Bandgap Engineering in High Temperature Semiconductors Boron

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C: Physical Processes in Nanomaterials and Nanostructures

Bandgap Engineering in High Temperature Semiconductors Boron-Rich Icosahedral Compounds Hongwei Wang, and Qi An J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02254 • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 25, 2019

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The Journal of Physical Chemistry

Bandgap Engineering in High Temperature Semiconductors Boron-Rich Icosahedral Compounds Hongwei Wang and Qi An* Department of Chemical and Materials Engineering, University of Nevada-Reno, Reno, Nevada 89557, United States *Corresponding author-Email: [email protected]

ABSTRACT: Bandgap engineering is essential for boron-rich icosahedral compounds for such high temperature applications as beta-voltaic devices and thermoelectrics, while the extreme complex chemical bonding in these icosahedral compounds leads to intriguing electronic properties. Here, we first employed quantum mechanics (QM) simulations to determine the electronic states that control the valence band maximum (VBM) and conduction band minimum (CBM) of these icosahedral compounds, as well as the detailed band structures. Then we examined the bandgap modulation by applying twin boundary, chemical substitution, structure arrangement, and hydrostatic pressure, with which the bandgaps of these icosahedral compounds can be engineered wider or narrower to a large extent. Particularly, we find that some icosahedral compounds show an increased bandgap with the applied hydrostatic pressure, an unusual phenomenon compared to the conventional inorganic semiconductors. Our study provides a fundamental understanding on the electronic properties of icosahedral solids and an effective way to tune their bandgaps for designing promising optical, thermoelectric, and beta-voltaic devices at extremely high-temperature and radiation condition.

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1. INTRODUCTION Icosahedral boron and boron-rich compounds are mainly composed of 12-atom boron clusters in which boron atoms occupy the 12 vertices of icosahedra1, displaying such promising properties as super hardness, high-melting temperature, and radioresistance2. The ability of icosahedral boron-rich compounds to survive in extreme environments make them potential useful for various advanced device applications3. One primary use is Beta-voltaic cells which utilize energy from a radioactive source of Beta particles to generate electricity and heat2-3. The beta-voltaic devices made with conventional semiconductors tend to undergo very serious radiation damage which can be circumvented by replacing them with icosahedral boron-rich semiconductors. The long-life and low-power characters of these icosahedral compounds are particularly well-suited for military and spacecraft applications. Another important application of icosahedral boron-rich compounds is in thermoelectric energy conversion4, generating electrical power from solar heat or recycle waste thermal energy5. Some boron-rich semiconductors have been found to possess large Seebeck coefficients6, high electrical conductivities, and very low thermal conductivities7. These are essential prerequisites to achieve high efficiency thermoelectric energy conversion5. Since the energy conversion through radiation and thermoelectricity highly depends on the systematic electronic structures, it is essential to examine the band structures and band gaps of icosahedral boron-rich semiconductors and perform band engineering to optimize their engineering performance. The boron-rich compounds alpha boron (α-B12), boron carbide (B4C), boron suboxide (B12O2) and boron subphosphide (B12P2) have similar crystal structure in which the doped elements C, O and P form the multiatomic chains linking to adjacent icosahedra. The different types of bonding interactions between chain and icosahedral atoms in these boron-rich systems


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result in unusual electronic properties8-10. Boron carbides possess a wide range of energy gaps between 0.48 and 2.5 eV reported by experiment9, 11-12, which have attracted more attention in contrast to other boron-rich compounds. Moreover, boron carbide is also found to display a pressure-dependence energy gap13, which is opaque at the ambient condition but becomes transparent at high pressure. The abundant electronic behaviors in boron carbides is due to their complex structure configurations and various stoichiometries. Ektarawong et al. found the one B atom of the icosahedron in B4C boron carbide tends to be substituted by one C atom able to be randomly distributed over all polar sites of the icosahedron14. In addition, the complex intericosahedral arrangements such as CBC, CBB and B□B(□ represents vacancy) may coexist in the actual boron carbide structures15-16, which has been investigated by Werheit and his coworks. The mixture of ~10% B□B arrangements, < 2% C–B–B chains and ~90% CBC chains with 100% B11C icosahedron13, 15 is responsible for the experimentally observed B4.3C structure formula, the carbon-rich limit composition of boron carbide compounds16. The electron transition levels introduced by above configurational disorder and chain-related defects in B4.3C compound, accounting for the wide-range bandgap, have been systematically studied by Werheit with theoretical analysis recently11. Furthermore, Hushur et al. proposed the optical transition in B4.3C compound results from the reduced structural defects by high pressure13, which enable to stabilize the defect-free B4C boron carbide with wide energy gap. Although the electronic performances for the boron-rich compounds have been investigated both theatrically and experimentally before, the intrinsic electronic properties of semiconductors are usually not attractable for practical applications. For example, their bandgaps need to be reduced to raise the usage efficiency of sunlight for the photocatalysis17-20 or increased for shortwavelength optical applications, ultraviolet photodetectors and resisting radiation damages21.


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Several effective approaches, such as carrier transport through interface heterojunction22-23, introducing gap state with composition substitution19, mechanical-strain induced structure distortion18,

26,

24-25,

and band edge modulation by

have been utilized to tailor electronic

properties in the traditional semiconductors and novelly discovered two-dimensional materials27. Within these methods, their electronic conductivities, light-emitting properties and the visible light-induced photocatalytic efficiencies have gained significant improvements28. However, the research on how to tune electronic properties in boron-rich icosahedral compounds has not been considered so far because of intriguing structure and bonding characters in these materials. Hence it is necessary to explore the bandgap engineering in these boron-rich systems to design more advanced devices, in combination with exciting electric, thermal, and mechanical performances. In this study, we focus on the electronic structures of icosahedral boron-rich compounds αB121,

29,

B12O230, B12P231-32, B4C9,

33

and B14C19, which are investigated by means of first-

principles method. The effects of twin boundary, high pressure, chemical substitution and structure rearrangement on electronic properties are considered at the present work. As for the boron carbide, we only consider the major constituent (B11C)CBC in B4.3C compound, the chainrelated defects are not considered in our work. We select three reprehensive structures of the (B11C)CBC system studied by Ektarawong14 to investigate the configuration disorder effect on electronic structures. The first one is the lowest structure configuration with the substituted C atom at the polar site in the icosahedron; the second one is the lowest structure configuration with the substituted C atom at the equatorial site in the icosahedron; and the third one is the structure configuration with a chain contained three C atoms. We believe that mechanism of the modulated bandgap by configuration disorder in these three structures is similar to that in other


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structure configurations. We find that the VBM and CBM electronic states in the icosahedral boron-rich compounds display the localized character, which are distributed over the intraicosahedral and chain chemical bonds respectively and are capable of tuning with the external physical or chemical conditions. As a result, the VBM and CBM electronic states correlated with these chemical bonds are readily tailored to a large extent as well. Based on the mechanisms, the design principles are established for the bandgap control in boron-rich icosahedral compounds.

2. STRUCTURAL AND ELECTRONIC PROPERTIES FROM FIRST-PRINCIPLES CALCULATIONS Figure 1a-d shows the schematic crystal structures of four typical boron-rich compounds α -B12, B12O2, B12P2 and B4C. Here we considered the ground state structure polar (B11Cp)CBC for B4C34. The B12 icosahedral units in α-B12 are interlinked via six strong two-center-two-electron (2c-2e) and six weak three-center-two-electron (3c-2e) bonds (see Figure 2). This results in 13 intra-icosahedral bonds within B12 icosahedron, satisfying the Wade’s rule35-36. The icosahedral atoms connected by 2c-2e and 3c-2e are called polar and equatorial atoms respectively (see Figure 2), which locate at the polar and equatorial sites in the icosahedron. For element doped systems B12O2, B12P2 and B4C, the doped atoms form a two-atom or three-atom inter-icosahedral chain which links with three neighboring icosahedra through the equatorial atoms. The more detailed structure information is shown in Figure 2. The two-atom or three atomic chains in both B12P2 and B4C will transfer electrons to the two-electron deficient B12 or one electron deficient B11C icosahedral units, forming 13 intra-icosahedral bonds and satisfying Wade’s rule34,

37.

However, in B12O2, the O atom attracts electrons from B12 icosahedron because of its larger electronegativity than B, leading to electron deficient in B12 icosahedron38.


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Since the icosahedral boron-rich compounds can be classified to the special molecular solids, named inverted molecular solids, the bonding character has a significant effect on the band structures of these compounds. To clarify this effect, we examined the band structures of these compounds using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid exchange functional39 which has been proven to be capable of obtaining more accurate bandgaps than Perdew-BurkeErnzerhof (PBE) functional40. The simulation details can be found in the Supporting Information (SI). The calculated band gaps of the B rich compounds are in the range of 2.0 to 3.5 eV, as listed in Table 1, indicating that all of these systems are semiconductors. In particular, the predicted bandgaps for α-B12 and B12P2 are 2.18 and 3.40 eV, respectively, which agree very well with experimental measurements of 2.00 and 3.35 eV41-42, indicating the reliability of HSE06 functional. The calculated band structures and charge density isosurfaces of four selected compounds are displayed in Figure 1a-d. The VBM is marked with blue color and CBM is marked with yellow color. The charge density analyses indicate that the VBM electronic states originate from the intra-icosahedral bonding within the B12 units for α-B12, B12O2, B12P2, while it stems from the inter-icosahedral bonding between neighboring icosahedra in B4C. The CBM electronic states are determined by the inter-icosahedral 3c-2e bonding in α-B12, antibonding interactions between two chain P atoms in B12P2, and antibonding interactions between the chain-carbon and chainboron atoms in B4C. However, in B12O2 the CBM electronic state is also determined by the intraicosahedral multicenter bonding. The unique CBM electronic state in B12O2 arises from the electron deficiency in B12 icosahedra because chain O atom attracts electrons from B12 icosahedron38.


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3. BANDGAP MODULATION BY CHEMICAL AND MECHANICAL CONDITIONS Understanding band structures of boron rich compounds is essential for bandgap engineering for widely engineering applications. Here we apply four realistic approaches to investigate the bandgap engineering in B-rich compounds: (1) twin boundary engineering, (2) composition modulation, (3) structure arrangement, and (4) pressure engineering. 3.1. TWIN BOUNDARY Twin boundaries (TBs) with low interfacial energy generally exist in crystalline materials, which has been extensively observed in B-rich compounds30,

33.

Therefore, it is necessary to

investigate the dependent of band structures on TBs for boron-rich compounds. Here, we focus on three twinned structures of boron rich compounds τ-B12, τ-B12O2 and τ-B12P2 (Figure 3a). The computed band structures of these boron-rich compounds are shown in Figure S1-S3 of SI and the bandgaps are given in Table 1. The bandgaps of α-B12, B12O2, are almost unaffected by TBs, whereas the τ-B12P2 has a bandgap increasement of 0.4 eV compared to the perfect B12P2 crystal. In order to understand the different electronic behaviors, we utilized the crystal orbital Hamilton population (pCOHP) approach to analyze the chemical bonds correlating with the VBM and CBM states for both perfect and twinned boron-rich compounds. The pCOHP provides a straightforward view onto orbital-pair interactions, capable of a quantitative measure of bonding strength. The negative and positive parts of pCOHP represent bonding and antibonding contributions to the chemical-bond strength43. Obviously, the bandgaps are determined by the lower limit of the CBM-bonding pCOHP above the Fermi level and the upper


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limit of VBM-bonding pCOHP below the Fermi level (See Figure S4 in SI). The pCOHPs of B12P2 and τ-B12P2 shown in Figure 3b indicate that the lower limit of antibonding-state edge responsible for CBM is higher than that in B12P2, which accounts for the wider bandgap of τB12P2. Meanwhile the upper limits of bonding-state edge responsible for VBM are almost the same in B12P2 and τ-B12P2 (see Figure S1 in SI). Since the CBM electronic states of B12P2 and τB12P2 both reside in the P-P chain bonds (See charge density in Figure 3c), the bandgap difference between B12P2 and τ-B12P2 originates from the chain bonding interactions. The length of P-P bonds remains the same in both B12P2 and τ-B12P2, but one B-P bond connecting intericosahedra chain and B12 icosahedron is shortened by 0.02 Å for τ-B12P2. The contracted B-P bond would enhance the bonding interaction between chain and icosahedron, which increases the antibonding level as well as the bandgap. It is worth to notice that each P atom with five valence electrons donates one electron to the B12 icosahedron, and the remaining four electrons form the sp3-hybridization with the surrounding three equatorial B atoms and one chain P atom44. This accounts for the chain P-P bonding interaction affected by B-P bond. To verify this, the P-P chemical bonding orbitals were obtained with a method of Solid State Adaptive Natural Density Partitioning45 (SSAdNDP). As shown in Figure 3c, the shape of CBM charge densities are quite similar comparing the P-P antibonding orbitals for both B12P2 and τ-B12P2. The relevant orbital compositions analyzed by the natural bond orbital (NBO) method46 are shown in Figure 4. The P-P antibonding orbital consists of about 25% s orbital and 75% p orbital, indicating the character of sp3-hybridization. Moreover, the wavefunction of CBM electronic state was plotted for B12P2 in Figure S5 of SI

47.

The peaks of the wave function are concentrated at both

equatorial B and chain P sites and exhibit the antibonding character, which is consist with the above charge density and orbital analyses. Since the B12 icosahedron is stiffer than inter-


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icosahedra P-P chain10,

48,

the VBM orbital distributed over intra-icosahedral bonds is less

sensitive to the external influence, which accounts for less varied energy edge of VBM electronic state in τ-B12P2. As for the α-B12 its VBM electronic orbitals reside in the B12 icosahedrons while the CBM electronic orbitals are related to 3c-2e bonds (see Figure 2). However, the 3c-2e bond length is pretty similar in both α-B12(2.00 Å) and τ-B12(2.00 Å), leads to the smaller bandgap difference between α-B12 and τ-B12. Both the CBM and VBM electronic orbitals of B12O2 and τ-B12O2 sit inside the B12 icosahedron because of the electron deficiency in B12 icosahedron38. Therefore, the bandgap of τ-B12O2 is exact the same as the B12O2. Our results suggest that nanotwin is not an effective way to perform bandgap engineering when the B12 icosahedron is electron deficiency (B12O2) or the chain-icosahedral interaction weakly depends on the twinned structure (α-B12). 3.2. COMPOSITION SUBSTITUTION Composition modulation has been proved to be an effective approach to tailor the band edges in semiconductors21, 28, even the continuous tuning of the band gap22. Hence, we calculated the electronic structure for B12S2 which can be regarded as the S substituted B12O2. Although the bandgap of B12O2 is not affected by TB, it undergoes a decrease of 0.74 eV after the S substitution (Table 1). Figure 5a shows the CBM bonding pCOHPs and charge density isosurfaces of CBM electronic state for B12O2 and B12S2. The lower limit of antibonding-state edge above the Fermi level in B12S2 has a large downwards shift in contrast to B12O2, and the upper limit of VBM-bonding pCOHPs below the Fermi level are equal by coincidence (see Figure S6 in SI). Therefore, the bandgap modification by composition modulation in B12O2 should originate from chemical bonding associated with the CBM electronic state. As mentioned


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above, the CBM electronic orbital of B12O2 locates at the center of B12 icosahedron instead of the inter-icosahedra chain. The reason can be attributed to the O atoms with higher electronegativity tend to attract electrons from its surrounding equatorial B atoms

38, 44,

which leave the positive

holes dispersing over the adjacent B atoms. The valence charges of the oxygen, polar and equatorial boron atoms in B12O2 obtained through the Bader analysis49 are about 8.0 e, 3.0 e, and 2.3 e, respectively. This suggests the O atoms have attracted electrons from the equatorial B atoms to form the close shell electronic configuration. The holes caused by B-O bonding interactions create unfilled orbitals at the equatorial B atoms, which correspond to the CBM electronic states. As shown in Figure 5b, the CBM charge density of B12O2 lies in the plane of equatorial B atoms with vertexes toward the six B-O bonds, corresponding to the six-center Bbonding orbital situated in the B-O plane. The analysis of charge density and SSAdNDP bonding orbital show a good agreement with the above discussion for the origin of CBM electronic states in B12O2. The CBM electronic orbital of B12S2 has the same character with that of B12O2. However, the lower electronegativity of S results in the weaker strength of B-S bond. This leads to the lower hole densities around the equatorial B atoms (Figure 5b) as well as the decreased CBM energy edge. 3.3. COMPOSITION CONCENTRATION Besides the composition substitution, the effect of the composition concentration on electronic property is also investigated for B4C compounds. B4C exhibits a wide range of carbon solid solubilities ranging from 8% to 20%. Therefore, it is important to investigate how the C concentration affects the bandgaps and band structures. The polar B11C-CBC composed of one C-atom substituted B12 icosahedron at the polar site and one C-B-C chain is the ground-state structure configuration of B4C9, 50, which possesses a wide bandgap of 3.84 eV. The kink-B14C1


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with a lower C concentration and a kinked B-B-C chain has a largely reduced bandgap of 2.01 eV in contrast to (B11C)p-CBC, indicating that the stoichiometry play an important role in the electronic structure of B4C. The B11C1 icosahedron in polar B11C-CBC compound becomes oneelectron deficient owning to the C-atom substitution at the polar site, and it accepts one electron from the B atom in the CBC chain. The two C atoms in the CBC chain form the sp3hybridization with the surrounding three equatorial B atoms and one chain B atom44, and the one B atom in the CBC chain form the sp-hybridization with the two C atoms. All bonding orbitals are completely filled in (B11Cp)-CBC making it a rather stable compound. These chain bonding information for B11C-CBC was also confirmed by the NBO analysis shown in Figure 4. As for the kink-B14C1, the two B atoms in C-B-B chain forms a 3c-2e bond with the connected B12 icosahedron, satisfying the Wade’s rule51. The bonding pCOHPs, charge densities, and SSAdNDP orbitals of CBM for polar B11C-CBC and kink-B14C1 are shown in Figure 5c and Figure 5d. As shown in Figure 5d, the CBM electronic state of the polar B11C-CBC stems from the antibonding interaction between C and B atoms in the C-B-C chain. Similarly, the CBM electronic orbital of the kink-B14C1 also resides in the chain B-B bonds and exhibits the 3c-2e bonding character. In addition, the VBM electronic states of polar B11C-CBC and kink-B14C1 both originate from the bonding orbitals of the two-center inter-icosahedral B-B bonds (see Figure S7 in SI), expecting to possess the closed VBM electronic state edges. Since the weak 3c2e bond between C-B-B chain and B12 icosahedron in B14C1 leads to a lower CBM energy edge, the bandgap of polar B11C-CBC determined by the inter-icosahedral B-B bonding state and the chain C-B antibonding state should be larger than that of kink-B14C1. The lower limit of CBMbonding pCOHPs above the Fermi level in kink-B14C1 is much smaller than that in polar B11CCBC (Figure 5c), showing a good agreement with the above discussions.


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3.4. STRUCTURE REARRANGEMENT Molecular crystal with the same structural formula may possess numerous structural configurations9, 52. Particularly, B4C possesses three possible configurations: (1) (B11Cp)-CBC; (2) equatorial (B11Ce)-CBC; and (3) (B12)-CCC52-53. Although (B11Cp)-CBC is the ground state structure, it is important to explore the effect of various configurations on the electronic property since these configurations may exist in experimental samples. In the chain B12-CCC, each chaincenter C atom with four valence electrons donates two electrons to the B12 icosahedron, and the chain-end C atoms form the sp3-hybridization with the surrounding three equatorial B atoms and one chain-center C atom with two valence electrons left. Similarly, the one chain-end C atom in the equatorial B11C-CBC forms the sp3-hybridization with the surrounding two equatorial B atoms, one C atom at equatorial site and one chain-center B atom, whereas the other chain-end C atom performs the sp3-hybridization with the adjacent three equatorial B atoms and one chaincenter B atom. The above details for the orbital hybridization of chain atoms in chain B12-CCC and equatorial (B11Ce)-CBC were also well consistent with the NBO analysis in Figure 4. The bandgaps of equatorial B11C-CBC and chain B12-CCC have significantly changed compared to that of polar B11C-CBC (Table 1). Especially for the chain B12-CCC, its bandgap is reduced by 1.31 eV in contrast to polar B11C-CBC. The atomic structures, CBM bonding pCOHPs, charge density isosurfaces and SSAdNDP bonding orbitals of CBM electronic state for these three structural configurations are shown in Figure 6a,b. The SSAdNDP and charge density analysis indicates that the CBM electronic state of the chain B12-CCC stems from the antibonding interaction between the chain-center and chain-end C atoms. For equatorial B11C-CBC, its CBM electronic state originates from the antibonding interaction between the chain-center B and chain-end C atoms. The lower limit of CBM-bonding pCOHP above the Fermi level for the


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chain B12-CCC has an evident low-energy shift in contrast to the polar B11C-CBC (Figure 6b), which attributes to the weaker C-C bond and results in the smaller bandgap in the chain B12CCC. With regard to the equatorial B11C-CBC, the chain-end C atom neighboring the C atom at equatorial site forms a bit longer chain C-B bond compared to polar B11C-CBC (Figure 6a). Therefore, the strength of chain C-B bond in equatorial B11C-CBC should be weaker than that in polar B11C-CBC, leading to the slightly lower edge of the CBM bonding pCOHP and smaller bandgap for equatorial B11C-CBC (Figure 6b). We also analyzed the electronic property for another structure configuration of B14C1, liner B14C1 in which the atoms of the inter-icosahedral C-B-B chain form a straight line (Figure 6c). The bandgap of liner B14C1 is 0.42 eV smaller than that of kink B14C1, which is given in Table 1. As shown in Figure 6c, the CBM charge densities of kink and liner B14C1 structures reveal a bonding character of CBM electronic state which is different from that of B4C and B12P2. The SSAdNDP bonding orbitals indicate that the CBM electronic states of kink and liner B14C1 compounds both stem from the 3c-2e bonding interactions. Moreover, the B-B bond responsible for CBM electronic state possesses a longer length in kink B14C1, which results in a relative weaker bonding strength of chain B-B bond. The strong bonding interaction can lower the bonding state and lift the antibonding state. Hence the stronger chain B-B bond in liner B14C1 causes the lower bonding CBM energy edge as well as the smaller bandgap (Figure 6d). Moreover, the chemical bonds responsible for VBM energy edge all lies on the B12 icosahedron in the above B4C and B14C1 compounds, which are less important to the bandgap modulations (see more details from Figure S8, S9 in SI). 3.5. EXTERNAL PRESSURE


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It is well known that the mechanical loading conditions such as external pressure and epitaxial strain can generate the large impacts on electronic, optical, magnetic properties through contracting or stretching interatomic distances in solid-state materials54-56. The mechanical strain has been widely applied to tune the electronic structures in some novel semiconductors, in which many exiting phenomena like direct and indirect bandgap transition, enhanced electronic motilities and largely modulated bandgap widths have been discovered26-27. However, it is difficult to find the proper substrates to impose a wide range of strain to the complex boron-rich compounds because of their strong covalent bonds. Thus, we utilized the hydrostatic pressure to tune the bandgaps at the present work. The bandgaps of α-B12, B12O2, kink B14C1 and linear B14C1 under the hydrostatic pressure of 30 GPa are listed in Table 1, which are 1.58eV, 3.22 eV, 2.46eV and 2.08eV respectively, exhibiting a significant change compare to those of equilibrium states. Here we focus on the CBM states analysis because VBM electronic orbitals of these discussed boron-rich compounds sitting on the intra-icosahedral B-B bonds or the intericosahedral bonds linking to polar B atoms are also less sensitive to pressure, due to their less compressibility shown in Figure S10-S13 of SI. The CBM bonding pCOHPs and charge density isosurfaces of CBM electronic state for the α-B12, B12O2, kink B14C1 and linear B14C1 are shown in Figure 7. For α-B12, the inter-icosahedral 3c-2e bonds accountable for the CBM electronic state undergo an evident compression with external pressure, and the charge density in the midst of these 3c-2e bonds is also increased, indicating the pressure enhanced bonding interactions for CBM electronic state. As a result, the CBM energy edge of α-B12 will move toward to the Fermi energy as the pressure increases, which account for the pressure induced bandgap reduction (Figure 7a). As mentioned above, the CBM electronic state of kink B14C1 arises from the B-B bonding interactions, but it transfers to another B-B bond after the pressure applied (Figure 7b),


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due to the complex chain structure. The B-B bonds responsible for the CBM electronic state are stretched by 0.1 Å after the pressure applied. Therefore, the pressure weakened CBM bonding interactions lead to an upper shift of the CBM energy edge and increased tendency for bandgap. Similar, the CBM electronic state of liner B14C1 transforms the bonding state of a shorter B-B bond (1.56Å) to that of an adjacent longer B-B bond (2.00Å) under external pressure (Figure 7c). As a result, the weaker bonding interaction of CBM electronic state causes an increased bandgap for liner B14C1 as well. However, the CBM electronic state of B12O2 exhibits the antibonding character (Figure 7d), thus the pressure shortened B-O bonds make the CBM energy edge move far away from the Fermi energy, resulting in the increased bandgap with pressure (Figure 7d).

4. CONCLUSION In summary, we have investigated the bandgap modulation by twin boundary, composition modulation, structure arrangement, and high pressure in boron-rich icosahedral compounds. The VBM electronic states determined by the intraicosahedral or the strong two-center intericosahedral B-B bonds are insensitive to the external conditions. The bandgap controls for boronrich icosahedral compounds are mainly achieved through the altered CBM electronic states which arise from the bonding interactions of the inter-icosahedral chain bonds. The twinning boundary and external pressure can effectively modify the length and strength of chain bonds which shift the related bonding or antibonding states at CBM to tune the bandgaps. As for the composition modulation, it can introduce the new type of chemical bonds in the inter-icosahedral chain to change the CBM electronic states as well as the bandgaps. In general, the high pressure tends to reduce the bandgaps in conventional solid-state compounds57. This is due to the application of hydrostatic pressure decreasing the interatomic distance and increasing the electronic hopping interaction t. Consequently, the one-electron bandwidths around the Fermi


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level proportional to t are also increased, leading to the reduced energy separation between the VBM and CBM electronic states57. However, the boron-rich icosahedral compounds belong to the inverted molecular solids, their electronic states around the Fermi level are decided by the local chemical bonds. For the CBM electronic states with bonding character, the boron-rich icosahedral compounds tend to reduce bandgaps with pressure; for the CBM electronic states with antibonding character, they incline to increase bandgaps with pressure. These unusual electronic properties make the boron-rich icosahedral compounds potential to be the candidate materials for new generation electronic device and photocatalysis applications. ACKNOWLEDGMENTS This work was supported by the National Science Foundation (CMMI-1727428) and Ralph E. Powe Junior Faculty Enhancement Awards from Oak Ridge Associated Universities (ORAU).

SUPPORTING INFORMATION The Supporting Information includes (i) computational methods, (ii) band structures for icosahedral boron-rich compounds, (iii) bonding pCOHPs and electronic orbitals for VBM electronic states.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected].


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ORCID Qi An: 0000-0003-4838-6232 Hongwei Wang: 0000-0001-6603-9731

Notes The authors declare that they have no competing financial interests.

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Figures

Figure 1. Atomic structures, band structures and partial charge density isosurfaces of (a) α-B12, (b) B12O2, (c) B12P2 and (d) B4C. The blue and yellow isosurfaces represent the VBM and CBM electronic states.


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Figure 2. (a) Schematic view of B12 icosahedral unit in α-B12. (b) The three-center intericosahedral bonds formed by equatorial B atoms in α-B12. (c) The two-center inter-icosahedral bonds formed by polar B atoms in α-B12. (d), (e) Schematic illustration of B12 icosahedral unit and inter-icosahedral chain in B12P2. (f), (g) Schematic view of B12 icosahedral unit and intericosahedral chain in polar B4C.


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Figure 3. (a) Atomic structure of τ-B12P2. (b) pCOHP analysis for the bond interactions associated with the CBM electronic states in B12P2 and τ-B12P2. (c) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM electronic states of B12P2 and τB12P2. The bond length is in the unit of angstrom. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals.


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Figure 4. Hybridization function (%) of the chemical bonds belonging to the inter-icosahedral chains for (a) B12P2, (b)B6O, (c) polar B4C, (d) chain B4C, and (e) equatorial B4C.


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Figure 5. (a) pCOHP analysis for the bond interactions associated with CBM electronic states in B12O2 and B12S2. (b) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM electronic states of B12O2 and B12S2. (c) pCOHP analysis for the bond interactions responsible for CBM electronic states in B4C and B14C1. (d) Partial charge densities (yellow isosurfaces) and chemical bonding orbitals for CBM electronic states of B4C and B14C1. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals.


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Figure 6. (a) Atomic structures, partial charge densities (yellow isosurfaces), and chemical bonding orbitals for CBM electronic states of B4C. (b) pCOHP analysis for the bonding interactions associated with the CBM electronic states in B4C. (c) Atomic structures of B14C1, partial charge densities (yellow isosurfaces), and chemical bonding orbitals for CBM electronic states of B14C1. (d) pCOHP analysis for the bonding interactions associated with the CBM electronic states in B14C1. Polar, Chain, and Equatorial mean three different structure configurations of B4C. Kink and Linear represent two different structure configurations of B14C1. The bond length is in the unit of angstrom. The red and blue isosurfaces represent the positive and negative phases of the chemical bonding orbitals.


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Figure 7. The pressure dependent pCOHPs for (a) α-B12, (b) Kink-B14C1, (c) B12O2 and (d) Linear-B14C1. The yellow isosurfaces stand for the partial charge densities for CBM electronic states. The bond length is in the unit of angstrom.


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Table 1. Lattice parameter, volume, structure symmetry and bandgap of the boron-rich icosahedra compounds. τ and p represent the twinned and high-pressure structures, and superscript index Expt. Stands for the experiment results.

B12 τ-B12 p-B12 B12O2 τ-B12O2 p-B12O2 B12S2 B12P2 τ-B12P2 Polar- B11C-CBC Chain- B12-CCC Equatorial-B11C-CBC Kink-B14C1 𝑝-Kink-B14C1 Linear-B14C1 p-Linear-B14C1

a (Å) 5.026 5.064Expt. 4.870 4.853 5.124 5.146Expt. 5.359 4.928 5.324 5.221 5.256Expt. 5.965 5.182 5.160 5.163Expt. 5.178 5.062 4.829 5.103 4.893

b (Å)

−

c (Å)

−

8.798 − −

16.019 − −

8.732 − − −

8.684 − − −

8.583 5.182 −

18.899 5.031 −

5.178 5.111 4.917 − −

5.145 5.184 4.920 − −

Volume (Å3) 85.744 87.834Expt. 686.376 76.872 101.625 102.484Expt. 406.400 91.551 123.325 120.800 123.222Expt. 967.497 107.381 109.681 109.419Expt. 107.781 108.945 95.938 107.785 95.960

Space group R3m

Bandgap (eV) 2.18indirect

Cmcm R3m R3m

2.21indirect 1.58indirect 2.89direct

Cmcm R3m R3m R3m

2.89indirect 3.22direct 2.15indirect 3.40indirect

Cmcm Cm R3m

3.80indirect 3.84indirect 2.53direct

Cm P1 P1 R3m R3m

3.51indirect 2.01indirect 2.46indirect 1.59indirect 2.08indirect


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Table of Contents Graphic


36

Bandgap Engineering in High Temperature Semiconductors Boron

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