# Haptic Sensation-Based Scanning Probe Microscopy: Exploring Perceived Forces
for Optimal Intuition-Driven Control

M. Freeman  R. Applestone  W. Behn  V. Brar<EMAIL_ADDRESS>Department of
Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, United
States

(August 30, 2024)

###### Abstract

We demonstrate a cryogenic scanning probe microscope (SPM) that has been
modified to be controlled with a haptic device, such that the operator can
‘feel’ the surface of a sample under investigation. This system allows for
direct tactile sensation of the atoms in and on top of a crystal, and allows
the operator to perceive, by using different SPM modalities, sensations that
are representative of the relevant atomic forces and tunneling processes
controlling the SPM. In particular, we operate the microscope in modes of (1)
conventional STM feedback, (2) energy-dependent electron density imaging, (3)
q-plus AFM frequency shift based force sensing, and (4) atomic
manipulation/sliding. We also use software to modify the haptic feedback
sensation to mimic different interatomic forces, including covalent bonding,
Coulomb repulsion, Van der Waals repulsion and a full Lennard-Jones potential.
This manner of SPM control creates new opportunities for human-based intuition
scanning, and it also acts as a novel educational tool to aid in understanding
materials at an atomic level.

††preprint: AIP/123-QED

##  I Introduction

Scanning probe microscopy (SPM), including scanning tunneling microscopy (STM)
and atomic force microscopy (AFM), is a powerful imaging technique that can be
used to visualize the atomic structure of materials and the wavefunctions of
electrons, as well as to manipulate individual atoms and molecules on the
surfaces of materials.Bian  _et al._ (2021); Binnig and Rohrer (1987); Chen
(2021) These imaging methods work by using piezoelectric motors with sub-Å
resolution to manipulate the position of an atomically sharp tip across a
smooth material surface, where tip-surface contact is maintained using a
feedback loop based on tunneling current, oscillation frequency shifting, or
other measurable parameters that change with tip-sample separation. Under
standard operating conditions, the tip is raster scanned slowly across a
surface and a full image is developed over the course of minutes to hours,
depending on the specific imaging modality. More rapid, but less visual,
measurements can be performed by continually scanning across the same path on
the sample as some parameter is varied, or the tip can be simply parked over a
specific spot of a surface to monitor changes as they happen in real time.
During manipulation procedures, however, the tip is carefully lowered into the
surface to either change its surface structure, or to pick up atoms/molecules
or trap them beneath it.Stroscio and Eigler (1991); Foster, Frommer, and
Arnett (1988) Subsequent movement of atoms/molecules is performed by dragging
them along the surface while moving the tip along a fixed path.Lyo and Avouris
(1991); Eigler, Lutz, and Rudge (1991); Ternes  _et al._ (2008)

In all of the above operational modes, live information about the tip height
and feedback parameters can be monitored by the operator by inputting their
values into an oscilloscope. This allows for instantaneous changes in the tip
or sample to be observed, and it also permits for precise placement of the tip
relative to some surface feature by ‘blindly’ moving the tip in sub-Å steps
and monitoring — for example — the tip height as it is altered by individual
surface atoms. This later capability allows for manipulation to be performed
without first obtaining sub-Å resolved images, which would be prohibitively
time consuming. During manipulation itself, a live feed of the scanning
parameters is necessary for assessing if an atom/molecule is on the tip —
which appears as a change in height — or if an atom/molecule is following the
tip — which can be known by observing the current noise; while an oscilloscope
can be used for such observations, it is more common to convert the tunneling
parameters into an audible sound with, for example, the tip height and
tunneling current represented by a particular pitch.Weiss and Stranick (2008);
Stroscio and Celotta (2004) This approach is often more intuitive and, in some
cases, can provide a clearer picture of the tip and sample conditions.

Recently, commercial haptic feedback technologies have proliferated as a
effective way in which to interact with a virtual space. Haptic feedback arms
allow a user to move a cursor in a simulated 3D space, where contact with a
virtual object results in a force imparted on the hand of the operator. These
devices are used extensively as tools for designing 3D virtual objects,
performing robot-assisted surgeries, training for medical and dental
operations, controlling robot arms in dangerous environments, and other
applications.Sheridan (1992) They can be interfaced with any tool that
exhibits motor-controlled $xyz$ motion and provides some positional feedback.

Shortly after the innovation of piezo-controlled SPMs, efforts were made by
several groups to interface them with haptic control arms as a way to ‘feel’
the surfaces being probed.Hatamura and Morishita (1990); Hollis, Salcudean,
and Abraham (1990); Taylor  _et al._ (1997); Falvo  _et al._ (1998); Sitti and
Hashimoto (1998) Those experiments, which included both STMs and AFMs, allowed
users to feel coarse features on the surfaces of materials, including
protruding quantum dots and step edges, with characteristic heights as small
as 2nm. Subsequent demonstrations showed that haptic-controlled AFMs could be
used to sense and manipulate carbon nanotubes and large biomolecules, such as
viruses, fibrin, and DNA.Guthold  _et al._ (1999); Reiner (1999); Guthold  _et
al._ (2000); Rubio-Sierra  _et al._ (2003); Sitti and Hashimoto (2003); Jobin
_et al._ (2005); Falvo  _et al._ (1998) These experiments allowed the sensing
of both lateral and vertical tip-sample forces as small as 1nN. Guthold  _et
al._ (2000) Later implementations also showed how haptic-controlled AFMs could
be used to precisely position micron-sized beads,Lim  _et al._ (2009); Xie,
Haliyo, and Régnier (2009); Hou  _et al._ (2013); Schmid  _et al._ (2012)
sense semiconductor devices,Lim  _et al._ (2009) and sense the distance
dependence of AFM tip-surface interactions. These later experiments were
particularly useful for instructional purposes as the correlation between tip-
surface and pen-hand interactions made it easier for students to understand
forces between material interfaces. Marchi  _et al._ (2005); Tse  _et al._
(2010); Bolopion  _et al._ (2013); Millet  _et al._ (2013)

Most early haptic-SPM experiments were performed in ambient conditions, where
it is difficult to maintain consistent tip and sample conditions, and where
surface adhesion forces introduced from interfacial molecules can be
significant. Haptic experiments using optical tweezers provided a means of
bypassing those challenges, with demonstrations showing reliable manipulation
of trapped beads near and around barriers, and force sensing down to
1pN.Pacoret  _et al._ (2009); Pacoret, Bergander, and Régnier (2010); Pacoret
and Regnier (2013) More recently, ultra-high vacuum (UHV) STM measurements —
where surface impurities were eliminated — that included haptic arm control
were performed on atomically smooth Au(111) surfaces with adsorbed C60
molecules.Perdigão and Saywell (2011) That work demonstrated that when STM
feedback is controlled with tunneling current rather than tip-sample forces,
the tunneling current could reliably be used to set the haptic arm force,
allowing the operator to feel atomic step edges, and to even manipulate C60
molecules. Other UHV experiments used camera tracking of hand movement to
control an STM/AFM tip to manipulate PTCDA molecules on an Ag(111) surface.
Green  _et al._ (2014); Leinen  _et al._ (2016) Those experiments lacked
force-feedback, but they demonstrated the effectiveness of hand-control in
choosing optimal SPM tip trajectories.

Here we expand on those previous works by integrating a haptic feedback arm
with a cryogenic, UHV SPM equipped with a quartz tuning fork sensor that can
be used for both operation as a frequency modulated AFM and STM. The ultra low
temperature environment of the surface enables highly stable scanning
conditions that we utilize to demonstrate several operational modes, including
the linking of the haptic force to (1) tunneling current, (2) changes in
tuning fork frequency and (3) local electron density. We also explore the use
of different feedback-force (‘feeling’) functions, which create different
tactile sensations that can be used to mimic different atomic forces, and to
optimize the ease of operation. Additionally, we demonstrate the ability to
manipulate the positions of individual CO molecules with atomic resolution,
such that the operator can feel as the molecules skip between atomic lattice
sites.

##  II Methods

Figure 1: The operational setup used for the haptic-SPM controller. The haptic
device, controlled via a dynamic-link library written in C/C++, and the
Nanonis control hardware, controlled via Nanonis’s SPM control software, both
connect to a desktop computer. Both of these interface via a LabVIEW program
on the computer, which handles signal processing and the main GUI. The user
moves the pen, and the xyz-positional data from the haptic device is mapped to
control the xyz-position of the pen. Meanwhile, signals like the tip
z-position, tunneling current, or cantilever frequency shift are converted
into a force, applied to the haptic device, and felt by the user.

###  II.1 Hardware and Software

All measurements were performed in a commercial SPM (CreaTec GmbH) with
Nanonis (SPECS GmbH) electronics and software. The SPM is operated in UHV
conditions at 4.5K using a qPlus quartz tuning fork sensor with a conductive
PtIr wire tip that allows for dual AFM/STM imaging. A Touch X haptic device
(also called a haptic pen) from 3D Systems was used for all experiments. The
device is operated via device drivers, calibration software, and the
OpenHaptics 3.5 application programming interface (API) for the C/C++
languages. It possesses a workspace of 160 W $\times$ 120 H $\times$ 120 D mm,
a maximum force output of 7.9 N, and a positional resolution of 1100 dots per
inch (dpi) — nearly double the resolution of haptic devices used in previous
experiments.Perdigão and Saywell (2011) Such high resolution is ideal for
obtaining smoother-feeling surfaces and forces.

There are three interconnected software components that allow the haptic
device to communicate with the STM/AFM: (1) The Nanonis SPM control system,
which is controlled through a LabVIEW-accessible API, and allows signal values
(e.g., tip positional data, current, and oscillation frequency shift) and
control parameters (e.g., tip position, tip bias) to be both read and
controlled in LabVIEW; (2) a custom dynamic-link library developed using the
OpenHaptics API, and coded in C++, which allows positional and force
parameters to be read and written to the haptic device via LabVIEW; and (3) a
LabVIEW GUI program used to interface the two, processing signals from each
device. The LabVIEW GUI and dynamic link library can be found at
www.github.com/HapticSPM.

The synthesis of these hardware and software components results in the
complete haptic controller, as shown in Fig. 1.

###  II.2 Operational Basics

There are two general modes of operation with which experiments were
performed: read mode and write mode. In read mode, the haptic pen only
controls the tip motion in the horizontal $xy$ plane, while the tip height is
controlled via conventional STM/AFM feedback. The force on the haptic pen is
then determined by reading a signal of interest (e.g., tip z-position, LDOS,
cantilever frequency shift, etc.) while the feedback is on and referencing it
to the z-position of the haptic pen; if the pen travels below a virtual,
scaled version of the sample defined by the signal, it is pushed upwards. For
example, if the feedback-determined tip-height is chosen as the signal, then
the relative value of the actual SPM tip-height and the virtual tip height is
used to set the force on the pen. The ‘feel’ of the sample (i.e., force as a
function of distance) is determined by a function of the form

$f(z_{pen})=\left\\{\begin{array}[]{ll}k\lvert z_{pen}-aS_{fb}\rvert&\quad
z_{pen}\leq aS_{fb}\\\ 0&\quad z_{pen}>aS_{fb}\end{array}\right.,$ (1)

where $S_{fb}$ is the signal of interest with feedback on, $a$ is the gain
setting controlled in LabVIEW, and $z_{pen}$ is the z-position of the haptic
pen in mm. When the haptic pen is held ‘above’ $aS_{fb}$, it experiences no
force, but as the position of the pen hits $aS_{fb}$ and then goes below it,
it experiences a spring force with an adjustable stiffness $k$. It is
important to note, however, that the force-distance relation described in Eq.
1 need not be linear; the overall ‘feeling’ of the sample can be changed by
altering the form of this function as described later in Sec. IV. This mode of
operation is similar to the ‘augmented reality mode’ used in previous haptic-
AFM implementations.Vogl, Ma, and Sitti (2006); Guthold  _et al._ (2000)

In write mode, the haptic pen controls the horizontal xy-position, as well as
the vertical z-position of the tip. The force on the haptic pen is determined
by the function $f(S)$, which is entirely dependent on the signal of interest
$S$ without feedback, with the tip height set by the position of the pen. As
an example, if the tunneling current is chosen as the signal of interest, then
as the pen (and thus, tip) moves downward and approaches the surface, the
tunneling current increases; this current is converted to an upwards force,
which the user interprets as a hard surface.

The force functions discussed above are varied depending on the signal of
interest, and are described explicitly in the next sections.

In normal use, a square region of interest is chosen on the surface of the
sample using the standard Nanonis SPM control software. This region’s location
and size are then used by the haptic device to convert the millimeter-scale
horizontal movement of the pen to the angstrom-scale horizontal movement of
the tip. The workspace of the pen is confined using hard-coded, vertical walls
to a $16$ cm $\times$ $16$ cm horizontal area in the middle of the pen’s range
of motion. This effectively confines the user of the haptic device to the
square region of interest on the sample. The sample surface is often slanted
relative to the axes of movement of the scanning probe, and thus a planing
algorithm must be used to ‘flatten’ the surface, such that the horizontal
movement of the pen is mapped to tip movement along the plane of the surface.
This algorithm is implemented by having the user choose 3 points and fitting a
plane to the force-defining signal at each of those points.

In both modes, it is possible to configure the perceived height of features on
the surface by changing the desired level of positional scaling, which allows
the user to feel differently-sized surface features. Thus, larger surface
features like step-edges and smaller features like individual molecules/atoms
are able to be felt in a more user-friendly way, without sacrificing the
ability to feel only one or the other.

Finally, a drag force was implemented to smoothen the user’s movements in an
attempt to eliminate all but deliberate pen motions. This force was determined
by the function $\mathbf{F}_{drag}=-c\mathbf{v}$, where $\mathbf{v}$ is the
velocity of the haptic device cursor and $c$ is an arbitrary constant. As an
additional safety measure, the maximum speed of the STM/AFM tip could be
configured such that the tip is only allowed to travel at less than a given
speed. Beyond limiting unwanted rapid motions of the STM/AFM and the haptic
device, this feature was found to be essential for fine-grained operations
like molecular manipulation.

##  III Modes of operation

We tested our haptic-SPM controller on an atomically flat Cu(111) surface
cleaned by repeated cycles of sputtering with Ar ions (500 V, 7 $\mu$A) for 10
minutes and annealing around 400 C for ten minutes. The crystal was allowed to
cool after annealing cycles and before each sputtering cycle. After loading
the sample into the SPM, carbon monoxide molecules were deposited on the
sample in situ via a UHV leak valve. The sample was analyzed using a variety
of different haptic-SPM configurations, described below.

###  III.1 STM Topography-Based Force

Figure 2: An example of both ‘STM topography-based’ (top) and ‘STM current-
based’ (bottom) operations. In (a) and (c) the pen position is plotted in
three dimensions alongside the corresponding STM imagery. Linecuts that
compare $z_{stm}$ and $z^{F}_{pen}$ as well as the force on the pen for
topography-based operations are shown in (b). Linecuts comparing the current
vs. pen force as the tip traverses a molecule in current-based mode is shown
in (d)

In this operational mode, the STM feedback controller remains on, adjusting
the z-position of the tip to maintain a constant ‘setpoint’ current. The
haptic controller is operated in read mode, such that the haptic pen controls
only the $xy$-position of the STM tip. The force exerted on the pen is
determined by Eq. 1 with $S_{fb}=z_{stm}$, where $z_{stm}$ is the height of
the tip relative to the plane of best fit in nm. $az_{stm}$ can be understood
as the STM tip height read and projected into the virtual haptic space.

Since the pen can move above $az_{stm}$, its z-position may or may not
correspond to the surface topography. Thus, $z_{pen}^{F}$ is used to
distinguish the case in which the user is applying a constant finite downward
force on the pen and the pen height would closely correspond to the surface
topology.

Fig. 2a shows the three-dimensional path of the haptic device
$z_{pen}^{F}(x_{pen},y_{pen})$ acquired using this mode of operation while
transiting a carbon monoxide (CO) molecule on Cu(111). The data is plotted
alongside the STM surface topography, and Fig. 2b directly compares a linecut
of the STM topography to $z_{pen}^{F}(x_{pen},y_{pen})$, showing good
agreement. This indicates that the haptic pen is able to reliably feel sub-
nanometer features.

There are a noticeable discrepancies between the actual STM topography and the
user-perceived surface, which originate from different sources. First, the STM
topographic data contains a slope that is representative of the actual slope
of the sample, while the path of the haptic pen is flat. This is due to the
slope correction algorithm described in Section II.2. Second, there is a 1 -
20 ms delay between when the STM signal value changes and when the haptic
device writes the corresponding force. This delay is combined with a delay
caused by the reaction time of the user, causing the haptic pen and SPM tip to
be out-of-sync. Third, in order for $z^{F}_{pen}$ to match $z_{STM}$ the user
must maintain a constant force on the pen during the entire movement, and
small deviations are inevitable. Finally, piezo drift differently affects the
$z_{stm}$ and $z^{F}_{pen}$ profiles, since the former is obtained at a
constant scan speed, and the latter’s scan speed is controlled by the user,
and generally non-constant.

###  III.2 STM Current-Based Force

The next method of operation we describe implements a current-based force,
where the STM feedback is turned off and the haptic controller is operated in
write mode, meaning the pen controls the tip position in all dimensions. The
arm produces an upwards force proportional to the tip tunneling current, which
increases with decreasing tip-sample separation. The force function used is

$f(I_{tun})=I_{tun}/I_{set}$ (2)

where $I_{tun}$ is the tunneling current, $I_{set}$ is an arbitrary current
chosen by the user, which the pen tends to maintain during use.

We found setting the tip force directly to the tunneling current created
difficult operating conditions when feeling large features, where small
changes in tip height led to large changes in force that the haptic arm could
not produce at sufficient rates to maintain stable tunneling; it was also
difficult to avoid tip crashes since the maximum force of the haptic pen could
easily be reached with small changes in the tip height. To mitigate these
problems, the vertical z-position of the pen was further processed using the
equation

$z_{stm}(z_{pen})=\left\\{\begin{array}[]{ll}b(\exp{(\frac{1}{b}[z_{pen}-z_{thresh}])}-1)+z_{thresh}&\quad
z_{pen}\leq z_{thresh}\\\ z_{pen}&\quad z_{pen}>z_{thresh}\end{array}\right.$
(3)

where $b$ is a scaling constant (nm), and $z_{thresh}$ ($nm$) is the
z-position at which the tunneling current surpasses a predetermined current
threshold (chosen to be about 20 pA in experiments shown here). Eq. 3 acts as
a configurable ‘floor’ past which the STM tip can only travel a few tens of
picometers, regardless of how much further the haptic pen position $z_{pen}$
travels. This prevents problems feeling large features by dramatically
decreasing the degree to which the haptic arm moves the pen towards the
surface after a certain threshold height is met. This correction also assists
the operator in maintaining a constant tip height at $z_{thresh}$, since the
transition to different functional forms on either side of $z_{thresh}$ can be
easily felt by the user. When the composition of Equations 2 and 3 is
considered, force as a function of pen height is at first exponential, then
becomes linear as the force approaches the maximum force.

A representative contour of $z_{pen}^{F}(x_{pen},y_{pen})$ obtained using a
current-based force is shown in Fig. 2c, along with the corresponding
topography obtained using standard STM imaging. We find that the topography is
less-well reproduced in comparison to using the topography-based force
described in the previous section, and we attribute that difference to the 1 -
20ms communication delay between the haptic pen and STM, which makes it
difficult for the user to maintain a perfectly constant current. Fig. 2c,
meanwhile, compares the force on the haptic pen against the tunneling current
as the user traverses the tip across an individual CO molecule. Here we find
good agreement, with the current/force decreasing as the tip moves into the
CO-defined dip (due to the tip moving further from the surface as it goes off
an edge) and increasing as it moves out.

It is found that the topography-based mode described in Section III.1 is
easier to control and acquires better data than the current-based mode. In
both modes, the user attempts to maintain a constant downward force on the
pen, establishing a feedback loop between the human, the haptic device, and
the STM. However, in the current-based mode, human errors and inefficiencies
in this loop affect the tip $z$-position and, by extension, the signal that
sets the force, which can feel erratic. Such processes include slow reaction
times of the user, random hand movements, communication delay between the
haptic pen and the STM, and microscopic changes to the SPM tip or sample. On
the other hand, in topography-based mode the tip $z$-position is controlled
via electronic feedback, which is unaffected by user-error, and can quickly
correct for changes in tunneling conditions (the typical feedback time
constant is 30$\mu$s). An additional caveat of the current-based mode is that
it is necessary to know some approximate parameters of the signal of interest
(i.e. how the signal varies with tip-sample separation) before operation in
order to appropriately scale the position and force mapping — this is not
necessary when operating in topography-based mode.

Despite the above drawbacks, current-based force imaging is significantly more
useful when a 4-dimensional understanding of the signal of interest is desired
($x$, $y$, $z$, and $I_{tun}(x,y,z,V)$); the topography-based mode is only
able to provide information about a single, 3-dimensional contour of the
signal of interest ($x$, $y$, and $z_{stm}$), and is thus more limited in its
capacity to convey information about the surface. For example, current-based
imaging could allow the operator to feel changes in the electron decay
constant associated with different bandsStroscio, Feenstra, and Fein (1986) or
different molecular orbitals. Stroscio  _et al._ (1995); Calleja  _et al._
(2004); Picone  _et al._ (2010); Tange  _et al._ (2010); Woolcot  _et al._
(2012); Takahashi  _et al._ (2016)

Fig. 3 shows a comparison of force as a function of $z_{pen}$ when lowering
the pen into the surface (taken to be at $z_{pen}=0$ mm). The current-based
force exhibits a relationship initially indicative of the tunneling current’s
exponential dependence on surface proximity and then becomes linearized at
$z_{pen}=z_{thresh}=0$ mm due to Eq. 3, while the topography-based force
exhibits a simple, linear relationship.

Figure 3: Force as a function of $z_{pen}$ for the (a) STM topography-based
force and the (b) STM current-based force.

###  III.3 STM LDOS-Based Force

The tip-sample distance in an STM is typically maintained by using the
tunneling current as the feedback parameter, however, the force on the haptic
arm can be defined by any measurable value. For example, the energy dependent
local density of electronic states (LDOS) is one property that is commonly
measured in STM experiments to provide direct visualization of electron
wavefunctions and interference patterns. The LDOS at any particular point of
the sample is proportional to the tip-sample conductance at the tunneling
voltage, and is commonly measured using a lock-in amplifier. By converting the
lock-in signal to a force written to the haptic controller operating in read
mode, the user is able to feel the voltage-dependent local electron density as
it varies across the sample.

This mode of operation uses Eq. 1 with $S_{fb}=LDOS_{stm}(V)$, and the gain
variable $a$ having units of mm/V (the lock-in outputs a voltage that is
proportional to the sample conductance). Thus, the contour felt by the
operator, $z_{pen}^{F}(x_{pen},y_{pen})$, is defined by the local sample
conductance, which depends on the tunneling bias. An example is shown in Fig.
4a, where $z_{pen}^{F}(x_{pen},y_{pen})$ of a particular path is plotted on
top of an LDOS image of the Cu(111) surface, which reveals standing waves
created by the interference pattern of the copper surface state. Fig. 4b,
meanwhile, directly compares the trajectory of the haptic pen with the
corresponding linecut of the LDOS image, showing excellent agreement.

We note that, unlike STM-derived topography, the LDOS changes dramatically
with the applied bias, and those changes reveal the rich behavior of the
electrons in the material. In the case of Cu(111), LDOS images taken at
higher/lower sample biases reveal shorter/longer wavelength standing wave
patterns due to the different momenta of the participating electrons.Crommie,
Lutz, and Eigler (1993a) Moreover, LDOS images of molecules can reveal the
internal structure of the different molecular orbitals. Soe  _et al._ (2009);
Repp  _et al._ (2005); Itatani  _et al._ (2004); Lu  _et al._ (2003) These
properties are all accessible to haptic force based sensing.

Figure 4: An example of the LDOS-based mode in which the haptic pen was
operated. The pen position is plotted in three dimensions alongside
corresponding LDOS imagery is shown in (a); a direct linecut comparison is
shown in (b).

Figure 5: An example of the three AFM-based modes in which the haptic pen was
operated. The pen position plotted in three dimensions alongside the
corresponding AFM imagery is shown in (a) and (c); a direct linecut comparison
is shown in (b) and (e), while (d) compares frequency shift and force.

###  III.4 AFM Topography-Based Force

In this mode of operation, the feedback of the system remains on, and the tip-
sample distance is maintained at a constant height by linking the feedback to
the frequency shift of the AFM cantilever ($\Delta f$), which changes
depending on the tip-sample distance, and the specific tip-sample interactions
(i.e. electrostatic, Van der Walls, etc…). The haptic controller is operated
in read mode, with $x$ and $y$ positions of the AFM tip controlled directly
via the pen, and the force on the pen is set by Eq. 1, where $S_{fb}=z_{afm}$.
The cantilever oscillation phase was 2.47 degrees, and the oscillation
excitation voltage was 2.97 mV.

Figure 5(a) shows the three-dimensional path of the haptic pen with constant
force $z_{pen}^{F}(x_{pen},y_{pen})$ acquired using an AFM topography based
force while transiting over a CO molecule on Cu(111). The data is plotted atop
the associated AFM image, and Fig. 5(b) directly compares
$z_{pen}^{F}(x_{pen},y_{pen})$ to a linecut of the topography.

This mode of operation performs similarly to the STM topography-based mode
described in Sec. III.1, however, the perceived properties are fundamentally
different since the STM is sensitive to conductivity and the AFM is sensitive
to interatomic forces. These differences are apparent in the measurements of
CO molecules: they are felt as protrusions in AFM topography mode since they
physically protrude from the surface and interact with the AFM tip, while they
are perceived as dips in STM topography mode since the locally lower the
surface conductivity.

###  III.5 AFM $\Delta f$-Based Force

In this configuration, the pen was operated in write mode, using a force based
on the frequency-shift of the AFM cantilever. The function used was

$f(\Delta f)=\left\\{\begin{array}[]{ll}0&\quad\Delta f\leq\Delta
f_{setpoint}\\\ k\log{(\Delta f/\Delta f_{setpoint})}&\quad\Delta f>\Delta
f_{setpoint}\end{array}\right.,$ (4)

where $\Delta f$ is the measured frequency-shift of the cantilever, $\Delta
f_{setpoint}$ is a value chosen by the user at which the pen begins to feel a
force, and $k$ is a scalar which sets the gain. We note that if the force on
the pen is linked directly to $\Delta f$, the applied force on the pen is
maxed out too quickly and the operator can easily crash the tip. Using the
logarithmic, step-like form shown in Eq. 4 makes it easy to hold the tip at a
particular setpoint, while still enabling tip-sample force perception as the
tip is lowered further.

Force perception obtained while transiting a molecule in this mode is shown in
Fig. 5c, while Fig. 5d directly compares the perceived force to $\Delta f$.
The major benefit of this mode of operation is that the pen force is directly
linked to the actual physical force between the tip and sample (which
establishes $\Delta f$). This allows the user to feel the different forces
that determine the AFM tip-sample interaction; this ability has previously
been shown to be valuable in educational settings.Marchi  _et al._ (2005); Tse
_et al._ (2010); Bolopion  _et al._ (2013); Millet  _et al._ (2013)

It is found that the comparative usefulness between the AFM topography-based
mode and the AFM $\Delta f$-based mode is identical to the corresponding STM
modes, as discussed at the end of Section III.2. In particular, topography-
based operation is more stable, while $\Delta f$-based scanning provides more
opportunities for studying the surface properties via tactile sensation.

###  III.6 AFM $\Delta f$-Based Force at Constant Height

The last mode of operation we demonstrate is frequency-shift based, for which
controller feedback was turned off, but the tip is fixed to move in a flat
plane that is established by fitting topographic data obtained first by
imaging the surface in standard feedback mode. Local changes in surface
topology raise or lower the frequency shift from resonance of the AFM
cantilever and this signal was converted to a force on the haptic device in
read mode. This method of imaging — which is especially effective when $\Delta
f$ is a non-monotonic function of $z_{afm}$ — has been shown to be effective
in obtaining atomically-resolved images of surfaces and, for CO functionalized
tip, in imaging atomic bonds withing molecules. Gross  _et al._ (2009);
Giessibl (2019, 2003)

The force on the haptic pen transiting two CO molecules in this mode is shown
in Fig. 5e, plotted atop the associated direct measurement of $\Delta f$ from
the Nanonis software. We note that here we plot the raw value of $\Delta f$
rather than the absolute value, which would reveal peaks instead of dips.

Table 1: The specific functions used to configure how the surface feels. The constants $\rho$, $\tau$, $\sigma$, and $\epsilon$ were all chosen to provide the a force curve confined to a 30 mm range between zero force and the maximum force (3 N).  Force | $\varphi(r)$
---|---
Linear | $\rho r$
Covalent | $\exp(\rho r-\tau)-\epsilon$
Coulomb | $\frac{\sigma}{(\rho r-\tau)^{2}}-\epsilon$
Van der Waals | $\frac{\sigma}{(\rho r-\tau)^{7}}-\epsilon$
Lennard-Jones | $-4\epsilon\left(\frac{6\sigma^{6}}{(\rho r-\tau)^{7}}-\frac{12\sigma^{12}}{(\rho r-\tau)^{13}}\right)$

Figure 6: Force as a function of $z_{pen}$ for each force investigated,
including (a) linear force, (b) covalent bonding force, (c) Coulomb force, (d)
Van der Waals force, and (e) Lennard-Jones force. All curves are shifted such
that the surface is at $z_{pen}=0$ mm.

##  IV Feeling functions

Figure 7: An example of the forces experienced while transiting a CO molecule
using different ’feeling functions’. A linecut of the molecule imaged using
conventional STM is shown in (a); a comparable path was taken with the haptic
pen applying a (b) linear force, (c) covalent bonding force, (d) Coulomb
force, (e) Van der Waals force, and (f) Lennard-Jones force. The subjective
feel corresponding each function is written under each plot.

Determining how the surface feels when using the haptic controller is an
important parameter that is decided by the subjective preference of the
operator and/or a distance-dependent SPM signal. In absolute terms, the feel,
or ’feeling function’ ($f(z_{pen})$), is set by how the force exerted by the
haptic pen depends on the pen height, but that dependence can be varied over a
wide range of parameter space. In sections III.1, III.3, and III.4,
$f(z_{pen})$ was set to be linear and spring-like, and independent of the
actual SPM signal dependence on height; Meanwhile, in Secs. III.2, III.5, and
III.6 $f(z_{pen})$ was directly linked to the raw SPM signal, or a
logarithmic/exponential function of it. There is, however, substantial leeway
in choosing a ’feeling function’ that is engineered to impart sensations that
deviate from the SPM signal vs. height function, with the only technical
constraint being that it must prevent drastic force vs. tip height
dependencies which can lead to unstable operation. Otherwise, it can be chosen
to either provide the best feel to the user, or to mimic a particular
interatomic force. In the later case, the force felt on the pen would
represent the forces that a theoretical atom or molecule would feel if scanned
across the surface.

Figure 8: An example of controlled manipulation of CO on Cu(111) using the
haptic device. Shown is (a) an illustration of a CO molecules being laterally
dragged over the Cu(111) lattice by an STM tip (b) linecuts of $z^{F}_{pen}$
and $z_{stm}$ obtained during the lateral dragging process, which show atomic
corrugations due the preferred binding of the CO molecule to the top of the Cu
atoms, and (c) before and after images of the same area, in which CO molecules
were moved to spell out ‘hi’ in Unified English Braille.

The idea of exploring different feeling functions is also motivated by studies
that show that the psychometric function for compliance discrimination (i.e.,
perceived stiffness as a function of the actual stiffness) is roughly
logarithmic, and on the order of N/mm.Jones and Tan (2012) This seems to
suggest that force-functions will yield significantly different perceptions
than what might be initially predicted; just because force as a function of
distance is exponential, for example, does not mean the surface will ‘feel
exponential’ to the user.

To investigate the effect of modifying $f(z_{pen})$ on the haptic pen
operation, we used different ‘feeling functions’ while probing the properties
of an individual CO molecule. All measurements were performed in the mode of
STM Topography-Based Force (Sec. III.1), with Eq. 1 modified to mimic
different interatomic forces. The ‘feeling functions’ used were of the form:

$f(r)=\left\\{\begin{array}[]{ll}\varphi(r)&\quad r\geq 0\\\ 0&\quad
r<0\end{array}\right.,$ (5)

where $r\equiv az_{stm}-z_{pen}$ is defined to be the penetration distance,
and $\varphi(r)$ takes on the various forms as described in Table 1. These
feeling functions impose sensations on the hand of the operator that simulate
the forces experienced by different species of molecules interacting with the
surface, depending on the valence state, bond structure, charge, and size.
These different functions also modify the user’s ability to control the haptic
pen as they change the apparent shape and ‘hardness’ of surface features,
which affects the user’s reaction time.

In order understand the effect of these different feeling functions, we plot
the the force experienced by the user as a function of pen height in Fig. 6
for each individual functional form. In Figure 7 we plot the perceived force
using each function while transiting a CO molecule. We note that while the
magnitude of force fluctuations is similar between different feeling
functions, the tactile sensation are different, as described in the figure.
For example, using a full Lennard-Jones type potential holds the haptic pen in
place, allowing the user to feel competing repulsive and attractive forces as
they transit the surface. The spherical Coulomb potential, meanwhile, which
mimics the force between two charged point particles, creates a ‘soft’
sensation, with minimal pushback from the surface. In general, the description
of these forces is necessarily both subjective and qualitative in nature and
all provided stable operation.

##  V Manipulation

The controlled manipulation of atoms and molecules with an SPM is a powerful
capability that enables the atom-by-atom engineering of nanosystems.Bartels,
Meyer, and Rieder (1997); Stroscio and Celotta (2004); Crommie, Lutz, and
Eigler (1993b); Eigler and Schweizer (1990) Haptic SPM control is especially
useful for such a use case, as the operator can find the target atom/molecule,
perform manipulation and interrogate the resulting structure without having to
conduct a time-intensive raster scan after each manipulation attempt. To
demonstrate this capability, we used haptic SPM control to manipulate the
positions of CO molecules on a Cu(111) surface. In these experiments, the
system was operated in ’STM topography-based force’ mode, as described in Sec.
III.1. The STM tip is first positioned on top of an individual CO molecule,
and the lateral control of the haptic arm is momentarily paused to minimize
uncontrolled movements. Next, the STM tip is brought close to the molecule by
increasing the setpoint current of the feedback and lowering the tunneling
bias, with typical values of 10nA and 1mV, respectively. Concurrently, the
z-position of the tip is monitored for fluctuations, which indicate that the
molecule is partially bound to the tip.Stroscio and Celotta (2004) Lateral
movement is then re-enabled, and the user can ‘drag’ the molecule to the
desired location upon which the tip is raised by increasing the bias and
lowering the setpoint current to typical values of 50mV and 1nA, leaving the
molecule on the surface.

An example of this manipulation process is shown in Figure 8, where we plot
$z^{F}_{pen}$ during the lateral sliding process of CO molecule. During the
movement, the atomic lattice of the underlying fcc Cu(111) surface (with a
lattice constant of 3.597 Å Davey (1925)) becomes resolved in STM measurements
and can be perceived by the haptic pen due to the preferentially binding of
the tops of the Cu atomic compared to the hollow site, which causes the CO to
’skip’ between atomic sites.Bartels, Meyer, and Rieder (1997); Stroscio and
Celotta (2004); Ternes  _et al._ (2008) This process causes the CO molecule to
dynamically alter the local conductivity during the sliding process, allowing
the atomic lattice to be felt by the operator. We found the process of
manipulation to be reliable, and it was used to manipulate many molecules with
high rates of success. Images before and after the manipulation of 5 CO
molecules are shown in Fig. 8c, with the latter spelling out ‘hi’ in Unified
English Braille. We note that one distinct advantage of haptic-SPM is that
during the manipulation process, it is easy to ’feel’ around the surface to
find molecules, without needing to re-scan the areas or to search for atoms by
monitoring the height of the SPM tip visually. This makes atomic manipulation
less time consuming and more intuitive than conventional SPM operation.

##  VI Discussion and Outlook

In general, the performance of our haptic-SPM was constrained by a number of
factors, which we discuss as following.

One limitation of the specific haptic device used in this work is its
relatively small range of motion in the $xy$ plane. Operations were limited to
a 16 cm $\times$ 16 cm area, meaning that, for a large enough area of
interest, small surface features were scaled down significantly and were more
difficult to feel. A haptic device with a larger range of motion could address
this issue by keeping the scale of horizontal movement constant, and
increasing/decreasing the allowed range of motion for larger/smaller areas of
interest, respectively. This would effectively allow the user to feel both
large and small surface features at the same time, without sacrificing
movement range for surface scale.

Another limitation is the discrepancy in the operating frequency of the
Nanonis control software and the haptic pen. While the haptic pen updates at a
rate of 1 kHz, the Nanonis control software is only capable of sending values
to LabVIEW at a rate of 100 Hz. This results in the pen moving over many
points before refreshing, limiting the pen from fully taking advantage of its
0.02 mm positional resolution. A faster control software operating frequency
would yield significantly smoother operation, allowing larger areas and
features to be felt at higher resolutions and speed. Ultimately, the control
software’s refresh rate is limited by the time constant of the feedback
controller (typically $\leavevmode\nobreak\ 30\mu s$), meaning there is a
maximal resolution capable of being achieved.

Regardless of these technological limitations, our results show that the
haptic controller described in this work provides a useful and intuitive way
of interacting with a cryogenic, UHV STM/AFM. The variety of modes in which
the device was successfully operated exemplifies the wide range of possible
use-cases, and shows that the haptic SPM controller is an effective way to
feel, simulate, and interact with nanoscale surfaces and features.

Such a control system could be especially useful for educational and
accessibility purposes. Tactile feedback can help develop more intuition about
the operational principles of SPM technology than traditional sight-based
methods, primarily due to the high correlation between tip-surface and pen-
hand interactions. Haptic operations also provide near-instantaneous feedback
when compared to obtaining time-intensive raster scans, facilitating fine-
grained operations like molecular manipulation. Scanning probe microscopy is
essential for the study and engineering of nanoscale systems, and further
refinement of haptic-SPM controllers will only serve to make interacting with
such instruments more ergonomic and more accessible to the layperson.

###### Acknowledgements.

Work by M. F. and R. A. was supported by the National Science Foundation
(NSF), Division of Materials Research (RAISE DMR) under Award No. 1839199.
Work by W. A. B. and V. W. B. was supported by the Office of Naval Research
under Award No. N00014-20-1-235.

## Author Declarations

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

M. Freeman and R. Applestone: data curation, investigation, methodology,
software, visualization, writing - original draft, writing - review and
editing. W. Behn: data curation, investigation, supervision. V. Brar:
conceptualization, funding acquisition, project administration, supervision,
writing - original draft, writing - review and editing.

##  VII Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request or from:
https://github.com/HapticSPM/data.

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