## Abstract

First principles hybrid functional calculations have been carried out to study electronic properties of GaAs with Bi alloying effects. It is found that the doping of Bi into GaAs reduces the bandgap due to the intraband level repulsions between Bi induced states and host states, and the Bi-related impurity states originate from the hybridization of Bi-6*p* and its nearest As-4*p* orbitals. With the increase of Bi concentration in GaAs, the bandgap decreases monotonously. The calculated optical properties of the undoped and Bi-doped GaAs are similar except the shift toward lower energy of absorption edge and main absorption peaks with Bi doping. These results suggest a promising application of GaBi_{x}As_{1-x} alloy as semiconductor saturable absorber in Q-switched or mode-locked laser.

© 2012 OSA

## 1. Introduction

Semiconductor saturable absorber Q-switched all-solid-state lasers are desirable for many potential applications in remote sensing, ranging, micromachining, and nonlinear wavelength conversion. In comparison with other saturable absorbers, GaAs has the advantages of stable photochemical property and saturable absorption, good thermal conductivity, non-degradability, and high damage threshold [1–4]. Since the operating photon energy at 1.06 μm wavelength is far below the bandgap of GaAs, the absorption at this wavelength in the GaAs saturable absorber is believed to be due to the deep donor EL2 defects [5]. However, the concentration of EL2 deep-level defects is very low, and it is a challenge to control the amount of EL2 defects in GaAs saturable absorber to design its Q-switching parameters, such as linear loss, non-linear loss, recovery time, and modulation depth.

Alloying is an effective way of modifying the properties of a material and is highly desirable for bandgap engineering applications. It is known that replacement of a small amount of anion species in GaAs by isovalent impurities, such as GaN_{x}As_{1-x}, GaP_{x}As_{1-x}, GaSb_{x}As_{1-x}, and GaBi_{x}As_{1-x}, leads to dramatic changes in its optical and electrical properties. Among these, the ternary alloy GaBi_{x}As_{1-x} is currently under investigation for a variety of potential device applications [6, 7]. GaBi_{x}As_{1-x} has been successfully grown by metal organic chemical vapor deposition (MOCVD) [8, 9], and quite recently by molecular beam epitaxy (MBE) [10–14]. On the theoretical side, the calculated electronic properties of GaBi_{x}As_{1-x} show that doping of Bi can reduce the bandgap of GaAs [15–19], and the effect is more significant than alloying different III-V compound semiconductors at the same concentration. This makes GaBi_{x}As_{1-x} a promising new semiconductor saturable absorber, and it has a very high possibility to be used in all-solid-state Q-switched and mode-locked lasers. However, results of previous conventional first-principles calculations on GaBi* _{x}*As

_{1-}

*have not been consistent [15–19]. The complex Bi-related electronic states in GaBi*

_{x}_{x}As

_{1-x}have been scarcely investigated and their presence, energy position, and composition evolution are still under debate. Therefore, further theoretical investigation on the electronic and structural properties of GaBi

_{x}As

_{1-x}, using the state-of-the-art computational method, is necessary in order to explore applications of GaBi

_{x}As

_{1-x}as saturable absorber in future Q-switched or mode-locked lasers.

It is well known that density functional theory (DFT) using the local density approximation (LDA) or the generalized gradient approximation (GGA) often severely underestimates bandgaps of semiconductors. Hybrid functional has been widely used in first principles calculations to correct the bandgap [20]. In this paper, by first principles calculations based on DFT as implemented in the Vienna *ab initio* simulation package (VASP) [21, 22] with a modified Heyd-Scuseria-Ernzerhof (HSE) hybrid exchange-correlation functional, the electronic properties and the band structure of GaAs, GaBi, and the ternary alloy GaBi_{x}As_{1-x} have been obtained. The Bi-related impurity states were found located below the valence band maximum (VBM), which results in the bandgap reduction in GaBi_{x}As_{1-x}.

## 2. Method of calculations

We have calculated the electronic properties of GaAs, GaBi, and the ternary alloy GaBi_{x}As_{1-x}, in which super-cells of 64 atoms were used. The calculations were performed using the plane-wave projector augmented-wave (PAW) [23, 24] method applying the semilocal Perdew-Burke-Ernzerhof (PBE) [25] exchange-correlation functional and the Heyd-Scuseria- Ernzerhof (HSE) [26] hybrid functional as implemented in VASP code. Hybrid functional were mixed by about 25% nonlocal Hartree-Fock and 75% semilocal exchange, and the HSE screening parameter [27] was set to a value of 0.2 Å^{−1}. The outermost *s*- and *p*-electrons of the As atom, the outermost *s*-, *p*- and *d*-electrons of the Ga atom, and the Bi atom were treated as valence electrons. The electronic wave functions were expanded into plane-waves with a cutoff energy of 300 eV. Brillouin-zone was sampled by 2 × 2 × 2 Г-centered mesh, and a small Gaussian broadening σ = 0.05 eV was used, such that the peaks of the defect states are resolvable from the valence band continuum, for the calculations of density of states (DOS).

## 3. Bi-related impurity states in GaBi_{x}As_{1-x}

The band structure and the total DOS of the perfect GaAs has been shown in Ref [28], from which we can see that the perfect GaAs has a direct bandgap of 1.5 eV at the Г point. However, from the band structure and the total DOS of the perfect GaBi in Fig. 1 , we can see that a very small overlap between the bottom of the conduction band and the top of the valence band in the band structure of GaBi, and noticeable density of states at the Fermi level in the total DOS. Therefore, it can be concluded that GaBi has no bandgap, and is expected to exhibit characteristics of a semimetal [15].

Figure 2
shows the band structure and the total DOS of GaBi_{x}As_{1-x} for x = 3.125%, from which a bandgap of 1.36 eV is found, and the conduction band structure is very similar to that of perfect GaAs. However, three new defect bands (D1, D2 and D3) related to the doped Bi atoms are found in valence band (highlighted in color), which will be referred to as impurity states. In contrast with the VBM of perfect GaAs, the valence band of GaBi_{x}As_{1-x} broadens and the VBM moves up towards the Fermi level due to the intraband level repulsions, resulting in a reduced band gap.

The origin of these impurity states can be explored by using the local density of states (LDOS), as shown in Fig. 3
, in which Figs. 3(a) and 3(b) show the total DOS of perfect GaAs and GaBi_{x}As_{1-x}, respectively, and Fig. 3(c) is the LDOS of the Bi atom in GaBi_{x}As_{1-x}. It can be seen clearly that the impurity states in Fig. 3(b) (highlighted by red line) and those of Bi atom (the four peaks highlighted in red in Fig. 3(c)) are located at the same positions. Charge transfer between Bi and surrounding Ga atoms induces new electronic states located at 0.33~1.27 eV below the VBM. These impurity states result in the reduction of GaAs bandgap, and also are the transition states to assist photon absorption.

In order to further understand the forming mechanism of the defect bands, the partial band decomposed charge density calculations for the defect bands are performed, as shown in Fig. 4
. Figure 4(a) shows that the defect band D1 originates from the hybridization of the Bi-6*p _{z}* orbital and the 4

*p*orbitals of the nearest As

_{z}_{1}atom and As

_{2}atom; Fig. 4(b) shows that the defect band D2 is mixed by the Bi-6

*p*orbital and the 4

_{x}*p*orbital of the nearest As

_{x}_{3}atom; and Fig. 4(c) shows that the defect band D3 is formed from the Bi-6

*p*orbital hybridized with the 4

_{y}*p*orbital of the nearest As

_{y}_{4}atom. Therefore, from the shape of orbital isosurfaces, we can speculate visually that the Bi-related defect bands originate from the hybridization of Bi-6

*p*and its nearest As-4

*p*orbitals.

## 4. Bandgap of GaBi_{x}As_{1-x} with different Bi composition

We also investigate effects of Bi concentration in GaBi_{x}As_{1-x} on the related electronic structure. Figure 5
shows the calculated band structures of GaBi_{x}As_{1-x} with different Bi concentrations. From Fig. 2 and Fig. 5, we can see that the band gap of GaBi_{x}As_{1-x} decreases from 1.36 down to 1.09 eV, as the Bi concentration increases from 3.125% to 12.5%. The bandgap reduction is a result of intraband level repulsions between the Bi impurity levels (red lines in Fig. 5) and other levels of the host.

The bandgap versus composition x for GaBi_{x}As_{1-x} is plotted in Fig. 6
(black line). We found that the dependence of the bandgap (*E _{g}*) of GaBi

_{x}As

_{1-x}on Bi composition

*x*can be well described by a 3rd-order polynomial, ${E}_{g}=1.52-5.386x+16.596{x}^{2}-12.734{x}^{3},$ for

*x*values ranging from 0 to 0.15 (red curve in Fig. 6). By setting

*E*to 1.17eV (photon energy at 1.06 um) and solving the equation numerically, we can obtain that the photon at the wavelength of 1.06 um can be absorbed in GaBi

_{g}_{x}As

_{1-x}with the Bi concentration of about 8.97%.

## 5. Optical absorption spectra

Figure 7
shows the absorption coefficients of perfect GaAs, GaBi_{x}As_{1-x} (x = 1/32), and GaBi_{x}As_{1-x} (x = 1/16). The inset of Fig. 7 is the magnified absorption edges that move to the lower energy after Bi doping, which are in good agreement with the above band structure results. It is known that the absorption edge is mainly from the interband transitions between the top of the valence band and the bottom of the conduction band. For the absorption edge of GaAs, it was due to the transitions from As 4*p* states to Ga 4*s* states, while for GaBi_{x}As_{1-x} the transitions were from As 2*p* and Bi 6*p* states to Ga 4*s*. Beyond the absorption edges, the both doped spectra of GaBi_{x}As_{1-x} have two main peaks, which show obvious redshifts compared with the corresponding peaks of GaAs.

From Fig. 7, it can be seen that the calculated optical properties of the undoped and Bi-doped GaAs are similar except the shift toward longer wavelength of absorption edge and main absorption peaks with Bi doping. Therefore, the incorporation of Bi into GaAs leads to a reduction of the optical bandgap, but does not change the good saturable absorption property of GaAs.

## 6. Conclusion

In summary, via first-principles calculations, we show that bandgap engineering of GaBi_{x}As_{1-x} can be realized by tuning Bi the concentration. The incorporation of Bi into GaAs leads to a reduction of bandgap, and the gap decreases with the increase of Bi concentration, due to the Bi induced intraband repulsions. The Bi alloying induced bandgap narrowing effect may make the absorption of light in GaBi_{x}As_{1-x} more efficient, suggesting that GaBi_{x}As_{1-x} alloy a promising new semiconductor saturable absorber in Q-switched or mode-locked laser in the future.

## Acknowledgments

This work was partially supported by the National Science Foundation of China (60876056, 21173134), the founding of the National Municipal Science and Technology Project (No. 2008ZX05011-002), the China Postdoctoral Science Foundation funded project (20090461210), and the Postdoctoral Special Innovation Foundation of Shandong Province (200903067).

## References and links

**1. **Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: a new material to accomplish passively mode-locked Nd:YAG laser,” Appl. Phys. Lett. **60**(4), 419–421 (1992). [CrossRef]

**2. **T. T. Kajava and A. L. Gaeta, “Q-switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. **21**(16), 1244–1246 (1996). [CrossRef] [PubMed]

**3. **J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S.-C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd:YVO_{4} laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. **35**(5), 299–307 (2001). [CrossRef]

**4. **J. Gu, F. Zhou, W. Xie, S. C. Tam, and Y. L. Lam, “Passive Q-switching of a diode pumped Nd:YAG with GaAs output coupler,” Opt. Commun. **165**(4-6), 245–249 (1999). [CrossRef]

**5. **A. L. Smirl, G. C. Valley, K. M. Bohnert, and T. F. Boggess, “Picosecond photorefractive and free-carrier transient energy transfer in GaAs at 1μm,” IEEE J. Quantum Electron. **24**(2), 289–303 (1988). [CrossRef]

**6. **T. Tiedje, E. C. Young, and A. Mascarenhas, “Growth and properties of the dilute bismide semiconductor GaAs_{1−x}Bi_{x} a complementary alloy to the dilute nitrides,” Int. J. Nanotechnol. **5**, 963–983 (2008). [CrossRef]

**7. **A. R. Mohmad, F. Bastiman, C. J. Hunter, J. S. Ng, S. J. Sweeney, and J. P. R. David, “The effect of Bi composition to the optical quality of GaAs_{1−x}Bi_{x},” Appl. Phys. Lett. **99**(4), 042107–042109 (2011). [CrossRef]

**8. **K. Oe and H. Okamato, “New semiconductor alloy GaAs_{1-}* _{x}*Bi

*grown by metal organic vapor phase epitaxy,” Jpn. J. Appl. Phys.*

_{x}**37**(Part 2, No. 11A), L1283–L1285 (1998). [CrossRef]

**9. **K. Oe, “Characteristics of semiconductor alloy GaAs_{1-}* _{x}*Bi

*,” Jpn. J. Appl. Phys.*

_{x}**41**(Part 1, No. 5A), 2801–2806 (2002). [CrossRef]

**10. **B. Fluegel, S. Francoeur, A. Mascarenhas, S. Tixier, E. C. Young, and T. Tiedje, “Giant spin-orbit bowing in GaAs_{1-x}Bi_{x.},” Phys. Rev. Lett. **97**(6), 067205–067208 (2006). [CrossRef] [PubMed]

**11. **S. Francoeur, M. J. Seong, A. Mascarenhas, S. Tixier, M. Adamcyk, and T. Tiedje, “Band gap of GaAs_{1−}* _{x}*Bi

*, 0<*

_{x}*x*<3.6%,” Appl. Phys. Lett.

**82**(22), 3874–3876 (2003). [CrossRef]

**12. **S. Tixier, M. Adamcyk, T. Tiedje, S. Francoeur, A. Mascarenhas, P. Wei, and F. Schiettekatte, “Molecular beam epitaxy growth of GaAs_{1−}* _{x}*Bi

*,” Appl. Phys. Lett.*

_{x}**82**(14), 2245–2247 (2003). [CrossRef]

**13. **E. C. Young, M. B. Whitwick, T. Tiedje, and D. A. Beaton, “Bismuth incorporation in GaAs_{1−}* _{x}*Bi

*grown by molecular beam epitaxy with in-situ light scattering,” Phys. Status Solidi*

_{x}**4**(5c), 1707–1710 (2007). [CrossRef]

**14. **K. Alberi, O. D. Dubon, W. Walukiewicz, K. M. Yu, K. Bertulis, and A. Krotkus, “Valence band anticrossing in GaBi_{x}As_{1−}* _{x}*,” Appl. Phys. Lett.

**91**(5), 051909–051911 (2007). [CrossRef]

**15. **A. Janoti, S. H. We, and S. B. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B **65**(11), 115203 (2002). [CrossRef]

**16. **Y. Zhang, Z. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B **71**(15), 155201 (2005). [CrossRef]

**17. **D. Madouri, A. Boukra, A. Zaoui, and M. Ferhat, “Bismuth alloying in GaAs: a first-principles study,” Comput. Mater. Sci. **43**(4), 818–822 (2008). [CrossRef]

**18. **A. Abdiche, H. Abid, R. Riane, and A. Bouaza, “Structural and electronic properties of zinc blend GaAs_{1-x}Bi_{x} solid solutions,” Physica B **405**(9), 2311–2316 (2010). [CrossRef]

**19. **J. Hwang and J. D. Phillips, “Band structure of strain-balanced GaAsBi/GaAsN superlattices on GaAs,” Phys. Rev. B **83**(19), 195327 (2011). [CrossRef]

**20. **J. Heyd, J. E. Peralta, G. E. Scuseria, and R. L. Martin, “Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional,” J. Chem. Phys. **123**(17), 174101 (2005). [CrossRef] [PubMed]

**21. **G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. **6**(1), 15–50 (1996). [CrossRef]

**22. **G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B Condens. Matter **54**(16), 11169–11186 (1996). [CrossRef] [PubMed]

**23. **P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B Condens. Matter **50**(24), 17953–17979 (1994). [CrossRef] [PubMed]

**24. **G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmented-wave method,” Phys. Rev. B **59**(3), 1758–1775 (1999). [CrossRef]

**25. **J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. **77**(18), 3865–3868 (1996). [CrossRef] [PubMed]

**26. **J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. **118**(18), 8207–8219 (2003). [CrossRef]

**27. **A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, “Influence of the exchange screening parameter on the performance of screened hybrid functionals,” J. Chem. Phys. **125**(22), 224106 (2006). [CrossRef] [PubMed]

**28. **D. C. Li, M. Yang, Y. Q. Cai, S. Z. Zhao, and Y. P. Feng, “First principles study of the ternary complex model of EL2 defect in GaAs saturable absorber,” Opt. Express **20**(6), 6258–6266 (2012). [CrossRef] [PubMed]