8210
J. Phys. Chem. B 2000, 104, 8210-8216
Etching of GaAs(100) Surfaces by Cl2: Quantum Chemical Calculations on the Mechanisms Arndt Jenichen*,† and Cornelia Engler Institute for Surface Modification, Permoserstrasse 15, D-04303 Leipzig, Germany, and UniVersity Leipzig, Wilhelm-Ostwald-Institute of Physical and Theoretical Chemistry, Linne´ strasse 2, D-04103 Leipzig, Germany ReceiVed: February 24, 2000; In Final Form: June 9, 2000
For the interpretation of experimental findings and the development of concrete mechanisms of the GaAs etching by chlorine, quantum chemical calculations were executed with molecular models of local structures of flat surfaces and steps with various chlorinations. Desorption energies and, partly, desorption barrier heights of Ga2, GaClm (m ) 1-3), As2, As4, and AsCln (n ) 1-3) are calculated by the density functional theory (B3P86). The obtained data agree well with qualitative and quantitative experimental findings and allow to explain the reaction behavior. Chlorine molecules preferably bond to Ga atoms than to As atoms. At steps, Cl atoms can pass over from As to Ga atoms between the first and second layer by overcoming small barriers. In general, the desorption energies of GaCln and AsCln (n ) 1-3) species show a characteristic behavior with increasing number of chlorine atoms at neighboring positions of the desorbing species. The reaction product distribution can be interpreted in dependence upon the temperature and the Cl2 concentration at the surface: Under deficient chlorine concentration (high temperatures), the GaCl and As2 desorption and, under high chlorine concentration (low temperatures), the GaCl3 and AsCl3 desorption is preferred. In agreement with experiments, the desorption energies of the essential reaction products increase in the order: AsCl3, GaCl3, GaCl, and As2. GaCl2, AsCl2, AsCl are relatively stably bound at the surface.
1. Introduction The controlled removal of surface atoms by reactive gasphase speciessthe chemical dry etchingscan be used for fabrication of microscopic structures on surfaces. The reaction of Cl2 with GaAs surfaces is one of the mostly investigated etching processes. Reviews were given by Yu and DeLouise1 as well as by Simpson and Yarmoff.2 A model that gives the mechanism and reproduces qualitative and quantitative experimental results does not exist up to now. For the investigation of mechanisms the experiments provide the surface composition after interruption of the etchant gas exposure,3-6 the reaction product distribution in dependence on the temperature,7-13 and, possibly, estimates of the activation energies of desorption for the product formation.12-14 All the chlorinated species GaCln and AsCln (n ) 1-3) were detected on the GaAs surfaces. For the thermal etching of the GaAs(100) surface by Cl2, the gas-phase products GaCl, GaCl3, AsCl3, As4, and As2 were found by most of the authors.7,8,11,12 Some differences were reported: Balooch et al.9 found AsCl, but not As2 and As4. Ludviksson et al.10 showed that small amounts of GaCl2 desorbs at 240 K. Houle11 also found AsCl2, GaCl2, and As3. French et al.13 registered no As4. The desorption temperatures of the species increase in the following order: AsCl3, GaCl3, GaCl, As2. Activation energies for desorption were estimated from the temperature-programmed desorption data.12-14 They can be connected with larger errors because the preexponential factor is assumed to be 10-13. * Corresponding author. E-mail:
[email protected]. Fax: 49-341-9736399. † Present postal address: University Leipzig, Wilhelm-Ostwald-Institute of Physical and Theoretical Chemistry, Linne´strasse 2, D-04103 Leipzig, Germany.
The essential theoretical investigations were presented by Ohno. Reference 15 demonstrates that an exchange reaction between Cl and As atoms and the insertion of Cl atoms in GaAs bonds could be responsible for initiation of the breakup of the GaAs crystal. In ref 16 the dissociative chemisorption of Cl2 at the GaAs(001) surface, as first step of etching, is investigated using the density functional theory and a six-layer slab model. On the Ga-rich GaAs(001)-(4 × 2) surface, the Cl2 was found to dissociate without potential barrier over the Ga dimer. The dimer bond is being simultaneously broken resulting in formation of GaCl with two back-bonds to the As layer below. On the As-rich (2 × 4) surface, on one hand, the Cl2 dissociation over the As dimer is an activated process and does not break the As dimer and, on the other hand, Cl2 dissociation over the As dimer vacancy is barrierless and exothermic. Theoretical investigations on the reverse desorption processes, as deposition or epitaxial crystal growth, can give interesting results. Fukunishi et al.17 calculated potential energy curves for the deposition of As2 using cluster models, where the As2 attacks Ga atom on top. For the removal of As2, which is bound on a flat GaAs(001) surface, an activation energy of 43.5 and a desorption energy of 20 kcal/mol was obtained by MP2 calculations. The removal of As2 out of a flat GaAs(001) surface requires 141.6 and 132.0 kcal/mol, respectively. Mochizuki et al.18 calculated the potential energy curve for the GaCl desorption with a small cluster model ((H2As)2GaCl). The activation energy of desorption is 60.2 kcal/mol obtained by the MRSDCI+Q method. Kunsagi-Mate et al.19 calculated the potential energy curve for the desorption of As dimers. They obtained an activation energy of 53.7 kcal/mol and a desorption energy of 36.6 kcal/mol by the MP2 method and a simple cluster model (H8As2Ga5As2).
10.1021/jp0007383 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/03/2000
Etching of GaAs(100) Surfaces by Cl2
J. Phys. Chem. B, Vol. 104, No. 34, 2000 8211
Figure 1. 4 × 2-dimer model. Examples for (A) free Ga-rich surface, (B) fully monochlorinated Ga-rich surface, (C) free As-rich surface, and (D) fully monochlorinated As-rich surface. The atoms marked with an asterisk (*) are fixed at positions determined by experimental data and are not optimized.
The aim of this study is the reaction modeling of the GaAs (100) surface etching by Cl2. Desorption energies and, partly, the related barrier heights are calculated using quantum chemical methods and molecular models representing local chemisorption structures with surroundings. These energies are compared with experimental data, as surface compositions, desorption temperatures, and estimated activation energies of desorption. Concrete reaction mechanisms are set up. At first the selected molecular models and quantum chemical methods are presented. Then the results are discussed in comparison with the experimental findings for low and high temperatures and chlorination.5 2. Models The formation and desorption of probable chemisorption surface structures is investigated in this study. The consideration of the surroundings, as flat surface or steps as well as free structures or various chemisorption, is important for the selection of the models. The distinction between high and low chlorination must also be considered for the modeling. That results from the experimental findings (see, e.g., ref 8): The etch rate increases with the temperature. The highly chlorinated species are desorbed under low temperatures. The non- and lowly chlorinated species are preferentially desorbed under high temperatures. One can conclude that under low temperatures little chlorine is consumed due to the low etch rate. Therefore, sufficient chlorine is available for chemisorption. The opposite results for the high temperatures. The high etch rate causes a strong consumption of Cl2. Therefore, a deficient chlorine concentration at the surface leads to lowly chlorinated surface structures. All the investigations are done for the Ga-rich and the analogous As-rich surface. For the selection of the concrete model structure, the electron counting model20 is considered, so that no unreal charge accumulates at the surface. The investigations are restricted to surface atoms (Ga, As) that have up to two bonds to atoms of the bulk. A third bond is possible to a neighboring atom of the same type (dimer or bridge structures). Therefore, two models are distinguished:
(X) The (4 × 2)-dimer model (Figure 1) is used for the modeling of the Ga2, As2, Cl2, GaCl and AsCl desorption from the free or lowly halogenated surface. The (4 × 2)-structure models a reconstructed surface and allows also to consider the desorption from the flat surface (middle) and from a step (edge). (Y) The (3 × 1)-monomer model (Figure 2) is used for the simple modeling of highly chlorinated surface structures with GaClm and AsClm (m ) 1-3) species. This model does not allow dimers as starting structures. Two types are distinguished for this model: (Y1) The flat surface model (Figure 2A,C) with two neighboring surface atoms are used for the modeling of a plane surface site. (Y2) The step model (Figure 2B,D) with one neighboring surface atom models a step into [110] direction. The outside atom of the second layer at the step can bind a chlorine atom. Each model is subdivided into two regions: (1) The reaction area is geometry-optimized. (2) The environment bath is fixed at the experimental bulk geometry. The dangling bonds into the bulk are saturated by hydrogen atoms. The H atoms are situated on the imaginary Ga-As bonds. Fixed atoms are marked by asterisks (*) in Figures 1 and 2. After the removal of atoms, the remaining clusters are reoptimized in the same manner as the full clusters. Additionally, dimerization of the second layer atoms is allowed. 3. Methods The reaction energies and the related barrier heights for the chemisorption/desorption of molecular structures are calculated using quantum chemical methods and molecular models of local surface structures. For the calculation of the energies, the density functional theory (DFT) is suitable. Dissociation energies of relevant diatomic molecules calculated by different DFT methods show that the B3P86 method provides data, which agree well with experimental, and other theoretical values. The B3P86 is a hybrid method with parameters combining Becke’s exchange functional21 and Perdew’s correlation functional.22 The
8212 J. Phys. Chem. B, Vol. 104, No. 34, 2000
Jenichen and Engler
Figure 2. (3 × 1)-monomer model. Examples for (A) fully monochlorinated Ga-rich surface (1/1/1),a (B) GaCl2 at a step of a Ga-rich surface with monochlorination of the surroundings (1/2/-1),a (C) AsCl2 on a flat As-rich surface with trichlorinated neighboring atoms (3/2/3),a and (D) AsCl3 at a step of an As-rich surface with trichlorination of the neighboring As atom and monochlorination of the outside Ga atom (3/3/-1).a The atoms marked with an asterisk (*) are fixed at positions determined by experimental data and are not optimized. a(left/middle/right): number of Cl atoms at the surface atoms (positive number) or at subsurface atoms of steps (negative number).
geometry optimizations of the individual species are done on the Hartee Fock (HF) level. The electronic core potentials (ECP) and the valence double-ζ basis set of Wadt and Hay23 are used for the geometry optimizations. For the energy calculations, a 6D set of polarization functions is added to the non-hydrogen atoms. The undetermined exponents are optimized in calculations of diatomic molecules in the HF-optimized atomic distances. The following values were applied: Ga, 0.16; As, 0.27; Cl, 0.6. The barrier heights for chemisorption/desorption reactions of molecules are obtained by the procedure of Ohno.16 The transition state is the point of the highest B3P86 energy along the restricted HF-optimized reaction path. In respect to the known deficiencies of the density functional methods for calculation of transition state energies, one has to assess those data with care. But at the moment we see no chance to use higher correlated ab initio methods. Frequencies were not calculated by reason for the partial optimization. The GAUSSIAN98 program system24 is used for the (B3P86/LanL2DZ(6D)//HF/ LanL2DZ) calculations.
4. Results and Discussion For determining the mechanisms of etching processes, the reaction with the lowest barrier must be found for each of the considered structures. At first, the reaction energies are calculated for all the probable desorption reactions. Secondly, the barrier height for the reaction with the lowest desorption energy is calculated. If it is smaller than the next higher desorption energy, one can assume that this reaction path is the most probable one. Otherwise, one has to calculate also the barrier height for the next higher energy and so on. In this paper the barrier heights, if calculated, are presented behind the desorption energies within brackets. 4.1. Free and Lowly Chlorinated Surface: Dimer Model. 4.1.1. Ga-Rich Surface: Ga2, Cl2, and GaCl Desorption. Table 1 contains the desorption energies and the related barrier heights for the Ga-rich (100) surface obtained with the (4 × 2)-dimer model. This model allows to study the chemisorption/desorption of Cl2 at the middle, edge, and outside position as well as the desorption of Ga2 and GaCl from the middle and edge position
Etching of GaAs(100) Surfaces by Cl2
J. Phys. Chem. B, Vol. 104, No. 34, 2000 8213
TABLE 1: Desorption Energiesa and Related Barrier Heightsa,b of Cl2, Ga2, and GaCl from Unchlorinated and Low Chlorinated Ga-rich (100) Surfaces Calculated by the Dimer Model (See, e.g., Figure 1A,B) local surface structures on the dimer model a b c d e f a
Cl2 desorption
middle
edge
outside
Ga2 2GaCl Ga2 2GaCl
Ga2 2GaCl 2Ga Ga2Cl2 2GaCl
2As 2As 2AsCl 2AsCl 2AsCl 2AsCl
2GaCl
middle
edge
111
111
99
121 116
113
Ga2 or GaCl desorption outside
46 (55) 63 (70) 76 87
middle
edge
115 56 105 43 (43)
145 57 113 45 (45) 31 (37)
15 (15)
Energies in kcal/mol. b Barrier heights within brackets.
TABLE 2: Desorption Energiesa and Related Barrier Heightsa,b of Cl2, As2, and AsCl from Unchlorinated and Low Chlorinated As-rich (100) Surface Calculated by the Dimer Model (See, e.g., Figure 1C,D) local surface structures on the dimer model a b c d e f g h i j k a
Cl2 desorption
middle
edge
outside
As2 2AsCl As2 2AsCl As2 2AsCl As2 2AsCl
As2 As2 2AsCl 2AsCl As2 As2 As2Cl2 As2Cl2 As2
2Ga 2Ga 2Ga 2Ga 2GaCl 2GaCl 2GaCl 2GaCl 2GaCl 2GaCl 2GaCl
As2 As2Cl2
middle
edge
As2 or AsCl desorption outside
51 (63) 45 (59)
47 (59) 44 (56)
47 (61) 46 (61)
76 (81) 76 (82) 59 (74)
93 (93) 91 122 123 (123) 119 145
middle
edge
103 74 93 66 51 (51) 46 (60) 84 62 (62)
88 107 65 72 93 (93) 88 81 79 59 (66)
-15 (
