Structure and bonding of iron-acceptor pairs in silicon

a49v322a

Structure and Bonding of Iron-Acceptor Pairs in Silicon

S. Zhao,

Texas Instruments Inc., Dallas, TX, 75243

J. F. Justo, L. V. C. Assali,

Instituto de Física, Universidade de São Paulo,

CP 66318, CEP 05315-970, São Paulo, SP, Brazil

and L. C. Kimerling

Massachusetts Institute of Technology, Cambridge, MA, 02139

Received on 23 April, 2001

Iron-acceptor pairs (Fe-A, A = B, Al, Ga, and In) in silicon were investigated using an ionic-based model, which incorporates the valence electron cloud polarization and the lattice relaxation.Our results are generaly in good agreement with the experimental trends among the Fe-A pairs, describing the increase in the pair donor energy level with increasing A principal quantum number and decreasing pair separation distance, and the pair configurational symmetries.

Iron pairs with acceptor impurities in silicon [1], forming electrically active centers. The properties of these pairs, such as the configurational structure and the positions of the energy levels in the band gap, have been investigated by electron paramagnetic resonance (EPR) and deep level transient spectroscopy (DLTS) [2] over the last thirty years. These pairs have been identified as consisting of a substitutional acceptor (A_s) with an iron (Fe_i) at either the nearest neighbor (T1, á111ñ symmetry) or the next nearest neighbor (T2, á100ñ symmetry) tetrahedral interstitial site. According to an ionic model, used to explain the experimental data, the Fe_iA_s pairs are formed by a positively charged iron ( or ) and a negatively charged acceptor ().

The ionic model fails in describing several trends among the Fe_iA_s pairs, such as the pair stability and the related positions of the acceptor and donor electronic levels [3]. Adding an elastic energy term to the point charge interaction, Kimerling et al. [4] explained the pair structures observed by the experiments. They noticed that large acceptor impurities provide strong repulsion enough to compete with the Coulomb attraction so that the Fe_i stays at a T2 site (and not at a T1 site) next to the acceptor. Our model incorporates a new interaction in the point charge Coulomb interaction, a short range attractive component to simulate the valence electronic cloud polarization [5]. The repulsive interaction between Fe_i and A_s or Si is approximated by a softened Lennard-Jones type potential, and the silicon crystal is treated as a dielectric medium. The results are compared to the experimental data on configurational symmetries and deep level positions. Our model captured several trends on the pairs observed by experiments [2], showing an increase in the pair donor energy level with increasing principal quantum number of A_sand decreasing pair separation distance, opposite to results obtained by Kimerling et al. [4].

When the separation between Fe_i and A_sis comparable to their ionic radii, the electronic cloud of one ion is strongly perturbed by the field of the other, causing an induced polarization on that electronic cloud. Our polarization model (PM) includes a short range attractive component to the Coulomb interaction to describe the electronic cloud polarization. As an estimation to the induced electronic cloud polarization effect, we take the valence electronic cloud as a charged spherical surface at certain radius around the radial peak position of the valence electronic charge density. Then, similar to the interaction between two conducting spheres, the electrostatic interaction can be written as (r º r_Fe–A)

where a₁ and a₂ are the valence electronic cloud spherical surface radii, q₁ and q₂ are the net ionic charges.

The calculations were performed using 279 Si atoms, one A_s, and one Fe_i. The distance r_Fe–A is changed along á111ñ direction (passing through T1 and T4 sites) and á100ñ direction (passing through T2 site) to find the potential curves for , , and . The minimum of each curve V_min(), V_min(), and V_min() is the ground state for , , and , respectively. The model predicts the Fe_iA_spair configurational symmetries by determining the energetically favorable sites for Fe_i.

Fig. 1 shows the potential curves along á111ñ and á100ñ directions for , and . According to Figs. 1a and 1d, stable Fe_iB_s and metastable Fe_iIn_s pairs have á111ñ-trigonal symmetry, while stable Fe_iIn_s and metastable Fe_iB_s pairs have á100ñ-orthorhombic symmetry. The á111ñ-trigonal symmetry can be assigned to stable , , , and pairs, while metastable , , , and pairs show á100ñ symmetry (Figs. 1b and 1c). In addition, Figs. 1b and 1c predict that the stable pair exhibits á100ñ symmetry, while the stable pair has equal probability to show either á111ñ-trigonal or á100ñ-orthorhombic structures. The assignments for stable and metastable structures are in good agreement with the EPR and DLTS observations [2]. The stable configuration switches from á111ñ-trigonal to á100ñ-orthorhombic for Fe_iA_s pairs going from B_s to In_s, and is related to an increase in repulsion between A_s and Fe_i.

The minimum of each curve can be used to compute the pair acceptor and donor levels. For Fe_i at near neighbor T sites relative to A_s, the donor level ()^0/+ is given by

where E_n is the top of the valence band and is the minimum of the potential curve at near neighbor sites of . The pair acceptor level ( )^-/0 is obtained by adding the difference V_min()-V_min() to the donor level. For isolated Fe_i, at remote sites relative to A_s, V_min()-V_min()=0.38 eV, which is consistent with experimental data that only one donor level at E_n+0.38 eV exists in the band gap. In our model, the difference between V_min() and V_min() for isolated Fe_i arises from the elastic energy caused by electron shell overlap between atoms. Fig. 2 shows the donor (0/+) and acceptor (-/0) levels for the transitions as computed by our polarization model for Fe_i sitting at T1 (Fig. 2a) or T2 (Fig. 2b) sites. Our results for the pair donor and acceptor levels agree very well with the known experimental data for the (0/+) and (-/0) transitions.

The PM predicts the correct magnitudes and trends of the donor level for the T1 site (E_T(1)) and the T2 site (E_T(2)) pairs with increasing A_s size and decreasing r_Fe–A as observed in experiments, while the point charge model would give an opposite trend. According to our model, repulsion and polarization from A_s should give a maximum contribution at the T1 site and yield the greatest variation in Fe_iA_s pair energy levels. This is consistent with the experimental data that E_T(1) displays the greatest sensitivity to A_s identity and E_T(2) shows relative uniformity. The PM suggests that the pair acceptor level ( )^-/0 should become shallower in the band gap as A_s goes from B_s to In_s, while recent experimental data [6] suggest that this level is almost constant for A_s.

The pair binding energies are shown in Table I. The model predicts a trend of monotonic decrease with increasing A_s size for both and . The increase in binding energy due to valence electronic cloud polarization competes with the repulsive interaction so that the model gives nearly constant binding energies for both and , consistent with experimental data [3,7,8]. Lattice relaxation clearly plays an important role in determining the pair binding energy.

The relative population of Fe_iA_s pairs in a certain charge state at T1 and T2 sites (R₁₂) is calculated, based on a Boltzmann distribution at thermal equilibrium:

where DE₁₂ = E_min(T2)– E_min(T1) is the energy difference for Fe_i at the T1 and T2 sites, and Z is the site degeneracy. The relative site populations for the pairs are compared with results from metastability experiments in Table II. Our model provides a good description of the energy differences between the T1 and T2 sites (DE₁₂) for all the pairs. The calculated N(1)/N(2) ratios at T = 200 K, around the temperature of the observed structural transformation [8,9], also agree very well with the experimental data.

In summary, our model captures several effects within the ionic model framework: (i) trends among the Fe_iA_s pairs revealing a deepening of the donor level in the band gap with increasing principal quantum number of A_sand decreasing pair separation distance r_Fe–A; and (ii) configurational symmetries and the bistability of the pairs. However, the deviations at E_T(1) between measured and calculated data suggest that other interactions are still missing. The deviations could come from the limitations of the ionic models at near neighbor T sites. The bulk, treated as dielectric medium, can still be valid for the space between a T4 site and the A_s, and between a T2 site and the A_s. However, at the T1 site, the screening would hardly be effectively described by the bulk dielectric constant, since one of the Fe_i first neighbors is the A_s. Covalency involving the Fe_i, A_s, and surrounding Si atoms may also play an important role, as pointed out by first-principles calculations [11,12,13]. Although a complete understanding on the properties of the pairs should be established with more detailed experiments and calculations, our model is important in identifying the contribution of each interaction for the pair formation.

Acknowledgments

This work is supported by the NREL under contract No. XD-2-11004-4. JFJ and LVCA thank the Brazilian agencies FAPESP and CNPq for financial support.

References

[1] G. W. Ludwig and H. H. Woodbury, Solid State Phys. 13, 223 (1962).

[2] A. A. Istratov, H. Hieslmair, and E. R. Weber, Appl. Phys. A 69, 13 (1999).

[3] L. C. Kimerling and J. L. Benton, Physica 116B, 297 (1983).

[4] L. C. Kimerling, M. T. Asom, J. L. Benton, P. J. Drevinsky, and C. E. Caefer, Mater. Sci. Forum 38-41, 141 (1989).

[5] S. Zhao, L. V. C. Assali, J. F. Justo, G. H. Gilmer, and L. C. Kimerling, J. Appl. Phys. 90, 2744 (2001).

[6] P. Tidlund, M. Kleverman, and H. G. Grimmeiss, Semicond. Sci. Technol. 11, 748 (1996).

[7] W. Wijaranakula, J. Electrochem. Soc. 140, 275 (1993).

[8] A. Chantre and D. Bois, Phys. Rev. B 31, 7979 (1985).

[9] A. Chantre and L. C. Kimerling, Mater. Sci. Forum 10-12, 387 (1986).

[10] H. Takahashi, M. Suezawa, and K. Sumino, Mater. Sci. Forum 83-87, 155 (1992).

[11] L. V. C. Assali and J. R. Leite, Mater. Sci. Forum 10-12, 55 (1986); 38-41, 409 (1989); 83-7, 143 (1992).

[12] L. V. C. Assali and J. F. Justo, Phys. Rev. B 58, 3870 (1998).

[13] J. F. Justo and L. V. C. Assali, Int. J. Mod. Phys. B 13, 2387 (1999).

Publication Dates

• Publication in this collection
  26 Nov 2002
• Date of issue
  June 2002

History

• Received
  23 Apr 2001