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SEMICONDUCTORS VOLUME 33, NUMBER 9 SEPTEMBER 1999 Effect of local vibrations on the H and D atom densities at a Si surface I. P. Ipatova and O. P. Chikalova-Luzina A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia K. Hess Beckman Institute, Illinois State University, Urbana, Illinois USA ͑Submitted March 1, 1999; accepted for publication March 2, 1999͒ Fiz. Tekh. Poluprovodn. 33, 1100–1101 ͑September 1999͒ The equilibrium surface densities of passivating adatoms for a silicon crystal in equilibrium with H2 or D2 gas are calculated. The difference in the surface densities of H and D adatoms is determined by the difference in their local surface vibrations. The equilibrium deuterium surface densities are an order of magnitude higher than the hydrogen surface densities. © 1999 American Institute of Physics. ͓S1063-7826͑99͒01909-2͔ In this paper we calculate the surface densities of hydro- function of a crystal with adatoms written in terms of the gen H ͑or deuterium D͒ atoms on a silicon surface in equi- frequency distribution function: librium with H ͑or D ) gas. The chemical potentials of H 2 2 ប(H,D) ͑ ͒ ͑ ͒ loc or D on a surface and the chemical potentials of H or D in (H,D)ϭT ln n(H,D)ϩ3T lnͫ 2 sinh ͬϩ . ͑2͒ gas are required to describe the equilibrium. In addition to surf 2T (H,D) the electronic contribution, the chemical potential of a H ͑or Here n(H,D) are equilibrium H or D adatom surface densities. D͒ adatom possesses a vibrational contribution, which is de- Since the binding energies of the isotopes are the same, i.e., termined by the dynamics of a crystal lattice with impurities. ϭ , the difference in the chemical potentials for H and The chemical potential of H ͑or D͒ in gas is known from the H D D arises because of the difference in the frequencies of their thermodynamics of diatomic gases. The condition that the local vibrations, (H)Þ(D) . chemical potential of an adatom is equal to the chemical loc loc The chemical potentials for H and D gas are obtained potential of H ͑or D͒ in gas at thermodynamic equilibrium from the condition of equilibrium for the dissociation reac- makes it possible to find the equilibrium H ͑or D͒ surface tion H ϭ2H ͑or D ϭ2D) and from the chemical potential density. It is shown that the surface density of D adatoms is 2 2 of a molecule consisting of two identical atoms5 an order of magnitude higher than that of H adatoms. For simplicity, an unreconstructed ͑100͒ silicon surface with the 1 (H,D)ϭ ͫT ln P Ϫc T ln TϪ T symmetry of a simple square lattice is considered. We as- gas 2 (H2 ,D2) p (H2 ,D2) sume that an adatom with mass M H ͑or M D) lies above a surface silicon atom with mass M and is bound with the ប(H2 ,D2) ϩ ϩ ͬ. ͑3͒ silicon atom by a force constant ␥. For low adatom density, 2 0 in the nearest-neighbors approximation the following charac- Here P and P are the pressures of the corresponding teristic equation can be obtained for determining the frequen- H2 D2 1 cies of local vibrations of adatoms: gases, c p is the specific heat at constant pressure, 3/2 ␥2 IH M H Ϫ 2 ϭ ͑ ͒ ϭ ͫ 2 ͩ 2 ͪ ͬ 1 G͑ ͒ 0, 1 H ln , 2Ϫ2 2 ប5 2 0 where 2ϭ␥/M (H,D), and G(2) is the diagonal element of I M 3/2 0 D2 D2 the Green’s functions matrix for a semi-infinite crystal.2 ϭlnͫ ͩ ͪ ͬ D2 ប5 2 In the numerical calculations of the frequencies of the local vibrations from Eq. ͑1͒ it was assumed that the force are, respectively, the chemical constants of hydrogen and constant ␥ is, to a high degree of accuracy, equal to the deuterium gases; I and I are the moments of inertia and H2 D2 effective force constant for central forces in a Si–Si bond at (H2) (D2) 4 and the vibrational frequencies of H2 and D2 the surface, i.e., ␥ϭ8.8ϫ10 dynes/cm. The experimentally molecules, and 0 is the binding energy of a molecule in gas. measured values of the frequencies of surface vibrations Substituting the chemical potentials ͑2͒ and ͑3͒ into the con- (H)ϭ ϫ 14 Ϫ1 of adatoms are used below: loc 3.96 10 s and dition of thermodynamic equilibrium (D)ϭ ϫ 14 Ϫ1 ͑ ͒ loc 2.83 10 s Ref. 4 , which are somewhat different ͑ ͒ (H)ϭ(H) ͑ ͒ from the frequencies calculated from Eq. 1 . surf gas , 4 The following chemical potentials for the H and D ada- (D)ϭ(D) ͑ ͒ toms are obtained from the vibrational part of the partition surf gas , 5 1063-7826/99/33(9)/2/$15.00 1002 © 1999 American Institute of Physics Semiconductors 33 (9), September 1999 Ipatova et al. 1003 gives an equation for the surface densitites n(H) and n(D). effect has been observed in Ref. 6, where hydrogen passiva- (H) (D) Since the local vibrational frequencies loc and loc satisfy tion of a silicon surface was replaced by deuterium passiva- ប(H) , ប(D)ϾT and since I /I ϭM /M , the ratio of tion. loc loc H2 D2 H2 D2 the adatom densities is I. P. Ipatov and O. P. Chikalova-Luzina thank the Rus- sian State program ͑code 0.12͒ ‘‘Surface Atomic Struc- (D) M 5/4 ប͓(H)Ϫ(D͔ n H2 3 loc loc tures,’’ the Russian State program ‘‘Leading Science ϭͩ ͪ expͫ ͬ (H) M 2T Schools’’ ͑Grant 96.15-96.348͒, and the Russian Fund for n D2 Fundamental Research ͑Grant 98-02-18295͒. ប(D2)Ϫប(H2) ϫexpͫ ͬ. ͑6͒ 4T 1 S. L. Cunnigham, L. Dobrzynski, and A. A. Maradudin, Phys. Rev. B 7, 4643 ͑1997͒. The first exponential factor, which contains the difference in 2 E. W. Montroll, A. A. Maradudin, G. H. Weiss, and I. P. Ipatova, Theory the local vibrational frequencies of H and D, makes the main of Lattice Dynamics ͑Academic Press, New York, 1971͒. (H)Ͼ(D) , the deu- 3 L. Miglio, P. Ruggerone, and G. Benedek, Phys. Scr. 37,768͑1988͒. contribution to this expression. Since loc loc 4 terium density is much higher than the hydrogen density. V. A. Burrows, Y. J. Chabal, G. S. Higashi, K. Raghavachary, and S. B. Christman, Appl. Phys. Lett. 53, 998 ͑1988͒. Our calculation showed that at temperatures Tϭ600 5 L. D. Landau and E. M. Lifshitz, Statistical Physics ͑Pergamon Press, Ϫ700 K typical of this technology this ratio is of the order of New York; Nauka, Moscow, 1976, Chap. 9͒. 10. It is entirely likely that the difference in the dynamics of 6 I. C. Kizilyalli, J. W. Lyding, and K. Hess, IEEE Electron Device Lett. 18, ͑ ͒ the vibrations of H and D isotopes is one of the factors that 81 1997 . explains the large isotopic effect in MOS transistors. This Translated by M. E. Alferieff SEMICONDUCTORS VOLUME 33, NUMBER 9 SEPTEMBER 1999 Irradiation as a possible method for producing SiC heterostructures A. A. Lebedev*) A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia ͑Submitted March 1, 1999; accepted for publication March 2, 1999͒ Fiz. Tekh. Poluprovodn. 33, 1102–1104 ͑September 1999͒ Certain aspects of the physics of heteropolytypic junctions based on silicon carbide are examined. It is known that the introduction of certain impurities into the growth zone during epitaxy of silicon carbide results in the growth of films whose polytype is different from that of the initial substrate. It is also known that these impurities lead to the formation of certain deep centers in the band gap of the conductor. Analysis of published data performed in this paper shows that irradiation of SiC with various charged particles also leads to the formation of these deep centers. It is assumed that under certain experimental conditions transformation of the polytype of the already grown epitaxial SiC structure is possible under the action of irradiation and subsequent annealing. © 1999 American Institute of Physics. ͓S1063-7826͑99͒02009-8͔ The term ‘‘silicon carbide’’ denotes essentially an entire sity of the substrate͒. It was found in Ref. 5 that the use of class of semiconductor compounds, since SiC can crystallize 6H-SiC Lely substrates with high dislocation density ͑of the in various modifications — polytypes. The polytypes of SiC order of 105 cmϪ2) in the standard ͑for growth of 6H-SiC with the same chemical composition can differ substantially layers͒ sublimation epitaxy process results in the growth of with respect to their electrical properties. For example, the 3C-SiC epitaxial layers. band gaps range from 2.4 ͑3C-SiC͒ to 3.3 eV ͑2H-SiC͒. This In Refs. 1 and 6 heteropolytypic epitaxy processes were makes silicon carbide a promising material from the stand- attributed to the stoichiometric composition of various poly- point of producing various types of heterostructures. types of SiC. Previously, it was observed that the concentra- It was found in Refs. 1–3 that when certain impurities tion ratio ͓Si͔/͓C͔ varies in different polytypes of SiC and are introduced into the growth zone of SiC layers, epitaxial decreases with increasing percentage of hexagonality. It was films with a polytype different from that of the substrate shown that the ratio ͓Si͔/͓C͔ was 1.046, 1.022, and 1.001 for employed can be obtained.