Structural studies of phosphorus induced dimers on Si(001)

0.35 MB·English

by  Prasenjit Sen

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Structural studies of phosphorus induced dimers on Si(001)
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n
Prasenjit Sen
a
Harish-Chandra Research Institute
J
Chhatnag Road, Jhunsi, Allahabad 211019, INDIA.
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2
Bikash C. Gupta and Inder P. Batra

] University of Illinois at Chicago
ci 845 W. Taylor Street, Chicago Illinois 60607, USA.
s
- Renewed focus on the P-Si system due to its potential application in quantum computing and
l
r self-directed growth of molecular wires, has led us to study structural changes induced by P upon
mt placement on Si(001)-p(2×1). Using first-principles density functional theory (DFT) based pseu-
dopotentialmethod,wehaveperformedcalculationsforP-Si(001)system,startingfromanisolated
.
t Patomonthesurface,andsystematicallyincreasingthecoverageuptoafullmonolayer. Anisolated
a
P atom can favorably be placed on an M site between two atoms of adjacent Si dimers belonging
m
to the same Si dimer row. But being incorporated in the surface is even more energetically benefi-
- cial due to the participation of the M site as a receptor for the ejected Si. Our calculations show
d that up to 1 monolayer coverage, hetero-dimer structure resulting from replacement of surface Si
n 8
atomswith Pisenergetically favorable. Recentlyobservedzig-zagfeatures inSTMarefoundtobe
o
consistent with thisreplacement process. Ascoverage increases, thehetero-dimersgive way toP-P
c
ortho-dimers on the Si dimer rows. This behavior is similar to that of Si-Sid-dimers but are to be
[
contrasted with theAl-Aldimers, which are found between adjacent Si dimers rows and in a para-

1 dimerarrangement. UnlikeAl-SisystemP-Sidoesnotshowanyparatoorthotransition. Forboth
v systems, the surface reconstruction is lifted at about one monolayer coverage. These calculations
5 help us in understandingthe experimentaldata obtained using scanning tunneling microscope.
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5 PACSnumbers: 68.43.Bc,73.90.+f,73.20.-r
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6 INTRODUCTION aries. AtslightlybelowaMLPcoverage,Wangetal. ob-
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serveSi-Si,Si-PandP-Pdimers. Atstilllowercoverages,
/
t there are ‘significant’ numbers of Si-Si and Si-P dimers,
a Phosphorous-doped Si is the back-bone of micro-
m while there are some P-P dimers. Kipp et al. [10] us-
electronic technology. Recently, P-Si system has gen-
ing STM, X-ray photoemission spectroscopy (XPS) and
- erated renewed interest due to its potential application
d totalenergycalculationsconcludethatafterlowtemper-
in quantum computers [1, 2, 3] and growth of molecular
n ature PH3 adsorption there are dimers on the surface.
o wires on Si surfaces [4]. It is also of fundamental in-
It is not conclusive whether these are P-P, Si-P or Si-Si
c terest to compare the behavior of P-P dimers with Si-Si
dimers, though they expect P-P dimers to be dominant
v: and Al-Al dimers on the Si surfaces, a lot having been atlowtemperatures. Boththesegroups(Wangetal. and
i understood about the last system [5, 6, 7].
X Kipp et al.) observe similar ‘bright’ features above Si-Si
r Phosphine gas (PH3) is used as the source of P in surface dimers in their STM images at low P coverages.
a most applications. Yu et al. [8] concluded from their ex- Wang et al. claim these to be indicative of Si-Si dimers,
periments that around 6750 C, all hydrogen atoms from while Kipp et al. claim these to be P-P dimers. Cur-
PH3 are desorbed and the surface is a monolayer (ML) son et al. [11], from their STM studies, conclude that at
P covered Si(001) with the formation of P-P dimers. low P coverages, the surface, in fact, contains Si-Si and
Wang et al. [9] did a scanning tunneling microscopy Si-P dimers, thus supporting Wang et al.’s conclusions.
(STM) and Auger electron spectroscopy (AES) study of Kippet al. alsofound that after PH3 adsorptionat6250
phosphorous-terminatedSi(001)surfaceclosetoamono- C, there are only symmetric P-P dimers on the surface.
layer P coverage. They find mostly P-P dimers, along At the maximum P coverage,they find defects like miss-
withsomeSi-Pdimersonthe surface. Theyalsofindde- ing dimer rows. From thermal desorption spectra of P
fects in the P-P dimer rows as well as anti-phase bound-
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fromtheSi(001)surface,HiroseandSakamoto[12]claim METHOD
that at low coverages (< 0.2 ML), there are mostly Si-
P dimers on the surface. Above 0.2 ML coverage, P-P, Calculations were performed using pseudopotential
Si-P dimers and defects coexist on the surface. Lin et methodwithinDFT.WeuseVASP[17,18]forourcalcu-
al. [13] in their core-level photoemission and STM stud- lations. Thewavefunctionsareexpressedinaplanewave
ies find that at ∼700 K the surface is interspersed with basiswithanenergycutoffof250eV.TheBrillouinzone
chains of P-P dimers. At ∼ 800 K the hydrogen atoms integrations are performed using the Monkhorst-Pack
desorb completely and one observes partial replacement scheme [19]. Ionic potentials are represented by ultra-
of Si atoms by P. soft Vanderbilt type pseudopotentials [20]. We use the
generalized gradient approximation (GGA) [21] for the
Thus apart from some differences in the details, most exchange-correlation energy. The preconditioned conju-
experiments agreethatafter the hydrogenfromPH3 has gate gradientmethod (as implemented in VASP) is used
beendesorbed,thesurfaceconsistsmostlyofP-Pdimers for wave function optimization and conjugate gradient
athigher coverages. Atlow coveragesthere is agreement is used for ionic relaxation. We use a (2 × 2 × 1) k-
that P replaces Si atoms and gets incorporated into the pointmeshforour(4×4)surfacesupercell,whileforthe
surface, but one would like to have a more detailed un- (2×2) surface supercell, we use a (4×4×1) k-point
derstanding of the structure. mesh. Convergence with respect to energy cutoff and
number of k points has been previously tested for simi-
There have been a few theoretical studies address- lar systems [22, 23]. When making comparison between
ing the question whether PH3 adsorbs dissociatively or binding energies of structures with same supercell size,
molecularly on Si(001) [14, 15, 16]. To our knowledge, it is expected that the errors due to cutoff and k-point
there are no systematic theoretical studies of P-covered mesh will cancel.
Si(001) surface as a function of coverage. Since it is the The Si(001)−p(2×1) surface is represented by a re-
P atoms which are important in applications, one would peated slab geometry. Each slab contains 5 Si atomic
like to understand their interaction with and structure layers with hydrogen atoms passivating the Si atoms at
on the Si(001) surface. the bottom layer of the slab. Consecutive slabs are iso-
lated from each other by a vacuum space of 9 ˚A. The
Therefore, we study stable atomic structure of P- Si atoms in the top four atomic layers are allowed to re-
covered Si(001) surface starting from a low coverage up lax, while the bottom layer Si atoms and passivating H
to a ML. Apart from finding the most favorable bind- atoms are kept fixed in order to simulate bulk-like ter-
ing site for a P ad-atom on this surface, we study P-P mination. We reproduced the energetics and geometry
dimers on Si(001) in detail because they turn out to be of the p(2×1) reconstructions of a clean Si(001) surface
a more favorable arrangement compared to isolated P using the above parameters [24].
atoms. We also compare the structure and energetics of Ourcalculationsprovidecohesiveenergyofasupercell
P-Pad-dimerswithAl-Alad-dimersaboutwhichmuchis composed of given set of atoms,
known. Wearriveattheimportantconclusionthatunlike
E [SC]=E [SC]−E [atoms] (1)
C T A
Al-Si system, P-Si system always prefer an ortho-dimer
structure and does not show a para to ortho transition where EC[SC] is the cohesive energy of the super-
with increasing coverage. Since P-Si hetero-dimers have cell, ET[SC] is the total energy of the supercell, and
been observed in experiments, we have also studied the EA[atoms] is the total energy of all the isolated atoms
energetics of replacement of surface Si atoms with P. In thatconstitutethesupercell. ThusEC[SC]istheenergy
fact, at low P coverages, this replacement of surface Si gained by assembling the given supercell structure from
atoms is a more favorable arrangement than adsorption the isolated atoms. We define the binding energy (BE)
of the P ad-atoms or dimers above the surface. Inter- of n P atoms, EB as,
estingly,the brightlines andzig-zagfeaturesobservedin
E =E [Si]−E [Si+nP] (2)
B C C
ref. [11] are related to this replacement process. In what
follows, we discuss the methods used, and the results of where E [Si] is the cohesive energy of the Si slab, and
C
our calculations in detail. E [Si+nP] is the cohesive energy with n P atoms ad-
C
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sorbed/incorporatedintotheslab. Thecohesiveenergies RESULTS AND DISCUSSIONS
of the Si slab with and without P are calculated in the
same supercell with fully relaxed atomic configurations. Inthesubsequentsubsections,wepresentresultsofour
Written in terms of the total energies, it is easy to see calculations in detail. We calculate the energetics of P
from eqn. 1, that the BE can be expressed as, adsorption on the surface, and replacement of surface Si
atoms by P when we haveanisolatedP ad-atom,andat
E =E [Si]−E [Si+nP]+nE [P] (3)
B T T A 1 1 1
, , and a full ML coverages.
8 4 2
It should be noted that in orderto comparestabilities
of two structures, one should compare their formation
energies (FE), which, in case of an ‘interstitial’ impurity Isolated P ad-atom
(in this case, added P atoms may replace Si atoms in
the slab, but they all remain within the system) can be As stated earlier, for P atoms on the Si(001) surface,
written as [25] we have considered two possibilities: they get adsorbed
on the surface or they replace Si atoms and get incor-
E =E [Si+nP]−E [Si]−nµ (4)
form T T P porated into the surface. In the first case, we have cal-
whereE [Si+nP]isthe totalenergyofthe Sislabwith culated the BE of a single P ad-atom adsorbed at four
T
the n P atoms, E [Si] is the total energy of the Si slab, symmetry sites on the p(2×1) asymmetric Si(001) sur-
T
and µ is the chemical potential of phosphorous in its face. The symmetry sites are: i) dimer site (D) on top
P
reference state. In the case when different structures be- of the Si surface dimer, ii) the site vertically above the
ing comparedhave equalnumber of Si and P atoms, one second layer Si atom between two atoms of adjacent Si
can see from eqns 3 and 4 that comparing their FE’s dimers belonging to the same dimer row (M), iii) cave
is equivalent to comparing their BE’s, since difference in site (C) between two Si surface dimers perpendicular to
FE’sisjustthenegativeofthedifferenceinBE’s. Also,if thedimerrowsandiv)quasi-hexagonalsite(H)half-way
the referencestate is takento be agasofisolatedatoms, between two Si surface dimers along a dimer row. These
which is probably appropriate in MBE conditions, then sites are marked in fig 1. We used a (4×4) surface su-
theFEofastructureisjustthe negativeofits BE.How- percell. The large size of the supercell ensures that the
ever, in case of a ‘substitutional’ impurity, when a Si interaction between a P atom in our supercell and its
atom replaced by a P atom leaves the system and goes periodic images are small and the BE represents that of
to a reservoir (again assumed to be a gas of isolated Si an isolated P atom. While studying BE of a P ad-atom
atoms), the formation energy is given by [25] at these sites, we relax the P atom, and the top four Si
layers. The BE values of the P atom at these sites are
Eform = ET[(N−1)atomSislab+P] givenintableI. IntableIwealsogiveBEofonePatom
1
− ET[NatomSislab] in a (2×2) surface cell correspondingto 4 ML, which is
discussed in detail later.
+ E [Si]−E [P]
A A The M site turns out to be the most favorablesite for
Again, from eqn 1, it is easy to see that this is equal an isolated P ad-atom. This is also the most favorable
to the difference between the cohesive energies of an N- site for an isolated Si ad-atom on Si(001) first discov-
atom Si slab in which one Si is replaced by a P atom, ered by Brocks et al. [26]. Here P ad-atom binds to two
and a the clean N-atom Si slab. Si atoms belonging to two different dimers in the same
In this work, we mostly study stabilities of various surface dimer row. These bonds are of equal length (2.3
structureshavingthesamenumberofSiandPatoms,as ˚A) with Si-P-Si bond angle ∼ 1120, suggesting that P
suggested by experiments. Hence comparing their BE’s likes to be close to a tetrahedrally bonded configuration.
serves the purpose, higher BE implying a more stable Another significantobservationis that the P ad-atomat
structure. In case of an isolated P being incorporated the M-site is only 2.26 ˚A away from the second layer
in the Si slab, we also compare stabilities of these two Si atom. This is a bond similar in character to the Si-P
structures: 1. the ejected Si remains in the slab; and 2. bonds at the surface as seen in the charge density plot
it goes to a reservoir. For this, we do have to compare in fig. 2(a). Thus the second layer Si atom bonded to P
the FE’s, as discussed in the next section. becomes five-fold coordinated probably accompanied by
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(a)
First layer
X C
Second layer P
2.3 A
XM Third layer 2.26 A 2.44 A Si
+ + Si
M Above 2nd layer
X X
D H
C Cave site
y[110]
D Dimer site
(b)
H Hollow site
−
x[110]
P
FIG. 1: Symmetry sites on the p(2×1) asymmetric Si(001) 2.3 A 2.3 A
surface at which binding properties of an isolated P ad-atom Si 3.84 A Si
arestudied. TheSiatoms marked‘+’areatagreaterheight
compared to their partners in the same dimer. This system
size is for illustration only. Calculations have been done on
different system sizes as discussed in thetext.
(c)
weakeningofitsbondswithotherSiatoms. Thisweaken- P
iantgthofebMondsistecoisstbseenneefircgiya,lbeunterPgebteicinaglly3-cfoolmdpcaoroerdditnoatthede 2.3 A 2.3 A
Dsite,wherethePad-atomisonlytwo-foldcoordinated. Si 2.48 A Si
ItisalsofoundthatwhenthePatomisattheDsite,the
0
Si-P-Si bonds make an angle of 64 . This angle is much
smaller than an idealtetrahedralangle of 1090. So there
is a bond rotation on the P atom at the D site which
costs energy. An interplay of these factors makes the M
FIG. 2: (Color online) Charge density contour plots in the
site more favorable by 0.2 eV compared to the D site. plane of the P ad-atom and the Si atoms it binds with. (a)
We showthe chargedensity contourplotsinthe planeof P ad-atom at the M site bonded to a second layer Si atom
thePad-atomandthetwosurfaceSiatomsitbindswith and a surface Si atom; (b) P ad-atom at the M site bonded
at the M and D sites in fig 2(b) and (c). The nature of totwosurfaceSiatomsofadjacentdimersinthesamedimer
row; (c) P ad-atom at the D site bonded to two Si atoms of
P-Sibonding at the two sites is similar,so it is the bond
rotation at the D site, and rearrangement of bonds the thesame surface dimer.
second layer Si atom forms, that make the M site more
favorable. can have dramatic effects on its binding properties on a
Energetically,MandDsitesarefollowedbytheHand substrate[5]. Thus while theMsite wasfoundto be the
C sites. At the H and C sites, the P ad-atom can bind most favorable site as stated before, for an Al ad-atom,
to four and two surface Si atoms respectively. However, H site turned out to the most favorable [6, 26].
beinganspelement,andhavingasmallatomicradius,it WhenthePatomgetsincorporatedintothesurfacewe
cannot take full advantage of all the neighboring surface replaceoneoftheSiatomsinasurfacedimerona(4×4)
Si atoms. Hence H site turns out to have a lower BE cellbyP.AsfortheejectedSiatom,itcaneithergotoa
than the M and D sites. The C site has the lowest reservoir, or bind with the Si surface at some other site.
BE. It has been seen before that the size of an ad-atom Experiments support the latter scenario [11, 16]. How-
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TABLE I: BE (eV/atom) for an isolated P ad-atom at dif-
dfeirffeenrtenstymcomveertargyess.ites on a Si(001)-p(2×1) surface at two II(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)I(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)IV
site isolated P 1 ML
4
MD 55..7555 55..7535 VII(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
H 4.76 4.74
C 3.73 4.45
V(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)VI
ever,forthe sakeofcompleteness,wehavecomparedthe (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)I(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
energetics of these two scenarios, as discussed later. In VII(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)I(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)
caseswhereitremainsinthesystem,weplacetheejected
Stiiaaltgoemomaettvriaersioaursessitheoswonnitnhefigsu3rf.acSet.aTrthinegpforsosmibltehiensie- (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)II(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
geometries, the ejected Si atom, top four atomic layers
FIG.3: Startingatomicgeometriesforstudyingincorporation
(including the incorporated P) are relaxed in all direc-
of one P atom into a (4×4) surface cell. The incorporated
tions. It turns out that the energetically most favorable
P atom is shown in dark color. Shaded circles show possible
position for the ejected Si atom is geometry I marked in
positions of the ejected Si atom, while open circles are the
fig3. ThisagreeswiththeresultsofWilsonetal.[16]. In Si atoms in the slab. The movements of the Si-P dimer and
the final relaxed geometry, the Si-P hetero-dimer moves Si-Sidimers neighboring it are indicated by thearrows.
by ≈0.6 ˚A alongh¯1¯10icomparedto the Si-Si dimers on
the clean surface. The adjacent Si-Si dimer, on the side
of the ejected Si, moves by ≈ 0.35 ˚A along h¯1¯10i. The atom in a surface dimer, and the ejected Si going to a
twoSi-Si dimersneighboringthese two dimersalso move reservoir that is assumed to be a gas of Si atoms. As
by ≈0.1˚A alongh¯1¯10i. As noted, this movementofthe arguedin the METHOD section,the FE in the firstcase
dimers relative to the original surface dimers propagates is just the negative of its BE, ı.e., −6.1 eV. The FE in
along the dimer row up to at least 2 dimers away from the second case, calculated as discussed in eqn. 5, turns
the Si-P dimer (the maximum distance observable in a out to be −1 eV. Since higher FE means a less stable
4×4 cell). The BE of the P atomin geometry geometry structure,clearly,itismorefavorablefortheejectedSito
I is 6.1eV. The BE’sof the P atominallthe geometries remainwithinthesystem,aconclusionthatmatcheswith
studied are givenin table II. Most importantly, compar- experimentalobservations. Inallsubsequentdiscussions,
ingtwosituationswithanisolatedPatomonthesurface: we assume that all the ejected Si atoms remain in the
(i) when the P atom is adsorbed at the M site, and (ii) system.
when it forms a P-Si heterodimer with the ejected Si in
geometry I, the latter case is found to be more favor-
able by 0.4 eV. It is interesting to note that geometry I 1 ML P Coverage
8
is reminiscent of Si ad-atom having M as the most fa-
vorable site [26]. The participation of M site makes Si 1
At a ML coverage, again we consider two
8
replacementafavorablescenario. This is consistentwith
possibilities–P atoms replacing surface Si atoms, or they
theobservationthatatlowcoverages,Patomsgetincor-
being adsorbed on the surface.
porated into the Si surface.
When the P atoms are adsorbed on the surface, we
Wenowaskwhetheritismorefavorablefortheejected put 2 P ad-atoms on a (4×4) surface supercell. Phos-
Si to remain in the system, or to go to a reservoir. For phorous being a pentavalent atom, even after binding to
this, we compare the FE’s of the following structures: 1. one or two surface Si atoms, we expect two P ad-atoms
geometry I discussed above; 2. a P atom replacing a Si to dimerize if possible. This is borne out by our calcula-
6
whileAl-Aldimersprefertoresidebetweensurfacedimer
TABLEII:BEineVperPatomincorporatedintotheSi(001)
rows[6, 7], P-Pdimers findit favorableto adsorbontop
surfacewiththeejectedSiatomatdifferentsitesasdiscussed
of dimer rows. We did study a P-P para-dimer in be-
in thetext.
tween two surface dimer rows, and the binding is found
geometry BE to be substantially weaker with a BE of 5.4 eV per P.
Also, in the case of Al-Al dimers, at low coverages, the
I 6.1
para-dimerconfigurationwasfoundtobemorefavorable,
II 5.2
while for P, ortho-dimer is more favorable. On the other
III 5.4
hand,foraSi-Siad-dimeronSi(001),Brocksetal. found
IV 5.4
that a para-dimerona surface dimer rowis only slightly
V 4.9 morefavorableby0.1eVcomparedtoanortho-dimer[5]
VI 5.2 (as this energy difference is the limit of the accuracy of
VII 5.4 their calculations). As we have found, a P ad-atom at
VIII 5.1 the M site forms a bond with the second layer Si atom
directly below it. This bond length is, in fact, slightly
shorter than the bonds the P ad-atom makes with the
surface Si atoms(see fig 2). This causes weakening of
1 1
tions at ML, as we discuss later. Hence, at ML, we
4 8 bondsbetweenthesecondlayerSiandotherSiatoms,as
considerpossiblepositionsofaP-Pdimer. Thepara-and
we have already argued. One can view a para-dimer be-
ortho-dimer arrangements are shown in fig. 4. We find ingformedbydimerizationoftwoPad-atomsontwoM
thatthe ortho-dimeris amorefavorableconfigurationof
sites between two Si-Sidimers in the same surfacedimer
the P-P dimer, with a BE of 6.3 eV per P atom. The
row. This stretches the P-second layer Si bonds, while
binding of the para-dimer turns out to be weaker with a
thebondsbetweenthesecondlayerSiandotherSiatoms
BE of 5.9 eV per P atom.
are still weak. The overall effect is a net energy cost. In
theortho-dimerorientation,thePad-atomsdonotaffect
any second layer Si atoms, while they still dimerize and
bind with four surface Si atoms. This situation turns
out to be more favorable. In case of a Si ad-atom at
the M site,the distance betweenthe Siad-atomandthe
secondlayerSiisfoundtobegreaterthanbulkSi-Sidis-
tance, and also greater than the distance between the Si
ad-atom and surface Si atoms [26]. Hence a Si ad-atom
at the M site has negligible effect on the second layer Si
atom. Thuseveninapara-dimerorientation,thereisnot
much energy costin stretching the ad-atom-secondlayer
bonds, and, in fact, para-dimer becomes more favorable
for Si ad-dimers.
Aside-viewoftheP-Portho-dimerontheSi(001)sur-
face is shown in fig 5. The P ad-atoms symmetrize the
two adjacent Si-Si surface dimers, but do not break the
dimers. Phosphorous atoms having smaller atomic radii
ortho para
than Si atoms, the P-P bond length is smaller (∼ 2.27
FIG. 4: Thepara- and ortho- orientations of a P-P dimeron ˚A). Hence the two adjacent Si-Si dimers are drawn in
theSi(001) surface at 1 ML studied in this work. closer to the P-P dimer along h1¯10i direction compared
8
totheirpositiononthep(2×1)-asymmetricreconstructed
Itisinterestingtocomparetheseenergeticswiththose surface. The Si-P distance in this case turns out to be
of Al-Al dimers on the Si(001) surface. The biggest dif- ∼2.3 ˚A.
ference between P-PandAl-Al dimers onSi(001)is that When two P atoms are incorporated, the ejected Si
7
2.3 A 1.95 A In this geometry the dangling bonds of the four surface
2.27 A Siatoms,abovewhichthe ejectedSiatomsdimerize,are
saturated. The ejected Si atoms are also 3-fold coordi-
[0 0 1]
nated. Thislargereductionofdanglingbondscausesthis
geometry to be the most favorable. In geometry I, the
next most favorable arrangement, the ejected Si atoms
[1 1− 0] do not dimerize. In this geometry, four dangling bonds
of the surface Si atoms are saturated, but the ejected Si
FIG. 5: Side-viewof the local geometry around a P-Portho- atoms are only 2-fold coordinated. In geometries II and
dimer adsorbed on Si(001). The P-P dimer is found to be IValso,afterrelaxation,theejectedSiatomsformasym-
symmetric.
metric dimers with Si-Si dimer distances of 2.38 ˚A and
2.41 ˚A respectively. However, in these two geometries,
the surface Si atoms are quite far from the ejected Si’s.
atoms are placed at various sites on the surface and the
Thus there is not much energy gain from bonding with
geometriesstudiedinthispaperareshowninfig6. Start-
surface Si atoms. This causes II and IV to be lower in
ing from these geometries,the ejected Si atoms, and top
BE.TheBE’sforallthegeometriesaregivenintableIII.
four atomic layers are relaxed. After relaxation, geome-
TABLEIII:BEperPatomforPincorporatedintotheSi(001)
surface at 1 ML.Thegeometries refertovariouspositions of
8
(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) IV (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) theejected Si atoms as discussed in the text.
geometry BE
I 6.0
(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) III (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) II 5.6
III 6.4
IV 5.7
(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) II (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)
(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) I (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) Again, what is interesting to note is that the geom-
etry with P atoms incorporated into the surface has a
lower energy. Therefore, at low P coverages, it is more
favorable for P atoms to replace surface Si atoms. The
ejected Si atoms prefer to go in positions where the next
layerofSiatomswouldbeabovethestartingsurface,and
FIG. 6: Starting atomic arrangements for incorporation of
twoPatomsinto(4×4)surfacecell. ThePatomsaredenoted form asymmetric dimers. This suggests that the bright
by dark circles. Shaded circles show possible positions of the lines seen in the STM images, along with the Si-P het-
pair of Si atoms displaced by the P atoms. Small arrows erodimers are, in fact, ejected Si-Si dimers, and not P-P
indicate that thetwo ejected Si atoms form a dimer. dimers. ThisisconsistentwithCursonetal.’sinterpreta-
tion of the lines perpendicular to the surface dimer rows
tryIIIturnsouttobethemostfavorablewithaBEof6.4 in their STM images as Si-Si dimer chains [11]. This
eV per P atom. Note that geometry III is an ortho- ori- also supports Wang et al.’s interpretation of their STM
entationoftheSi-Sidimerontopofasurfacedimerrow. images [9].
But it is known that the energy difference between the Curson et al. have observed some zig-zag features in
para- and ortho- configurations is small (∼ 0.1 eV) [5], their STM images [11]. There is also a bright spot asso-
and hence either structure may be seen in experiments. ciated with this feature as seen in those images. There
Inthefinalconvergedgeometry,thetwoejectedSiatoms could be two possible origins of these, (i) P-Si hetero-
formanasymmetricdimerwithaSi-Sidistanceof2.39˚A. dimer, which, as already mentioned, move by 0.6 ˚A rel-
8
ative to the Si-Si dimers, or (ii) the ejected Si atom in
geometry I in fig. 3. Charge density contours in a hori-
zontalplane approximately∼1 ˚A above the Si-P dimer
(without the ejected Si atom at I) are shownin fig. 7. A
zig-zag feature is distinctly visible. There is also an ex- (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)II(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)III(cid:0)(cid:1)(cid:0)(cid:1)
cesschargedensityonthePatominthe displaceddimer
which can appear as a bright spot in STM. In a charge
density plot (not shown here) on a similar plane ∼ 1 (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
˚A above the ejected Si in geometry I, only the Si atom 2 4V 6
is seen and no zig-zag features, since the surface dimer ~ 0.1 A ~ 0.1 A
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)
rows are not visible any more. From these observations (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)
[1 1 0] IV I
we conclude that the zig-zag features and the associated
bright spots can be attributed to Si-P hetero-dimers. 1_ 3 5
[1 1 0]
0.35 FIG. 8: Initial geometries for two P-P dimers on a (4×4)
supercell studied in thiswork. Given onedimerin a position
0.3
indicatedbythedarkcircles,fivepossiblepositionsareshown
0.25 fortheseconddimer. MovementsoftwosecondlayerSiatoms
0.2 (marked2and6)whenonlythedarkdimerispresentonthe
0.15 surface are also shown.
0.1
0.05
second dimer along h1¯10i once we have moved it along
FIG.7: (Coloronline)Chargedensitycontourplotsinaplane h110ibytwolatticespacings. Ontheotherhand,putting
∼ 1 ˚A above the Si-P dimer. The displacement of the Si-P two dimers only one lattice spacing apart, either along
dimergivesitazig-zagappearanceinSTM.Largerchargeon h110i or h1¯10i costs energy. Thus structures IV and V
thePatomisalsovisible. Thiscangiverisetotheassociated are less favorable than II or III, IV being costlier than
bright spot. V.
Inorderto understandwhystructuresIIandIIIturn
out be lower in energy than I, one has to look at the
structurearoundtheP-Pdimermoreclosely. Aswehave
41 ML P coverage already mentioned, top layer Si-Si dimers neighboring a
P-P dimer are drawn closer to it. On the other hand,
At 1 ML P coverage also we study both the there are six second layerSi atoms (marked1-6 in fig 8)
4
possibilities–Pgettingadsorbedonthesurface,orgetting immediately neighboring a P-P dimer (marked by dark
incorporatedinto the surface. For eachof these possibil- circles in that figure). Of these, two second layer atoms
ities, we do calculationson two different system sizes–(i) (2 and6)actuallymoveawayfromthe P-Pdimer,while
oneP atomona(2×2)surfacecell, (ii)fourP atomson the others remain in their ideal positions as on a bare
a (4×4) surface cell. surface. When two P-P dimers are put in structure I,
When we have four P ad-atoms adsorbed on a (4×4) the second layer Si in between them (6 in this case) is
cell, they would form two P-P ortho-dimers. Various frustratedsincethetwodimerstendtopushitinopposite
reasonablepositionsoftwoP-Pdimersareshowninfig8. directions. This causes strain in the structure. There is
The BE’s for the relaxed structures starting from these no such problem once the P dimers are separated by at
atomic configurations are given in table IV. The dimers least two lattice spacings along h110i, in which case all
prefertobeseparatedbyatleasttwolatticespacings(of secondlayerSiatomsneighboringthePdimerscanrelax
thesquarelatticeontheunreconstructedSi(001)surface) freely. ThefactthatstructuresIIandIIIhavethe same
along the h110i direction. In fact, there is essentially no energy also indicates that this relaxation of the second
difference in energy between structures II and III. This layer Si atoms is a crucial mechanism in optimizing the
shows that there is no further energy gain in moving the structure. Once that has been achieved in structure II,
9
there is no further energy gain in moving the second P P ad-atom. While putting four P atoms on a (4 ×4)
dimer two lattice spacings along h1¯10i. surface cell, there can be several possibilities. However,
1
we are guided by our calculations at ML, where we
8
found that two ejected Si atoms prefer to dimerize on
TABLE IV: BE values in eV per P atom for two P-P dimers
top of and perpendicular to surface Si dimer row. We
presentona(4×4)surfacesupercellofSi(001) startingfrom
thus incorporated all the four P atoms in the dimers in
various initial atomic geometries as discussed in thetext.
a row of our (4×4) cell, and put the ejected Si atoms
above the other dimer row. The starting configuration
geometry BE
is shown in fig 9. In the relaxed geometry, the ejected
I 6.2 Si atoms formtwo asymmetric dimers,as expected. The
II 6.3 BE turns out to be 6.2 eV per P atom. There is slight
III 6.3 energygainrelativetothe(2×2)cellduetodimerization
IV 5.7 of ejected Si atoms.
V 5.8
In structures IV and V, two P dimers are put one
lattice spacing apart in the initial configuration. Atomic
relaxationstartingfromthesegeometriesindicatethatit
is energetically highly unfavorablefor two P-Pdimers to
come so close to each other at this coverage. There is a
repulsionbetweenthe twodimersandthey tendto move (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)
away from each other. (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
1
Now we presentour results for ML P coveragestud-
4
ied with one P ad-atom on a (2×2) surface supercell.
We put the P ad-atom at M, D, H, and C sites. A
look at table I shows that BE’s at M, D and H sites
are essentially the same as those for an isolatedSi atom.
However, binding at the C site is significantly stronger
in the present case. At M, D and H sites, an isolated P
atomisalreadyreasonablystronglybondedtotheneigh-
boring surface Si atoms. However, the P-Si bonding at
the C site is rather weak, which leaves the isolated P
1 FIG. 9: Starting geometry for the four ejected Si atoms
ad-atom with localized electrons on it. At ML, the P
4 (shaded circles) when four P atoms (dark circles) are incor-
atom finds other P atoms at nearby C sites, which gives porated in a (4×4) surface cell.
these localized electrons a channel to delocalize. This
delocalization lowers the kinetic energy of the electrons,
1
and makes the binding stronger. We also find that at
4
ML coverage, two P-P dimers on a (4×4) surface cell NowacomparisonofBE’sforPadsorbedandPincor-
have a stronger binding than a single P ad-atom on a porated geometries shows that at 1 ML, P adsorptionis
4
(2 × 2) surface cell. This shows that dimer formation more favorablethan P incorporationby 0.1 eV. Thus we
byPad-atomsonthe Si(001)surfacesignificantlylowers reach the significant conclusion that at a critical cover-
their energy. age whose value lies between 1 ML and 1 ML, P atoms
8 4
In case of P incorporation into the surface, when we prefertogetadsorbedonthesurfaceandformP-Portho-
have one P atom on a (2×2) surface cell, the ejected dimers, rather than getting incorporated in the surface.
Si is placed in geometry I as explained in fig 3. The Note that, while at 1 ML P adsorption is more favor-
4
ejected Si and top four atomic layers are relaxed. In the able, in experiments, it is not surprising to find some P
converged geometry, the BE is found to be 6.1 eV per incorporation concurrently.
10
1 and full ML P coverage
2
(a) (b)
1 (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
At 2 ML also we calculated the energetics of P incor- (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
poration into Si(001) surface, though it is expected that
(cid:0)(cid:1)(cid:0)(cid:1)II (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
adsorption would be more favorable at this coverage. In (cid:0)(cid:1)(cid:0)(cid:1) (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) I (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
fact, that is what we find in our calculations. In order (cid:0)(cid:1)(cid:0)(cid:1)
to study adsorption at 1 ML P coverage, we put two (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
P ad-atoms in a dimerize2d position on a (2×2) surface (cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)
cell. WeagaincalculatedenergiesofP-Ppara-dimerand
ortho-dimer on top of a surface dimer row. These two ortho para ortho(III) para(IV)
geometries are shown in fig. 10(a). It turns out that the
FIG. 10: Two P atoms (dark circles) on a (2×2) surface
ortho-dimer is a more favorable configuration. The P-
P dimer distance is found to be 2.27 ˚A while the Si-P cell at half monolayer coverage. (a) Para- and ortho-dimer
configurations of two adsorbed P-P dimer; (b) two P atoms
distance is 2.34 ˚A. The underlying Si dimers are sym-
replacetwosurfaceSiatoms(shadedcircles),whichareshown
metrized,butthe Si-Sidimerdistance stillremainstobe in four different initial geometries.
2.33˚A.ThusthelocalgeometryandbondingaroundaP-
P ad-dimer is similar to that found around an ad-dimer
1
in case of ML with a similar value for the BE. The
8
BE turns out to be 6.3 eV per P atom. The para-dimer
it is unfavorablefor two P-Pdimers to come too closeto
configuration has a BE of 5.9 eV per P. So we find an-
each other on the surface. Some of this strain could be
othercrucialdifferencebetweenAl-AlandP-Pdimerson
released by missing P-P dimer rows as found in experi-
Si(001). Al-Aldimersshowedatransitionfromapara-to
ments. However,since we are studying full ML coverage
ortho- orientation with increasing coverage [7], but P-P
with a (2×2) surface supercell, we cannot explore this
dimers always prefer an ortho- orientation.
possibility in our calculations.
In order to study P incorporation, we replace two Si
atomsintwodimersona(2×2)surfacecellbyPatoms.
ThereareseveralpossibilitieswheretheejectedSiatoms
can go. We have considered four possible arrangements
for two ejected Si atoms that are shown in Fig. 10(b).
The geometry I and the ortho-dimer geometry (III) of
the Si atoms turn out to be very close in BE. The BE of
geometryIIIis5.97eVperPatomandthatofgeometry
I is 5.95 eV per P atom. The para-dimergeometry (IV)
has a BE of 5.45 eV per P atom. Geometry II turns
out to be the least favorablewith a BE of 5.12 eV per P
atom.
Atone ML coverage,we put fourP atoms ona (2×2)
surface supercell. Again, a symmetric dimer-row struc-
tureofthePad-atomsturnsouttobethemostfavorable
FIG. 11: Four P ad-atoms (dark circles) forming two dimers
one. This is same as the structure found for a ML As- ona(2×2)surfacecellatafullMLcoverage. Reconstruction
covered Si(001). The geometry of a full ML P covered of the underlyingSi(001) surface is lifted.
Si(001)isshowninfig.11. TheP-Pdimerdistanceinthe
the relaxed structure is calculated to be 2.3 ˚A. The Si-P
distanceisfoundtobe2.38˚A.TheBEforP-Pad-dimers
is found to be 6.4 eV per P atom at full ML coverage. OurfindingsthatathighercoveragesPadsorptionbe-
Another important feature seen at this coverage is that comes more favorable, and that P ad-atoms prefer to
the reconstruction of the underlying Si surface is lifted, formdimers, are consistent with the conclusionsreached
just as was found for As on Si(001). We have seen that by Yu et al. and Wang et al. [8, 9].