Localised vibrational modes of hydrogen-impurity complexes in GaAs

Physica B 170 (1991) 413-416 North-Holland

Localised vibrational modes of hydrogen-impurity complexes in GaAs P.R. Briddon and R. Jones Department of Physics, University of Exeter, Exeter, EX4 4QL, UK

The results of ab initio calculations performed on the complexes formed between hydrogen and donor and acceptor atoms in gallium arsenide are reported. The equilibrium geometries and electronic properties are presented. A parameter free determination of the vibrational properties of the entire defect complex has been performed allowing a more complete comparison with infrared absorption experiments to be made. Local structural distortions far larger than previously expected are proposed explaining the absence of certain absorption lines.

1. Introduction There has recently been a great deal of interest in the properties associated with hydrogen (H) when incorporated in both pure [1] and doped [2-5] semiconductors. Most of the experimental effort [2, 3] and almost all of the previous theoretical treatments [4, 5] have focussed on the hydrogen passivation of shallow impurities in silicon and little has been said about the situation in III-V materials such as gallium arsenide. The purpose of this study is to explore the different complexes formed in GaAs between hydrogen and the defects produced by substituting a Ga atom with Si (a donor) and Be (an acceptor).

2. Method The first-principles calculations presented used the local density functional theory with the ab initio pseudopotentials of Bachelet, Hamann and Schluter [6]. Hydrogen-terminated clusters of 56, 86 and 102 atoms were used. The methodology has been presented in detail elsewhere [7]. This procdure reproduces the bulk bond length and angle in GaAs to within 1-2%. An electronic density of states constructed was also found to be

in close agreement with experiment. The vibrational properties of GaAs and the defect complexes were then calculated by determining ab initio parameters for a Musgrave-Pople potential [7, 8].

3. The hydrogen-silicon complex Recently, detailed infrared absorption experiments have been performed which studied the complex formed between silicon donors and hydrogen [10]. Two hydrogen related lines at 896 and 1717 cm-~ were observed. Evidence that the H bonds directly to the silicon donor was provided by the observation of small changes of the frequency of the 1717cm -~ line due to the presence of the three different isotopes of silicon: ~' - 298i and 3OSi . - 8SI, In a previous publication [11] we have investigated the final state complex produced in this passivation process. Three possible high symmety sites for the hydrogen atom were considered: (a) the antibonding (AB) site of the silicon donor, (b) the "bond centred" ( B C ) - near the centre of one of the S i - As bonds, (c) the AB site of one of the four arsenic atoms

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I'.R. BrMdoH, R. Jone~

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which are nearest neighbours of the silicon atom. Details of the resulting microscopic structures have already been published I l l ] where it was reported that the AB site for the H atom had the lowest energy, with sites (b) and (c) being higher in energy by 11.4 and 0.8 eV, respectively. In the remainder of this section more details are given of the determination of the vibrational frequencies of the complexes. Second derivatives of the total energy of the cluster with respect to displacements of the silicon atom and its five nearest neighbours were evaluated. The dynamical matrix describing thc vibration of a cluster of many hundreds of atoms was then generated by using thc ab initio second derivatives for all elcments depending on the innermost six atoms and for the remainder using a valence force potential obtained for pure gallium arsenide using the same procedure as has been previously described for diamond by Jones 17]. The vibrational frequencies of the atoms in the complex were then obtained by diagonalising thc dynamical matrix in the usual manncr. It is readily verified that the frequencies converge if only a modest n u m b e r of atoms arc allowed to vibrate. In fact the results satisfactorily converged when only the silicon atom and the ncarest two shells of host atoms were allowcd to vibrate, with the remainder held stationary. Nevertheless, in the following calculation a further two shells were allowed to vibrate. A feel for the strengths of the bonds present in the defect complex can be obtained by fitting the second derivatives listed above to a 'local" valence force potential with parameters which are allowed to take different values from the bulk values and to vary from bond to bond. The potential energy of the crystal may then be written a s = q)d+.l..ct + q)r~.m.i,,d,,,

g r a v c - P o p l c form 181. q~,,.,~, then describes the bonding near the dcfecl. All thal rcmains is to choose a potcntia] that enables the "'raw ab initio sccond derivativcs'" to bc lifted adequately. In this study the following form has been choscn:

<,

+ ~k~;il

<

•

\" 21;

,,

.XO: t

l

+ ~k,r,',

\" 8ri, ._.,

,

.

wherc r,, is thc cquilibrimn bond length ill pure crvstallmc gallium arscnide and 3.r and .X0 denote the changes of cach bond length or bond angle from its own, individual, equilibrium value as determined by the ab initio program. Thc valence forcc constants wcrc determined bv a standard least squares lit to the second dcriw> tives and the resulting force constants arc given in table 1. It is clearly scen from this table how the uniquc, lengthened silicon-arsenic bond has a stretching force constant (k~) which is far weaker than that of the other three silicon-arsenic bonds (ke). in fact these bonds had a slightly increased force constant c o m p a r e d to that of a "'bulk'" gallium-arsenidc bond. This is to be expected as these bonds are sp ? in character and it is known that such bonds arc stronger than the sp s bonds found in pure GaAs. Thc vibrational frequencies were then readily evaluated by constructing and diagonalising the dynamical matrix. The quality of the litted

,

where q)r..... inder is the potential due to all the gallium and arsenic atoms in thc cluster and the sum excludes the silicon and hydrogen atoms and all bond stretching terms involving silicon-arsenic bonds, q~ has been chosen to have the Mus-

Table I Force constants ( c V / A ' ) describing the potential ncar ]I Si complex (AB structure). kI k~

1.476 11.774

k, k,

9.268 (I.362

k k,,

I0.272 2.056

P.R. Briddon, R. Jones / Hydrogen-impurity complexes in GaAs

potential can be tested by inserting the raw derivatives and checking that the frequencies do not change. The results of carrying out this procedure are given in table 2. An analysis of the corresponding eigenvectors showed that the Si modes corresponded to motion in the plane of the three As atoms. The remaining mode, associated with motion along the extended bond, fell into the one-phonon spectrum, thus accounting for it not being observed. The absence of this line may therefore be considered as indirect experimental evidence for such a large distortion. We then carried out a similar procedure for the BC structure (b) above. The larger clusters showed this defect to have a short (and therefore strong) S i - H bond being formed which, in contrast to experiment [10], gave rise to a high vibrational frequency for the H atom (2200 cm-~). The Si related vibrational frequencies were found to be 354 (A~), 424 and 428 (E) cm . These modes are slightly at variance with experiment as the singlet vibrational mode (354 cm 1) has not been observed. This provides an additional check as to the correct equilibrium site. To summarise then, these calculations have

415

therefore been able to identity the Si antibonding site as the preferred site for the hydrogen atom in the S i : H complex and have been able to reproduce the observed vibrational modes.

4. The hydrogen-beryllium complex We now turn to the neutralisation of acceptors. The first observation of this was by Johnson et al. [13], who showed that the depth of hydrogen or deuterium penetration and the depth to which the acceptors were compensated were equal to experimental accuracy. Once again, infrared absorption experiments have been performed [14] determining the LVMs of the H and Be atoms. Work by Stavola et al. [15] demonstrated that the complex possessed C3v symmetry with the symmetry axis along [1 1 1]. In this study, two such sites for the hydrogen atom were considered (a) near the centre of one of the four B e - A s bonds, and (b) at the antibonding site of one of the As atoms adjacent to the Be. It was found that site (a) had a lower energy by 0.3 eV and vibrational frequencies in close agreement with experiment. The properties of this complex are illustrated below in table 3.

Table 2 Vibrational frequencies (cm ~) of S i - H complex in A B configuration.

Si H "bend" H "stretch"

Raw derivatives

Fitted result

Experimental values

446.1, 449.0 1019.6, 1032.6 1829.9

456.35 982.4 1813.3

409.95 896 1717

Table 3 Structural and vibrational properties of the B e l l complex. Property

56 atom cluster

86 atom cluster

102 atom cluster

B e - H (/~,) A s - H (/~,) B e - A s (,~) A s ' - G a (/k) As-Be-As Ga-As'-Ga

1.78 1.54 2.19 2.43 119 ° 116 °

1.84 1.54 2.16 2.45 119° 117°

1.85 1.52 2.16 2.42 120 ° 117 °

H wag freq. (cm ~) Expt.: not seen H stretch freq. (cm ~) Expt.: 2037 cm

346383

495

301

2163

2018

2083

416

f'.R. Briddon. R. Jones'

ftydrogen-impurity comphwe~ in (;aAs

The close agreement illustrates the degree to which the results converged in cluster size. It was found that the H atom had a tendency to move slightly (~0.15,4,) off-axis, although the energy changes involved were very small (~0.01 eV). It seems very likely that the H wag mode falls into the one-phonon excitation spectrum, explaining why it has not been observed. The electronic acceptor-related level became doubly occupied and fell into the valence band explaining the removal of all electrical activity. The hydrogen atom was then inserted at the antibonding site of one of arsenic atoms surrounding the Be atom. The resulting A s - H bond length was 1.55 ,~, with the unique B e - A s bond lengthening to 3.29 A. The corresponding vibrational frequencies of the hydrogen atom were found to be 852, 853 (E modes) and 2069 cm (the A~ mode). The energy however was 0.3 eV higher than that of the " b o n d - c e n t r e d " structure above and this, together with the very high wag frequency effectively rules out this as the equilibrium structure of the Bell complex. 5. Conclusions To conclude, the calculations have established that, for the Si doped material, the stable site for hydrogen is the antibonding site, adjacent to the silicon atom. This model is similar to that postulated by Pajot et al. but with one major differe n c e - here the silicon is four-fold coordinated whereas those workers suggested that it should be five-fold coordinated. This has turned out to be a significant difference as it is just the broken bond that causes the "'missing" silicon mode to fall into the one-phonon spectrum. However, for Be doped material, the BC site is favoured. The stretching frequency of the B e - H bond has been reproduced together with a prediction that the unobserved mode falls into the onc-phonon band. These calculations have therefore been able to distinguish between different models previously put forward for the microscopic structure of d o n o r / a c c e p t o r complexes with hydrogen in

semiconductors. Quantitative agreement has been obtained with experimental values of the vibrational frequencies of both the hydrogen atom itself and the modes of the paired donor/ acceptor atoms.

Acknowledgements We would like to thank Ron Newman for encouraging us to carry out these calculations and for much helpful advice and Malcolm Heggie and Grenville Lister for many useful discussions.

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