diameter and ionicity would be one of criteria for the emergence of quatum confinement and help us to design nanodevices using nanowire twin-plane superlattices. In summary, we have theoretically predicted tunable band alignments in the heterojunction of twin-plane superlattices in semiconductor nanowires by utilizing the structuredependent quantum-confinement effect. The ability to form type I quantum wells by twin-plane superlattices in semiconductor nanowires open up new possibilities for band engineering within a single materials.
FIGURE 5. The critical diameter, in which the valence band offset at ZB/WZ nanowire interface becomes zero, obtained by a simple tight-biding method32 as a function of ionicity fi. Nanowires with the largest ZB structure content are adopted to obtain the VBM of nanowires including ZB structure.
electrons are confined in WZ structured nanowire forming type II quantum well. Therefore, type I quantum wells can be basically achieved in twin-plane superlattices of nanowires that are made from semiconductor materials with direct band gap at Γ point in the bulk phase. Furthermore, it should be noted that the CBM is located about 85% along Γ to X points in bulk Si. Because of this electronic structure, the quantum confinement effect in Si is slightly different from that in other material with direct band gap, and relatively small conduction band offset is achieved in Si nanowires. To find out the largest nanowires possessing straddling band alignment, we now estimate size dependence of the valence band offset in twin-plane superlattices on the basis of simple tight-biding method.32 Our calculations based on tight-binding approach shown in Figure 5 fairly reproduce the quantum confinement effect in which the VBM for the smallest case is lower than that in the bulk phase by ∼1.0 eV. However, the VBM of nanowire converges into the bulk value within 0.1 eV when the diameter is ranging 4-8 nm (see Figure S5 of Supporting Information). In accordance with this size dependence, the largest diameter possessing straddling band alignment is located ranging 4-8 nm. Assuming that the CBM in WZ-structured nanowire is always © 2010 American Chemical Society
Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific Research (No. 21560032) from the Japan Society for the Promotion of Science. Computations were performed at Research Center for Computational Science, National Institutes of Natural Sciences. Supporting Information Available. Summary of results for the electronic properties of nanowires with 6H and wurtzite structures (Tables S1 and S2), details of periodic model of nanowires with {111} side facets (Figure S1), ionicity dependence in the energy difference between valence band maximum and the bonding state (Figure S2), ionicity dependence of gap energy in nanowires (Figure S3), details of one-dimensional band structure of GaP nanowires (Figure S4), and size dependence in the valence band offset in semiconductor nanowires using tight-binding method (Figure S5). This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1)
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