Local spectroscopy and atomic imaging of tunneling current, forces and dissipation on graphite

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by  S. Hembacher

Local spectroscopy and atomic imaging of tunneling current, forces and dissipation on
graphite
∗
S. Hembacher, F. J. Giessibl, and J. Mannhart
Universit¨at Augsburg, Institute of Physics, Electronic Correlations and Magnetism,
Experimentalphysik VI, Universit¨atsstrasse 1, D-86135 Augsburg, Germany.
5
C. F. Quate
0
0 Stanford University, Ginzton Lab, Stanford CA 94305-4085, USA.
2 (Dated: accepted at PRL)

n Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive
a forcesmeasuredinatomic forcemicroscopy (AFM)aredirectlyrelated. Atomicimagesobtained in
J an attractive AFM mode should therefore be redundant because they should be similar to STM.

4 Here, we show that while the distance dependence of current and force is similar for graphite,
constant-heightAFM-andSTMimagesdiffersubstantiallydependingondistanceandbiasvoltage.

] We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at
i
c high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as
s sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic
-
friction.
l
r
t
m
The capability of scanning tunneling microscopy
.
t (STM) [1] and atomic force microscopy (AFM) [2] to
a
m resolve single atoms in real space makes them powerful
tools for surface science and nanoscience. When operat-
-
d ingAFMintherepulsivemode,protrusionsintheimages
n simply relate to the atoms because of Pauli’s exclusion
o law. In contrast, the interpretation of STM images is
c
more complicated. The Tersoff-Hamann approximation
[
[3], valid for tips in ans-state,interprets STM images as FIG. 1: (color) Crystal structure of graphite. The unit cell

1 a map of the charge density of the sample at the Fermi (green)consistsoftwolayerswithinequivalentbasisatomsα
v (white) and β (red). The α-atoms have direct neighbors in
energy. Depending on the state of the tip, atoms can ei-
5 the adjacent atomic layers as indicated by the dotted lines,
ther be recordedasprotrusionsor holes,andtip changes
4 theβ-atomsareaboveahollowsite(h). (a)Perspectiveview,
0 can reverse the atomic contrast [4, 5]. Theoretical pre- showingthreelayersformedbyhexagonalrings. (b)Topview
1 dictions regarding the relation of forces and tunneling with surface unit vectors u and v. The line Λ = −v +u
0 currents I state that tunneling currents and attractive connects theα, β and h lattice points, spaced by 142pm.
5
forces are directly related, thus AFM would not pro-
0
vide any new physical insights over STM. Chen [5] has
/
t concentrated at the β sites, and only these atoms are
a foundthatthesquareoftheattractiveenergybetweentip
‘seen’ by STM at low-bias voltages. The state-of-the-
m and sample should be proportionalto I with experimen-
artmethod for atomic resolutionforce microscopyis fre-
tal evidence in [6]. Hofer and Fisher [7] suggested that
-
quency modulation AFM (FMAFM) [11], where the fre-
d the interaction energy and I should be directly propor-
n quencyshift∆f ofanoscillatingcantileverwithstiffness
tional, experimentally found in [8, 9]. In this Letter, we
o k, eigenfrequency f and oscillation amplitude A is used
investigate the experimental relationships between tun- 0
c as the imaging signal [12, 13]. The bonding energy be-
: neling currents and conservative as well as dissipative
v tween two adjacent graphite layers at distance σ can be
forces for graphite probed with a W tip by performing
i approximated by a Morse potential
X local spectroscopy on specific lattice sites. While force
r spectroscopy on specific lattice sites [10] and combined V =E [ 2exp−κ(z−σ)+exp−2κ(z−σ)] (1)
a M bond −
force and tunneling spectroscopy on unspecific sample
with E 23meV and κ 8nm−1 per atom
positions [8, 9] have been performed before, the mea- bond ≈ − ≈
pair [14]. The ‘normalized frequency shift’ γ(x,y,z) =
surements reported here encompass site-specific spectra
kA3/2∆f(x,y,z)/f connectsthephysicalobservable∆f
of currents and forces, supplemented by simultaneous 0
and the underlying forces F with range λ, where γ
constant-heightmeasurementsofcurrentsandforcesthat ts ≈
0.4F λ0.5 (see Eqs. 35-41 in [13]). For covalent bonds,
allow a precise assessment of the validity of the theories ts
thetypicalbondingstrengthisontheorderof-1nNwith
regarding currents and forces in scanning probe experi-
λ 1˚A,resultinginγ 4fN√m,whereanegativesign
ments. ≈ ≈−
indicates attractive interaction. For graphite, the inter-
In graphite (see Fig. 1), the electrons at E are layer bonds are much weaker and the potential of Eq. 1
F
2
FIG.2: (color)Simultaneousrecordsofa)tunnelingcurrent,
b) frequency shift and c) damping. Image size 3nm × 1nm,
tip bias 100mV,scanning speed 40nm/s.
results in γ = 0.1fN√m. The interaction of a tip
min
−
atomwithagraphitesurfacemaybestrongerthanthein-
terlayerbondsbutshouldstillresultin γ <1fN√m,
min
−
posing a challenge for AFM imaging. True atomic reso-
lutionongraphitebyAFMhassofaronlybeenobtained
atlowtemperatures,firstbyAllersetal. [15]usinglarge-
amplitude FM-AFM with ∆f = 63Hz, f = 160kHz,
0
−
k = 35N/m and A = 8.8nm, thus γ = 11.4fN√m. In
−
spectroscopic measurements by the same group, a min-
imum of γ 60 fN√m has been observed (Fig. 1b
≈ −
in [16]). Because this value is more than two orders of
magnitudegreaterthantheestimateabove,itisexpected
thatlong-rangeforceshavecausedalargecontributionin FIG. 3: (color) Experimental spectra of I, γ and ∆Ets as a
thatexperiment. Here,weuseFMAFMwithsub-nmam- function of distance for a tip bias of 160mV. The insets are
plitudeswhichgreatlyreducestheinfluenceoflong-range logarithmic plots of I, −γ and ∆Ets. The grey curves are
forces[13]andenablessimultaneousSTMoperation[17]. taken at position ‘1’ in Fig. 4a), the black curvesat position
‘2’ and thered curvesat position ‘3’. Theinsets areviews of
We use a low-temperature STM/AFM operating at
I(z), γ(z) and ∆Ets(z) for −0.1nm< z < 0 on logarithmic
4.9K in ultrahigh vacuum [18]. The microscope uses
scales.
a qPlus sensor [19] for simultaneous STM/AFM oper-
ation (k = 1800N/m, f = 11851.75Hz, quality factor
0
Q = 20000). All data (spectroscopy and images) are in the log-scale insets. The correspondence between ex-
recorded at A = 0.25nm. The tip is prepared by dc perimental images and the lattice sites is established by
etching (3V) of a polycrystalline tungsten wire. The the analysis below. The current increases exponentially
frequency shift is measured with a commercial phase- in the distance regime from z = 0 to z = 100pm, fol-
−
locked-loopdetector(EasyPLLbyNanosurfAG,Liestal, lowed by a step-like increase for smaller distances. We
Switzerland). The instrument is thermally well con- assumethat the tip is essentially incontactto the upper
nectedto a liquidHe bathcryostatat4.2K,leadingto a graphite layer for distances smaller than -100pm. Given
drift rate of 20pm/hour. Non-conservative tip-sample thattheelectricalconductivityofgraphiteissmallatlow
≈
interactions lead to damping, and the energy ∆Ets that temperatures and small in z-direction, we conclude that
has to be provided for each oscillation cycle to keep A thestep-likeincreaseincurrentfordistancessmallerthan
constant is recorded simultaneously with I and ∆f. -100pm is caused by an increasing number of graphite
To check if the three data channels I, ∆f and ∆E layers becoming available for charge transport. The cur-
ts
are produced by the same tip atom, we have scanned an rent spectra in Fig. 3a) are maximal for most distances
area that contains a step edge (Fig. 2). The step edge on site ‘3’. Because site ‘3’ is a current maximum, we
appears at the same position in all three data channels, identify it as a β position.
thus the signals are produced by the same tip atom. The normalized frequency γ shift decreases down to
The physics of the interaction is best explored by a distance of 170pm, followed by a slight increase
≈ −
performing I, γ and ∆E -spectroscopy at the high- down to 550pm and a sharper increase for even
ts
≈ −
symmetry lattice sites. Figure 3 shows I(z), γ(z) and smaller distances. For z < 800pm, γ remains con-
−
∆E (z)takenat the α-, β- andh-lattice sites. All three stant because the cantilever remains in contact to the
ts
signals initially increase roughly exponentially, as shown sampleduring the entire oscillationcycle. Inthe z-range
3
from 0 to -100pm where the short-rangechemical bond-
ing forces start to emerge, the magnitude of γ increases
exponentially (see inset). It is believed, that the short-
range forces between AFM tips and graphite originate
from van-der-Waals forces [16] with their typical 1/z7-
distance dependence. The experimental data shows that
whenthe interatomicdistanceapproachesthe atomicdi-
ameters, an exponential force dependence prevails.
The damping signal initially also increases exponen-
tially for z < 0, reaches a plateau for z < 170pm,
−
decays to zero from z < 600pm and remains zero for
−
z < 800pm because the cantilever remains in contact
−
for the whole oscillation cycle. This points to a damp-
ing mechanism as described by Prandtl [20] and Tom-
linson [21], where the energy loss is caused by a pluck-
ing action of the atoms on each other. The energy loss
per cycle is simply related to the maximal attractive
force F andthe stiffness of the sample k with
tsmin sample
∆E =F2 /(2k ) [22].
ts tsmin sample
The insets are logarithmic plots of I(z), γ(z) and
∆E (z) for 0.1nm< z < 0, showing an almost expo-
ts
−
nential distance dependence in that range. For the tun-
neling current, we find a decay constant κ = 13nm−1
I
at the β-site and κ = 15nm−1 at sites ‘1’and ‘2’, lead-
I
ing to an apparent barrier height of 2eV. The decay
≈
constant of γ and thus the interaction potential (Eq. 39
in [13]) is κ =12nm−1 at the β-site and κ =16nm−1
γ γ
atsites‘1’and‘2’. Thedecayconstantsforκ andκ are
I γ
equal within the measurement accuracy,thus the theory
by Hofer and Fisher [7] appears to hold for the interac-
tionofWwithgraphite. Thedampingsignaldecayswith
κ = 20nm−1 at the β-site and κ = 30nm−1 at
∆Ets ∆Ets
sites ‘1’and ‘2’ as expected from an energy loss propor-
tional to the square of the attractive force.
The normalized frequency spectra shown in Fig. 3b)
are rather similar, expect for the grey curve recorded
at site ‘1’. In the distance regime from 600pm to
−
800pm,thegreycurveisshiftedby 40pm. IftheC
− ≈−
sampleatomsandtheWtipatomareassumedtobehard
spheres with a diameter of 142pm and 273pm respec-
FIG. 4: (color) Constant-height measurements of I, γ and
tively, the W tip atom could protrude 56pm deeper on
∆Ets in attractive and repulsive distance regimes for a tip
topofthe hollowsites thanatα orβ sites. We therefore bias of 160mV (a-c) and -60mV (d-f). The hexagons show
conclude that position ‘1’ (grey curves)corresponds to a the proposed positions of α (white) and β (red) atoms. The
hollowsite(hinFig. 1(b)). Interestingly,Fig. 3c)shows brightnessisproportional to|I|,γ and∆Ets. Theinset inc)
that the dissipation is significantly larger on the hollow left shows a higher harmonic image [23], indicating that the
tipstateisnotperfectlysymmetricwithrespecttothez-axis.
site than on top of α or β sites. The three data chan-
nels were acquired simultaneously and the range from
z = 1.7nm to 0.6nmandbackto 1.7nm wasramped
− −
within 60s. The sequence of the three sites was scanned were supplemented by constant height scans at various
three times, so a totalof6 spectra wascollectedfor each z-positions shown in Fig. 4. Figures 4a)-c) show I, γ
α-, β- and h-site. While the drift rate of our instrument and ∆E at a tip bias of 160mV in the fully attrac-
ts
is very low, piezo creep caused z-offsets of consecutive tive mode at z 100pm (a), in a weakly repulsive
≈ −
scans. These offsets were calibrated by comparison with regime at z 350pm (b) and a fully repulsive mode
≈ −
constant-height scans which provide precise cross refer- at z 750pm (c). If the attractive interaction be-
≈ −
ences for I, γ and ∆E at the α-, β- and h-sites for a tweentipandsamplewasonlymediatedbytheelectronic
ts
given z-value. The local spectra at high-symmetry sites states that contribute to the tunneling current, the I-
4
and γ-images in Fig. 4a) should be exactly inverse. Evi- images [27].
dently, this is not the case. We therefore conclude, that This work is supported by the Bundesministerium fu¨r
electronic states that do not contribute to the tunnel- Bildung und Forschung (project EKM13N6918). We
ing current may contribute to attractive interaction. In thank M. Herz for discussions and K. Wiedenmann and
the repulsive regime shown in Fig. 4c), the repulsion H. Bielefeldt for help in the construction of the micro-
is strongest above the α sites, almost as strong on the scope.
β sites, and weakest on hollow sites, in agreement with
with Fig. 3a) and the Pauli exclusion law. The current
has a local maximum on top of the β sites, and ∆E
ts
hasapronouncedmaximumatthe hollowsites. Because
∗
Electronic address: [email protected]
of the long time scales involved in damping measure-
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