Electronic properties of pseudocubic IV–V compounds with 3:4 stoichiometry: Chemical trends

Chemical Physics Letters 501 (2010) 47–53

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Electronic properties of pseudocubic IV–V compounds with 3:4 stoichiometry: Chemical trends Tie-Yu Lü, Jin-Cheng Zheng ⇑ Department of Physics, Institute of Theoretical Physics and Astrophysics, Fujian Key Lab of Semiconductor Materials and Applications, Xiamen University, Xiamen 361005, China

a r t i c l e

i n f o

Article history: Received 28 August 2010 In final form 26 October 2010 Available online 28 October 2010

a b s t r a c t We perform first-principles calculations based on density functional theory and quasiparticle GW approximation to investigate the chemical trends in mechanical and electronic properties of twelve IV3V4 compounds (IV = C, Si, Ge, and Sn; V = N, P, and As). Our results indicate that these compounds are semiconductors, with the exception of C3P4 and C3As4. While Ge3P4 and Ge3As4 appear to be semimetals within local density approximation, but are, in fact, semiconductors with indirect band gaps, as revealed by GW calculations. We propose an empirical formula of band gaps for IV3V4 compounds that depends only on the nearest-neighbor distance and electronegativity difference. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction IV3V4 (IV = C, Si, Ge, and Sn; V = N, P, and As) compounds have recently attracted much attention due to their desirable physical properties for various potential applications, such as mechanical engineering, photoelectric, and photovoltaic applications. For example, Cohen et al. predicted a zero-pressure bulk modulus (B0) of b-C3N4 in excess of that of diamond [1]. Zhang et al. reported that graphitic carbon nitrides (g-C3N4) had a photovoltaic effect and were promising in solar energy conversion [2,3]. The high fracture toughness, hardness, and wear-resistance of Si3N4-based ceramics are used in cutting tools and antifriction bearings [4]. Ge3N4 has been experimentally demonstrated to be a good candidate for applications in photodiodes, optic fibers, and protective coatings, as well as others [5–9]. Recently, one of the authors and Feng’s group also investigated the structural properties of group-IV phosphides and arsenides using first principles calculations based on density functional theory (DFT) in local density approximation (LDA) or general gradient approximation (GGA) and predicted that their most stable phases are pseudocubic structure [10–15]. The band gaps of IV3V4 compounds range from 0 eV (C3P4) [11] to 6.4 eV (C3N4) [16], which covers the entire solar spectrum (0  4 eV). Therefore, IV3V4 compounds and their alloys are potential candidates for photovoltaic applications. Through literature review, we have found that there are still several unclear issues about these compounds, such as: (1) What factors determine the trends of structural parameters and bulk ⇑ Corresponding author. E-mail address: [email protected] (J.-C. Zheng). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.10.055

modulii of IV3V4? (2) What are the accurate values and the trend of the band gaps of IV3V4, which are important for photoelectric and photovoltaic engineering? In order to address these issues, we perform first-principles calculations to study the structure and electronic properties of IV3V4 compounds in the pseudocubic structure and investigate the trends when the components change across the periodic table.

2. Computational details The calculations have been implemented in the framework of DFT. The plane-wave method as implemented in ABINIT code [17] was employed. Pseudopotentials were generated using the scheme by Troullier and Martins [18]. Both LDA [19] and GGA [20] are used for the exchange–correlation effects, and the energy cutoff of 30 Hartree is chosen for plane-wave function’s expansion. The k-points of 5  5  5 for Brillouin zone sampling are generated using the Monkhorst–Pack scheme [21]. The cell parameters and atomic positions are optimized simultaneously. For self-consistent field iterations, the convergence tolerance for geometry optimization is set when the difference in total energy, the maximum ionic Hellmann–Feynman force, the stress tensor, and maximum displacement reduce to 1.0  106 Hartree/cell, 2.0  105 Hartree/ Å, 0.02 GPa, and 5.0  104 Å, respectively. It is known that there is a band-gap problem of semiconductors in LDA [22,23]. GW approximation (GWA) [24,25] has been considered as a good solution to this problem. In this Letter, GW calculations are performed as a ‘one-shot’ correction to self-consistent LDA and GGA calculations. This approach, denoted G0W0, has been successful in many applications to solids.

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3. Results and discussion 3.1. Ground states properties The unit cell of pseudocubic structure contains seven atoms, which exhibits P42m symmetry with three internal parameters (u, v and w) for the group-V atom (see Figure 1 Inset). The optimized lattice parameters, and atomic positions are listed in Table 1 and 2, respectively. Firstly, we examine the chemical trends for internal parameters of IV3V4 compounds. The internal parameters characterize the displacements of IV or V atoms, and therefore, they can be regarded as a measurement of imperfectness of the pseudocubic structure. Table 2 shows that after relaxation, group-IV atoms remain in the ideal positions, as shown in Figure 1. The group-V atoms then relax toward the vacant site. The crystal symmetry of space group P42m leads to the relationship: u = v and u + w = 0.5 [15], thus leaves only one independent parameter u. In Table 2, from C3P4 to C3As4, u becomes smaller, while in Si3V4, Ge3V4 and Sn3V4 (V = N, P, As), the substitution of N by P or As results in an increase of u. We find that u is mainly determined by the lattice parameters and the electronegativity difference (Dv) between group-IV and group-V atoms. The larger lattice constant (i.e., larger volume) provides more space for group-V elements to displace, leading to a larger u. On the other hand, as Dv increases, the IV–V bonding becomes stronger, and group-V elements are dragged back to the ideal position, as in the perfect zincblende structure. Secondly, we discuss the chemical trends of the lattice constants and bulk modulii for pseudocubic IV3V4. For lattice constant, it becomes smaller (larger) when the compounds consist of lighter (heavier) elements. The bulk modulii B0 are determined by fitting the calculated total energies to Murnaghan–Birch [26,27] equations of state. Compared with GGA results, the LDA bulk modulus is larger. This is attributed to the well-known LDA problem of overbonding. Most B0 of IV3V4 agrees with previous results, but those of C3P4 and C3As4 are much smaller. In order to analyze the difference, we thus calculate B0 using different occupation methods for comparison. The optimized lattice constants and atomic positions are nearly the same using either insulating occupations or metallic occupations. Using insulating occupations, B0(C3P4) are 175 GPa with LDA, or 151.1 GPa with

GGA, which is consistent with previous results [28,29]. However, our result and previous calculated results [11,28–31] predict that C3P4 is a metal. Therefore, we then calculate B0(C3P4) using metallic occupations, and obtain B0(C3P4) = 135.4 GPa (LDA) or 131.4 GPa (GGA), which are smaller than modulii found using insulating occupations. Interestingly, with metallic occupation, C3P4 has lower total energy and smaller curvature than that with insulating occupation. B0 is very sensitive to the curvature of total energy with respect to volume. It therefore causes the difference of B0 between semiconducting and metallic occupations. This is the same case for C3As4. LDA predicts that Ge3P4 and Ge3As4 are metals, but GGA and GWA predict these compounds to be semiconductors. So, we calculate B0 of Ge3P4 and Ge3As4 with insulating occupations. As the group-IV element evolves from C to Sn, the lattice constant of the unit cell increases and B0 decreases. The same trends are observed when the group-V element evolves from N to As. This is mainly due to the increased atomic radius and reduced strength of interatomic interaction, as can be deduced from the Cohen’s empirical formula B0 = 0.25Nc(1971–220k)d3.5, where Nc is the average coordination number, and k = 0, 1, and 2 for groups IV, III–V, and II–VI, respectively [1,32,33]. From the calculated results using Cohen’s formula with Nc = 24/7 for group-IV (k = 0) and group-III–V (k = 1) compounds in pseudocubic structure (Figure 2), one can find that B0 of IV3V4 compounds, except C3N4, are less than those of III–V compounds, while B0 of all IV3V4 compounds are much smaller than those of IV compounds, when they have the same d. Thus, if we calculate B0 of IV3V4 directly using Cohen’s formula, it is hard to obtain a reasonable value of k for IV3V4 in order to fit the DFT data. Given that pseudocubic structure differs from perfect zincblende structure in terms of large displacement, Cohen’s formula should be modified for IV3V4 compounds. Therefore, in what follows, we describe a procedure to obtain a new empirical formula for IV3V4 compounds. IV3V4 with pseudocubic phase can be considered to be, in some sense, between group-IV covalent and III–V ionic semiconductors. So, we set k = 0.5 for IV3V4 compounds. We then find that the number of chemical bonds in a pseudocubic unit cell is 0.875 times of that in a corresponding zincblende unit cell. As we mentioned previously, the displacement of group-V atoms in pseudocubic structures may be an important factor responsible for a decrease in B0. In order to quantify this effect, we define a displacement factor as 4|u0.25|. Here, u is the internal parameter for V atoms, |u0.25| is the displacement of V atoms (compared with the ideal position in a zincblende structure), and 4 is the number of V atoms in one unit cell. We can then define an imperfect factor a = 0.125 + 4|u0.25|, which characterizes both the defects and the displacements. Therefore, we obtain,

B0 ¼ ð1971  220kÞd

Figure 1. The trends of cohesive energy E (Hartree/unit cell) calculated by LDA as a function of molecular weight (g/mol) for IV3V4 compounds. Inset shows the pseudocubic structure model.

3:5

ð1  aÞ

ð1Þ

where k = 0.5, d is nearest-neighbor distance, and parameter u is listed in Table 2. The results for IV3V4 compounds obtained using Eq. (1) are given in Figure 2a. Clearly, C3P4 and C3As4 are anomalous in this series for this type of scaling. This is possibly because C3P4 and C3As4 are metallic while others are semicondutors, the metallicity may reduce B0 of compounds in this group, as we dicussed above. For example, B0 of C3P4 is predicted to be 163.7 GPa from Eq. (1), which differs from LDA value using insulating occupations by 6.5% or using metallic occupations by 17%. It would be appropriate to include a metallization factor in order to analyze mechanical properties of C3P4 and C3As4 compounds. Figure 2b plots a cohesive energy (Ecoh) vs d curve for IV3V4 compounds. Ecoh becomes smaller as d becomes larger. This is because the larger d leads to the larger lattice constant and thus lower the binding energy. A similar behavior has also been reported for

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T.-Y. Lü, J.-C. Zheng / Chemical Physics Letters 501 (2010) 47–53 Table 1 Lattice constant (Å) and bulk modulus B0 (GPa) for IV3V4 compounds in pseudocubic structure. Present work

Other calculations

LDA

GGA

LDA

GGA

a(Å) c(Å) B0(GPa)

3.3976 3.4002 430.7

3.4467 3.4467 410.7

3.415a; 3.4232b; 3.44c; 3.42d; 3.39e 3.423a; 3.4232b; 3.44c; 3.42d; 3.39e 445.9a; 448b; 430c; 424.1d

a(Å) c(Å) B0(GPa)

4.0575 4.0606 222.2

4.1222 4.1253 205.3

4.05d 4.05d 221.8d

a(Å) c(Å) B0(GPa)

4.2452 4.2485 182.2

4.3806 4.38 340 149.5

4.251f 4.251f 147.06f

a(Å) c(Å) B0(GPa)

4.6418 4.6448 130.9

4.8338 4.8352 106.4

4.731g 4.724g 116g

a(Å) c(Å) B0(GPa)

4.1399 4.1430 135.4

4.2100 4.2114 131.4

4.101a; 4.1e; 4.1016h 4.106a; 4.1e; 4.101h 209.2a

4.13i 4.13i 158i; 158j; 161j

a(Å) c(Å) B0(GPa)

4.9862 4.9861 78.8

5.0908 5.0907 69.6

4.961k 4.978k 91k

5.027k; 5.038m 4.998k; 5.038m 77k; 74.28m

a(Å) c(Å) B0(GPa)

5.1007 5.1008 60.8

5.2641 5.2642 54.5

5.142m 5.142m 61.83m

a(Å) c(Å) B0(GPa)

5.4224 5.4257 50.5

5.6346 5.6379 39.8

5.531m 5.504m 47.51m; 36n

a(Å) c(Å) B0(GPa)

4.5132 4.5167 87.0

4.6303 4.6329 80.3

4.589o; 4.6115p 4.596o; 4.6138p 116.5054p

a(Å) c(Å) B0(GPa)

5.2483 5.2514 67.6

5.3838 5.3869 59.7

5.357o; 5.3676p; 5.2743q 5.358o; 5.3793p; 5.2755q 68.4555p; 63.49q

a(Å) c(Å) B0(GPa)

5.3402 5.3936 52.1

5.5234 5.5786 46.3

5.499o; 5.5116p; 5.3270q 5.518o; 5.5116p; 5.3267q 59.5772p; 58.77q

a(Å) c(Å) B0(GPa)

5.6294 5.6763 47.3

5.8684 5.8694 41.2

5.848o; 5.8629p; 5.7034p 5.849o; 5.8633p; 5.7051q 51.0608p; 44.35q

C3N4

Si3N4

Ge3N4

Sn3N4

C3P4

Si3P4

Ge3P4

Sn3P4

C3As4

Si3As4

Ge3As4

Sn3As4

a b c d e f g h i j k m n o p q

Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.

[30]. [41]. [42]. [43]. [31]. [44]. [45]. [11]. [28]. [29]. [12]. [37]. [14]. [15]. [34]. [38].

II–VI, III–V, and IV semiconductors. Our finding of the trend is in good agreement with previous calculations [34] for V3As4

compounds. For IV3P4 and IV3As4, the relationship between Ecoh and d can be obtained as,

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Table 2 The calculated atomic positions (u,v,w) of V in pseudocubic IV3V4 compoundsa, and electronegativity difference (Dv) between IV and V using the Pauling scale.

C3V4 Si3V4 Ge3V4 Sn3V4 a

V V V V

(u,v,w) (u,v,w) (u,v,w) (u,v,w)

Dv(V-C) Dv(V-Si) Dv(V-Ge) Dv(V-Sn)

Nitrides (V = N)

Phosphides (V = P)

Arsenides (V = As)

(0.2451,0.2451,0.2549)0.49 (0.2393,0.2393,0.2607)1.14 (0.2432,0.2432,0.2568)1.03 (0.2412,0.2412,0.2588)1.08

(0.2758,0.2758,0.2242)-0.36 (0.2789,0.2789,0.2211)0.29 (0.2837,0.2837,0.2163)0.18 (0.2885,0.2885,0.2115)0.23

(0.2725,0.2725,0.2275)-0.37 (0.2810,0.2810, 0.2190)0.28 (0.2846,0.2846,0.2164)0.17 (0.2903,0.2903,0.2107)0.22

The internal coordinate (u, v, w) is (0.0, 0.0, 0.0) for IV1, and (0.5, 0.0, 0.5) for IV2.

C point. Most GGA band structures are similar to those of LDA.

Figure 2. (a) Bulk modulus fitted by LDA data and calculated by Eq. (1) as a function of nearest-neighbor distance of IV3V4 compounds. The dashed and dotted lines are calculated by the Cohen empirical formula with k = 0 and k = 1, respectively. (b) Cohesive energy calculated by LDA as a function of nearest-neighbor distance of IV3V4 compounds; the fitting trend Ecoh = 3.267d0.931.

Ecoh ¼ 3:267d

0:931

;

ð2Þ

as shown in Figure2b. The trend is similar with compounds in rock salt structure (Ecoh / d1) [35,36], but a slightly smaller power value (0.931) is found for IV3V4 compounds. The deviation of power value from unit is due to the imperfectness of pseudocubic structure. 3.2. Electronic properties We now turn to the the trends of band structure for IV3V4 compounds. The DFT-LDA band structures are displayed in Figure 3. The LDA, GGA, and GWA band gaps of IV3V4 compounds are listed in Table 3. Where possible, we have included the results of other ab initio calculations. In Figure 3, it can be seen that all the materials are semiconductors in LDA except for C3P4, C3As4, Ge3P4, and Ge3As4, which show metallic properties. Among these semiconductors, C3N4 and Sn3N4 are direct band-gap semiconductors at the

However, Ge3P4 and Ge3As4 are found to be semiconductors with narrow band gaps, namely, 0.19 and 0.12 eV, by GGA calculations, respectively, agrees well with other GGA results [15,34,37,38]. In Table 3, one can find that GGA band gaps of Ge3N4 and Sn3N4 are much smaller than those of LDA. This is unusual because in many semiconductors the band gap predicted by GGA is normally larger than that calculated by LDA. Moreover, we predict that Sn3N4 is a direct band gap semiconductor at the C point using LDA, while it is an indirect band gap semiconductor by GGA calculation, with valence band maximum (VBM) at the A point, and conductor band minimum (CBM) at the C point. To check whether this unusual result is related to the computational convergence, we then repeat the calculations with larger kinetic energy cutoff (40 Hartree) and more k points (8  8  8). We find that the band gap differences between LDA and GGA for Ge3N4 (0.9 eV) and Sn3N4 (0.6 eV) are almost independent on the convergence parameters. We further notice that the optimized lattice constants of Ge3N4 and Sn3N4 by LDA are smaller than those by GGA. This trend is found in many materials due to the well-known overbinding problem in LDA. We thus calculate the band structures of Ge3N4 and Sn3N4 by LDA at GGA-optimized lattice constants (equivalently applied a tensile strain). In this case, we find that the band gap of Ge3N4 decreases from 2.35 to 1.39 eV, becoming smaller than the GGA band gap (1.43 eV) at the same lattice constant, while Sn3N4 is predicted to be a metal (the band gap is 0.06 eV in the GGA calculation with the same lattice constant). These calculations show that the different equilibrium lattice constants are the main cause of the differences of band structures of Ge3N4 and Sn3N4 between LDA and GGA. To confirm our speculation, we have performed further calculations for Ge3N4 using the full-potential linearized augmented plane wave method (FLAPW) [39]. The FLAPW band gap of Ge3N4 is 2.32 eV within LDA (1.49 eV within GGA), agree well with the pseudopotential results. This indicates that the band structures of Ge3N4 and Sn3N4 are very sensitive to lattice parameters, and thus suggests the possibility of band gap tunability by strain engineering. We also found that, similar to the LDA case, the GW band gaps of Ge3N4 and Sn3N4 are very sensitive to lattice parameters. When the volume of Ge3N4 is reduced to 93% of the equilibrium volume, the GWA band gap increases to 4.3 eV, while the gap decreases to 2.6 eV when the volume increases to 110% of the equilibrium volume. The GWA band gap of Sn3N4 has the similar trend to that of Ge3N4. Furthermore, the exchange–correlation–functional dependent band gap predicted for Ge3N4 and Sn3N4 provides an interesting test stone for further experimental varification. It is well known that LDA and GGA underestimate the band gaps of semiconductors. To overcome this shortcoming, we performed quasiparticle GWA calculations. We find that Ge3P4 and Ge3As4 are indeed semiconductors and with an indirect band gap in GWA calculations. However, for C3P4 and C3As4, even GWA is still not able to open a band gap. In Figure 3, it can be seen that C3P4 is metallic in LDA, as the valence band and conductor band overlap at the C point. At the Z, A, M, and R points, the band gaps of C3P4 are larger than zero. We have calculated GWA-LDA band gaps of C3P4 at these points. At the Z, A, M, and R points, DE (DE ¼ EGWA  ELDA g g ) are 0.43, 0.25, 0.33, and 0.26 eV, respectively.

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Figure 3. Electronic band structure of IV3V4 compounds calculated using LDA. The top of the valence band is set to be zero.

Table 3 Calculated band gap Eg (eV) of IV3V4 compounds using LDA, LDA-GWA (i.e., LDA results with GW correction), GGA, and GGA-GWA (GGA results with GW correction). Other LDA or GGA calculations from literature are also listed for comparison.

C3N4 C3P4 C3As4 Si3N4 Si3P4 Si3As4 Ge3N4 Ge3P4 Ge3As4 Sn3N4 Sn3P4 Sn3As4 a b c d e f g h i j k

Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.

LDA (eV)

LDA-GWA (eV)

Other LDA calculations (eV)

GGA (eV)

GGA-GWA (eV)

2.53 0 0 2.70 0.10 0.19 2.35 0 0 0.60 0.57 0.44

4.19 0 0 4.42 0.74 0.60 3.74 0.57 0.24 1.61 1.20 0.79

2.43a;4b 1.15a;

2.54 0 0 2.76 0.37 0.39 1.43 0.19 0.12 0.06 0.84 0.41

3.99 0 0 4.25 0.93 0.7 2.49 0.54 0.36 0.68 1.29 0.7

3.5b <0f 2.5i

0.458j

Other GGA calculation (eV) 0c 0d,e 0.134f; 0.33g 0.42d; 0.414e; 0.445h 0.17g 0.16d; 0.248h; 0.159e 0.83g; 0.836k 0.39d; 1.039h; 0.38e

[30]. [43]. [28]. [15]. [34]. [12]. [37]. [38]. [44]. [45]. [14].

Average DE is equal to 0.32 eV. This correction could not make the minimum of the conduction band larger than the maximum of the valence band. Therefore, it is reasonable that the GWA band gap of C3P4 is negative. The band gap correction for C3As4 is similar to that of C3P4. The reason for C3P4 (or C3As4) being metallic may be that the electrons filling the bands just below the Fermi level form a covalent C–P (or C–As) bond, they are very delocalized, and the bonding is metallic in nature [31].

The band gaps of IV3V4 are significantly improved by GWA, as listed in Table 3 and illustrated in Figure 4a. For comparison, we also presented the GWA-LDA and GWA-GGA corrected band gap in Table 3. From Table 3, we can find that band gaps of GWALDA and GWA-GGA agree well with each other, except for Ge3N4 and Sn3N4. This may be attributed to the difference in electronic properties of Ge3N4 and Sn3N4 between LDA and GGA, as we discussed above.

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gap of material is a complex issue. There are many factors, such as crystal structure, lattice constant, electronegativity of the element, temperature, and so on, that can affect the band gap of material. We find that band gaps of IV3V4 increase with the bond length decreasing and Dv increasing. We fit the relation between band gaps (eV) of IV3V4 compounds, bond length d (Å), and electronegativity as expressed below: 1:7

Eg ¼ bðDvÞd

Figure 4. (a) LDA and GWA band gap as a function of molecular weight of IV3V4 compounds. (b) GWA-LDA band gaps as a function of bond length and electronegativity following Eq. (3).

We found that the shape and band width of band structures obtained by LDA are slightly modified by GW correction with energy variation of about 0.5 eV. Taking pseudocubic C3N4 with largest band gap as an example, GW corrections for band gap (i.e., DEg) at C, A, M, R, and Z, points are 1.7, 1.5, 1.9, 2.0 and 1.5 eV, respectively. The band width at C point is 25.2 eV by LDA and it is increased to 25.9 eV by GW correction, with energy shift of about 0.7 eV (2.7%). For materials with smaller band gaps, the energy difference related to band gap correction at different k points and the shape and band width is smaller accordingly. From above data analysis, we can conclude that the well known scissors operation can give reasonable accuracy and can be applied in the case when the detailed band structure shape variation is not important. For the sake of comparison, our calculated LDA results of band gaps are also presented together with GWA band gaps in Figure 4a, where the trend can be seen more clearly. From C3V4 to Si3V4, the band gap increases, while the band gap decreases from Si3V4 to Ge3V4. From Ge3N4 to Sn3N4, the band gap decreases, also, but then increases from Ge3P4 (Ge3As4) to Sn3P4 (Sn3As4). The trend of GGA band gaps is similar to the trend of band gaps of LDA. Figure 4a shows that the trend differs from that of the band gaps of II–VI, III–V, and IV semiconductors [40]. In general, the band gap becomes smaller as the molecular weight becomes larger, but this general trend does not hold for group-IV phosphides and groupIV arsenides: an anomalous ‘v’ shaped band gap is found as a function of molecular weight, as shown in Figure 4a. Indeed, the band

þc

ð3Þ

where b is a group-IV-dependent parameter, b(C3N4) = 17, b(Si3V4) = b(Ge3V4) = 10, and b(Sn3V4) = 1.7. Dv is listed in Table 2. The final parameter c is 1 for Sn3V4, and 0 for other IV3V4 compounds. Generally, for semiconductors, strong ionicity of bonds corresponds to large band gaps; the band gap and the bond length grow into nearly inverse proportion. In Eq. (3), b(Dv) represents the ionicity of chemical bonds. b of IV3V4 decreases from 17 to 1.7, as a group-IV element evolves from C to Sn. This may be attributed to the addition of metallic characteristic of bonds, when C is substituted by Si, Ge, and Sn. Figure 4b shows the comparison of band gaps calculated by GWA-LDA and predicted by Eq. (3). Our empirical formula can accurately reproduce the GWA-LDA band gaps. Eq. (3) can also indicate that C3P4 (Dv = 0.36) and C3As4 (Dv = 0.37) are metals. These GWA-corrected band gaps for IV3V4 compounds are reported for the first time. We note that our results agree well with the available corrected band gaps for IV-arsenides [34] (with a different correction method), which in some sense verifies the reliability of our GWA results. It is interesting to see that the range of IV3V4 energy gaps predicted by our GWA calculations is from 0 eV to more than 4 eV, covering the entire solar spectrum. This makes IV3V4 compounds and their alloys attractive candidates for potential applications in the solar cell and photoelectric industry. The possibility of solar energy conversion using a member of the IV3V4 group, graphitic carbon nitrides [2,3], makes our proposal of IV3V4 compounds for solar energy application more reasonable. Thus our accurate prediction of band gap, a key factor for solar cell design, may be useful for photovoltaics and other emergent applications. 4. Conclusions We have investigated the chemical trends for structural and electronic properties of IV3V4 compounds in pseudocubic structures based on DFT + GW calculations. Trends for relationship among cohesive energy, bulk modulus and nearest-neighbor distance of IV3V4 compounds are obtained. A modified empirical formula was proposed to accurately calculate the bulk modulus of IV3V4 compounds in pseudocubic structure. The relationship between the band gap and molecular weight of IV3V4 compounds is quite different from that of semiconductors and insulators in groups II-VI, III-V, and IV. Specifically, for IV-phosphides and IVarsenides, there is an anomalous ‘v’ shape in the band gap as a function of molecular weight. IV3V4 compounds in pseudocubic structure are found to be semiconductors, with the exception of C3P4 and C3As4. An empirical formula was proposed to predict band gaps in terms of the electronegativities of elements and bond lengths of compounds. A proposal of IV3V4 compounds for solar energy application is made and the possibility of band gap tunability by strain engineering is suggested. Acknowledgements The authors are grateful for the discussions with Huiqiong Wang (Xiamen University). This work is supported by the Minjiang

T.-Y. Lü, J.-C. Zheng / Chemical Physics Letters 501 (2010) 47–53

Scholar Distinguished Professorship Program through Xiamen University, Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090121120028), and the Natural Science Foundation of Fujian Province, China (Grant No. 2009J01015). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]

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