computations of stm images of zinc-blende gan(0 0 1) surface

Vacuum 63 (2001) 75}81

Computations of STM images of zinc-blendeGaN(0 0 1) surface

Wojciech KaminH ski, Barbara Stankiewicz*, Leszek Jurczyszyn

Institute of Experimental Physics, University of Wroc!aw, pl. Maksa Borna 9, 50}204 Wroc!aw, Poland

Abstract

Theoretical study of the formation of STM images of the GaN(0 0 1)-(2�2) surface is presented. Calculation of thetunnelling current between the tip and the substrate is based on the non-equilibrium Green-function formalism.Tunnelling current and conductance, calculated for W and Al tips, and di!erent voltages and distances, are analysed. Oursimulations show that for both considered tips, the topography of images, given by unoccupied surface states, correctlyreproduces a (2�2) reconstruction of the substrate surface. Presented results con"rm the important role of the tunnellingthrough d orbitals of the W tip in the process of the STM image formation. � 2001 Elsevier Science Ltd. All rightsreserved.

Keywords: STM simulations; �-GaN

1. Introduction

In recent years, the properties of gallium nitridesurfaces have been intensively investigated. Numer-ous experimental and theoretical studies have pro-vided valuable information about the electronicand atomic structure of di!erent surfaces of thissemiconductor. The (0 0 1) surface of �-GaN hasbeen investigated most intensively, as this surfaceemerges at the MBE crystal growth [1}8]. On theother hand, it has been proven that this material isextremely di$cult for STM observations. Conse-quently, the number of STM measurements of GaNsurfaces is relatively small. In particular, there is

*Corresponding author. Tel.: #48-71-201343; fax: #48-71-3287365.E-mail address: [email protected] (B. Stankiewicz).

a lack of high-resolution images. Amongst thoseavailable, the STM images obtained by Wassermeieret al. [9,10] appear to be of the highest quality. Thisexperiment has been performed for zinc-blendeGaN(0 0 1) surface, and the images received showtwo types of surface reconstruction, which might

appear in this case, i.e. the (2�2) and (�10��10)reconstruction. The simulations of STM processes,also presented in [9], have been directly based onthe calculation of local density maps of the highestoccupied and lowest unoccupied states. This simpli-"ed approach is helpful for the interpretation ofimages obtained in the experiment, but it does notprovide any information about the formation of anSTM image in such a di$cult case as the scanning ofthe GaN surface. Therefore, in this work we presenta theoretical study of the coherent multichanneltunnelling of electrons in the system formed by anSTM tip and the GaN(0 0 1)-(2�2) surface.

0042-207X/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 1 7 3 - 7

Fig. 1. Local density of surface states at a surface Ga atom ofa gallium-covered GaN(0 0 1) surface. Solid line* total densityof states, dashed line * density of states projected on an s or-bital, dotted line * density of states projected on a p

�orbital.

2. Method of calculation

Calculation of the tunnelling current between thetip and the substrate is based on the non-equilibriumGreen-function formalism developed by Keldysh[11]. This approach allows to study the coherenttunnelling through di!erent orbitals of the tip}sub-strate system. Since it is not based on any perturba-tion theory, it is accurate even for small distancesbewteen the tip and the sample. The method isdescribed in detail in [12]. It is shown there that tocalculate the tunnelling current we only need toknow the matrices of the Green functions and thedensity of states for the tip and the sample, when thetip and the sample do not interact, as well as thematrix of hoppings between di!erent orbitals of theatoms from both parts of the system, when the tipand the sample are in contact.

In the present work, calculations of the electronicstructure of the tip have been performed withthe help of the cluster-Bethe-lattice method [13].The top part of the tip is represented by a "ve-atompyramidal cluster (with a single atom at the apex),while the in#uence of the rest of the tip is simulatedby a Bethe lattice connected to this cluster. Self-consistency has been assured here by imposing a lo-cal charge neutrality at each atom of the cluster.Calculation of hopping interactions has been per-formed using the Bardeen's expression for the tun-nelling current between particular orbitals [12].

To calculate the electronic structure, the Greenfunctions and the density of states of a GaN crystal,the slab model and linear combination of atomicorbitals (LCAO) method have been used. Calcu-lations have been performed for the (0 0 1) orientedslab of thickness of four molecular layers. The (2�2)surface reconstruction has been assumed for bothsurfaces, as suggested in [3]. The sp� model Hamil-tonian and second-neighbour approximation withneglected overlapping of orbitals [8] have been used.The one-electron wave functions have been con-structed as a linear combination of 4s and 4p or-bitals of gallium, and 2s and 2p orbitals of nitrogen.Interactions between all nearest neighbours, as wellas the second neighbours of gallium type havebeen included, but interactions between nitrogen-type second neighbours have been neglected.Semi-empirical parameters describing the electronic

structure of bulk GaN crystal have been obtained[8] by "tting to the results of LMTO calculations[14], corrected to reproduce experimental positionof the main band gap edges. The energy scale isrelative to the vacuum level. To calculate the densityof states in the succeeding atomic layers, the one-center parameters have been modi"ed self-consis-tently to include the changes of the potential of slabions with respect to that in the bulk of the crystal.Changes in the potential, in turn, result from the lackof adequate number of neighbouring ions at bothsurfaces of the slab, as well as from the di!erentdistances between atoms in the Ga surface layer ascompared to that inside the crystal, and also fromthe resulting charge density shift [8].

3. Results

The STM system formed by an Al or W tip andthe (2�2)-reconstructed gallium-covered zinc-blende GaN(0 0 1) surface has been considered. Re-sults have been obtained from the simulation of theprocess of tunnelling through states localized at thissurface. Since the Fermi level in this case is locatedvery close to the lower edge of the surface-state band(Fig. 1), simulations of the STM process have beenperformed mostly for the unoccupied surface states.

76 W. Kamin& ski et al. / Vacuum 63 (2001) 75}81

Fig. 2. STM images of GaN(0 0 1) gallium-covered surface simulated for the W tip (bias equal to 0.7 V), and the following tip}sampledistances: (a) 4 As , (b) 5 As , (c) 6 As .

Figs. 2 and 3 present sets of images simulated inconstant-height mode. These images have been builtup by the evolution of the current tunnelling to allunoccupied surface states (at a bias equal to 0.7 V).They have been obtained for three di!erent tip-sample distances (4, 5 and 6 As ), and for W (Fig. 2)and Al (Fig. 3) tip. Figs. 2 and 3 clearly show that forboth tips and for all considered distances the imagesof a similar topography are obtained. In each case,the dominating features are located at the surfacegallium dimers, reproducing correctly a (2�2) re-construction of the GaN(0 0 1) surface, and being inagreement with the image of unoccupied states

received in STM experiments [9,10]. These featuresare oriented along the dimer axis, but the atomicstructure of the dimer can be well recognized onlyfor images received with a tngsten tip at small dis-tances (Fig. 2a). For greater distances, the resolutionof simulated images becomes worse, so already fordistances about 6 As , the atomic structure of galliumdimers is virtually invisible, in accordance with theresolution level of STM images received in experi-ment. The comparison of images obtained withW and Al tips indicates that the details of atomicstructure are better reproduced by using the tung-sten tip for all the considered tip}sample distances.

W. Kamin& ski et al. / Vacuum 63 (2001) 75}81 77

Fig. 3. The same as in Fig. 2, but for the Al tip.

This better resolution is mainly caused by the tun-nelling through d orbitals of the tungsten tip. Theanalysis of the current contributions connected withthe tunnelling through di!erent orbitals of the tipapex atom (Figs. 4a and 5a) shows the importantrole of d orbitals of a W tip (especially d

��). Tunnell-

ing through this channel gives the largest contribu-tion to the total current and reproduces the chargedistribution at the substrate surface more accuratelythan the tunnelling through sp orbitals of an Al tip(Fig. 5a).

Figs. 4b and 5b show that for both tips (i.e. for theW as well as the Al tip) the protrusion correspondingto the surface dimer is built up mainly by the tunnell-

ing through p�

orbitals of Ga atoms (which areoriented perpendicular to the surface). The contribu-tion coming from s orbitals of the substrate is muchweaker, while the p

�-p

�contributions are negligible.

The sequence of images presented in Fig. 6 illus-trates the evolution of conductance connected withthe tunnelling of electrons between the Fermi level ofthe tip and the states localized at the GaN(0 0 1)surface, of four di!erent energies: !0.1 (occupiedsurface state), 0.0, 0.2 and 0.5 eV. In all the cases, thetip}sample distance is equal to 5 As . The comparisonof these images clearly shows that the conductancedepends critically on the energy of surface states. Inparticular, near the upper edge of the surface-states


Fig. 4. Evolution of the current along the dimer axis, for the W tip, bias eqal to 0.7 V (tunnelling to unoccupied surface states) and thetip}sample distance equal to 5 As : (a) Components of current #owing through W tip orbitals. Solid line denotes the total current, whilecross, dash-dot, dashed, and dotted lines correspond to d, p

�, s, and p

�-p

�current contributions, respectively. (b) Current components

#owing through GaN surface orbitals. Solid line denotes the total current, while dashed, dash-dot, and dotted lines correspond to s, p�,

and p�-p

�current contributions, respectively.

Fig. 5. Evolution of the current along the dimer axis, for the Al tip, bias eqal to 0.7 V (tunnelling to unoccupied surface states), and thetip}sample distance equal to 5 As : (a) Current components #owing through Al tip orbitals. Solid line denotes the total current, whiledash-dot, dashed, and dotted lines correspond to p

�, s, and p

�-p

�current contributions, respectively. (b) Current components #owing

through GaN surface orbitals. Solid line denotes the total current, while dashed, dash-dot and dotted lines correspond to s, p�

and p�-p

�current contributions, respectively.

band the conductance creates the topography verydi!erent from the real atomic structure ofa GaN(0 0 1) surface (Fig. 6d) * in contrast surfacestates with lower energies (Figs. 6b and c). Thismeans that the localization properties of unoccupiedsurface states from the upper part of the bandare di!erent from those of the other states formingthis band.

4. Summary

We have presented here a theoretical study of theformation of an STM image of unoccupied surfacestates at the GaN(0 0 1)-(2�2) surface, based onthe analysis of the tunnelling current and theconductance, calculated for di!erent voltagesand tip}sample distances. The results of STM


Fig. 6. Conductance, for the W tip and the tip}sample distance equal to 5 As , from the Fermi level of the W tip into the states on GaNsurface of energy (with respect to the GaN Fermi level): (a) !0.1 eV, (b) 0.0 eV, (c) 0.2 eV, (d) 0.5 eV.

simulations show that, for all the considered distan-ces, the topography of images given by unoccupiedsurface states correctly reproduces the (2�2) recon-struction of the substrate surface. The atomic scaleresolution is received only for a tungsten tip andsmall distances (5 As and less). For greater distances(6 As and more) the details of dimer atomic structureare practically lost, which agrees with the resolutionlevel of STM images received in experiment.

Consequently, the images received with a tungstentip provide a better resolution than those obtained

with an Al tip, which is mainly caused by tunnellingthrough d orbitals of the W tip. This con"rms theimportant role of d orbitals of the tip in the processof imagining of the substrate surface, in accordancewith [15}19].

Acknowledgements

This work was supported by the University ofWroc"aw under Grant No. 2016/W/IFD/98.


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computations of stm images of zinc-blende gan(0 0 1) surface

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