Segregation of impurities in GaAs and InAs nanowires
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A p r Segregation of impurities in GaAs and InAs nanowires
M. Galicka, R. Buczko, and P. Kacman
Institute of Physics, Polish Academy of Sciences, Al. Lotnik´ow 32/46, 02-668 Warsaw, Poland
Using ab initio methods based on the density functional theory, we investigate the segregationand formation energies for various dopants (Si, Be, Zn, Sn), commonly used to obtain p- or n-type conductivity in GaAs and InAs nanowires. The distribution of Au and O atoms, which may beunintentionally incorporated during the wire growth, is also studied. The calculations performed fornanowires of zinc blende and wurtzite structure show that the distribution of most of the impuritiesdepends on the crystal structure of the wires. For example, it is shown that the same growthconditions can lead to lower energy for Si substituting Ga (donor) in the wire of wurtzite structureand substituting As (acceptor) in the wire of zinc blende structure. In contrast, we obtain thatgold and oxygen atoms always tend to stay at the lateral surfaces of GaAs and InAs nanowires,in agreement with experimental findings, while for beryllium the lowest energies are found whenthe impurities are located in sites in the center of the wurtzite wire or along the [1 , ,
1] axis fromsurface to the center of the zinc blende wire, what can explain the recently observed diffusion of thisimpurity into the volume of GaAs wires.
PACS numbers: 63.20dk, 61.72uj, 62.23Hj, 61.72sh
I. INTRODUCTION
Successful realization of most of electronic nanodevicesrequires a high carrier concentration so as to reach suf-ficient conductivity. The excellent properties of III-Vsemiconductors, in particular the high electron mobilitywhich can be obtained in GaAs and InAs, turns nano-wires (NWs) from these materials into natural candi-dates for building blocks of such high speed applications.The properties of semiconductor NWs differ from thoseof their parent bulk materials due to quantum confine-ment and surface related effects – pure semiconductorNWs usually have low concentration of carriers. Thus,the application of semiconductor NWs in novel electronicdevices requires controllable p-type and n-type doping.This task still remains a big challenge to the grow-ers, despite substantial efforts, both experimental andtheoretical.
Most of the publications describing dop-ing of III-V NWs focus on InAs NWs. In these structuresthe surface Fermi level is pinned in the conduction band.This makes n-type conductivity in InAs NWs easy to ob-tain at the expense of difficulties in p-type doping. Incontrast, in GaAs NWs the Fermi level at the surface ispinned approximately in the center of the band gap andboth, controlled p- and n-type doping, can be produces.Doping of GaAs NWs grown by molecular beam epitaxy(MBE) has been demonstrated in different means. Cz-aban et al. used Be and Te as p- and n-type dopantprecursors respectively, while Fontcuberta i Morral etal. pointed out that Si may act as both, acceptor anddonor, by just changing the operating temperature dur-ing growth as shown before for 2D epitaxial growth ofGaAs. The incorporation of Si and Be into GaAsNWs was investigated in a further study. Recently, theuse of tetraethyl tin as a precursor material for successfuln-type doping of GaAs NWs, grown by metal organic va-por phase epitaxy, was reported. Moreover, it occurredthat not only specific growth conditions but also the crys- tal structure of the wires may lead to different incorpo-ration behavior than known for planar layers.
Thiswas shown in particular for the group IV element, silicon,which is known to be amphoteric in III-V compounds.Namely, it was found that although under typical MBEgrowth conditions Si acted as n-type dopant for GaAs,p-type conductivity was obtained in Si-doped GaAs NWswhich adapted wurtzite (wz) structure in similar growthconditions. As mentioned above, doping of NWs was studied the-oretically by several groups. They focused, however,mainly on silicon NWs (see Ref. 19 and the referencestherein). There are very few publications which describetheoretically, incorporation of non-magnetic dopants inGaAs and InAs NWs. To our best knowledge, doping ofGaAs NWs was considered only in Ref. 8, where only Sidoping of wz structure GaAs NWs was studied. In con-trast, Cl`audia dos Santos and co-authors considered Cdand Zn doping of InAs NWs having the zinc-blende (zb)structure. In Ref. 9 the studied NWs were extremelythin (with diameters of 1 nm) and their lateral surfaceswere passivated with hydrogen atoms. Recently, the roleof the surface dangling bonds and the effect of molecularpassivation on doping of InAs NWs was also studied byHaibo Shu et al.
In this paper we report a systematic theoretical studyof several dopants, which are usually used to obtain p-or n-type conductivity in GaAs and InAs NWs, i.e., Si,Be, Sn and Zn. In contrast to the previous papers, weassume that the surface atoms are not saturated by fo-reign atoms. This assumption is justified by the fact, thatwe consider incorporation of dopants during the growthprocess in high vacuum conditions, e.g., MBE. To checkwhat is the preferential location of a given dopant in thewire, i.e., to answer the question whether it is possible toexplain the problems of doping of III-V NWs by segrega-tion phenomena, we study the energy of the wire with theimpurity situated in different sites. Such analysis provedalready to be very useful, e.g., for predicting conditionsto obtain ferromagnetism in GaAs NWs with magneticMn ions. In Ref. 20 it was shown that the distributionof Mn ions and thus the electric and magnetic proper-ties of (Ga,Mn)As NWs depend strongly on the crystalstructure. Since the III-V semiconductor NWs can growin both, zb and wz structures, we consider here bothtypes of wires to check whether the crystal structure hasan impact on the distribution of the studied impuritiesin GaAs and InAs NWs. Finally, we consider the distri-bution of Au and O atoms in the studied NWs. Oxygencan be used for n-type doping of GaAs but also un-intentional incorporation of O atoms in GaAs wires hasbeen reported in the literature. On the other hand, goldcan defuse into the wire from the catalyst particle duringAu-assisted vapor - liquid - solid (VLS) growth. This isknown to be a serious problem in Si NWs. Althoughit seems that the unintentional incorporation of Au inGaAs and InAs wires is much lower the measured Audoping values can make ballistic transport through thenanowires difficult to obtain. This makes the study ofthe distribution of Au atoms in the wires very important.It should be mentioned here that to avoid Au incorpo-ration self-catalyzed growth of GaAs and InAs NWs hasbeen pursued by several groups (see, e.g., 27–30).
II. METHODOLOGY
In our calculations the doping of the wires is performedby substituting one cation or anion in the elementary cellof the NW with an impurity atom. One foreign atom inthe elementary cell of the studied NWs corresponds to aconcentration of impurities in the range from ∼ ∼ ab initio methods, based on the density functional theory (DFT).The energy of the wire with the dopant occupying the siteexactly at the center of the wire cross section is taken asa reference point, i.e., as zero on the energy scale. Thesegregation energy is defined by the difference betweenthe energy of the NW with an impurity at a given siteand the reference energy: E S = E doped NW − E center doped NW . (1)Thus, the negative value of the segregation energy fora dopant atom at a given site means that this impurity a)b)FIG. 1. (Color online) Cross section of an a) wz NW withdiameter d=2.8 nm and b) zb NW (d=2.4 nm). The greenballs show the 10 nonequivalent sites, which we consider assubstituted by a dopant. The blue balls denote Ga(In) atoms,gray - As atoms. The darker colors denote atoms in the deeperdouble layer. prefers to substitute the host atom at this particular siterather than be at the center of the wire. In contrast,positive segregation energy values denote the situationwhen substitution of an atom in the center of the NWwill be energetically more favorable. Let us mention thatin a study of doped Ge wires, performed with use ofa similar method, the values of formation energy, i.e.,energy needed to insert the impurity atom (taken from areservoir) into a given NWs site, from which the originalatom has been removed (to a reservoir), were shown todepend strongly on the size of the simulated supercell andthat segregation energy, being a relative quantity, is freeof these systematic inaccuracies. However, by the studyof segregation energies we can only answer the questionwhere an impurity prefers to stay within the wire. Toanswer the question for which impurity the energy costof substituting a host atom is lower, one has to comparetheir formation energies, which depend on atomic andelectronic chemical potentials. The formation energy Ωof a neutral impurity X can be calculated according tothe formalism proposed by Northrup and Zhang, Ω = E tot [ X ] − E tot [ N W ] + µ Ga/As − µ X , (2)where E tot [ X ] is the total energy derived from the calcu-lation of the nanowire with an impurity X , E tot [ N W ] isthe total energy of undoped nanowire. The term µ Ga/As denotes the chemical potential of the corresponding sub-stituted Ga or As atom, while µ X denotes the chem-ical potential of the impurity atom. Our analysis isperformed with an assumption of thermal equilibriumconditions of the impurity region with the surroundingnanowire, i.e., µ bulkGaAs = µ Ga + µ As . (3)Using µ i ≤ µ bulki with i ∈ Ga, As, X and the definitionof the heat of formation of GaAs∆ H = µ bulkGa + µ bulkAs − µ bulkGaAs , (4)we can limit the range of possible values of ∆ µ to − ∆ H ≤ ∆ µ ≤ +∆ H . The quantity ∆ µ is the difference betweenthe chemical potentials of Ga and As and is given by∆ µ = ( µ Ga − µ As ) − ( µ bulkGa − µ bulkAs ) . (5)Thereby, the situation ∆ µ = +∆ H corresponds to Ga-rich growth conditions, while ∆ µ = − ∆ H correspondsto As-rich conditions.As mentioned above, we incorporate the dopants intoGaAs and InAs wires of both wz and zb crystal struc-tures. The only considered NWs are those grown along[0001] direction (wz) and along [111] axis (zb), becausea vast majority of III-V NWs grow only along these di-rections. It has been also shown theoretically that thesegrowth directions and the types of facets presented inFig. 1 constitute the most stable configurations of GaAsand InAs NWs. It is well known that with ab initio methods only very thin NWs, much thinner than the realones, can be simulated. This can lead to overestimationof the side surfaces’ effects in the results, deceptive whensuch calculations are used to determine, e.g., the crys-tal structure of thicker wires. This problem is, however,not so important in our study, in which we try to answeronly the question: is there any energy difference betweenthe wires with an impurity situated at the side facets andwith the impurity inside the core of the wire. The diame-ter test, in which we considered zb wires of several diffe-rent diameters, 0.9 nm, 1.4 nm, 1.8 nm and 2.4 nm, hasshown that for the two highest diameters the obtainedsegregation energies are practically the same. Similarly,the results do not depend considerably on the diameterin wz NWs with diameters from 2.0 nm to 2.8 nm. Con-gruous studies reported in Ref. 5 also indicate that for diameters larger than approximately 3 nm the P impuritylevels inside the Si NWs recover bulk characteristics. Inthe following, all the presented results are for the thick-est wz NWs with diameters of 2.8 nm and the thickest(2.4 nm) zb wires. As already mentioned, we assumethat the surface atoms are not saturated by any foreign,for example, hydrogen atoms, because we study the pro-cess of NWs growth and incorporation of the impurities.Still, for the calculations of the density of states of al-ready doped wires and discussion about the positions ofthe Fermi level, the side facets of the wires have beenpassivated by partial atomic charges of hydrogen atoms.The calculations are performed using the Vienna ab initio simulation package (VASP).
Each of theinitial structures is cut out from an appropriate bulk ma-terial, in either zb or wz structure. The wz elementarycell is doubled along the c direction, to guarantee thatthere is enough separation between the impurity ion andits periodic images. Thus, the smallest supercell used inour study contains 122 atoms (zb) whereas the largest(wz) 384 atoms. For different dopants a plane wave basisset is adopted with different cutoff energies: for Si thecutoff energy was equal to 307 eV, for Be – 375 eV, Sn– 261 eV, Zn – 346 eV, Au – 287 eV and O – 500 eV. Ineach case all the energies and chemical potentials are cal-culated with these cutoff values. These cutoff energies aresufficient to ensure that the results do not depend on thesize of the plane wave basis. The k-points are generatedwith a (1 × × n ) mesh, where n ≥
50 ˚A /c and c is theunit cell dimension in the growth direction. The inter-action between the valence electrons and the ionic coresis included using the projected augmented wave method(PAW). The exchange correlation energy is calculatedwithin the generalized gradient approximation (GGA).The atomic positions leading to minimum energy are de-termined with relaxation of all atomic positions as wellas of the unit cell dimension in the growth direction, andwith full reconstruction of the NW’s surfaces. In eachsimulation process the atomic coordinates are relaxedwith a conjugate gradient technique. The criterion thatthe maximum force is smaller than 0.01 eV/˚A is used todetermine the equilibrium configurations. Neither pres-sure nor temperature are included in our calculations.
III. RESULTS
The distribution of gold in the cross-section of InAswires was studied experimentally using a technique calledpulsed-laser atom probe tomography. In Ref. 25 it wasshown that Au atoms accumulate in a shell at the lateralsurfaces of the wire. We start our study by consideringAu impurities in InAs NWs to check if our calculationscan describe this experimental finding. We analyze InAsNWs with an Au atom in various cation sites and focuson the search of the impurity positions for which thesegregation energy is the most negative, i.e., the sites inwhich the energy cost of substituting the cation by anAu atom is lower than in the other nonequivalent sites.In Fig. 2 the results for both wz and zb InAs as wellas GaAs NWs are presented. In this and all followingFigures the diameters of the wz NWs equal to 2.8 nmand of zb NWs to 2.4 nm. In all Figures the calculatedvalues of segregation energy are connected by a line toguide the eye. a)b)FIG. 2. (Color online) The segregation energy in a) wz (dia-meter 2.8 nm); b) zb (diameter 2.4 nm) InAs (green) andGaAs (blue) NWs as a function of different Au atom posi-tions.
As one can see in Fig. 2, in both wz and zb NWs theAu atoms tend to accumulate near the lateral surfaces.In wz structure the energy is the lowest for the dopantoccupying the threefold coordinated sites 1 and 4, thecorner sites of the sidewall facets. In NWs of zb struc-ture the most energetically favorable for Au atom is tosubstitute the cation in position 1, i.e., the cation withextra dangling bond in the corner of the cross-section ofthe wire. Analogous results are obtained for oxygen, an-other element, which can be unintentionally incorporatedduring the growth, as shown for GaAs wires in Fig. 3.The difference between the energy of the wire with anAu or O atom at the lateral surface and at the centerof the wire is significant, from ca 0.6 eV for gold in wzInAs NWs to nearly 3 eV for oxygen in GaAs zb NWs.Thus, both these impurities should indeed be trapped atthe lateral surfaces of the wires. In zb NWs we note thatthe segregation energy decreases with the distance fromthe center of the wire monotonically along the different crystallographic axes, as shown for example in the insetto Fig. 3 for two nonequivalent [1 , ,
1] directions. a)b)FIG. 3. (Color online) The segregation energy in a) wz; b)zb GaAs NW as a function of different O atom positions. Inthe inset to b) the segregation energies for the O atom insubsequent sites along the two nonequivalent [1 , ,
1] lines areshown
Next, we consider Si doping in GaAs NWs. As alreadymentioned, since Si is a group IV element in III-V com-pounds it can serve either as a donor, by substitutingthe cation, or as an acceptor, by occupying the anionsite. We therefore analyze the NWs with the Si atomin various cation and anion sites. In Fig. 4 the resultsfor both wz and zb NWs are presented. We recall thatSi-doped GaAs NWs of wz structure were already stu-died by Ghaderi et al. in Ref. 8. These authors con-sidered only four dopant positions in a wz NW, i.e., onecenter-like, two surface threefold (distinction is made forcorner or middle of facets positions), and one subsurfacefourfold coordinated position. Our results presented inFig. 4a, which are obtained for many more Si positionsin a thicker wz GaAs NW, fully confirm the conclusionof Ref. 8. Namely, the four-coordinated subsurface po-sitions are the most energetically favorable locations forSi acting as a donor as well as an acceptor. The seg-regation in these sites is, however, not as strong as forAu or O atoms (ca -0.2 eV). The calculated segregationenergies for Si-doped GaAs NWs of zb structure, which,we recall, were not considered by the authors of Ref. 8,are presented in Fig. 4b. As one can notice by compar- a)b)FIG. 4. (Color online) The segregation energy in a) wz; b) zbGaAs NW as a function of different Si atoms positions. ing Fig. 4a and b, the spread of the segregation energyvalues is considerably larger for zb wires ( ± . µ in which the same growth conditions lead to lowerenergy for Si substituting Ga in the wire of wz structureand substituting As in the wire of zb structure.Next, we have calculated the density of states (DOS)for Si-doped GaAs nanowires. In wz structure wires Siacts as expected, i.e., as a donor when substituting Ga a)b)FIG. 5. (Color online) The formation energy Ω of GaAs NWwith Si impurity in the center of a) wz NW, b) zb NW as afunction of the value ∆ µ . and as acceptor when substituting As. Impurity bandsare located close to valence band maximum (VBM) andconduction band minimum (CBM) for Si acceptors anddonors, respectively. The passivation of the lateral sur-face have almost no influence on the position of thesestates, similarly to what was shown for CdTe NWs of wzstructure in the paper of T. Sadowski. In contrast, innot passivated zb NWs we observed surface states in theband gap and the impurity states (for both Si at As andGa sites) located at these surface states. After satura-tion the surface states disappear and the impurity statesmove close to VBM and CBM, for Si atom substituting ananion or cation atom, respectively, inside the wire core.In Fig. 6 a) we show the density of states calculated forH-passivated zb GaAs nanowire with Si substituting theGa atom in the wire’s center position 21. The situa-tion is quite different when Si substitutes the Ga atom inposition 1, in the corner of the wire cross-section. For un-passivated nanowires (part b of Fig. 6) Si states and theFermi level are again pinned at the surface states in theband gap, as for the other impurity positions in zb NWs. a)b)c)FIG. 6. (Color online) The density of states calculated forzb GaAs NW with Si substituting Ga atom in the site 21 a)and site 1, c) and b), (site numbers as denoted in Fig.1). TheDOS presented in part b) is for the NW with unpassivatedlateral surfaces; the results in parts a) and c) are for NWswith lateral surfaces passivated by H atoms. Zero on energyscale denotes always the Fermi level.
However, after passivation the Fermi level moves to theVBM (compare part c of Fig. 6), what indicates thatin this position Si will not behave as an n-type dopant.As the segregation energies suggest that most of the Siatoms are trapped around these corner positions, this be-havior can explain the observed dominance of p-type inSi-doped GaAs NWs. In the next step we compare the segregation energy obtained for Si-doped GaAs NWs with the segregationenergy in wires doped with beryllium, one of the mostwidely used acceptors in GaAs. Results obtained for Be-doped GaAs NW of wz and zb structure are presented inFig. 7. As shown in the Figure, in wz NWs the distribu- a)b)FIG. 7. (Color online) The segregation energy in a) wz; b) zbGaAs NW as a function of different Be atom positions. tion of Be atoms should be again quite homogenous, butin this case the lowest energy corresponds to the situa-tion where the impurity substitutes an atom inside thewire. Again, in zb GaAs NWs the lowest value of thesegregation energy (-0.4 eV) was obtained when Be sub-stitutes the Ga atom with an extra dangling bond in site1. It should be noted, however, that this is much weakersegregation than obtained in zb GaAs NWs for Si, and ofcourse Au and O. Therefore, these results seem to be inagreement with the experimental observation that eventhough Be atoms accumulate in the shell of zb GaAsNWs, it should be possible to dope the NWs almost ho-mogeneously during axial growth. It is also interestingto note that for some reason the lowest energies of the zbGaAs wires with Be atoms are found when the impuri-ties are located in sites along the [1 , ,
1] axis (from thecenter of the wire to the cation with extra dangling bondat the corner of the lateral surface). This is in contrastto the situation presented in Fig. 3 for oxygen and goldimpurities. The low energy cost of incorporation of Bealong the [1 , ,
1] axis can explain the recently observeddiffusion of this impurity into the volume of the zb GaAsNWs, interpreted in Ref. 41 as an alternative incorpora-tion path.Finally, the comparison of formation energies for Beincorporation into the GaAs NWs, presented in Fig. 8,shows that it should be much easier to dope with beryl-lium the NWs with zb structure than those with wz crys-tal structure. It shows also that the formation energiesfor Be are much lower than for Si.
FIG. 8. (Color online) The formation energy Ω of zb and wzGaAs NW with Be impurity as a function of the value ∆ µ . As mentioned before, the as grown InAs NWs are usu-ally n-type. Doping with several acceptors, like Be or Zn,have been tried to obtain p-type conductivity in theseNWs.
In Fig. 9 we present the comparison of segrega-tion energies obtained for InAs NWs doped with Si, Beand Zn atoms as a function of their different locations.The study of segregation energy for different acceptors inInAs NWs shows that in these wires, similarly to GaAsNWs, wz structure should lead to a more homogeneousdistribution of impurities. Inside the wire, in the core,all impurity positions are energetically equivalent in bothstructures. In the shell, Be and Zn prefer to be in themiddle of the sidewall of the wire, substituting three-fold coordinated cations, while Si, substitutes fourfoldcoordinated anion at the NW’s lateral surface (site 6),as presented in Fig. 10. One can understand this dif-ference by recalling that Zn and Be occupy the cationpositions while Si, should substitute an anion to serveas an acceptor. The relaxation of the atom positions atthe wire lateral surfaces leads to different reconstructionof bonds for cations and anions, as shown in Ref. 32 forpure III-V NWs. The most important result of this studyis, however, the fact that in InAs NWs of wz structurethe segregation energy for Be atoms is not negative forany of the considered positions. Also for Si in wz InAsNWs the segregation energy for the impurity in site 6,although negative, is close to zero (-0.06 eV). Thus, wecan conclude that the best precursor for p-type doping ofInAs NWs should be beryllium but using Si can also beeffective, provided the wz crystal structure of the wires a)b)FIG. 9. (Color online) The segregation energy for Si, Be andZn acceptors in various positions in wz (a) and zb (b) InAsNW.FIG. 10. (Color online) The most energetically favorable po-sitions of Zn, Be and Si acceptors at the lateral surfaces of wzInAs NW. is assured.In Ref. 43 it was shown, by capacitance measurements,that the concentration of carriers in InAs NWs can beincreased by n-type doping with Sn. In Fig. 11 the seg-regation energy obtained for InAs NWs doped with Sn ispresented. The results for Sn in wz InAs wires are verysimilar to that for Si-doped InAs NWs, presented above.Tin ions distribute fairly homogeneously across the wzwire. Although for Sn the most favorable is to substitutethe fourfold coordinated cations at the wz NW’s late-ral surface, the segregation energy is again very small.This result seems to agree with the observed increase ofthe carrier concentration and the surface charge densityin Sn-doped wz InAs NWs. It should be noted thatin Ref. 3 it was shown that the Sn precursor increases a)b)FIG. 11. (Color online) The segregation energy of a) wz; b)zb InAs NW as a function of different Sn positions. the stacking fault density in wz NWs, ultimately at highflows leading to a zb crystal structure with strong over-growth and very low resistivity. In agreement with thisobservation we obtain that in zb NWs, analogously toother dopants in this material, Sn atoms do not incor-porate into the wire but stay at the lateral surface, withparticular reference to atoms with extra dangling bond(Fig. 11b).In contrast, our calculations performed for GaAs NWsshow that in this material Sn atoms tend to segregateto the lateral surfaces in both wz and zb structures (seeFig. 12). Thus, although our calculations performed forSn impurities in III-V wires agree with the observationthat doping with tin can be used to increase the con-centration of electrons in InAs wires, they suggest thatusing Sn for n-type doping of GaAs NWs can be muchless efficient. IV. CONCLUSIONS
Nanowire growth processes usually rely on the vapor -liquid - solid (VLS) mechanism normally assisted by golddroplets or self assisted on a SiO/SiO surface. Dopingthese structures during such complex growth process isdifficult to understand and control. It is, however, al-ready widely accepted that there are two distinct path- a)b)FIG. 12. (Color online) The segregation energy of a) wz; b)zb GaAs NW as a function of different Sn atoms positions. ways for dopant incorporation into semiconductor NWs:the VLS mechanism, in which the dopant atoms first dis-solve in the catalyst and are then transported across theliquid - solid interface to the core of the NW, and thevapor - solid (VS) mechanism, when dopant atoms aredirectly deposited on the lateral NW surfaces. In Ref.44 it has been suggested that these two mechanisms pro-ceed at different rates – namely, the latter predominatesand leads to a much higher concentration of dopants inthe shell of the NW than in the core. This conclusionwas based on the experimentally observed accumulationof gold atoms close to the lateral surfaces of InAs NWs as well as phosphorus in Ge NWs. Radovanovic and co-workers, when studying GaN wires doped with Co andCr, have also concluded that adsorption on the lateralsurface is the main doping mechanism of the semicon-ductor NWs. Finally, the conclusion that Be atoms aremostly incorporated into the zb GaAs NWs from the sidefacets and that the incorporation through the Ga dropletis negligible are made in Ref. 41. It should be also men-tioned that the very recently reported beautiful model, in which B-doped Si NWs were considered, has shownthat 2D diffusivity along the solid-liquid NW interfaceplays also a considerable role in impurity incorporation.In this paper we show, by means of first-principles cal-culations of the total energy of doped GaAs and InAsNWs, that indeed most of the commonly used impuritiesfor p- and n-type doping should accumulate near the sur-faces of the NW. It should be, however, emphasized thatthis result does not depend on the growth mechanism,because in our calculations only the differences in for-mation energies for various dopant positions have beentaken into account. Thus, it shows that even for incorpo-ration of the dopants into the core, via VLS mechanism,the segregation of impurities to the surfaces should takeplace. The only exceptions are wz GaAs as well as wzInAs NWs doped with Be – in these the segregation en-ergy is positive for all studied cation sites substituted byBe atoms.We note that the degree of segregation depends con-siderably on the NW’s host material, crystal structure ofthe wire and of course the particular dopant. Our calcu-lations show that in NWs of zb structure the segregationfor the most common dopants is much higher than inNWs of wz structure. The studied impurities in zb NWsshould remain either at the lateral surfaces, where theyprefer to substitute the atom with extra dangling bond,or should be trapped at the subsurface, in the vicinity ofthe atom with additional dangling bond. At these posi-tions the segregation energies in zb GaAs NWs are lowerthan in the core by ca 0.4 eV for beryllium, but by even1.5-3 eV for gold and oxygen. It is also shown that atthese positions Si atoms do not act as donors even whensubstituting Ga cations - this result is in agreement withthe observed predominance of p-type in Si-doped GaAsNWs. For gold and oxygen in wz wires the results aresimilar to those obtained for zb structure but with lower,though still high, segregation. With our calculations wehave thus confirmed the experimentally observed segre-gation of Au atoms to lateral surfaces. According toour results the same should be also observed for oxy-gen. In contrast, all other studied impurities distributemuch more homogeneously across the wz wire and Beeven prefers to substitute the Ga(In) ion at the center ofthe wire, as mentioned above. We can thus conclude thatour calculations suggest that growth conditions leadingto wz structure can help to avoid accumulation of im-purity atoms at the surface during the growth of dopedIII-V wires. It seems that the best choice for effectivep-type doping of both GaAs and InAs wz NWs is to useberyllium as a dopant, due to it’s low segregation. How-ever, the cost of substituting the host cation by Be atom,i.e., the formation energy, is lower in the zb than in the wz NWs. Finally, we observe that the different from otherimpurities behavior of Au and O can be attributed to thelarge electronegativity of these elements (3.5 for O and2.4 for Au) as compared to electronegativities of Ga, Inand all other studied dopants, which are in the range of1.5 – 1.8.As shown above, our results suggest that the energy ofa doped NW can be very different when the impurity po-sition inside the wire changes, especially in zb structure.Only in the case of oxygen and beryllium in GaAs NWssome regularities in these differences can be observed.In other cases the fluctuations of the segregation energyvalues seem to be random. These results were fully con-firmed by several tests, i.e., by repeating the calculationsfor the impurities in equivalent sites, by changing theNW diameter and finally by moving slightly the initialatomic positions. Recently, thanks to laser assisted atomprobe tomography the studies of the distribution of impu-rities in semiconductor wires have become possible. Ourresults may suggest that the observed inhomogeneities(compare, e.g., Ref. 19) may have a more fundamen-tal origin than just disorder. Neither the noticed trendsnor the other segregation fluctuations, which we are notable to explain in our approach, were reported before.It should be noted, however, that in all previous studiesthe segregation and/or formation energies in doped NWshave been calculated for at most 3-4 different impuritypositions. In our study the results for wz NWs with theimpurities in 16 different sites and for zb NWs in 21 dif-ferent sites have been compared - to our best knowledge,most of the nonequivalent sites considered here have notbeen studied before for any impurity.
ACKNOWLEDGMENTS
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