Shallow donors in diamond: Be and Mg

Computational Materials Science 44 (2009) 1286–1290

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Shallow donors in diamond: Be and Mg C.X. Yan a,b, Y. Dai a,*, B.B. Huang a, R. Long a, M. Guo a a b

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, PR China Department of Physics, Jining University, Qufu 273155, PR China

a r t i c l e

i n f o

Article history: Received 1 June 2008 Received in revised form 26 June 2008 Accepted 28 August 2008 Available online 7 October 2008 PACS: 81.05.Uw 61.72. y 61.72.Bb

a b s t r a c t The electronic properties of the impurities Be, Mg and the hydrogen complexes Be–H, Mg–H in diamond have been investigated by first-principle calculations. It is found that the interstitial Be- or Mg- doped diamond are of n-type metal conductivity character. Even at low impurity concentration the doped diamond also appears n-type behavior. The further results indicate that the interstitial Be or Mg doping diamond should be synthesized at H-poor conditions to obtain the n-type material because most of hydrogen atom may result in interstitial Be- and Mg- doped diamond p-type semiconductor or insulator. The substitutional Be and Mg show acceptor behaviors and may compensate other interstitial donors in diamond. Our results are very helpful to the research of n-type doping in diamond for the future experimental work. Ó 2008 Elsevier B.V. All rights reserved.

Keywords: Diamond n-Type conductivity

1. Introduction Diamond has recently attracted much attention due to its outstanding physical properties suitable for electronic device applications. The p-type material is easily achieved by boron doping. However, the lack of available n-type diamond material has hindered the use of diamond-based devices in electronic applications. It is crucial for diamond to attain an effective donor dopant. Various desired dopants, such as group I elements Li and Na, group V elements N, P, As and Sb, group VI elements O, S, Se and Te, have been independently doped or co-doped into diamond as donor dopants [1–12]. However, the expected n-type diamond material has not yet been obtained, which is one of the biggest challenges in diamond device development. For diamond, substitutional phosphorus (Ps) with a donor level at Ec 0.6 eV is the best donor to date, however, such a deep donor is problematic for application at room temperature [13–15]. Recently, Koizumi [16] has succeeded in growing high quality Pdoped diamond. However, the ionization energy of the phosphorus donor is large (0.57 eV), which is not suitable yet for application at room temperature. Nitrogen in diamond creates a deeper donor levels at Ec 1.7 eV due to the localization of the unpaired electron on a carbon dangling bond [4,17]. Consequently, the N-doped diamond is not expected to yield useful conductivities at room tem-

* Corresponding author. E-mail address: [email protected] (Y. Dai). 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.08.017

perature. It has been reported that sulfur (S) can generate a ‘‘shallow” donor state below the conduction band and may become a good donor dopant, but these results have not yet been reproduced unambiguously; and in theory it is still controversial whether the substitutional sulfur is a ‘‘shallow” or ‘‘deep” donor [8,18–20]. Prins has obtained an n-type layer with donor level of Ec 0.32 eV in oxygen-implanted diamond [2]. But hardly any theoretical work explains the phenomenon and the subsequent report on O-doped n-type diamond is little. For the study of Li and Na in diamond, the results showed that a deep level is introduced in the band gap of diamond, which indicated that Li and Na in diamond are unlikely to produce the valid n-type material [4,21,22]. Simultaneously, studies on the interaction between hydrogen and these donor candidate dopants [23–26] have been carried out to research the effects of hydrogen on the gap states associated with defects and related electronic properties. The available n-type diamond material has not yet been obtained. In addition, a shallow n-type material with activation energy of around 0.23 eV has been obtained by deuteration of p-type B-doped diamond [27–30]. However, the origin of shallow donor level is controversial [31–36], which hampers the valid controlling of n-type material synthesis. Despite the recent progress in the study of n-type diamond, it is not available and a hunt for effective donor dopants continues. Compared with the donor dopants mentioned above, group II elements Be and Mg have never received attention for several decades in the n-type doping of diamond both experimentally and theoretically, although they have been widely used in doping GaAs and AlxGa(1 x)As [37–39].

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2. Method

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In the present work, the geometry and electronic properties of diamond doped with Be, Mg and hydrogen complexes, respectively, have been studied by means of density functional theory. The results show that the interstitial Be- (Bei-) and Mg- (Mgi-) doped diamond appear n-type behaviors with metallic character. Even if the impurity concentration is low, the diamond doped with Bei and Mgi also appear n-type characters. It is found that hydrogen atom may result in Bei- and Mgi- doped diamond p-type semiconductor or insulator, which denotes that the impurity doping into diamond should be carried out at H-poor conditions. Both substitutional Be (Bes) and Mg (Mgs) in diamond show acceptor behaviors and act as compensation centers for n-type conductivity.

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In the present work, the calculations have been performed by the CASTEP code [40], in which a plane-wave basis set and a conjugated gradient electronic minimization were used. The conjugated gradient approximation (GGA) with ultrasoft pseudopotentials in reciprocal space was adopted and exchange-correlation potential was parametrized by the Perdew–Burke–Ernzerhof scheme (PBE) [41]. A cubic 64-atom supercell was used and all atoms in the supercell were allowed to move freely during the geometry optimization. Using periodic boundary, a plane-wave cutoff energy of 310 eV was employed. It has been shown that the results were well converged at this cutoff energy. The calculations were performed using the Monkhorst-Pack scheme for sampling in the Brillouin zone with a mesh of 4  4  4 special k points [42].

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3. Results and discussion

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3.1. Interstitial defect atom Xi

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Interstitial defect atom Xi (X represents Be or Mg) was placed at various initial sites including tetrahedral interstitial (Td) site. All atoms were allowed to move freely until the energy was minimized and the optimized structure is shown in Fig. 1. After geometry optimization, we find that the equilibrium location of Xi is the Td site. For the defect Bei with Td symmetry displayed in Fig. 1(a), the optimal bond length of Bei–C is 1.67 Å and the bond angle of C– Bei–C is 109.47°. For Mgi with Td symmetry shown in Fig. 1(b), the Mgi–C bond length and the C–Mgi–C bond angle are 1.75 Å and 109.47°, respectively. Figs. 2(a) and (b) show the calculated band structures of the diamond doped with Bei and Mgi, respectively. For the sake of the completeness and comparison purposes, the band structure of pure diamond (as seen in Fig. 2(c)) is also shown as a reference. In Fig. 2(a) for the diamond doped with Bei, it can be seen that the Bei introduces donor states mixing with the conduction band (CB) and the Fermi level EF lies in the CB, which means the Bei-

Fig. 2. The band structures of diamond with (a) Bei doping, (b) Mgi doping, (c) pure, (d) Bei doping consisting of 128 C atoms and (e) Bei doping consisting of 216 C atoms. The dot line represents the Fermi level EF.

Fig. 1. Optimized structures for diamond doped with (a) interstitial dopants Bei and (b) Mgi.

doped diamond is of n-type metal conductivity character. The band structure of Mgi-doped diamond is displayed in Fig. 2(b). Similar as Bei doping, the introduced Mgi-related impurity states also locate near and overlap with the CB. The Fermi level is pinned in the conduction band, which presents that the diamond doped with Mgi is of good n-type conductivity behaviors. To investigate the influence of Bei and Mgi doping concentration on the electronic properties of diamond, the geometry and electronic properties of the doped diamond consisting of 128 and 216 C atoms have been studied by the method mentioned above. Considering the similar electronic properties of Bei with Mgi, we only describe the electronic properties of Bei in 128- and 216-C supercells in detail. The optimized structures of the Bei-doped dia-

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C.X. Yan et al. / Computational Materials Science 44 (2009) 1286–1290

mond consisting of 128 and 216 atoms are both same as the doped diamond consisting of 64 atoms Fig. 1(a). The corresponding band structures of Bei-doped diamond are shown in Fig. 2(d) and (e), respectively. In Fig. 2(d), the impurity states introduced by Bei mix with the CB and the Fermi level lies in the CB. It denotes that the Bei -doped diamond still appears n-type behavior with metallic character as the doping concentration is only a half of original concentration. For the doped diamond consisting of 216 C atoms Fig. 2(e), the impurity levels locate and connect to the bottom of CB (BCB) and the Fermi level lies at the BCB, which indicates the doped diamond is n-type conductivity material. The results demonstrate that the dopant Bei is a shallow donor in diamond and the n-type diamond material may be achieved by doping Bei into diamond lightly as well as the n-type material with a metallic character can also be obtained by Bei doping into diamond heavily. The optimal structures of Mgi in 128- and 216-C supercell are both similar to that shown in Fig. 1(b). As similar to the Bei-doped diamond, the Mgi-doped diamond consisting of 128 C atoms also appears ntype behavior with metallic character and that consisting of 216 C atoms is also n-type conductivity material. It indicates that n-type diamond material and the one with metallic character may also be obtained by doping Mgi into diamond lightly and heavily, respectively.

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(Bei-Hcc)-doped

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Fig. 4. The band structure of diamond doped with Bei–Hcc complex. The dot line represents the Fermi level EF.

3.2. The Bei- and Mgi-hydrogen complexes (Xi–H) impurity states mix with the conduction band and the Fermi level locates in the CB, which indicates that the complex Bei–Hcc also acts as a donor center in diamond. The total density of states (DOS) and projected DOS are shown in Fig. 5 to explore the origin of the electronic structure for (Bei– Hcc)- doped diamond. It can be seen that the states near the Fermi level are mainly contributed by C 2s2, 2p2 and Be 2s2 states, which indicates that the n-type behavior of doped diamond results from the hybridization between C and Be orbits. However, the interaction between Hcc and Bei dopant is weak near the Fermi level. According to the analysis, Hcc atom has little effect on the electronic properties of Bei-doped diamond and thus the diamond containing (Bei–Hcc) complex still shows n-type behavior. The results demonstrate that the diamond doped with hydrogen complexes show n-type character when the interaction between H and dopant Xi is small. Otherwise, the diamond containing hydrogen complexes show p-type or insulator behavior. Therefore, Bei- and Mgi- doping into diamond should be performed at H-poor growth conditions to avoid the effect of H on dopant Xi.

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To understand the effects of hydrogen on the electronic properties and gap states associated with defects, we have also investigated the electronic structures of diamond doped with (Xi–H) complexes. The calculations demonstrate that all possible configurations of the (Xi–H) complexes show p-type or insulator behavior except the complexes (Bei–Hcc) and (Bei–Hbc). For the (Bei–Hcc) complex as shown in Fig. 3(a), the H atom is placed at the center between the nearest and the second nearest C atoms of dopant Bei. After geometry optimization, the Bei lies at C3v symmetry site. The Bei–C bond length is 1.67 Å and the C– Bei–C bond angle is 119.58°. The C–H bond lengths are 1.34 Å and 1.03 Å, respectively. The other is (Bei–Hbc) complex, the Bei also locates at the C3v symmetry site and the H atom sites at between Bei and C atoms, which is shown in Fig. 3(b). The optimal Bei–C bond length and the C–Bei–C bond angle are 1.66 Å and 104.31°, respectively. The Bei–H and H–C bond lengths are 1.19 and 1.53 Å, respectively. The electronic structure calculations indicate that both of the complex Bei–Hcc and Bei–Hbc introduce donor levels too and present similar results. For simplicity, only the band structure of diamond with complex Bei–Hcc is shown in Fig. 4. Compared with that of Bei–doped diamond Fig. 2(a), the introduced donor states are a little far away from the CB besides an occupied state at the middle of band gap and the Fermi level is a little shallow in the bottom of CB. But, it is still evident that the

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Energy (eV) Fig. 3. Optimized structures for diamond doped with (a) Bei–Hcc and (b) Bei–Hbc complexes.

Fig. 5. The total and projected DOS of diamond doped with complex Bei–Hcc. The dot line represents the Fermi level EF.

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states above the VB than Bes and shows p-type behavior too. As the same result, Mgi trapped at a C vacancy is not only passivated itself, but will also compensate other Mgi donors. 4. Conclusion

Fig. 6. Optimized structures of diamond doped with substitutional dopants.

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In conclusion, we have investigated the electronic properties of dopants Be, Mg and related hydrogen complexes in diamond. The results indicate that the Bei- or Mgi- doped diamond are n-type semiconductor with metallic character. Even if the impurity concentration is low in diamond, the n-type diamond can still be obtained. The Bei- or Mgi- doping of diamond should be carried out at H-poor growth conditions because H atom may lead to Bei- or Mgi-doped diamond p-type semiconductor or insulator due to the effect of H atom on dopant Xi. The diamond doped with substitutional Bes or Mgs shows p-type behavior, and the gap states introduced by Bes or Mgs may serve as compensation center for other interstitial donors in diamond. The results are helpful to the investigation of the available n-type diamond.

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Acknowledgements

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This work is supported by the National Science foundation of China under Grant 10774091, National Basic Research Program of China (973 program, 2007CB613302), Fund for Doctoral Program of National Education 20060422023 and the Natural Science Foundation of Shandong Province under Grant number Y2007A18.

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References

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Fig. 7. The band structures of diamond containing defect dopants (a) Bes and (b) Mgs. The dot line represents Fermi level EF.

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3.3. Substitutional defect atom Xs The interstitial Li and Na in diamond are possibly mobile and trapped at C vacancies [21,43,44]. As the same period neighboring elements with Li and Na respectively, it is possible to trap at vacancy sites for Bei and Mgi impurities. So we have also investigated the electronic properties for the substitutional dopants Bes and Mgs, namely, the cases of Bei and Mgi trapped at C vacancy sites. The optimized structures are shown in Fig. 6. For the Bes-doped diamond configuration in Fig. 6(a), the Bes lies in the Td symmetry site with the Bes–C bond lengths of 1.68 Å and C–Bes–C band angles of 109.47°. For the configuration of diamond with Mgs in Fig. 6(b), the bond length of Mgs–C and the angle of C–Mgs–C are 1.84 Å and 109.48°, respectively. The band structure of Bes–doped diamond is shown in Fig. 7(a). It is clearly shown that some of impurity gap states are introduced above the valence band (VB) and the Fermi level is pinned at the gap states, which indicates that the Bes serves as an acceptor center in diamond. Furthermore the Bes, as an acceptor center, may trap the electron released by the donor Bei in diamond, in which the trapped electron does not participate in conductivity in diamond. Thus, the acceptor Bes may compensate the donor Bei. The result means that if Bei is trapped at a C vacancy to form the Bes, it will become an acceptor from a donor, which demonstrates that the Bei trapped at a C vacancy is not only itself passivated, but also compensates other Bei donors in the case of multi-defects coexistence in diamond. For the diamond containing Mgs, the band structure shown in Fig. 7(b) presents that Mgs may introduce deeper gap

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