Substantial Band-Gap Tuning and a Strain-Controlled Semiconductor

Sep 22, 2016 - By first-principle calculations, we have systematically studied the effect of strain/pressure on the electronic structure of rutile lea...
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Substantial Band-Gap Tuning and a Strain-Controlled Semiconductor to Gapless/Band-Inverted Semimetal Transition in Rutile Lead/ Stannic Dioxide Fengxian Ma,†,‡ Yalong Jiao,†,‡ Guoping Gao,† Yuantong Gu,† Ante Bilic,§ Stefano Sanvito,⊥ and Aijun Du*,† †

School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Gardens Point Campus, Brisbane 4001, Queensland, Australia § CSIRO Data61, Molecular and Materials Modelling, Docklands 3008, Victoria, Australia ⊥ School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland S Supporting Information *

ABSTRACT: By first-principle calculations, we have systematically studied the effect of strain/pressure on the electronic structure of rutile lead/stannic dioxide (PbO2/SnO2). We find that pressure/strain has a significant impact on the electronic structure of PbO2/SnO2. Not only can the band gap be substantially tuned by pressure/strain, but also a transition between a semiconductor and a gapless/band-inverted semimetal can be manipulated. Furthermore, the semimetallic state is robust under strain, indicating a bright perspective for electronics applications. In addition, a practical approach to realizing strain in SnO2 is then proposed by substituting tin (Sn) with lead (Pb), which also can trigger the transition from a large-band-gap to a moderategap semiconductor with enhanced electron mobility. This work is expected to provide guidance for full utilization of the flexible electronic properties in PbO2 and SnO2. KEYWORDS: lead dioxide, stannic dioxide, strain effect, pressure effect, band-inverted semimetal

S

semimetals in electronics, namely, a strategy to widely tune their band structure.6 A Dirac semimetal normally has a single Dirac point defined by the lattice symmetry7 and can also be created via band inversion, which induces a pair of Dirac points in the Brillouin zone, as demonstrated in the most recent experiment by doping black phosphorus with potassium.8 The possibility of controlling the transition between semiconductors and semimetals is highly desirable because it would bring great flexibility in the design and optimization of optoelectronic devices. Rutile-type PbO2 (β-PbO2), a rare mineral plattnerite, has been known for over 100 years,9 and a number of investigations have been conducted both experimentally and theoretically to

emimetal materials, especially Dirac semimetals such as graphene, are promising candidates for electronic devices because they usually have conical band structures near the Fermi level, which enable them to achieve very high carrier mobility and conductivity. Electron and hole carriers in semimetal are supposed to give rise to many novel electronic properties including the relativistic Dirac Fermions with linear dispersion, unconventional superconductivity,1 and giant magnetoresistance.2 Therefore, the search for Dirac semimetals has attracted great attention in recent years.3,4 Unfortunately, the application of such semimetals, e.g., in planar field-effect transistors, is still limited because of their lack of a band gap, which strongly undermines the possibility of achieving large on−off current ratios.5 The ability to control the properties of Dirac materials, such as the band gap, is essential for the development of next-generation electronic devices. Hence, a significant challenge remains toward the application of © XXXX American Chemical Society

Received: August 8, 2016 Accepted: September 22, 2016

A

DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

37.5%, 50%, and 75% Pb concentrations, respectively, in PbxSn1−xO16. Standard DFT using both PBE and hybrid functional methods has been applied to evaluate the structural configuration of PbO2, and the calculated structural parameters are presented in Table 1. We find that PBE overestimates the

study its electronic properties. However, the physical properties of β-PbO2 have not been well understood because some experimental works report a metallic ground state,10−12 while others claim an optical band gap of up to 1.5 eV.13−15 On the theoretical front, Heinemann et al., using standard density functional theory (DFT), reported that PbO2 is intrinsically metallic, with the conduction band overlapping with the top of the valence band,16 while Payne et al. recently found that PbO2 is a semiconductor with a small band gap (0.2 eV) by using a hybrid functional method.17,18 As such, it is still too early to draw a conclusion on the nature of the electronic ground state of PbO2, and there is a pressing need for a careful reexamination of its physical properties. Moving up group 14 from Pb to Sn in the periodic table, we find SnO2, which also crystallizes in a rutile-type (β-)tetragonal structure but presents a large band gap (3.6 eV). SnO2 is part of another important group of materials with the potential for applications in solar cells because of their long-term stability and high carrier mobility.19,20 Furthermore, they have been proposed as alternative anode materials with high energy density and stable capacity retention in lithium-ion batteries.21 However, the large band gap of SnO2 limits its practical application. Therefore, reducing the band gap of SnO2 to a useful range will greatly extend its application in photovoltaics. In this work, systematic DFT calculations have been carried out to investigate the structural and electronic properties of βPbO2/SnO2. We find that the band gap of PbO2 can be substantially tuned and a transition between a semiconductor and a gapless/band-inverted semimetal (Dirac semimetal) can be realized by hydrostatic strain/pressure. Wide-band-gap SnO2 can also be turned into a moderate semiconductor and Dirac/ band-inverted semimetal with a small electron effective mass, thus extending its potential applications in nanoelectronics and photoelectronics. Furthermore, doping SnO2 with large Pb atoms is demonstrated to be effective in realizing strain in the experiment. Structural relaxation and electronic band-structure calculations were carried out using DFT, as implemented in the Vienna ab initio simulation package (VASP).22,23 The projector-augmented-wave method was used to describe the electron−ion interaction.24,25 The generalized gradient approximation, as parametrized in the Perdew−Burke−Ernzerhof (PBE) functional,26 and the state-of-the-art hybrid functional HSE0627 were employed to evaluate the exchange correlation energy. An energy cutoff of 400 eV for the plane-wave expansion and Monkhorst−Pack k-point meshes of 4 × 4 × 6 and 2 × 2 × 6 for a primitive unit cell and a 2 × 2 supercell, respectively, in the whole Brillouin zone were used in the calculation. During the geometry optimization of all structures, the atomic position and lattice vectors were fully relaxed until energy and forces were converged to 10−5 eV and 0.005 eV/Å, respectively. The electron effective mass is estimated from the curvature of the electronic band dispersion. The effective mass, m*, of the electrons at the conduction band minimum (CBM) can be obtained according to the formula m* = ℏ2

∂E 2 ∂k 2

Table 1. Crystal and Electronic Properties for PbO2 Calculated Using the PBE and HSE06 Functionals and Compared to Those of Existing Experiments experiment HSE (this work) PBE (this work) HSE (ref 20) PBE (ref 20)

c (Å)

Eg (eV)

4.951 5.010 5.067 4.960 5.060

3.383 3.380 3.441 3.376 3.455

0.080 metallic 0.23 metallic

m* (me) 0.80 0.11 0.18

a Here a/c, Eg, and m* represent the lattice parameters, band gap, and effective mass, respectively.

lattice constants by 2% compared to the experimental measured values.17 The prediction from PBE also suggests that PbO2 is a metallic material with an overlap of 0.7 eV between the valence and conduction bands at the Γ point (see Figure 1c). The HSE06 functional is known to successfully reproduce the structural and band-gap data for a wide range of metal oxide systems.28 It is also capable of predicting more accurate equilibrium lattice constants compared to those from PBE, as shown in Table 1. The calculated structural parameters of PbO2 by HSE06 are very close to the experimental results. The HSE06 calculation also shows that PbO2 has a small band gap (Figure 1b), which is consistent with previous work.17 From Table 1, we can find the value of the c axis to be close to the experimentally measured values, while the size of the a axis is slightly larger. Furthermore, both the present work and that of Scanlon et al.17 predict PbO2 to be a small-band-gap semiconductor, with a somewhat smaller band-gap value evaluated in the present study. Having identified the crystal geometry of PbO2, we investigated the effect of strain on its band structure. Figure 2 illustrates variation of the band gap as a function of strain. Clearly, the effect of strain is particularly notable at Γ(0,0,0) and R(0.0,0.5,0.5). Under tensile strain, as shown in Figure 2c,d, the energy levels of the CBM and valence band maximum (VBM) cross the Fermi level in opposite directions, suggesting a transition from a semiconductor to a band-inverted semimetal. The overlap gap is around −0.12 eV at the Γ point at a strain of 1% (see Figure 2d). The band-inverted point at the high-symmetric Γ point evolves into two Dirac points around Γ. Subsequently, with increasing tensile strain, the semimetallic state becomes more robust, as is evident from the overlap gap continuously rising up to −0.37 eV at a strain of 3% (see Figure 2e). It can also be seen that the Dirac points move along the Γ−Z and Γ−M lines when the tensile strain increases. The Dirac semimetal can further be verified from the density of states (DOS) of PbO2, as shown in Figure S1. One can observe that the DOS vanishes near EF, suggesting a well-defined semimetallic nature. These results strongly suggest that bulk PbO2, under a small tensile strain, is an example of a strainmodified Dirac semimetal. In contrast, when pressure strain (negative strain) is applied to PbO2, as shown in Figure 2a−c, the energy of the CBM at Γ point rises, inducing an enhancement of the direct band gap to

−1

( )

a (Å)

,

where E and k are the band energy and reciprocal lattice vector. For anisotropic materials, m* = mi*mj* where i and j label the transport direction (x, y or z). In addition, for the substitution of Sn by Pb in SnO2, we use a 2 × 2 supercell (Sn8O16) with one, two, three, four, and six Sn atoms substituted by Pb atoms corresponding to 12.5%, 25%, B

DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Figure 1. (a) Top and side views of the PbO2 crystal structure. The black and red spheres represent Pb and O atoms, respectively. Band structure of PbO2 calculated by using (b) hybrid HSE06 and (c) PBE functionals.

Figure 2. (a−c) Direct-to-indirect band-gap transition in β-PbO2 manipulated by hydrostatic pressure. (c−e) Transition from a semiconductor to a metal in β-PbO2 manipulated by hydrostatic tensile strain. (f) Band gap at the Γ point as a function of strain. The hydrostatic strain and pressure correspond to expansion and compression along three axes, respectively. The Fermi energy was set to zero.

0.30 eV at −1% (Figure 2b; the band gap will rise even further with increasing strain). In general, from Figure 2f, it is clear that the band gap of PbO2 is widely and continuously tunable in the range of +0.8 to −0.4 eV for strains in the 3% to −3% range. The gradual emergence of band inversion and Dirac points in PbO2 is particularly interesting. Therefore, PbO2 demonstrates a potential for applications in field-effect transistors with a high on−off current ratio. Furthermore, the dramatic response of PbO2 to strain and pressure points to its potential for pressure/ strain sensing applications. Finally, note that a very small pressure or tensile strain turns PbO2 into completely different electronic materials: a semiconductor or a band-inverted semimetal. These findings shed light on the long-standing controversies regarding its metallic/semiconducting properties,

given that the role of a small pressure or tension could be easily overlooked in the experiments. Variation of the band gap under strain can be explained by analyzing the orbital-resolved band structures, as shown in Figure 3. At zero strain, the dominant contribution to the VBM at the Γ point comes from the px and py orbitals of O, while the CBM at the Γ point mainly consists of the s orbitals of Pb, as shown in Figure 3a. With increasing tensile strain, the energy of the Pb s states decreases, while that of the px and py states of O rises in energy. This causes both the CBM and VBM to shift toward the Fermi level, touching each other at a critical strain, before their energies cross at a higher one. For strains beyond the critical one, those orbitals keep shifting away from the Fermi level gradually in opposite directions. This “shifting away” triggers the formation of a band-inverted semimetal with C

DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Figure 3. Orbital-resolved band structures of β-PbO2 under different strains of 0% (a) and 2% (b). The red dots represent contributions from the Pb s atomic orbital, and the orange and violet dots indicate contributions from the px and py orbitals of O. Larger dots mean higher contributions, while smaller ones indicate lower contributions. Smooth lines represent zero contribution.

Figure 4. (a−e) Transition from a semiconductor to a metal in β-SnO2 manipulated by hydrostatic strain. (f) Band-gap (red line) and electron effective mass (green line) at the Γ point as a function of strain. The Fermi energy was set to zero.

two Dirac points near the Γ point. Furthermore, with increasing tensile strain, the Pb−O bond length becomes larger, which indicates a weaker bonding strength between the Pb and O atoms. The decline of the bonding strength would therefore cause a decrease of the energy splitting between the bonding (VBM) and antibonding (CBM) states, which results in an upward shift of the bonding state and a downward shift of the antibonding state. In contrast, if pressure strain is applied, the energy of the Pb s states rises, resulting in a shift of the CBM away from the Fermi level and an increased band gap. At the same time, the smaller lattice under pressure leads to shorter Pb−O bond lengths and stronger interactions between the Pb and O atoms.

For β-SnO2, the equilibrium lattice constants and band gap are calculated with HSE06 to be a = 4.754 Å and c = 3.187 Å and 2.8 eV (more details can be found in Figure S2), respectively. These are in general agreement with the experimental values of a = 4.738 Å and c = 3.186 Å and 3.6 eV. In addition to the structure parameters, the strain effect on the band structures of SnO2 has also been investigated, as shown in Figure 4. The band gap of SnO2 decreases dramatically with increasing tensile strain. A moderate 4% strain is able to reduce the gap to approximately 1.5 eV, which is an ideal gap for solar-cell materials, indicating their promising applications as light absorbers. With a strain up to about 11%, the band gap gradually closes, and then SnO2 becomes a gapless semimetal, with the VBM and CBM touching each D

DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Figure 5. (a−c) Band structures of PbxSn1−xO2 with different Pb doping concentrations. (d) Band gap (red line) and effective mass (green line) as a function of the Pb doping concentration. The Fermi energy was set to zero.

other at the Γ point, indicating a transition from a semiconductor to a semimetal (Figure 4f). When the strain is increased above the critical strain of 11%, the CBM and VBM states (at the Γ point) cross over and continuously move away from the Fermi level. This triggers a transition from a gapless semimetal to a band-inverted semimetal with overlapped valence and conduction bands at the Γ point. Subsequently, with increasing tensile strain, the overlap gap keeps rising up to 0.3 eV at 12% strain. Such a large overlap gap should enhance the electron mobility at the conic point. It then turns out that the electronic properties of SnO2 are highly tunable via the application of hydrostatic strain. Such a flexible band gap manipulated by strain is expected to extend the potential of the material in applications. It is also evident from Figure 4 that the strain has a significant impact on the curvature of the dispersion relation at the band edges. It is known that the sharper dispersion relationship at the band edges is always accompanied with a smaller effective mass m*, which would therefore enhance the carrier mobility of the system. Thus, a change of the electron effective mass modified by strain is plotted in Figure 4f. At 0% strain, the electron effective mass is 0.22 me, which is in agreement with the experimental measurements by Button et al.29 With increasing tensile strain (Figure 4f), m* undergoes to a dramatic downward trend, reaching 0.15 me at 5% strain (this strain should be reachable in experiments) and 0.08 me at 10% strain (may be difficult to realize experimentally). Such a variation in the electron effective mass controlled by strain makes SnO2 a promising material for applications in highly sensitive optical and electromechanical sensors. The mechanism with which the electronic structure of SnO2 is controlled by strain is quite similar to that of PbO2,, as shown in Figure S3. We observe that the strain effectively manipulates the shift of the Sn s state in the CBM and thus induces bandgap reduction. Beyond the critical strain (11%), the CBM exchanges with the VBM, which consists of O px and py orbitals. This generates a transition from a semiconductor to a

band-inverted semimetal. As revealed by the orbital-resolved band structure (Figure S3), the VBM in SnO2 is mainly composed of O p orbitals, while the CBM derives from the Sn s orbital. Because Pb and Sn are elements belonging to the same group in the periodic table, we hypothesize that substitution of Sn by Pb in SnO2 should lower the energy of the CBM along with a limited effect on the energy of the valence band. Therefore, another effective strategy of reducing the band gap of SnO2 may be that of Pb doping. In addition, Pb doping may lead to an increase in the lattice constant of the unit cell due to the larger atomic size of Pb compared to Sn. Such an increase of the lattice parameter with Pb doping is very similar to that obtained by the simple application of tensile strain in the unit cell, so that we expect Pb doping to be an effective method to include tensile strain in SnO2 and hence to reduce the band gap as well as alter its electronic structure. Having discovered the substantial impact of strain on both PbO2 and SnO2, the Pb-doping effects on the structural and electronic properties of SnO2 are investigated. Parts a−c of Figure 5 demonstrate that increasing the Pb concentration significantly drives the CBM toward the Fermi level and therefore reduces the band gap of SnO2. Moreover, it also leads to elongation of the lattice constants, which is analogous to that obtained by the application of strain to this material (Figure S4). Finally, the effective mass shows a downward trend and changes from 0.22 me for SnO2 to 0.15 me for a 50% Pb-doping concentration. It should be noted that such a Pb-doping technique has been realized experimentally in the fabrication of the PbxSn1−xO2 film with 0 < x < 0.7.30 Therefore, the cation interchange is an effective method to tailor the electronic properties of SnO2 and PbO2. After the possibility of tailoring the electronic properties of SnO2 by two different tools, namely, strain and Pb doping, was explored, a further investigation was also performed where the two aspects are combined; i.e., strain is applied on a PbxSn1−xO2 alloy. Figure S5 illustrates the change of the band gap under several strains for SnO2 with 25% Pb doping E

DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

ACS Applied Materials & Interfaces

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(Pb2Sn6O16). In Figure S5a, the band gap for strain-free Pb2Sn6O16 is 2 eV, which is 1 eV smaller than that of pure SnO2. The band gap has a downward trend with the rising strain, as shown in Figure S5, which is quite similar to that of pure SnO2. However, the critical strain, for the semiconductorto-semimetal transition, is somewhat reduced (8%). As for the effective mass shown in Figure S5d, this decreases with increasing strain, reaching a very small value (0.10 me) for 6% strain. A relatively small Pb concentration in SnO2 has effectively lowered the critical strain for the transition. It can be expected that higher Pb concentrations, such as 50% and 60%, will further decrease the critical strain value and therefore make this transition easier to achieve in the laboratory. Last, the spin−orbit coupling (SOC) effect has also been considered in the current work. It is found that the gap of PbO2 at 0% strain remains open when SOC is introduced in the system (Figure S6), proving that the results yielded by the HSE06 method are highly reliable, and the conclusion will not be changed by using the HSE + SOC calculation. In summary, we have systematically investigated the electronic properties of PbO2 and SnO2 manipulated by strain and doping. We find that PbO2 is a small-band-gap semiconductor with light electron effective mass and its band structure is very sensitive to strain. Specifically, a small tensile strain (1%) turns it into a band-inverted semimetal, while a moderate pressure strain (−1%) induces a transition to a semiconductor. Our current results not only provide a good rationale for the conflicting works on PbO2 reported in previous literature, but also indicate the potential application of PbO2 in transistors with a large on−off current ratio due to the emergence of the semimetallic state. For SnO2, adding effective strain (11%) is also able to trigger the semiconductor-tosemimetal transition, and the critical strain can be further reduced via the substitution of Sn by Pb. Such a transition is expected to be instrumental for applications in optoelectronics. In addition, Pb doping, as an efficient technique to introduce strain in SnO2, is also capable of decreasing the effective electron mass and therefore enhancing the electron mobility in SnO2. Because semimetallic PbO2/SnO2 possesses many novel electronic properties, such as the relativistic Dirac Fermions, unconventional superconductivity, and giant magnetoresistance, the strain-controlled transition between a semiconductor and a semimetal coupled with the widely tunable band gap is expected to have great potential in building novel electronic and photonic devices. In addition, the dramatic response of rutile PbO2/SnO2 to strain/pressure points to its potential in pressure/strain sensing applications.

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Letter

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.D.). Author Contributions

‡ These authors contributed equally to this work. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge generous grants of high-performance computer time from computing facilities at Queensland University of Technology and Australian National Facility. A.D. greatly appreciates a Australian Research Council QEII fellowship and financial support of the Australian Research Council under Discovery Project DP130102420. F.M. also acknowledges support through a CSIRO top-up scholarship. A.B. thanks CSIRO for support through a Julius Career Award. S.S. thanks the European Research Council (Quest Project) for financial support.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b09967. DOS of PbO2 under 3% stain, band structure of SnO2 using the PBE and HSE06 functionals, orbital-resolved band structures for SnO2 under different strains, relative change of the lattice parameter of SnO2 at different concentrations of Pb doping, and band structure of Pb2Sn6O2 (SnO2 with 25% Pb-doping concentration) in the presence of strain (PDF) F

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DOI: 10.1021/acsami.6b09967 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX