Composition and reconstruction of the GaP{100}-(4 × 2) surface

Composition and reconstruction of the GaP{100}-(4 × 2) surface

surface science ELSEVIER Surface Science 365 (1996) 136-148 Composition and reconstruction of the GaP{ 100}-(4 x 2)surface M.M. Sung, J.W. Rabalais...

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surface science ELSEVIER

Surface Science 365 (1996) 136-148

Composition and reconstruction of the GaP{ 100}-(4 x 2)surface M.M.

Sung, J.W. Rabalais

*

Department of Chemistry, University of Houston, Houston, TX 77204-5641, USA Received 15 January 1996;accepted for publication 26 February 1996

Abstract The composition and reconstruction of the GAP{100}-(4x 2) surface has been studied by time-of-flight scattering and recoiling spectrometry (TOF-SARS) and low energy electron diffraction (LEED). Time-of-flightspectra of scattered and recoiled neutrals plus ions were collected as a function of crystal azimuthal rotation angle 6 and primary beam incident (polar) angle ~. Compositional analysis of the surface was obtained from 4 keV Ne ÷ scattering and recoiling spectra. Structural analysis was obtained from the azimuthal anisotropy of the 5-scans and the features of the a-scans using both 4 keV Ne ÷ and Kr ÷ for scattering and recoiling. The azimuthal 6-scans were simulated by means of a shadow cone focusing model and a classical ion trajectory model. The totality of this data shows that the (4 x 2) reconstruction of GaP is a Ga missing-row-trimerP dimer (MRTD) structure in which every fourth Ga(011) row is missing, the Ga atoms are trimerized along the (011) azimuth, and the 2nd-layer P atoms exposed in the (011) troughs are dimerized. This MRTD model is consistent with all of the data, is autocompensated, and has Ga intratrimer spacings of 3.2+0.2 .A and P intradimer spacings of 2.7+0.2 ]k. The results of the simulations suggest that the two end Ga atoms of the trimers are relaxed downward by a minimum of 0.2 A.. A missing-row-dimer(MRD) model, similar to that proposed for the GaAs (4 x 2) structure, in which every fourth Ga (011) row is missing and Ga dimers form along (011), was also considered. This MRD model is inconsistent with large portions of the experimental data and the simulations. The results are discussed in terms of the differences in the chemical bonds of phosphorus and arsenic.

Keywords: Computer simulations; Gallium phosphide; Ion-solid interactions, scattering, channeling; Low energy ion scattering (LEIS); Low index single crystal surfaces; Semiconductingfilms;Surface relaxation and reconstruction; Surface structure, morphology, roughness, and topography

1. Introduction The I I I - V s e m i c o n d u c t o r surface r e c o n s t r u c t i o n phases have been the focus of m a n y surface science investigations [-1 ], primarily due to the interesting chemistry a n d physics that is responsible for these structures a n d to the i m p o r t a n t technological applications of these surfaces. M u c h of the research has focused o n GaAs. As a result, the structures of * Corresponding author. Fax: + 1 713 7432709; e-mail: [email protected]

the G a A s reconstructions are n o w established to a high degree of certainty. It was only n a t u r a l that the structures of these G a A s reconstructions were extrapolated to other I I I - V c o m p o u n d s . It has recently been s h o w n [ 2 , 3 ] , however, that the I n P { 1 0 0 } - ( 4 x 2 ) r e c o n s t r u c t i o n is different from that of G a A s { 1 0 0 } - ( 4 x 2 ) . These cation-termin a t e d (4 x 2) surfaces are the most stable structures at elevated temperatures. It has been firmly established for G a A s [ 4 - 1 7 ] a n d InAs [ 1 8 - 2 2 ] t h r o u g h the use of several surface analysis techniques that the {100}-(4 x 2)

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M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

and -(2 x 4) reconstructions are of the missing rowdimer (MRD) type. The (4 × 2) phase contains Ga or In dimers in the 1st layer and the (2 × 4) phase contains As dimers in the 1st layer. These structures are characterized by a 2x period derived from dimerization of lst-layer atoms and a 4x period derived from the spatial arrangement of the Ga(In) and As dimer rows. The dimer or dangling bond direction is parallel to the missing-row (MR) direction. For the InP {100}-(4 x 2) surface, it has been shown [2,3] that the reconstruction consists of lst-layer In trimers with 2nd-layer P dimers exposed in the In missing row troughs. For this missing-row-trimer-dimer (MRTD) structure, which satisfies autocompensation requirements [ 1,23], the 2x period is derived from dimerization of 2nd-layer P atoms in the missing rows and the 4x period is derived from the spatial arrangement of the lst-layer In rows. In contrast with the MRD structure of GaAs and InAs, the lst-layer trimer or dangling bond direction is perpendicular to the MR direction. Schematic drawings of the cation terminated unreconstructed (1 × 1) and reconstructed MRD and MRTD (4x2) surfaces are shown in Fig. 1. The differences in the MRD and MRTD structures have been made apparent in a study [24] of the growth of an InAs (4 x 2) epilayer with MRD structure on an InP (4 x 2) surface with MRTD structure. Since a major difference in the MRD and MRTD structures is the formation of anion dimers in the latter, it is believed that the driving force towards a MRTD structure is the strong covalent bond that can be formed from phosphorus dimerization. If this premise is correct, the GAP{100}-(4×2) surface should also have an MRTD reconstruction similar to that of InP. Despite the fact that GaP is one of the most widely used visible light-emitting diode materials that is capable of operating at high temperatures, the surface structures of the reconstructed phases are not known [25-28]. The purpose of this paper is to present the results of a time-of-flight scattering and recoiling spectrometry (TOF-SARS) and low energy electron diffraction (LEED) study of the GAP{100}-(4 x 2) surface in order to identify the type of reconstruction and to determine the interatomic spacings in the reconstructed layer.

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[Ii MRTD (4x2) Fig. 1. Schematic models for the III-V {100}-(1 x 1) and -(4 × 2) cation-terminated surface reconstructions showing the missingrow-dimer (MRD) and the missing-row-trimer-dimer (MRTD) models. The unit cells are defined by dashed lines. The filled and empty dangling bonds are shown as dark and light parabolas and the dimer bonds are shown as dark ellipses.

2. Experimental and computational methods 2.1. T O F - S A R S measurements

The TOF-SARS technique and experimental procedures have been described in detail elsewhere [29]. The primary beams used were 4keV Ne ÷ and Kr ÷ and various scattering angles in order to facilitate separation of certain scattering and recoiling peaks. The pulse width was ,~ 50 ns, the pulse repetition rate was 30 kHz, and the average beam current density was ,-,0.5 nA/cm2. The angular notation is defined as follows: ~=beam incident

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M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

angle to the surface, 6=crystal azimuthal angle measured from the (011) azimuth, 0=scattering angle, ~=recoiling angle, and fl=scattering or recoiling exit angle from the surface. The surface was allowed to cool to room temperature for all data acquisition. Four types of TOF-SARS spectra were employed in the analysis. First, Kr + was employed at ~= 10° and 0 = 3 0 ° in order to facilitate sensitive recoiling of light impurities. This was used to check for impurities and to define the clean surface condition. Second, elemental analysis of the surface was obtained by detecting scattered Ne at ~ = 10°, 0 = 20 °, and random azimuthal directions between 6 = 0 ° and 90 °. These conditions of relatively small incident and exit angles favor scattering and recoiling from only the 1st layer and any exposed 2nd or 3rd layers. Azimuthal angles that were not aligned with any of the low index azimuths were chosen in order to avoid semichanneling and focusing effects. Third, surface Ga was investigated by detecting backscattered Ne at 0 = 163 ° and recoiled Ga at 0 = 3 0 °. At 0 = 163 °, 4 keV Ne quasi-single scattering from a P atom has a kinetic energy of only ~ 200 eV and is therefore not detected; only Ne backscattering from Ga is detected. Fourth, surface P was investigated by detecting P atoms that were recoiled [29] at ~ = 15° and ~ = 30 ° from quasi-single collisions of primary Kr +. The scattering (Is) and recoiling (It) intensities were obtained by integrating a time window of 0.2 #s centered at the scattered or recoiled peak maxima. Details of the method for determining the composition and orientation of III-V { 100} semiconductor surfaces using TOF-SARS have been published elsewhere [3].

2.2. Sample preparation The samples of undoped GAP(100) wafers (M.R. Semicon, Inc.) with an n-type carrier concentration of 5 x 1017 cm -3 were cleaned according to the procedure described by Weiss et al. [21], i.e., they were chemomechanically polished with a brominemethanol solution, rinsed in methanol, dried with nitrogen, and then transferred to the ultra-high vacuum (UHV) chamber. The (4 x 2) surface was obtained by using cycles of 300 eV Ar ÷ sputtering

(0.1 #A, 15 min, 30 ° incident angle) followed by annealing for 5 rain at 850 K. This surface exhibited a sharp (4 x 2) LEED pattern with no detectable impurities by TOF-SARS.

2.3. Simulations of scattering and recoiling Two types of calculations were used in order to simulate the experimental results: a shadow cone focusing model and a classical ion trajectory simulation model. The azimuthal angle &scans of Ga recoil from Ne were simulated using a shadow cone focusing model developed in this laboratory [30]. This simplified model was developed specifically for simulating f-scans where it is important to keep the computational time short so that several different surface structural models can be tested. Based on a binary collision approximation, the model assumes that the incident ion flux is focused by the shadow cones of the surface atoms. The resulting anisotropic flux that is distributed over the surface produces high recoiling intensities when atoms are aligned such that the focused flux from a shadowing atom is incident with the appropriate impact parameter of the scattering atom. Simultaneous focusing by several atoms, e.g., semichanneling [31], is included. Using a fixed incident angle, c~, azimuthal angle g-scans can be calculated on a PC-compatible computer in seconds. The classical ion trajectory simulation was carried out by means of a program called scattering and recoiling imaging code (SARIC) which was developed in this laboratory [3,32]. SARIC is based on the binary collision approximation (BCA), i.e., it models the trajectories of the energetic particles as a series of straight lines corresponding to the asymptotes of the scattering trajectories due to sequential binary collisions. The calculation is performed by solving Hamilton's equations of motion for an ion approaching a crystal lattice. This simulation was applied to 4keV Ne ÷ projectiles impinging on finite twodimensional slices of the GaP {100}-(4 x 2) surface along each principal azimuth to simulate the incident angle or-scans.

M.M. Sung, J. W. Rabalais/SurfaceScience365 (1996) 136-148

3. Results 3.1. Elemental analysis of the surfaces A typical T O F spectrum from a G a P surface that has some impurity hydrogen, carbon, and oxygen is shown in Fig. 2. The spectrum exhibits peaks due to K r scattering from G a atoms as well as recoiled P, H, C, and O atoms. These contaminants were removed by cycles of sputtering and annealing, after which a sharp ( 4 x 2 ) L E E D pattern was observed and the hydrogen, carbon, and oxygen peaks were no longer detected, as shown in Fig. 2. The relative G a and P elemental concentrations in the surface were obtained by collecting N e

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scattering spectra at 40 different r a n d o m azimuthal angles between 0 ° and 90°; an example spectrum is shown in Fig. 3. The Ioa and Ip peak intensities were obtained from the average of these 40 spectral intensities, from which concentrations were calculated after correcting for the different scattering and recoiling cross sections. These cross sections were calculated in the binary collision approximation using the Moli6re a p p r o x i m a t i o n to the potential function [ 33, 34]. The calculated cross sections are aG~=0.316 A 2 and a e = 0 . 1 8 2 ,~2, yielding an atomic concentration ratio of [ G a ] / [ P ] = 2.66. The GAP{100} surface can be terminated in either a G a or a P layer. The high [ G a ] / [ P ] ratio obtained confirms that the surface is terminated in a layer of G a atoms and that the exposed P atoms are m o s t likely in missing-row troughs.

3.2. Relating the (011) and (011) azimuths to the LEED pattern

] Go(S) The relation of the two principal crystal azimuths to the L E E D pattern can be established [ 3 , 3 5 ] from the differences in the relative intensities Ioa of G a scattering spectra and Ie of P recoiling spectra along the principal directions of

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Fig. 2. Portion of the TOF-SARS spectrum of the GaP{100}(4 x 2) surface showing the contamination on the surface after incomplete cleaning and after complete removal of the surface impurities. The conditions were: 4 keV Ar +; incident angle ct= 10° from the surface; scattering and recoiling angle 0=~b= 30°; azimuthal angle 6 = 40° from (011). Peaks due to Ar scattering from Ga [Ga(S)] and recoiling hydrogen, carbon, oxygen, and phosphorus [H(R), C(R), O(R), and P(R)] are observed before cleaning. The H, C, and O impurities are below the detection limit on the (4 x 2) surface.

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Fig. 3. Example of a TOF-SARS spectrum of the clean (4 x 2) surface with the beam aligned along a random azimuthal direction showing Ne scattering from gallium and phosphorus [Ga(S) and P(S)] and gallium recoiling [Ga(R)]. The relative intensities for scattering from Ga (Io,) and P (Ip), as determined from the average of 40 such spectra collected at random azimuthal directions between 6=0 ° and 90°, were used to determine the elemental composition of the surface. The conditions were: 4 keV Ne+; incident angle a = 5°; scattering angle 0 = 30°, and azimuthal angle 6=0°-90 °.

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M.M. Sung, J, W. Rabalais/Surface Science 365 (1996) 136-148

the LEED pattern. The atoms underlying the (011) azimuth are arranged differently from those underlying the (011) azimuth because the ideal bulk truncated surface of GAP{100} has only 180° symmetry with respect to the underlying bulk crystal, as can be seen from Fig. 1 The number of Ga and P atoms exposed to the ion beam is different along the (011) and (011) azimuths. At the low incidence angle of ~= 15° used in the comparison, only the lst- through 3rd-layer atoms or atoms exposed in missing row troughs are accessible to the ion beam. For the unreconstructed (1 × 1) surface, the ratio of these atoms within the unit cell for Ga is Ga_(011)/Ga(011)= 2/1 and the ratio for P is P(011)/P(011)=0/1. Therefore, higher Io, from Ga and lower IF from P can be expected for TOF spectra along the (0]-1) azimuth. Reconstruction with missing rows will naturally change these ratios, however the qualitative prediction of higher IG, and lower Ip along the (011) azimuth is unchanged. The Ga scattering and P recoiling spectra used for this comparison were collected along the two principal directions, labeled 4x and 2x, of the LEED pattern. These spectra are shown in Fig. 4. The intensity ratios obtained for IG, from Ga and Ip from P along the two directions of the (4 x 2) surface are IG,(2X)/IG,(4X)= 2.2 for Ga and Ip(2X)/Ip(4X)=0.33 for P. This establishes the 2x direction as the (011) azimuth and the 4x direction as the (011) azimuth. The value of the ratio for P is higher than expected for the unreconstructed surface, indicating that the reconstructed surface has Ga missing rows and P atoms exposed in these troughs. The orientation of the directions of the LEED pattern with respect to the underlying bulk crystal is important in determining a model for the reconstructed (4 x 2) surface, as will be shown in Section 4.2. 3.3. Surface periodicity of the (4 x 2) Ga and P atoms - azimuthal angle f-scans of Ga recoiled by Ne and P recoiled by Kr The surface periodicity of the Ga and P atoms was determined by monitoring IG~ for Ga and Ip for P as a function of the crystal azimuthal angle26. The azimuthal angle as defined before was 6 =0 ° for (011) and 6 =90 ° for (011). TOF spectra

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similar to those shown in Fig. 4, i.e., Ga data from Ne recoiling of Ga atoms and P data from Kr recoiling of P atoms, were used in making the azimuthal plots of Figs. 5 and 6. Minima and maxima are observed as a function of 6. The widths of the minima are related to the interatomic spacings along that particular direction. Wide, deep minima are expected from short interatomic spacings because of the larger degree of rotation about 6 required for atoms to emerge from neighboring shadows. The minima are coincident with lowindex azimuths where the surface atoms are inside of the shadowing or blocking cones cast by their aligned, closely spaced nearest neighbors, resulting in low Io, and Ip. As 6 is scanned, the atoms move out of the shadow cones along the intermediate 6 directions where the interatomic spacings between the atoms are long, resulting in an increase in IG, and Ip. Schematic diagrams of the MRTD surface illustrating the recoiling and blocking directions

M.M. Sung, J. IV.. Rabalais/Surface Science 365 (1996) 136-148

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are presented above the &-scans of Figs. 5 and 6. The positions of the observed minima together with those calculated for MRTD and MRD (4 x 2) structures are listed in Table 1. The calculated minima were obtained by varying the Ga-Ga intratrimer spacings AxG~ and the P-P intradimer spacings ,dye for MRTD and the Ga-Ga intradimer spacings zlxG, for MRD in order to optimize the fit with the experimental minima. All of the labeled minima have been reproduced several times in measurements involving three different GaP crystals. In general, the narrow, shallow minima observed

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for both Ioa and Ie at intermediate directions between the principal (011) and (011) azimuths is suggestive of a structure involving many different lst-neighbor distances, some of which are long relative to the lst-neighbor distances along the principal azimuths.

3.3.1. Ga recoiling from Ne The IGa &-scan was performed in the shadowing mode [29], i.e., a grazing incident angle (~= 5°) and small recoiling angle (~b= 30°) were used. The wide minima A and F are direct results of the short interatomic spacings between the lst-layer Ga atoms along the principal azimuths. Three distinct minima, labeled B1,2, C I , 2 , and E1,2, and a

M.M. Sung, J. W. Rabalais/SurfaeeScience365 (1996) 136-148

142

Table 1 Comparison of the positions of the experimental TOF-SARS minima of the azimuthal angle &scan for the GaP (4 x 2) surface with the positions calculated for a (4 x 2) reconstructed surface using the MRTD and MRD models Experimental TOFSARS minimaa

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a These angular positions correspond to the minima observed in the scans of Figs. 5 and 6. Each value represents the average of four independent measurements. b MRTD model: Ga missing-row-trimer P dimer with missing rows along (011) (Ga-Ga intratrimer spacing = 3.2 A; P-P intradimer spacing = 2.7 ,~). ¢ MRD model: Ga missing-row-dimer along (011) (Ga-Ga intradimer spacing = 3.3 ,~).

m i n o r minimum, labeled D, are observed at oblique angles to the principal azimuths. Each of the B1,2, Cla, and EL2 minima is a result of two closely aligned focusing a t o m pairs. The D m i n i m u m is only barely observable due to the semichannels which are closely aligned with this direction; these semichannels refocus the deflected particles along the D direction.

the lst-layer plane, the 6 rotation required for recoiling 2nd-layer P atoms to avoid the G a blocking cones is larger than that required for avoiding the P blocking cones. The Ip f-scan reveals the periodicity of the 2nd-layer P atoms. The wide, deep G m i n i m u m indicates t h a t very little P is accessible to the beam along ( 0 1 1 ) and that the P atoms are blocked predominantly by the m o r e massive G a atoms along this direction. The minor m a x i m u m located within this deep m i n i m u m is due to focusing and semichanneling [ 3 1 ] along the ( 0 1 1 ) direction. The m i n i m u m labeled M along ( 0 1 1 ) is narrow, indicating that the major influence on the recoiled P atoms is the less efficient blocking by neighboring in-plane P atoms.

3.3.3. Simulation of the azimuthal angle 6-scans The results of the s h a d o w cone focusing model simulation of the recoiling intensity Ioa using the M R T D model are shown in Fig. 5. The calculation uses the experimental values obtained for the G a - G a intratrimer spacing (3.2 A) and the P - P intradimer spacing (2.7,~). The best agreement between the simulated scan and the experimental scan was obtained after including relaxation of the two end G a atoms of the trimers (atoms 1,3,4,6,7,9 of Fig. 1) d o w n w a r d by 0.2 A, resulting in a buckled trimer. W i t h o u t such buckling, the G a atoms aligned along the B1,2 directions of Fig. 5 are in the same plane, resulting in extensive shadowing which would produce deep minima at those positions. The value of 0.2 A was the m i n i m u m a m o u n t of relaxation required to achieve agreement with the experimental scan. This simulation, therefore, suggests that the G a trimers have a buckled configuration.

Interatomic spacings - incident (polar) angle a-scans of Ne scattered from Ga 3.4.

3.3.2. P recoiling from Kr The Ip f-scan was performed in the blocking m o d e [ 2 9 ] , i.e., a relatively large incident angle ( a = 1 6 °) and small recoiling angle (~b=20 °) were used. The recoiled P atoms can be blocked by both neighboring G a and P atoms, although Ga, due to its greater m a s s , has a blocking cone that is 10% larger than that of P and therefore blocks more efficiently. Also, since the G a atoms are in

Information on the interatomic spacings along planes perpendicular to the surface was obtained [ 2 9 ] by measuring I r a for G a as a function of the incident angle a along the azimuthal directions 6 = 0 ° ( 0 1 1 ) and 90°(011). At grazing a, all atoms lie within the s h a d o w cones of their preceding neighbors [ 2 9 ] . As a is increased, subsurface layer atoms move out of the s h a d o w cones of the lst-layer

M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

atoms. When the impact parameter required for scattering into 0 becomes accessible, a sharp increase in IGa is observed due to focusing of ion trajectories at the edges of the shadow cones. A critical incident angle ~c, defined as the c~value at half peak height, can be related to the interatomic distance through use of the shadow cone radii [29]. Examples of such a-scans together with cuts through the two principal azimuths in planes perpendicular to the {100} surface are shown in Fig. 7. The nearest-neighbor Ga and P alignments in these planes for an MRTD structure are indicated in the diagrams on the right side of the a-scans. The I~a scan is particularly simple for the (011) azimuth where four distinct peaks are observed. For the (011) azimuth, a broad, low IG~ feature is observed for ~< 35 °, which is characteristic of overlapping peaks. The low overall intensity of the low portion of this scan is also indicative of the lower number of accessible Ga atoms along (011). The features observed in these incident angle

143

or-scans can be related to the interatomic spacings from the diagrams on the right side of Fig. 7 and the trajectory simulations of Figs. 8 and 9. First, consider the scan along the 4x (011> direction. The overlapping peaks A and B are at the positions expected for Ga-Ga shadowing and focusing along the lst-layer Ga atoms. Two overlapping peaks are observed because the reconstruction provides

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M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

two different G a - G a interatomic spacings along this azimuth and, hence, two different focusing angles (Fig. 8A and Fig. 8B). Peak C results from focusing by 2nd-layer P atoms onto 3rd-layer Ga atoms (Fig. 8C) and D results from focusing by lst-layer Ga atoms onto 5th-layer Ga atoms (Fig. 8D). Next consider the scan along the 2 x (011) direction. Since there is only a single type of Ga interatomic spacing along this azimuth, only a single intense peak labeled E is observed corresponding to lst-layer-lst-layer Ga shadowing and blocking (Fig. 9E). Peak F results from (Fig. 9F) 2nd layer P atoms focusing onto 5th-layer Ga atoms and peaks G and H both arise from lstlayer Ga atoms focusing onto 5th-layer Ga atoms. These features are all in accord with the structure of the MRTD model.

similar to those of InP [2] and different from those of GaAs and InAs [24].

4.2. Compatibility of the MRD and MRTD models with the data The experimental results are compared in this section with two models: (i) the Ga missing-rowdimer (MRD) model as proposed for the GaAsand InAs-(4x2) structures [1], in which every fourth Ga or In (011) row is missing; and (ii) the In missing-row-trimer P dimer (MRTD) model, as proposed [2] for the InP-(4 x 2) structure, in which every fourth In (011) row is missing, the In atoms are trimerized along (0_11), and the 2nd-layer P atoms exposed in the (011) troughs are dimerized.

4.2.1. Surface termination Both models are compatible with termination of the (4 x 2) surface in a layer of Ga atoms and having P atoms exposed in the troughs. 4. Model for the GaP (4 x 2) structure

4.1. Summary of experimental results for the (4 x 2) phase The results that are most essential in developing a model for the GAP(4 x 2) structure can be summarized as follows. The surface is terminated in a Ga layer, although P atoms are clearly exposed to the beam. The ratios of the accessible atoms along the principal azimuths are I~(2x)/I~(4x)---2.2 for Ga and Ir(2x)/Ip(4x)=0.33 for P. The 2x and 4x directions of the LEED pattern are aligned with the (011) and (011) azimuths, respectively. The positions of the minima listed in Table 1 and shown in Figs. 5 and 6 reveal the periodicity, or alignment, of neighboring Ga and P atoms. The G a - G a interatomic spacings are short along both principal azimuths and the P atoms are blocked predominantly by neighboring Ga atoms along (011) and by neighboring P atoms along (011). The ratios of accessible atoms along the principal azimuths and the .- and &scans for GaP are very

4.2.2. Alignment of the 2x and 4x LEED directions The MRTD model is consistent with the experimental result which aligns the 2x and 4x directions with the (011) and (011) azimuths, respectively. The MRD model aligns the 2x and 4x directions with the (011) and (011) azimuths, respectively. 4.2.3. Number of accessible atoms along the azimuths The ratios of the number of atoms accessible to scattering and recoiling in the lst-layer and the exposed 2nd- and 3rd-layers of the unit cell along the principal azimuths of the MRTD model are Ga(2x)/Ga(4x) = 14/6 = 2.2

(1)

and P(2x)/P(4x) = 2/8 = 0.25.

(2)

The values found experimentally (Section 3.) are: Ira(2x)/IGa(4X) = 2.2 for Ga

(3)

and

Ip(2x)/lv(4X)=0.33 for P.

(4)

M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

The higher Ira and lower Ip observed along the 2x direction are consistent with the experimental data and the assignment of this direction to the (011 > azimuth. For the MRD model, the numbers of atoms exposed in the lst- through 4th-layers of the unit cell are: Ga<2x)/Ga(4x> = 6/14

(5)

and P<2f>/P(4f> = 10/0,

(6)

145

fails to predict the L minimum. Increasing or decreasing AXGa results in even worse agreement. Concerning the P blocking pattern of Fig. 6, the MRTD model, predicts that 2nd-layer P atoms are blocked predominantly by neighboring Ga and P atoms along the 2x and 4x directions, respectively, as observed experimentally. The MRD model predicts that P atoms are predominantly blocked by Ga and P atoms along the 4x and 2x directions, respectively, in contradiction to the experimental result.

in contradiction to the experimental data.

4.2.5. Incident angles 4.2.4. Surface periodicity The Ga and P atomic alignments in the surfaces of the MRTD and MRD models were calculated for comparison to the positions of the minima observed in the f-scans of Fig. 5 and Fig. 6. These positions of the Ga shadowing and P blocking minima calculated from the MRTD model, in which the G a - G a and P - P spacings have been optimized for the best fit with the experimental minima, are listed in Table 1. This model provides agreement with all of the observed I6~ and Ip minima. The best fit is obtained for lst-layer Ga atoms that make a linear trimer along (011 > with lateral G a - G a spacings of 3.2_ 0.2 A, corresponding to a displacement of the two end atoms of the trimer by AXG~= 0.7 A from their equilibrium positions. The good correspondence between the observed and predicted I e minima indicates that 2nd-layer P atoms are exposed and dimerized along the (011) missing rows with intradimer spacings 2.7_ 0.2 ,A, or a displacement of each P atom by Ayp=0.6 ,A from their equilibrium positions. In order to compare the Ga and P periodicities in the MRD model with the data, the Ga atoms were dimerized along <011> and the P atoms in the troughs remained undimerized. The positions of the calculated minima for both Ga and P are listed in Table l for Ga displacements of AXG~=0.3 ,A from their equilibrium positions, i.e., 3.6 A intradimer spacing. The model predicts triple minima which are spread over a 11 ° span for the C position (a single narrow minimum is observed), angular positions for the El,2 and H minima which are in disagreement with the observed minima by more than the experimental uncertainty, and it

Cuts through the two principal azimuths of the MRTD model in planes perpendicular to the {100} surface are shown alongside the a-scans of Fig. 7. The nearest-neighbor atomic alignments in these planes are labeled and the approximate positions of the calculated focusing peaks are indicated below the scans. These positions were calculated from the angle of alignment of the focusing-scattering atom pair and the radius of the shadowing cone [32]_The Ga a-scan is particularly simple for the <011> azimuth where the four observed peaks are clearly predicted by the model. For the Ga <011 > azimuth, the model predicts two overlapping features for the broad structure observed at ~<35 °. All of the features of the 0t-scans are in qualitative agreement with the atomic alignment angles and spacings along the principal azimuths predicted by the MRTD model. Vertical relaxation in the outermost layers has not been included in the calculations of the peak positions. Inclusion of such relaxation would result only in small shifts in the calculated peak positions indicated in Fig. 7. The MRD association of <011> and (011) with the 2x and 4x directions, respectively, results in particularly complicated peak features for IGa along the 2x direction where dimerization of Ga would result in several closely spaced low a peaks. On the contrary, this azimuth exhibits particularly simple features (Fig. 7).

5. Discussion The_proposed MRTD model has P dimers along the (011) azimuth, and Ga buckled trimers along

146

M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

the (011) azimuth which reduces the number of P and Ga dangling bonds. The structure contains 0.25 of a monolayer of P atoms exposed in the Ga missing row troughs. The MRTD and MRD models can be compared through simple energetic arguments. Consider that the most stable reconstructed phase at a given temperature should have the smallest amount of dangling bonds and the largest amount of new bonds formed as a result of the reconstruction. The unit cell of the MRTD structure (Fig. 1) contains two filled P dangling bonds, four empty Ga dangling bonds, two P-P dimer bonds, and four Ga-Ga trimer bonds. The P dangling bonds are directed along the (2x) (011) direction and the Ga dangling bonds are directed along the (4x) (011) direction. The MRD unit cell contains four filled P dangling bonds, six empty Ga dangling bonds, and three Ga-Ga dimer bonds. The major expected energy changes [36] upon reconstruction are as follows. The total energy of the system should be lowered by an amount of the order A E b ,~ 1 eV per new bond per atom formed and ZlEr~0.01 eV per surface atom due to substrate relaxation. Based on this simple approach, the MRTD reconstructed surface should be stabilized by ,,~8AEb while the MRD reconstructed surface should be stabilized by ,-~6AE b. The lateral dimer and trimer bond lengths of P - P = 2 . 7 _ 0 . 2 A and G a - G a = 3.2_0.2 A, respectively, obtained from the analysis are in the expected range for such bond lengths. Considering the covalent (rco) and van der Waals trvdw) radii [37] of P (rco= 1.1 A and rvdw = 1.9 A) and Ga (rco=1.21 A and rvdw=2.0A), one would expect that the bond lengths would be in the ranges 2.2~
tion [39] using the MO LCAO Hartree-FockRoothan technique on GaP has found that the most stable surface structures obtained from the calculations agree with those predicted by electron counting rules. However, these calculations imply a mixed P - G a character of the filled and empty surface bands and partial occupancies of both P and Ga dangling bonds. In accord with electron counting rules, the filled (empty) surface bands have predominantly P (Ga) character. Due to the mixed character of the surface bands, the partial occupancy of the dangling bonds does not necessarily imply a metallic character of the surface electronic structure. It is well known [38] that the group V elements form dimer and tetramer molecules in the vapor phase. The covalent bond strengths [40] for the P2 and As2 dimer bonds are P - P = 5.07 eV and As-As = 3.96 eV. The bond strengths of the dimers in the missing-row troughs of the MRTD structure will be different from these since each phosphorus atom is bound in a distorted tetrahedral environment to two Ga atoms and one P atom, with its filled dangling bond at the other apex of the tetrahedron. Nevertheless, the large difference, i.e., 1.1 eV, in the bond strengths of the dimer molecules will also be reflected in the bond strengths of the dimers in the MRTD structure. This difference in the P-P and As-As bond strengths may be sufficient to stabilize the MRTD structure over the MRD structure for GaP and InP since the total energy difference between the two reconstruction phases may be small.

6. Conclusions

The major conclusions resulting from this compositional and structural investigation of the GaP{100}-(4x2) surface can be summarized as follows. (i) The reconstructed (4 x 2) phase is terminated in a Ga layer with 2nd-layer P atoms exposed in the Ga missing row troughs. (ii) All of the TOF-SARS, LEED, and simulation data are compatible with a Ga missing-row-trimer P dimer (MRTD) model in which every fourth Ga (071) row is missing, the Ga atoms are trimerized

M.M. Sung, J. W. Rabalais/Surface Science 365 (1996) 136-148

along the (011) azimuth, and the 2nd-layer P atoms exposed in the (011) troughs are dimerized. (iii) A missing-row-dimer (MRD) model, similar to that proposed for the GaAs (4 x 2) structure, in which every fourth Ga (011) row is missing, was also considered for the structure; this model is inconsistent with large portions of the data. (iv) The (2x) P dimer direction is coincident with the (011) azimuth and the (4x) Ga trimer direction is coincident with the (011) azimuth. (v) The MRTD model is autocompensated through trimerization of lst-layer Ga atoms and dimerization of 2nd-layer P atoms. (vi) The Ga intratrimer spacing is 3.2+0.2 A, contracted by 17% from the bulk G a - G a spacing, and the P intradimer spacing is 2.7+0.2 A, contracted by 30% from the bulk P - P spacing. (vii) A simulation of the azimuthal angle 6-scan for scattering from Ga indicates that the two Ga atoms at the ends of the trimers are relaxed vertically by a minimum of 0.2 ,A, resulting in a buckled trimer.

Acknowledgements This material is based on work supported by the National Science Foundation under grant no. CHE-9321899 and the R. A. Welch Foundation under grant no. E656.

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