Incoherent Transport through Molecules on Silicon in the vicinity of a Dangling Bond

0.54 MB·English

by  Hassan Raza

Incoherent Transport through Molecules on Silicon in the vicinity of a Dangling Bond
Hassan Raza
NSF Network for Computational Nanotechnology and School of Electrical and Computer Engineering,
Purdue University, West Lafayette, Indiana 47907 USA
School of Electrical and Computer Engineering, Cornell University, Ithaca New York 14853 USA
8 Kirk H. Bevan, Diego Kienle
0 NSF Network for Computational Nanotechnology and School of Electrical and Computer Engineering,
0 Purdue University, West Lafayette, Indiana 47907 USA
2
Wetheoretically studytheeffect of a localized unpaireddangling bond (DB)on occupied molec-
n
ular orbital conduction through a styrene molecule bonded to a n++ H:Si(001)-(2×1) surface. For
a
J molecules relatively far from the DB, we find good agreement with the reported experiment using
a model that accounts for the electrostatic contribution of the DB, provided we include some de-
8
phasingduetolow lyingphonon modes. However,for molecules within 10˚A totheDB, we haveto
2
includeelectroniccontributionaswellalongwithhigherdephasingtoexplainthetransportfeatures.

]
r PACSnumbers: 85.65.+h,73.20.-r,73.63.-b
e
h
t
o I. INTRODUCTION the I-V characteristicsof the styrene chain electronically
. by introducing a near-midgap state in the local density
t
a ofstates(LDOS)ofSiatoms4˚Aand8˚Aaway. Forthese
m Interest in atomic scale conduction continues to grow
molecules,this contributionwouldleadto anearly onset
atarapidpacebothintheengineeringandscientificcom-
- of conduction at approximately 0.5V (rather than 1.1V
d munities. The comparatively stable C-Si bond and the
due to the bulk Si band gap) as shown in Fig. 1. Since
n well characterized Si surface chemistry1,2 not only place
the DB wavefunction decays exponentially, this contri-
o organicmoleculesinanidealpositiontocomplementex-
c bution would be nearly absent for a molecule 12˚A away.
isting Si technology, but also offer a unique platform to
[ Apart from this, the effect on transport due to the DB
study scientific phenomena3,4 with experimental repro-
state would be pronounced when the highest occupied
3 ducibility. Notably, Si contacts may give rise to novel
v features such as negative differential resistance5,6,7, al- molecularorbital(HOMO)levelissufficientlybroadened
6 to form a significantoverlapwith the DB state as shown
though the mechanism is not yet established8.
2 in the inset of Fig. 2. Moreover, this effect would be
2 In Si technology, dangling bond (DB) defects in the diminished if the HOMO level is too far from the DB
7 form of Pb centers have created reliability issues - con- state.
0 sider, negative bias temperature instability in metal-
6
oxide-Si structures. However, one could engineer such
0
defects to be useful in novel devices. Recently Piva et
/
t al9 observedsignificantshifts in the onsetvoltagesalong
a
m a styrene chain as function of distance from a negatively The impact of dephasing due to low lying phonons on
charged unpaired DB on a n++ H:Si(001)-(2×1) surface
- experimentallyobservedlineshapesisfurtherexploredin
d usingscanningtunneling spectroscopy(STS). Inthis pa- thispaper. Inmolecularjunctions,thedominantphonon
n per, we theoretically study their results. A comparison
modes are the ones having low energy, which arise due
o betweencalculatedandexperimentallyobservedcurrent-
to the combined motion [translational, rotational, etc]
c
voltage (I-V) plots is shown in Fig. 1. The DB, being
: of the entire molecule relative to the contacts and have
v negatively charged, pushes molecular levels upward. A been discussed theoretically in Refs.11,12. Experimen-
i schematic energy level/band diagram is shown in Fig.
X tally, some evidence of the presence of these low lying
r 1. The onset voltage depends on the gap between the modes is available13,14,15. Since experimental results are
a equilibriumchemicalpotential(µo)andmolecularlevels. suggestive,adetailedstudyneedstobedonetoestablish
Giventhat the onsetvoltageis decreasingin the vicinity
it on a solid footing. These low lying phonon modes are
of the DB, one concludes that conduction is through oc-
exciteddue to inelastic electron-phononscattering. Sim-
cupied orbitals. The trend would have been reversed for
ilarly, the styrene should be able to vibrate, rotate and
unoccupied orbital conduction.
move with respect to the Si and tip contacts, and hence
Furthermore, observed onset voltages for molecules weexpectasimilartrend. Since~ω ≪k T atroomtem-
B
4˚A and 8˚A10 away from the DB are grouped together; peratureforthesemodes,weinclude their effectthrough
whereas a molecule 12˚A away has a distinctly different elastic dephasing for simplicity. Furthermore, broaden-
onset voltage. Electrostatically, one would expect them ing due to such modes could be large as in Ref.16. The
tofollowaninversedistancerelationship. Toexplainthe dephasing strength used in our calculation gives a com-
above discrepancy, we propose that the DB also affects parable broadening.
Vacuum 2
DB’s electronic
W(110) Tip contribution
tip inside band gap
DB Styrene Ec o electrostatic and electronic boundary conditions are set
U chain DB by the tip voltage and contact self-energies (ΣSi,tip) re-
DB sEtate Shift of HOMO spectively. Σs is the scattering self-energy. In a non-
Si v level due to DB’s orthogonalbasis for the elastic dephasing, the scattering
n++ H:Si(100)-(2x1) electrostatic
contribution broadening function is given as20:
0.4eV
Γ (E)=Σin+Σout ≈D SA(E)S (2)
s s s
0.08 whereΣinisthescatteringinflowfunctionandΣoutisthe
4Å, D=1.85eV2 s s
scattering outflow function. D is the dephasing strength
8Å, D=1.85eV2
0.06 which is a fourth rank tensor, but in our calculations it
A) 12Å, D=1.4eV2 is approximated by a scalar and is used as a fitting pa-
n
nt (0.04 rameter. TreatingD as a scalarwouldignorethe minute
e detailsofdephasingthatmaybe otherwisepresentwhen
r
ur a carrier gets scattered from one electronic state to an-
C0.02 other electronic state more strongly or weakly. A is the
Spectralfunctiondefinedasi(G−G†)=Gn+Gp,where
GnandGparetheelectronandholecorrelationfunctions
0
0 0.5 1 1.5 2 respectively. Using Eq. 2, the scattering self-energy is
Tip Voltage (V)
given as:
1 ∞ −Γ (y)/2 Γ (E)
Σ (E)= dy s −i s (3)
s π Z E−y 2
−∞
It has been shown21 that the real part of Σ (E) [cal-
s
culated by the Hilbert transform as shown in Eq. 2] is
about few meV for different organic molecule contacted
by Au(111) electrodes due to slowly varying Γ (E). We
s
FIG. 1: (color online) Calculated transport properties of a
expectittobesmallforthemoleculartransportthrough
styrenemoleculebondedtoan++ H:Si(001)-(2×1)surfacein
Si valence band due to slowly varying density of valence
thevicinityofanegativelychargedDB.Experimentaldatais
band states. However, this approximation may not be
indicatedby×marks9,10. Asafunctionofdecreasingdistance
appropriate for a one dimensional contact like carbon
fromtheDB,theonsetvoltagesshifttowardlowertipvoltages
nanotube or graphene nanoribbon due to van Hove sin-
implying occupied molecular orbital conduction. I-V plots
for molecules 4˚A and 8˚A away have grouped onset voltages. gularities. Giventhatthiscalculationiscomputationally
The electrostatic and electronic contributions of the DB are veryexpensiveandhassmalleffectonthefinalresults,we
included in these calculations. We assume a lower dephasing ignoretherealpartofΣs(E). SinceΣs,G,Gn(=−iG<)
strength (D) of 1.4eV2 for the molecule that is farthest from and Σin(= −iΣ<) depend on each other, we solve for
s
theDB, as compared to1.85eV2 for the closer ones. the abovefour quantities self-consistentlyalongwith the
Hatree self-consistent loop of the applied tip voltage.
TheelectronicstructureofSi(001)22,styrene23andthe
II. THEORETICAL MODEL AND
tip is calculated using Extended Hu¨ckel Theory (EHT).
ASSUMPTIONS
Importantly,EHT providesthe correctbulk Si band gap
(as compared to LDA7) and captures the surface and
We use the single particle non-equilibrium Green’s band structure effects accurately4,24,25. We incorporate
functionformalisminthemeanfieldapproximationusing an isolated DB in a H:Si(001)-(2×1) symmetric dimer
anon-orthogonalbasistomodelquantumtransportasin unit cell, composed of 64 Si atoms with 8 at the surface,
Ref.17. We extend this workbyincluding elasticdephas- out of which 7 are passivated and one is unpassivated
ing within the self-consistent Born approximation18,19. which has the dangling bond, as shown in the inset of
The time-retarted Green’s function is defined as: Fig. 4 (visualized using GaussView27). Additional sur-
face relaxation due to the DB is small26 and hence ig-
G=[(E+i0+)S−H −U −U −Σ −Σ ]−1(1)
d d DB Si,tip s nored. We calculate the surface Green’s function (g )
s
where H is the device Hamiltonian and S is the overlap recursively28 and find that the DB gives rise to a near-
d
matrix. U is the potential experienced by the molecule midgap state in the Si band gap similar to Ref.26. We
d
and consists of (1) Laplace potential due to applied tip assume a constant gs for the tip similar to Ref.5. How-
voltage,(2) Bandlineup potentialdue to the Fermilevel ever, Σtip is still energy dependent, since it is defined as
mismatch of n++-Si and tip contacts, (3) Hartree and [(E +i0+)S −H ]g [(E +i0+)S† −H†] where S and
1 1 s 1 1 1
Imagepotentials,duetonon-equilibriumstatisticsofthe H aretheoverlapandHamiltonianmatricesbetweentip
1
electrons on the molecular region. U is the poten- andstyrenemolecule. ForagoodSTStipwhichcangive
DB
tial due to the negative charge on the unpaired dangling atomic resolution, the last tip atom at the apex domi-
bond, which causes a shift in the molecular levels. The nates STS andhence we use a single tungsten (W) atom
3
as shown in Fig. 2(a). This apparent barrier height is

about 10eV with original parameters. Apart from this,
A)100 !" 2m ap the HOMO level of W atom lies at -10.73eV, whereas
n e#2!z Fit
nt ( "1 Å-1 the work function of W(110) tip is around 5.2eV, there-
re "4.3eV fore we have an offset of 5.53eV with respect to vac-
ur 10 ap uum. Similarly, the Si conduction band edge (Ec) ob-
C
el tained from EHT has an offset of 7.75eV. To calculate
n Transport the offset of styrene, we use the HOMO level obtained
n
u 1 Calculation from DFT-B3PW91/6-311g* calculations32 as a refer-
T
Exponential Fit ence,sincetheoccupiedstatesinDFT arerelativelywell
characterized33. To ensure a proper alignment with re-
4 5 6 7
(a) Tip Height - z (Å) specttovacuum,weshifttheHamiltoniansbytheabove-
mentioned offsets E for the systems i and j
offset−i,j
within EHT procedure as follows:
1
H = S (K H +K H +E +E ) (4)
ij ij i ii j jj offset−i offset−j
2
In order to match the experimentally observed onset

3D Electrostatic Calculation voltages,weshiftthemolecularlevelsby+0.5eV[shifted
0.6
Hyperbolic Fit toward the valence band minimum]. This shift is a one
0.7 time adjustment for all the molecules under considera-
STYRENE
V) 0.4 tion and hence it affects the onset voltages of all the
e
( molecules by an offset of +0.5V. Further changes in the
B eV
D onsetvoltagescomeduetotheDBpotentialU ,which
U DB
0.2 varies inverselywith distance of different molecules from
SILICON 0 theDB.Since,thedensityofstatesinsideHOMO-LUMO
U 2.4(eV) d(Å) (lowestunoccupied molecularorbital)gapis quite small,
0 DB
a shift of 0.5V can be caused by a very small change
10 20 30 40 50
(b) Distance from DB - d (Å) in Hartree potential at equilibrium due to small charge
transfer. However, the lineshapes of the calculated I-V
characteristicsare not sensitive to this shift and they re-
mainconvex[seeSec. III].Incorporatingthisshiftresults
in the HOMO levelbeing about 0.4eV below the valence
band edge [after incorporatingthe effect of Si contact as
FIG. 2: (color online) Tip modeling and electrostatic contri- well in the form of Si self-energy - the real part of the
butionoftheDB.(a)Tunnelcurrentasafunctionoftipheight self-energy shifts the molecular levels]. This means that
showing exponential decay, which gives an apparent barrier HOMOlevelisabout0.9eVbelowthe valencebandedge
height of 4.3eV. (b) A 3D continuum finite-element electro- before applying this shift. The position of HOMO level
static calculation showing a hyperbolic trend in the average in our study is different from Ref.3, where it is reported
potential, due to a negatively charged DB, along a styrene
to be about 1eV below the valence band edge. How-
chain. The insets show a contour plot potential profile 4˚A
ever, the difference in our case is that the styrene chain
away.
is inthe vicinity ofachargeddanglingbond whichcould
changelocalnatureofSi-Cbond. Thisgovernsthecharge
transferatequilibrium,whereasinRef.3,thereisnodan-
as tip. Transport quantities are then calculated through gling bond. Furthermore,we do notcalculate the charge
a single molecule. The molecularstructure is takenfrom transferatequilibrium,ratherusetheshiftinenergylev-
Ref.5, which reports structure for a styrene molecule on els due to charge transfer as an adjusting parameter. In
hydrogenatedSisurface. Thereisanimportantdifference short, there are two fitting parameters in these calcula-
between bonding geometry of styrene on hydrogenated tions, shift of energy levels [a one time adjustment] and
and unpassivated Si. For hydrogenated Si, one C atom dephasing strength D. These two fitting parameters are
of styrene bonds to one Si atom as shown in Fig. 1. For used to capture two independent features in the experi-
unpassivated Si, styrene goes through a cyclo-addition ment. The first one, i.e. shift of energy levels, is used to
process and the two C atoms on the styrene bind with quantitatively match the experimentally observed onset
two atoms of a Si dimer [not shown in this paper]. voltages and it does not affect the lineshapes observed
ForΣ ,theEHTparametersofthes-orbitalbasisset whether we include dephasing or not. The second pa-
tip
are modified29 (similar to Ref.30) to get an appropriate rameter, i.e. dephasing strength D, is used to reproduce
apparent barrier height (φ ). We obtain φ = 4.3eV theexperimentallyobservedconcave lineshapes. Thede-
ap ap
from the calculated I(z) plot31 with 2V applied at tip phasingaffectsthe onsetvoltageinaminorfashionsince
0.08
12Å, D=1.4eV2 4
12Å, D=0
)0.06 about one third of the tip voltage because tip is quite
A
n HOMO close to the molecule. Apart from this, the tip heights
nt (0.04 Conduction are modified34 to reflect actual changes during experi-
e mental data acquisition35 and hence tip heights are not
r
r used as adjustment parameters. Rather, it implies that
u
C0.02 our model is flexible to incorporate the very delicate ex-
perimental details.
ForcalculatingthepotentialduetotheDB,a3Dfinite-
(a) 00 0.5 1 1.5 2 element continuum calculation36 is performed by taking
Tip Voltage (V) intoaccounttheDB’sapproximateshape37. Thestyrene
chainisapproximatedbya100˚Along3Dboxwithwidth
and height corresponding to that of styrene and having
a relative dielectric constant of about 2.4. This box is
placed on a Si bulk having a relative dielectric constant
0.08 of about 12. An STM tip is placed about 1nm above
4Å, D=1.4eV2
the styrene chain in the form of a metallic sheet. An
8Å, D=1.4eV2 averageof the calculatedpotential(U ) takenoverthe
0.06 DB
A) 12Å, D=1.4eV2 lateral cross-sectionis included in our transport calcula-
n
nt (0.04 DtioBn.isAshpolwotnoinf UFDigB. a2s(ba).fuTnchteiopnotoefndtiiastlapnrcoefiflreoamcrtohses
re a molecule 4˚A away from the DB [shown in the inset of
r
u Fig. 2(b)], shows a weak electrostatic contribution in Si.
C0.02 Incorporating U in an averagedfashion ignores Stark
DB
effect within a single molecule due to chargeon the dan-
(b) gling bond. This may quantitatively affect the results in
0
0 0.5 1 1.5 2 aminorwaybecauseasseenintheinsetofFig. 2(b),the
Tip Voltage (V) danglingbondpotentialiscomparativelyconstantovera
single molecule, i.e within about 0.5-0.7eV. This simple
continuummodelseemstobesatisfactoryforcalculating
the electrostatics of the DB, because (1) the screening
effectofthe styrenechainshouldbesmallduetothe one
dimensional nature of the styrene chain. In particular,
occupiedstatesaremorelocalizedthanunoccupiedstates
FIG. 3: (color online) Effect of dephasing and electrostatic andhencethisscreeningisexpectedtobesmallforoccu-
contribution of the DB on transport properties. (a) Calcu- piedstatesconduction[acasediscussedinthispaper](2)
lated I-V plots for the molecule 12˚A away with and with- we obtain a hyperbolic dependence as a function of dis-
out dephasing. Without dephasing, the lineshape [red (dark tance from the dangling bond i.e. U ≈2.4(eV)/d(˚A),
DB
gray) dotted line] does not match with the experiment (blue
which is expected. For calculating the electrostatic con-
x marks). With D = 1.4eV2, there is a good quantitative
tribution, treating the charged DB, styrene chain and
agreement with the experiment. (b) Calculated I-V plots for
n++ doped Si in atomistic manner may result in quan-
molecules 4˚A, 8˚A and 12˚A away from the DB after incorpo-
titatively different U , however it is still expected to
rating UDB. DB
show a hyperbolic dependence and can be readily incor-
porated in our model. Such a change would result in
different onset voltages as a function of distance from
it broadens the energy levels and hence current starts
flowing at lower tip voltages. the dangling bond, however the reported lineshapes in
Sec. III would remain the same.
We solve the 3D Laplace’s equation using the finite-
element method to obtain the potential profile across Moreover, based on a finite-element MEDICI38 cal-
styrene due to the tip voltage. This method has been culation, we conclude that tip induced band bending
discussed in detail in Ref.17. This method also provides is also negligible. Additionally, dopants in n++ Si in-
the zero bias band lineup potential due to the Fermi troduce states approximately 50meV39 below E , which
c
level mismatch of 1.15eV between the tip and n++ Si. contribute weakly40 to transport for a tip voltage of
Solving for a 3D potential ensures that Stark effect is about 50meV. In our calculations, we ignore the above-
captured for the applied tip voltage. Furthermore, for mentionedeffects. TheHartreepotentialforthemolecule
the experimental conditions the molecular levels shift by is included via the complete neglect of differential over-
about one tenth of the applied tip voltage and/or Fermi lapmethod41. Imageeffectsareincorporated17 toensure
levelmismatch,sincethetipisquitefarfromthestyrene that self-consistencyis not over-estimated,which canal-
molecules. This scenario is different from the ones re- ter results significantly. In all of the above electrostatic
ported in Refs.5,6, where the molecular levels shift by calculations, the tip is taken to be a metal sheet having
×10-7 5
4Å 8Å 12Å
HOMO
DB
4Å away from DB Conduction
m)0.4 E =
8Å away from DB E c Si
o v
at Clean Bandgap 4Å
/
V
e 8Å
(/

S0.2
O
D
E E
l
a v c HOMO-1
oc (a) Conduction tip
L
0
-13.5 -13 -12.5 -12 -11.5
Energy (eV)
0.08
4Å, D=1.4eV2
8Å, D=1.4eV2
0.06
A) 12Å, D=1.4eV2
n
(
FIG.4: (coloronline)ElectroniccontributionoftheDB.The nt 0.04
calculatedlocaldensityofstatesofSiatoms,4˚Aand8˚Afrom re
r
the DB, shows that the DB introduces a near-midgap state. u
Inset shows thesurface portion of the unit cell used. C0.02
(b)
work function of 5.2eV - a value attributed to W(110) 0
0 0.5 1 1.5 2
tip. Tip Voltage (V)
III. DISCUSSION OF RESULTS
Atransportcalculationtostudytheeffectofdephasing
foramolecule12˚AawayfromtheDBispresentedinFig.
3(a). Without dephasing, the lineshape [red (dark gray)
FIG. 5: (color online) Effect of electronic and electro-
dotted line] does not match with the experiment [blue
static contributions of the DB on transport properties. (a)
(dark gray) × marks]. The lineshapes for the theoret- T(E,V)[ftip−fSi] plots (where T(E,V) is the transmission
ically calculated and experimentally observed I-V char- and ftip,Si are the Fermi functions for the contacts) for
acteristics are quite different. Experimentally observed molecules4˚A,8˚Aand12˚AawayfromtheDB.Formolecules
lineshapes are concave, whereas the calculated lineshape 4˚A and 8˚A away, there is conduction inside band gap due
has a convex character. For coherent transport, obtain- to electronic contribution of the DB. (b) Corresponding I-V
ing a convex lineshape is expected because it represents plots. Onsetvoltagesformolecules4and8˚Aawaymatchwell
with theexperiment,whereas lineshapes do not.
thatcurrentstartsflowingthroughalevelandthensatu-
rates when the level is fully inside the bias window. The
corresponding conductance peak [not shown] has a full
width half maximum (FWHM) of about 0.2eV. This is Since the local density of states (LDOS) of Si contact
roughlyequaltothecouplingbetweenstyreneandSicon- [see Fig. 4] increases with decreasing energy/increasing
tactbecausetipisquite farandhencethe I-Vcharacter- positive tip voltage, the current starts increasing in a
istics do not get affected much by the Hartree potential fashion proportional to the coupling to the Si contact,
due to the non-equilibrium carrier statistics. This small which is proportional to the LDOS of Si contact. In
coupling is expected since styrene binds with Si through this case, as can be seen in Fig. 4, the LDOS increases
only one Si-C bond and HOMO is localized on the aro- with decreasing energy as one goes away from the va-
matic ring of the styrene molecule, see e.g. Refs.9,44. lence band edge. The current increases with increasing
However, after including dephasing (with D = 1.4eV2), tip voltage in a concave manner because of this increase
notonly is the lineshape reproduced,but goodquantita- in LDOS of Si contact. This LDOS corresponds to in-
tive agreement with the experiment is achieved. creased surface Green’s function of Si and hence larger
This transition from a convex lineshape to concave Si self-energy Σ , which results in a higher current. In
Si
lineshape needs further discussion. The physical effect order to adjust for this, we have to use higher tip height
of dephasing is that it broadens the molecular levels. of8.67˚Ainourmodel,afterincludingdephasing,instead
6
of 7.79˚A for coherent transport to get the same current electrostatic contribution with D = 1.4eV2. The onset
level. Since experimentally tip heights in generalremain voltagesformolecules4˚Aand8˚Aawaymatchreasonably
to be unknown, this variation is acceptable. However, well with the experiment and are grouped together, but
relative tip heights are known experimentally. In the set the lineshapes still differ. There is an increasein current
of experiments we consider, these relative heights were at about 0.6V and then current tends to saturate. This
changed35 during experimental data acquisition for the is because contribution of the DB state is small in this
molecules 4˚A and 8˚A away from the DB and we include energyrange. Using a higher D of1.85eV2 for molecules
them in our model34. 4˚Aand8˚Aawaybroadensthemolecularspectraldensity
Using the same D for molecules 4˚A and8˚A awayfrom more and hence reproduces the experimentally observed
the DB, and including U , we obtain the I-V plots lineshapes as shown in Fig. 1. These molecules, being
DB
shown in Fig. 3(b). Although the lineshapes are similar at the end of styrene chain, may have more phonon de-
to the experimentally observed lineshapes, there is still grees of freedom thus resulting in a higher dephasing.
a significant mismatch in the onset voltages between ex- Another possible explanation could be that the dephas-
periment and calculation for molecules 4˚A and 8˚A away. ing processes inside the Si contact broaden the LDOS
Experimentally,theironsetvoltagesaregroupedtogether contribution of the midgap state. Further experimental
and are much smaller than the calculated ones. This is and theoretical work needs to be carried out to estab-
expected since the valence band edge corresponds to a lish a detailed understanding of the dephasing mecha-
tip voltage of about 1.1V and hence very small current nism. For example, conducting temperature dependent
shouldbeexpectedfortipvoltagesbelow1.1V.However, transport experiments would sharpen the spectroscopic
as can be seen in Fig. 3(b), experimentally conduction features with decreasing temperature, since D ∝ T for
starts from about 0.5V. We interpret this disagreement ~ω ≪ kBT. Apart form this, using different molecules
betweenexperimentandcalculationtobeinducedbythe with varying HOMO levels may give an insight into the
DB. Besides contributing electrostatically,the DB intro- electronic contribution.
duces a near-midgap state in the LDOS of Si atoms be-
Sincewearecalculatingtransportpropertiesofaniso-
neath the styrene chain extending up to be about 10˚A.
lated styrene molecule and comparing with the styrene
ThecalculatedLDOSforSiatoms4˚Aand8˚Aawayfrom
molecules embedded in a chain, the question arises if we
theDBisshowninFig. 4. Anear-midgapstateisclearly
are missing something. As far as one can obtain atomic
visible inside the band gap which is responsible for the
resolution with the tip which means that there is one
early onset of conduction at about 0.5V of tip voltage.
apex atom and the tip is above a styrene molecule, the
The local DOS contribution of the DB state exponen-
conduction from the tip to other styrene molecules in-
tially decays and is nearly absent for a styrene molecule
side the chain is expected to be small. Because styrene
about 12˚A away. molecules are about 4˚A away and if the tip is about
Inourtransportmodel,theDBistakentobefullyoc- 8˚A above the styrene molecule, the distance of the tip
cupiedunderequilibriumandnon-equilibriumconditions atomfromthenextstyrenemoleculewouldbeabout9˚A.
through inelastic processes inside the Si contact. This is Thisshouldresultinanorderofmagnitudelowercurrent
avalidassumptionsincetheenergeticlocationoftheDB through the next styrene molecule. Therefore, although
state is well below the chemical potential. Furthermore, the conduction along the styrene chain may be notice-
the electronic structure calculations are for intrinsic Si, able as discussed in Ref.3, since the tip is placed above
where the effect of dopants and charged DB is ignored a styrene molecule, the lowest conduction path is still
for simplicity, otherwise the calculations become com- through this particular styrene molecule and hence con-
putationally prohibitive. The effect of doping, however, ductionthroughtheneighboringstyrenemoleculeswould
is electrostatically included in our transport calculations still be small. However, if the tip is placed between two
by adjusting the equilibrium Si chemical potential. Be- styrene molecule [a case not discussed in this paper],
sides this, treating the DB state as charged is expected one has to consider transport though both the styrene
tocauseashiftinitsenergeticpositionwithinbandgap. molecules as well as tunneling between them. Since in
Since these states are thermally broadened on the order ourcase,the neighboringstyrenemolecules areexpected
of 0.5eV or more42 at room temperature and that the to remain in equilibrium, the effect of self-consistent po-
DB state is close to midgap, the results presented are tentialvariationintheneighboringstyrenemoleculescan
expected to be comparatively insensitive to this shift. be ignored as well. It should be noted that our case is
In Fig. 5(a), the bias dependent calculated transmis- different from that of a self-assembled monolayer device
sion T(E,V) through molecules 4˚A, 8˚A and 12˚A away contacted by a flat contact, because in this case all the
from the DB is shown. For molecules 4˚A and 8˚A away, molecules are expected to conduct and hence a molecule
there is finite conductioninside the bandgapdue to this would be affected by the self-consistent potential of the
DB state, which is absent for the molecule 12˚A away. neighboring molecules. The self-consistent potential of
For the molecule 4˚A away, at higher tip voltages, the the styrene molecule through which the conduction is
level below the HOMO level i.e. HOMO-1 level, also occurring could affect the neighboring styrene molecule
starts conducting. Fig. 5(b) shows the corresponding I- electrostatics and in return the perturbed neighboring
V characteristics after including the DB’s electronic and molecules could affect the self-consistentpotential of the
7
conducting molecule itself. Since, tip is far from the IV. CONCLUSIONS
molecule and self-consistent potential is small [although
not negligible], this effect is expected to be small. We have studied occupied level conduction through a
We also ignore the tilt angle of the styrene molecule styrene molecule in the vicinity of a negatively charged
with respectto the Si substrate as a function of distance DB on a n++ H:Si(001)-(2×1) surface. We put for-
from the dangling bond that may be present in reality. ward that the DB not only affect conduction through
It has been shown previously that the tilt angle for a styrene electrostatically within approximately 100˚A but
styrene chain in the absence of the dangling bond as a also electronically up to 10˚A from the DB by introduc-
function of distance from the end of the styrene chain ing a near-midgap state in the LDOS of neighboring Si
may lead to significant changes in the current flowing atoms. Dephasing is further expected to play a signifi-
through the styrene chain and hence the observed STM cant role in these experiments.
images. Thisendeffecthasbeenobservedexperimentally
for low bias and qualitatively reproduced theoretically
in Ref.3. This end effect vanishes at higher bias and is V. APPENDIX
still not well understood. As shown experimentally in
Ref.9, in the presence of a charged dangling bond at the In this section we show the derivation of Eq. 2. The
end of the styrene chain, this end effect is not present. scattering inflow function (Σin), outflow function (Σout)
s s
Therefore, assuming that the tilt angle of the molecules and broadening function (Γ ) are defined as19:
s
near the end of the chain does not change seem to be
a good approximation. However, a detailed quantitative
∞ d(~ω)
study is needed. It would also be interesting to analyze Σin,out(E)= Dem,ab(~ω)SGn,p(E+~ω)S+Dab,em(~ω)SG
how the low lying phonon spectrum gets modified for a s Z0 2π
styrene chain on Si surface in the presence of a dangling
bond, whereas previously phonon spectrum of a single
molecule on a substrate has been discussed11,12. The Γs(E)=Σisn+Σosut
inter-molecular interactions are expected to give rise to
new peaks in the phonon spectrum. ∞ d(~ω)
= Dem(~ω)S[Gn(E+~ω)+Gp(E−~ω)]S+Dab(~ω)S[Gn(E
Apart from this, there is a possibility that the neigh- Z 2π
0
boring styrene molecules may be electronically affecting
eachother. Althoughthestyrenemoleculesarenotchem- where Dem(~ω) = (N + 1)D (~ω) and Dab(~ω) =
o
ically bonded, there still may be some effect of broad- N D (~ω) are emission and absorption dephasing func-
o
ening. In particular, this effect has been theoretically tions respectively and are related by Dab/Dem =
addressed in Ref.3 where they conclude that it would exp(−~ω/k T). Nistheequilibriumnumberofphonons
B
be higher for unoccupied states than occupied states. givenbyBose-Einsteinstatisticsas1/[exp(~ω/k T)−1].
B
This conclusion is consistent with Ref.43, where based For ~ω ≪ k T, N +1 ≈ N ≈ k T/~ω by keeping first
B B
on DFT calculations, it has been reported that for oc- term in the Taylor series expansion of exp(~ω/k T) ≈
B
cupied states upto 80% of the wave-function is localized 1+~ω/k T, which leads to,
B
on the aromatic ring of the styrene molecule. Further-
more, the unoccupied states are also analyzed theoreti- Γ (E)= ∞ d(~ω)[Dem(~ω)+Dab(~ω)]SA(E)S
callyinRefs.44,45 reachingthesameconclusion. Itmeans s Z 2π
0
that hybridization along the chain for occupied state is
small and hence broadening caused by it is expected to and
be small. Another calculation in Ref.9 shows similar be-
k T
havior with additional information that for the energy Dem(~ω)≈Dab(~ω)=N Do(~ω)≈ ~Bω Do(~ω)
range correponding to tip voltages less than about +2V
[the voltage range discussed in this paper], the coupling Substituting these results in the above Eq. gives Eq. 2:
between the styrene molecules is small and hence they
attributetheexperimentalobservationoftheslopeeffect Γ (E)≈T ∞ d(~ω)2kBDo(~ω)SA(E)S
to this localizedchargeonstyrene moleculesin this volt- s Z 2π ~ω
0
age range. However, for larger energy range and for tip
D
voltagesgreaterthanabout+2V[acasenotdiscussedin | {z }
this paper],the spectraldensities onneighboringstyrene The presence of low lying phonon modes depends on
molecules start overlaping and charge density becomes many details (type of molecule, surface, bias voltage,
delocalized and hence slope effect vanishes. Since in our etc). This implies that not only the energy (~ω) of the
study, we are calculating transport properties for occu- phonon modes would change under different conditions,
pied states in 0-2V tip voltage range, this effect is ex- butalsotheassociateddephasingfunctionsD . Weleave
o
pected to be small in our voltage range of interest and thedetailedstudyofthesephononmodesforthestyrene
hence is not included in our calculations. chain on Si surface in the presence of a dangling bond
8
for future work and in this study, treat this effect in an acknowledge F. Zahid and T. Raza for Huckel-IV 3.017
averagemannerbyusingthe dephasingstrengthDasan codes. We also thank A. W. Ghosh and G.-C. Liang
adjusting parameter. for useful discussions. This work was supported by the
We acknowledge fruitful discussions with S. Datta, P. NASA Institute for NanoelectronicsandComputing and
G. Piva and R. A. Wolkow and thank the latter two for ARO-DURINT. Computational facilities were provided
sharingtheirexperimentaldatainelectronicformat. We bytheNSFNetworkforComputationalNanotechnology.
1 R.J.Hamers,R.M.TrompandJ.E.Demuth,Phys.Rev. 26 S. Watanabe, Y. A. Ono, T. Hashizume and Y. Wada,
B 34, 5343 (1986). Phys. Rev.B 54, R17308 (1996).
2 R. Wolkow and Ph. Avouris, Phys. Rev. Lett. 60, 1049 27 R. Dennington II, T. Keith, J. Millam, K. Eppinnett,
(1988). W. L. Hovell, and R. Gilliland, GaussView, Version 3.0
3 G. Kirczenow, P. G. Piva and R. A. Wolkow, Phys. Rev. (Semichem, Inc., ShawneeMission, KS,2003).
B 72, 245306 (2005). 28 M. P. L. Sancho, J. M. L. Sancho and J. Rubio, J. Phys.
4 G.-C.LiangandA.W.Ghosh,Phys.Rev.Lett.95,076403 F: Met. Phys. 14, 1205 (1984).
(2005) and references there-in. 29 Original ζ=2.341, Modified ζ=1.10427.
5 T.Rakshit,G.-C.Liang,A.W.GhoshandS.Datta,Nano. 30 J.Cerda,A.Yoon,M.A.VanHove,P.Sautet,M.Salmeron
Lett. 4, 1803 (2004). and G. A.Somorjai, Phys.Rev.B 56, 15900 (1997).
6 N. P. Guisinger, N. L. Yolder and M. C. Hersam, PNAS 31 L.Olesen,M.Brandbyge,M.R.Sorensen,K.W.Jacobsen,
102, 8828 (2005). E. Laegsgaard, I. Stensgaard and F. Besenbacher, Phys.
7 W. Lu, V. Meunier and J. Bernholc, Phys. Rev. Lett. 95, Rev.Lett. 76, 1485 (1996).
206805 (2005). 32 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuse-
8 J.L.PittersandR.A.Wolkow,Nano.Lett.6,390(2006). ria,M.A.Robb,J.R.Cheeseman,J.A.Montgomery,Jr.,
9 P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S.
Rezeq, S. Dogel, W. A. Hofer and R. A. Wolkow, Nature S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi,
435, 658 (2005). G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M.
10 P. G. Piva and R. A. Wolkow (private communication). Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M.
Experimentally, there is an uncertainty of ± half a dimer Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M.
spacingtodeterminetheDBcentre.Therefore,4˚Aand8˚A Klene, X.Li, J. E. Knox,H.P. Hratchian, J. B. Cross, V.
curves are more like 4±2˚A and 8±2˚A. Bakken,C.Adamo,J.Jaramillo,R.Gomperts,R.E.Strat-
11 N. Sergueev, D. Roubtsov and H. Guo, Phys. Rev. Lett. mann, O. Yazyev,A. J. Austin, R.Cammi, C. Pomelli, J.
95, 146803 (2005). W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth,
12 Y.-C. Chen, M. Zwolak and M. D. Ventra, Nano. Lett. 5, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dap-
621 (2005). prich,A.D.Daniels,M.C.Strain,O.Farkas,D.K.Malick,
13 J. G. Kushmerick, J. Lazorcik, C. H. Patterson, R. A.D.Rabuck,K.Raghavachari,J.B.Foresman,J.V.Or-
Shashidhar, D. S. Seferosand G. C. Bazan, Nano. Lett. tiz,Q.Cui,A.G.Baboul, S.Clifford, J. Cioslowski, B.B.
4, 639 (2004). Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,
14 H.S.Kato,J.Noh,M.HaraandM.Kawai,J.Phys.Chem. R.L.Martin, D.J.Fox,T.Keith,M.A.Al-Laham,C.Y.
B 106, 9655 (2002). Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill,
15 H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and
Alivisatos, P.L. McEuen, Nature 407, 57 (2000). J. A. Pople, Gaussian 03, Revision B.03 (Gaussian, Inc.,
16 A. Devosand M. Lannoo, Phys. Rev.B 58, 8236 (1998). Wallingford CT, 2004).
17 F. Zahid, M. Paulsson, E. Polizzi, A. W. Ghosh, L. Sid- 33 R. M. Martin, Electronic Structure: Basic Theory and
diqui, and S. Datta, J. Chem. Phys. 123, 064707 (2005). Practical Methods (Cambridge University Press, Cam-
18 S. Datta, Quantum Transport: Atom to Transistor (Cam- bridge, UK,2004).
bridge University Press, Cambridge, UK,2005). 34 8.79˚A, 8.73˚A and 8.67˚A for molecules 4˚A, 8˚A and 12˚A
19 G. D. Mahan, Phys. Rep.145, 251 (1987). away respectively unless otherwise stated.
20 F. Zahid, M. Paulsson and S. Datta, ”Electrical Conduc- 35 P. G. Piva and R. A. Wolkow (private communication).
tionthroughMolecules”,inAdvanced Semiconductors and DuringtheconstantcurrentSTM(not shown),theheight
OrganicNano-techniques (III),editedbyH.Morkoc(Aca- profileof thestyrenechain decreased 1.2±0.4˚A across its
demic Press, San Diego, CA, 2003). 60˚A length.Asthis constant current height contour(with
21 M. Paulsson, T. Frederiksen and M. Brandbyge, Nano the current feedback loop ’ON’) determined the start-
Lett. 6, 258 (2006). ing tip-sample separation prior to acquiring individual I-
22 J. Cerda and F. Soria, Phys. Rev.B 61, 7965 (2000). V curves (with current feedback loop ’OFF’), I-V curves
23 J. Howell, A. Rossi, D. Wallace, K. Haraki and R. Hoff- shown in Fig. 1, 3, and 5 in the present work and in Fig.
man, FORTICON8, QCPE Program 545, Department of 5(a)inRef.9wereacquiredwithdecreasingtip-samplesep-
Chemistry, Cornell University,Ithaca, NY 14853. aration as thedistance from theDB increased.
24 H. Raza, Phys. Rev.B 76, 045308 (2007). 36 COMSOL is a trademark of COMSOL AB (comsol.com).
25 D. Kienle, K. H. Bevan, G.-C. Liang, L. Siddiqui, J. I. 37 DB is approximated by a prolate spheroid with polar and
Cerda and A. W. Ghosh, J. Appl. Phys. 100, 043715 equatorial radius given by 1.5˚A and 1˚A respectively, esti-
(2006). mated with a B3PW91/6-311g* calculation. The relative
9
dielectric constant for the dangling bond is taken as 1. 42 T. Hitosugi, T. Hashizume, S.Heike,Y. Wada,S. Watan-
38 Technology Modeling Associates, Inc.: Sunnyvale, CA, abe, T. Hasegawa, K. Kitazawa, Appl. Phys. A 66, S695
TMA medici, two-dimensional device simulation program, (1998).
version 4.0 users manual (1997). 43 W. A. Hofer, A. J. Fisher, G. P. Lopinski and R. A.
39 S.M.Sze,PhysicsofSemiconductorDevicesCh.1 (Wiley- Wolkow, Chem. Phys.Lett. 365, 129 (2002).
Interscience, NY,1981). 44 G. P. Lopinski, D. D. M. Wayner and R. A. Wolkow, Na-
40 R. M. Feenstraand J. A.Stroscio, J. Vac. Sci. Technol. B ture406, 48 (2000).
5, 923 (1987). 45 J.-H. Cho, D.-H. Oh and L. Kleinman, Phys. Rev. B 65,
41 J. A. Pople and G. A. Segal, J. Chem. Phys. 44, 3289 081310(R) (2002).
(1966).