chapter 10 heated atomic force microscope cantilevers and their

Transcription

CHAPTER 10
HEATED ATOMIC FORCE MICROSCOPE CANTILEVERS AND THEIR
APPLICATIONS
William P. King,∗ Bikramjit Bhatia, Jonathan R. Felts, Hoe Joon Kim, Beomjin Kwon,
Byeonghee Lee, Suhas Somnath, & Matthew Rosenberger
Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign,
Urbana, IL 61801, USA
∗
Address all correspondence to William P. King E-mail: [email protected]
Atomic force microscope (AFM) cantilevers with integrated heaters enable nanometer-scale
heat flow measurements, materials characterization, nanomanufacturing, and many other applications. When a heated AFM cantilever tip is in contact with a substrate, the interface
is a nanometer-scale hotspot whose temperature can be controlled over a large temperature
range. Over the past decade, there has been significant improvements in the understanding of
heat flows within and from a heated an AFM cantilever. There have also been improvements
in the characterization and calibration of these heated AFM cantilevers. These advancements
have led to new heated AFM cantilever designs and have enabled new applications of heated
AFM cantilevers. This chapter describes research into heat transfer fundamentals, cantilever
technology, and applications of heated AFM cantilevers.
1. INTRODUCTION
The physical and chemical properties of matter depend on temperature, and the temperature dependence of materials properties has enabled many technologies. Manufacturing
technologies use melting, solidification, and phase change in the fabrication of metals,
glasses, polymers, and ceramics. Temperature-dependent chemical processes are used in
petrochemical production and also enable the polymerase chain reaction (PCR). Analytical techniques that measure the temperature dependence of materials properties include
calorimetry, thermogravimetry, rheometry, and dynamic mechanical analysis. Energy conversion processes that use thermoelectric or ferroelectric materials also depend on temperature. The characterization of these processes and the exploitation of these technologies
requires temperature control.
An atomic force microscope (AFM) cantilever having an integrated heater allows for
the control of temperature and heat flows at the nanometer scale. This nanometer-scale
temperature control enables the above thermal processing techniques and applications at
the nanometer scale. A heated AFM cantilever further enables fundamental studies of thermal transport at small length scales. This chapter describes the development of heated
AFM cantilevers, the fundamental heat transfer measurements made on and with heated
cantilevers, and the related technologies and applications for these cantilevers.
There is a rich history of thermal atomic force microscopy. Thermal analysis was
among the first applications envisioned for scanning probe microscopy,1−3 and has had
ISSN: 1049–0787; ISBN: 978–1–56700–222–6/13/$35.00 + $00.00
c 2013 by Begell House, Inc.
°
287
288
A NNUAL R EVIEW OF H EAT T RANSFER
NOMENCLATURE
d
Gss
Gliq
hair
hairgap
T
∆Tnoise
θSubstrate
θInterface
distance between cantilever and
substate [m]
tip-sample thermal conductance
through solid contact [nW/K]
tip-sample thermal conductance
through solid contact [nW/K]
effective heat transfer coefficient
between cantilever and
surrounding air [W/m2 K]
effective heat transfer coefficient
for air gap between cantilever and
substrate [W/m2 K]
temperature [◦ C]
noise temperature [◦ C]
nondimentional temperature of
substrate (Tsub – T0 )/(Theater – T0 )
nondimentional interface temperature
(Tinterface – T0 )/(Theater – T0 )
RTip
RContact
RSub
RGap
RSub2
∆x
∆R/R
τ
thermal resistance of tip
[K/W]
tip-sample contact thermal
resistance [K/W]
spreading thermal resistance
of substrate under contact
[K/W]
thermal resistance of air gap
between the tip and substrate
[K/W]
spreading thermal resistance
of substrate under air gap
[K/W]
spatial resolution [m]
topography sensitivity when
using heated cantilever
thermal time constant [s−1 ]
both research success and commercial success. Research successes include data storage,
where heated AFM cantilever tips could write data at unprecedented data density, and
arrays of heated AFM cantilevers could be independently operated for data writing and
reading.4,5 Other research successes include novel nanolithography techniques6,7 and materials property measurements.8,9 Some applications of thermal atomic force microscopy
have led to both research and commercial success, for example, scanning thermal microscopy,10 micrometer-scale thermal analysis (µTA),8 and nanometer-scale thermal analysis
(nano-TA).9
This chapter focuses on fundamentals and applications of AFM cantilevers that have
integrated heaters and thermometers. It includes work on thermal probe technologies that
does not strictly occur inside an AFM, since these technologies enable novel departures
from conventional probe microscopy. The chapter also includes related fundamental work
broadly relevant to the micro-/nanoscale heat transfer community. However, it does not focus on scanning thermal microscopy (SThM),10−13 and it does not review research where
a thermal element is not integrated into the cantilever or tip.
The chapter is organized into sections on heat transfer fundamentals, cantilever technologies, and applications of heated AFM cantilevers. The fundamentals section reviews
research on heat generation and heat flows within the cantilever and between the cantilever
and the environment. Special attention is given to heat flow within the cantilever tip and
between the tip and a nearby substrate, because this nanometer-scale heat flow reveals the
most interesting physics and also because the tip-substrate interface temperature is critical for many applications. The technology section reviews research on the design and
H EATED ATOMIC F ORCE M ICROSCOPE C ANTILEVERS AND T HEIR A PPLICATIONS
289
characterization of heated AFM cantilevers. There have been many concepts proposed for
heated AFM cantilevers, which must satisfy both fabrication requirements and requirements for thermal, mechanical, and electrical operation and systems integration. The applications section describes uses of heated AFM cantilevers in materials characterization,
nanomanufacturing, and many other areas. The review concludes with comments on future
challenges and opportunities for heated AFM cantilevers.
2. HEAT TRANSFER FUNDAMENTALS
The performance of a heated AFM cantilever depends on the temperature distribution
within the cantilever and cantilever tip. This section describes research into heat generation within the cantilever and heat flow from the cantilever. Figure 1 shows the heat flow
paths within and from a heated cantilever. This figure specifically applies to a heated cantilever with an internal resistive heater, but the general principles also apply to other types
of heated cantilevers. The heat generated near the tip flows either to the substrate or through
the cantilever and then to the substrate. Heat flows through the cantilever heater and legs
FIG. 1: Heat transfer from a heated cantilever and cantilever tip. Heat transfer from the
heaters is mainly due to conduction within the cantilever and cantilever tip, and through the
air near the cantilever. Heat transfer at the tip-substrate contact is mainly due to solid-solid
contact, although the presence of water at the tip-substrate interface can also affect the heat
transfer.
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by conduction, and from the cantilever to the environment by conduction and thermal radiation. The thermal conductance of the silicon heated cantilever is about 1 µW/K when
it is operated to heat a substrate as shown in Fig. 1.14,15 About 30% of the total heat generated flows from the heater, across the air gap, and into the substrate.14 The remainder
of the heat flows down the legs, although nearly all of this heat eventually flows into the
substrate. Usually, convection and radiation are negligibly small.
Figure 2 shows a thermal resistance network model that can be used to understand the
heat flows from the cantilever to the substrate and the associated temperature distributions
within the cantilever and at the sample surface.16−18 Similar thermal resistance networks
can model heat flow through the tip during SThM.10 For a typical silicon AFM tip and silicon dioxide substrate, RTip = 106 K/W, RContact = 107 – 108 K/W, and RSub = 108 K/W.
FIG. 2: (a) Thermal resistance network model and expected temperature profile on the substrate. (b) Nondimentional temperature profile on the surface of a silicon substrate coated
with a 100 nm–thick gold film. The silicon tip is 1 µm in height.
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For a cantilever operating in an air environment and having a tip height of about 1 µm,
RGap = 105 and RSub2 = 102 K/W.16,17 Therefore, the quantity of heat transferred through
the tip is much smaller than that through the air gap. However, the heat flux at the tipsample contact is large, such that the interface temperature at the contact is much higher
than the temperature rise by air conduction, θInterface > θSubstrate . For most substrates,
heat conduction across the cantilever-substrate air gap has a small effect on the tip-sample
interface temperature.17 Figure 2 also shows the temperature profile on the surface of a
substrate having a 100 nm–thick gold layer on silicon dioxide. Here, the silicon tip is 1 µm
tall. The temperature rise at the contact is much higher than the temperature rise away from
the tip, due to the high thermal conductivity of the tip and the high heat flux at the contact. The absolute value of the interface temperature at the contact depends on the thermal
conductivity of the substrate.17
2.1 Heat Generation within the Cantilever
The first reports of heated AFM cantilevers used a laser to heat the cantilever. The cantilever tip was in contact with a polymer substrate, and on laser heating, the hot tip could
make indentations into the polymer surface.3 The integration of a heating laser into an
AFM system can be challenging, but it allows nearly any cantilever to be heated.3,19−21
Cantilevers with integrated resistive heaters are less widely available than conventional
AFM cantilevers, but are easier to integrate into an AFM system. The first internal resistive heating of an AFM cantilever was achieved using a commercial piezoresistive cantilever having two doped silicon legs and was demonstrated by thermomechanical writing
on polymer and phase-change material.22
Metal wires or films fabricated onto the cantilever or cantilever tip can be used for resistive heating.10 The tip can be a single metal wire23 or a metal wire junction.24 The metal
junction can also serve as a thermocouple.25−30 In general, metal heaters are easy to fabricate, but thin metal films are limited in mechanical strength and maximum temperature.31,32
Metal layers fabricated onto a multilayer cantilever can induce unwanted thermomechanical bending.
Silicon AFM cantilevers with integrated resistive heaters can reach temperatures over
1000◦ C and have a thermal time constant as fast as 10 µs.33,34 These cantilevers also have
a large temperature coefficient of resistance (TCR) compared to metals, allowing sensitive
temperature measurement. Such cantilevers were developed for data storage,35−40 but also
have other applications as described in subsequent sections. Integrated heaters have also
been fabricated from diamond.41
2.2 Heat Transfer through the Tip
Many applications of heated AFM cantilevers depend on locally raising the temperature
at the tip-substrate interface. Heat transfer through the tip is either through the direct solid
contact or through a water meniscus formed near the contact. When the tip is not in contact
with but very near the substrate closer than the mean free path of the medium molecule,
ballistic conduction through the gap determines the tip-sample heat transfer.42 Thermal
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conduction through the tip-sample contact is essential for heated cantilever applications,
due to the small size of the contact and also due to thermal boundary resistance at the tipsubstrate interface.17,43 Table 1 shows tip-sample thermal conductance values that have
been estimated using both experiments and simulations. Typical thermal contact thermal
conductance is in the range 0.1–100 nW/K. For a tip radius of 30 nm, a typical contact
diameter is about 10 nm with a contact force of 10 nN. The spreading contact conductance
due to 10 nm contact on a polymer sample is 2 nW/K.
In humid air, a water meniscus forms at the tip-sample contact.10,26 For a wetting surface and relative humidity of 0.5, the liquid contact diameter is about 30 nm, somewhat
larger than a typical solid contact diameter of about 10 nm.17 Since the spreading conductance in the substrate is proportional to the contact diameter, the thermal conductance
of the liquid meniscus is 6 nW/K. Usually, the contact thermal conductance or spreading
contact conductance dominates the total thermal conductance through tip-sample contact.
Figure 3 illustrates two experimental investigations of heat flow through the tip. The
measurements are very similar, however, the first experiment was performed with a thermocouple tip and a heated substrate,44 while the second experiment was performed with a
heated tip and a thermocouple on the substrate.18 The tip was brought into and then out of
contact with the substrate, while the temperature and heat dissipation were recorded, along
with the cantilever deflection. Figure 3(a) shows the experimental result with a thermocouple SThM tip. The upper curves show the cantilever deflection as the cantilever approaches
TABLE 1: Tip-sample thermal conductance
G(nW/K)
26
Luo et al.
105
29 ± 6 (solid contact)
Shi et al.44
6.7 ± 1.5 (liquid contact)
Park et al.18
40
Nelson et al.9,17
100
Nelson et al.
100
9,17
Fletcher et al.16
10
Prasher et al.45
200–300
Shi et al.46
100
Lefêvre et al.135
1800
Zhang et al.42
9500
Remarks
Measured with SThM thermocouple tip
Measured with SThM thermocouple tip
Measured with silicon tip heated
cantilever
Expected from nano-TA experiment
Calculated for silicon heated tip contact
Pt-Au nanothermocouple at
tip-substrate contact
Simulation with ballistic phonon transport from silicon nanowire (D = 20 nm)
to Si substrate
MD simulation on silicon through 10
nm–diameter orifice
Wollaston wire probe with tip radius of
5–15 µm
Ballistic air conduction between Wollaston wire probe and substrate in separation within 200 nm
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FIG. 3: Cantilever deflection and temperature response as a function of tip vertical distance
over a substrate. (a) The temperature response is the thermocouple tip temperature divided
by the substrate temperature.44 (b) The electrical resistance of a silicon heated cantilever,
the cantilever deflection, and the voltage of a surface nanothermocouple.18
or retracts from the sample, while the lower curve shows the corresponding temperature
response. The heat conduction through contact is initiated by liquid contact, and rises by
increasing the contact force that is responsible for the solid contact diameter. The solid contact conductance was 29 nW/K, and liquid film conductance was 6.7 nW/K. Significantly
more heat flows through the solid than the liquid, owing to the difference in conductance
and also the difference in heat transfer area. Figure 3(b) shows the results of a similar experiment for a silicon heated cantilever.18 The upper curve is the cantilever deflection and
the lower two curves are the cantilever voltage and electrical resistance, which indicate the
cantilever temperature. The contact thermal conductance was 40 nW/K for tip radius of
20–50 nm.
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Theoretical treatments of thermal contact conductance through a nanometer-scale constriction provide insights into heat flow through a heated AFM cantilever tip.17,43,45,46 At
room temperature, the phonon mean free path in pure crystalline silicon is approximately
250 nm, while the thermal constriction of the tip is somewhat smaller, and so a continuum
description of heat transfer does not accurately model the heat flow. Considering ballistic
phonon transport, the thermal conductance for a silicon nanowire of diameter 20 nm and
length 1 µm was calculated to be 200–300 nW/K.45 Molecular dynamics (MD) simulation
estimated the thermal conductance through a 10 nm orifice on highly n-doped (Nd = 3
× 1020 /cm3 ) silicon to be 100 nW/K. Interface temperature at the tip-sample nanocontact
was measured experimentally and supported the theoretical results.16
2.3 Heat Transfer to the Surroundings
A typical AFM cantilever has a Biot number less than 10−4 , so heat transfer within a microcantilever can be modeled as 1D.20,47 The temperature distribution measured along a
silicon cantilever is exponential, confirming the appropriateness of this model.34 Cantilever
thermal conductance is an important parameter to determine the cantilever temperature for
a given power consumption. Table 2 summarizes the effective heat transfer coefficients
between the cantilever and surrounding air, hair , which have been investigated experimentally and numerically. The reported hair are ∼103 W/m2 · K, at least 100 times larger than
for natural convection in air.48 The large heat transfer coefficient is due to the large heat
capacity of the surrounding air relative to the cantilever heat capacity, as well as the large
surface-to-volume ratio of the microcantilever.49,50
When the cantilever is in air, heat transfer to the air is dominated by conduction rather
than convection, since the Grashof number is about 10−3 . However, when a heated cantilever is operated in water, the Grashof number can be 0.1, and there can be significant
buoyancy-driven fluid motion. Average fluid velocity in the plane of the microcantilever
was measured to be 105 µm/s when the cantilever heater was 65◦ C.51 Small-scale conduction and convection from the heated cantilever to the nearby environment is a topic that
merits further research.
When the cantilever is operated near a substrate, the cantilever thermal conductance is
higher than when it is operated away from a substrate.30,52−55 The effective heat transfer
coefficient is hairgap = kair /d, on the order of 10 kW/m2 K for a tip height of 1–10 µm.
Many heated cantilevers have a tip smaller than 10 µm, and are operated at a cantileversubstrate angle of 10 deg, and thus in general hairgap > hair near the heater region.
Heated cantilevers have been operated not only in the air, but also in different environments such as partial vacuum,14 low temperature,56 and liquid.51,57,58 The heat transfer
between a heated cantilever and its gaseous surroundings is a function of the Knudsen
number, Kn, which is the ratio of the mean free path of the medium to the gap where the
heat flows through. Mostly, the air gap is much larger than the mean free path of the surrounding medium, i.e., Kn < 1, thus the conduction through the gap is in the continuum
regime. The continuum assumption is not appropriate at the very end of the tip where the
air gap is smaller than 1 µm, or when the cantilever is operated in vacuum. Operating the
heated cantilever in partial vacuum revealed that the air conduction becomes negligibly
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TABLE 2: Cantilever effective heat transfer coefficient
hair (W/m2 K)
Chui et al.64
Hu et al.49
Shen et al.194
Serrano et al.195
Toda et al.196
Narayanaswamy et al.20
Lee et al.14
Park et al.61
Kim et al.62
Nelson et al.52
Kwon et al.118
Remarks
0.1 W/m K for two 8 µm–wide
3000
legs (experiment)
Al heater on SiNx membrane
2700
(experiment)
70 nm Au and 450 nm SiNx bi500
material cantilever (experiment)
Raman spectroscopy on silicon
2500 (25◦ C), 5500 (450◦ C)
heated cantilever (experiment)
90
nm Au and 300 nm SiNx bi1670 (20◦ C), 3900 (143◦ C)
material cantilever (experiment)
70 nm Au and 530 nm SiNx bi3400
material cantilever (experiment
and simulation)
Silicon heated cantilever (ex3400 (Air), 44 (1 mbar)
periment and simulation)
Silicon heated cantilever (ex800 (leg), 1000–3000 (heater)
Finite element simulation of sil2000 (leg), 7000 (heater)
icon heated cantilever (simulation)
Silicon heated cantilever, used
for temperature calibration (ex3100
850–1200 (Al-SiNx , Au-SiNx ) Bimaterial cantilevers (experi500 (Al-Si)
ment and simulation)
small at pressures less than 1 mbar.14 Direct simulation Monte Carlo (DSMC)59 and a
quasi-ballistic heat transfer model60 assessed the subcontinuum conduction, finding that
the heat flow is in the continuum regime for an air gap larger than about 1 µm. The thermal
conductance of heated cantilevers changes from 24 W/K in air to 137 W/K in deionized
water.58
Usually, thermal radiation heat transfer from a heated cantilever is negligibly small
compared to the other heat transfer mechanisms. When the cantilever is operated at 1000◦ C
in air and assumed to be a blackbody, radiative heat transfer is only 2% of the total heat
flow. When operated in vacuum under the same conditions, radiative heat flow is 6% of the
total heat flow. Thus for most practical operating conditions, radiation can be ignored.
2.4 Cantilever Measurement Resolution
Measurements with heated AFM cantilevers can be characterized by temporal resolution, temperature resolution, spatial resolution, and force or displacement resolution. The
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cantilever has at least three time constants: mechanical, thermal, and electrical. The mechanical time constant is the inverse of the resonant frequency of the cantilever. The thermal time constant represents the speed of heating and cooling. The electrical time constant
describes the electrical response of the cantilever and its on-chip interconnects. Typically,
the thermal time constant is longer than the mechanical or electrical time constants.
Heated cantilevers have several time constants that are classified based on the heating
source, cantilever temperature distribution, or the specific region of the cantilever. The
external time constant is the time taken for the cantilever and the environment to come to an
equilibrium, while the internal time constant is the time taken to achieve uniform cantilever
temperature.10 A “fast” time constant is used to describe the time taken by the cantilever to
thermally respond to an instantaneous change in heater power, and it is on the order of 100
µs.61 Correspondingly, the “slow” time constant is the time for the cantilever to come to
thermal equilibrium, and can be as long as 2.5 ms. The time constant associated only with
the heater is much smaller than all other time constants due to its small thermal inertia, and
is ∼1 µs.61 FEM simulations provided insights into these separate time constants and their
respective heat flow mechanisms.62
Figure 4 shows cantilever thermal time constant measured as the cantilever response
to a current pulse,22,36,63 or the periodic cantilever response to a sinusoidal current.61
With the pulsing method, the time constant is the time taken for the cantilever temperature to reach 70% of the maximum temperature. For the periodic heating method, the
time constant is the inverse of the frequency where the periodic temperature is 30% of
the maximum.61 The time constant is ∼35 µs by both methods. Figure 4(c) shows the
electrical resistance and power dissipation of a silicon heated cantilever as a function of
the cantilever temperature. The cantilever resistance rises with temperature and then drops
suddenly. The temperature coefficient of resistance (TCR) varies with cantilever temperature and is on the order of 6000 ppm/◦ C.34 A positive feedback mechanism exists in doped
semiconductor materials wherein the number of thermally generated intrinsic carriers from
silicon rise with cantilever temperature and these carriers in turn increase the cantilever
heating.64 The point at which the thermally generated intrinsic carriers dominate carriers
from dopants is called thermal runaway.34 Thermal runaway occurs at around 500–600◦ C
for doped silicon, where the TCR changes from positive to negative.
The heated cantilever thermal time constant can be reduced by decreasing the heat capacity of the cantilever heater.65 The cantilever heating time can be decreased by reducing
heat flow from the heater by means of thermal constrictions, however, this can increase
cantilever cooling time.40,41,61,62,66 Contacting the tip to a substrate increases heat transfer from the cantilever.22,53 Table 3 shows a summary of the thermal time constants of
several cantilevers. When the cantilever is operated in a cryogenic environment, the cantilever thermal time constant decreases by a factor of three because the specific heat of
silicon is reduced.56
An understanding of the noise spectrum is necessary to calculate the fundamental temperature or topography resolution limits of the cantilever.10,67,68 The dominant source of
noise for heated cantilevers transitions from 1/f noise to Johnson noise at 10 kHz.67 The
Johnson noise floor of a typical heated cantilever is 0.3–1.7 µK/Hz1/2 over the temperature
range of 296–781 K,67 and the temperature resolution of the same heated cantilever near
297
FIG. 4: (a) Transient temperature response of heated cantilever during a step change in
heating power. (b) Periodic cantilever temperature during periodic heating measured using the 3ω method. (c) Measured cantilever electrical resistance and heating power as a
function of cantilever heater temperature.
room temperature is 100 mK in DC and 5 mK in AC.68 One study that used the cantilever
heat flow to measure nanotopography obtained about 1–3 nm vertical topography resolution, which corresponds to about 50–150 mK temperature resolution.53 Usually, the heated
cantilever has a voltage drop that is much larger than the thermal noise (Johnson noise)
voltage; therefore, the temperature resolution of it is larger than the calculated thermal
noise.
The cantilever spatial resolution is the minimum feature size or measurement volume
that is heated by the cantilever tip, depending on the application. The spatial resolution can
be larger than the contact area between the tip and sample. For manipulation or surface
298
TABLE 3: Cantilever thermal time constant
τ (µs)
280
Park et al.61
2500 (settling time constant)
56
Park et al.
1000 (settling time constant)
Dai et al.194
89
Bae et al.62
0.45
Drechsler et al.40
7–11
Rothuizen et al.196
10
Kim et al.20
1–10
Mamin22
350 (in contact)
450 (away)
Remarks
Silicon heated cantilever at room
temperature
Silicon heated cantilever at 77 K
Silicon heated cantilever with 100
nm heater
All-diamond heated cantilever
Silicon heated cantilever with
thermal constriction
Increased thermal constriction
Silicon heated cantilever in contact with silicon substrate
Silicon heated cantilever on silicon substrate
modification using a heated cantilever, the spatial resolution is the final feature size after processing. The minimum feature size for indents formed with a heated tip are 10–
50 nm,4,21,38,39,69 and the minimum feature size for thermal nanolithography is in the
range 30–100 nm.6,70−72 For temperature-dependent mechanical property measurements,
the spatial resolution can be defined as the size of the tip-sample contact. The spatial resolution of temperature-dependent contact stiffness of a polymer was about 20 nm.73 For
SThM, the noise equivalent spatial resolution,10 ∆x = ∆Tnoise /(dT /dx), is the minimum
distance leading to distinguishable temperature change that is larger than noise and is usually larger than the contact diameter. The ultimate spatial resolution of SThM is about
50 nm13,30,54,74 since measuring thermal phenomena requires sufficient volume to reach
equilibrium.
3. CANTILEVER TECHNOLOGY
Advancements in microfabrication and characterization technologies have enabled significant improvements in the design, operation, and use of heated AFM cantilevers. Miniaturizing the thermal element has enabled decreased thermal time constants and improved
spatial resolution,3,22,75,76 and has provided the ability to apply large temperatures with
minimal sample damage.9 Integrating the thermal element into an AFM cantilever allows
simplicity and scalability compared to external methods of heating or sensing. These advancements in heated cantilever technology have in turn enabled a variety of applications
and enhanced the understanding of cantilever heat transfer fundamentals.
3.1 Cantilevers with Metal Heater-Thermometers
The first cantilevers with integrated heating used metal heating elements. Figure 5(a) shows
a cantilever tip that is a loop of Wollaston wire having a portion of the silver casing etched
299
FIG. 5: SEM images of thermal probes and cantilevers with metallic heater-thermometers.
(a) Wollaston probe with a metal resistive heater-thermometer element at the tip.139 (b)
Platinum thermoresistive element fabricated by electron beam deposition having four legs
and a sharp needle at the apex.75 (c) AFM cantilever with a platinum/chromium-nickel
thermocouple junction on a silicon dioxide tip.80
away to create a small platinum filament tip. Such a metal tip can locally apply heat to
a surface and measure the material response with spatial resolution on the order of 0.1–
10 µm.77,78 To improve the spatial resolution with a miniaturized heating element, several
cantilever designs have been proposed that integrate the heating element into the cantilever.
Figure 5(b) shows a cantilever with a resistive filament structure fabricated at the cantilever free end.75,79 Electron beam deposition of platinum formed a filament structure
that was 2–5 µm tall and had a diameter of 30–100 nm with a sharp needle structure at
the apex. The development of batch fabrication processes allowed reproducible and lowercost cantilever production.77,78 A nanometer-scale thermocouple junction integrated on an
AFM cantilever can generate heat for thermal properties measurement.80−82 Figure 5(c)
shows a cantilever having a platinum/chromium-nickel thermocouple junction tip with radius smaller than 100 nm.80 The integrated thermocouple junction at an AFM cantilever
tip could monitor the temperature and heat the sample, simultaneously. This thermocouple
junction exhibited an electrical resistance of 100 Ω and thermoelectric voltage sensitivity
of 16 µV/K.
3.2 Silicon Cantilevers with Doped Heater-Thermometers
Cantilevers with solid state heaters are often U-shaped and have a heater element at the
cantilever free end.36 Current flowing through the resistive element causes resistive heating
and temperature rise. Silicon cantilevers have advantages over metal cantilevers, since they
are more resistant to wear and fatigue, and allow higher operating temperatures. Silicon
heated cantilevers can also be batch fabricated with sharp tips.
300
The design of a heated AFM cantilever involves the optimization of parameters such
as cantilever material and geometry, and dopant element and concentrations to suit the
intended cantilever performance characteristics. Many cantilevers with doped heaters are
made of silicon,34,35,83 and some are made of diamond.41 Typical heated cantilevers are
about 100 µm long and the cantilever thickness varies from 100 nm to a few microns
while the smaller lateral heater dimension varies from <100 nm to a few hundreds of
microns.34,40,41,65,66,84−86 Phosphorous, boron, and antimony are commonly used dopants,
and silicon cantilevers have a typical dopant concentration of 1016 –1018 cm−3 in the resistive heater region and 1020 cm−3 in the cantilever legs and interconnects.16,34,35,41,83 The
room temperature electrical resistance of heated cantilevers ranges from 1 to 5 kΩ, with
most of the electrical resistance arising from the heater region. It is possible to design the
cantilever heater to be higher or lower than this range, however, higher electrical resistance
requires higher heating voltage, and lower electrical resistance in the heater region results
in heating in the cantilever legs.36 It is desirable to have low electrical resistance in the
cantilever legs and interconnects such that the heat generation is localized in the cantilever
heater. The practical lower limit on the electrical resistance of the legs is about 100 Ω for
each leg.
Several electrical, thermal, and electrothermal metrics can be used to characterize the
performance of heated cantilevers. The power dissipated from microcantilever heaters is
typically in the range of 1–10 mW and is an important design consideration for applications
such as data storage.34,40,66,85 The heater thermal time constant determines the response
rate of the heater, and varies from 0.1 µs to a few hundreds of microseconds.34,35,40,41,65,66,85
The cantilever geometry, material, and doping determine the electrical resistance, power
dissipation, and temperature distribution of the cantilever. Smaller heaters combined with
slender cantilever legs dissipate less power and can heat and cool rapidly. Cantilever temperature sensitivity is the cantilever signal per change in temperature and is approximately
0.0011 K−1 .68 The temperature sensitivity is the smallest step change in temperature that
can be measured in a given integration time, and it is typically around 5 mK.68 The thermal topography sensitivity is defined as the normalized change in the cantilever electrical
resistance for a unit change in cantilever vertical displacement, and it varies from 0.05 ×
10−5 to 10−1 nm−1 .53,87−89 Imaging resolution is the smallest vertical displacement that
can be resolved by the cantilever in the thermal image, and is typically 0.1–20 nm.53,87−89
Innovative heated cantilever designs have yielded significant performance gains. Figure 6(a) shows a cantilever where the leg regions close to the heater are constricted to reduce heat loss from the heater.36 The thermal time constant of this cantilever was 0.8 µs and
that of cantilevers without constricted legs was ∼10 µs. Figure 6(b) shows a cantilever with
a 100 nm–wide nanoheater element developed for fast heater dynamic response that was
fabricated using a combination of photolithography and controlled annealing techniques.65
Figure 6(c) shows a nanoheater cantilever where the heater and leg widths were reduced
using electron beam etching techniques to achieve a 4× reduction in power consumption compared to similar-sized cantilevers.40 Figure 6(d) shows a cantilever with separate
heater elements optimized for thermal reading and writing of data bits along with a capacitive platform for electrostatic actuation of the cantilever.33,69 Separating the read-heater
from the tip enabled the heater to be operated at high temperatures without damaging the
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FIG. 6: Examples of cantilevers with integrated heater thermometers. (a) Cantilever with
constricted leg regions around the heater to improve heater dynamic response.35 (b)
Cantilever with a 100 nm–sized heater for speed and heat localization.65 (c) Cantilever
with a nanoheater and reduced heater and leg dimensions to reduce cantilever power
consumption.40 (d) Cantilever with two heaters optimized for data reading and writing
along with a capacitive platform for electrostatic actuation.69 (e) Dual-heater cantilevers
for data storage having silicon nitride straps to link cantilever sections to minimize heat loss
from the heaters.66 (f) All-diamond heated cantilever with minimized tip wear.41 (g) Silicon
heated cantilever with diamond-coated tip with low tip wear and resistance to fouling.91 (h)
Electrothermal cantilever with integrated n-p-n diode capable of independently controlling
tip voltage and temperature.94
surface. Furthermore, the write-heater was made smaller to reduce the heater thermal time
constant. Offsetting the cantilever 8 µm from the free end of the cantilever containing the
read-heater reduced the heater-surface distance to 250 nm, thereby enabling a high ∆R/R
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topography sensitivity of 5 × 10−5 nm−1 . Figure 6(e) shows a similar heated cantilever
optimized for minimal power consumption without compromising the topography sensitivity and data-reading bandwidth.66 Silicon dioxide straps were used in place of silicon arms
to link different cantilever sections to reduce the heat loss from the heater regions. A ∆R/R
topography sensitivity of 2 × 10−4 nm−1 was achieved for cantilever power dissipation
on the order of 1 mW, which was a 6× improvement over similar heated cantilevers.53
A similar design approach was explored where a thermal isolation layer was sandwiched
between the heater and the cantilever legs.90 The thermal resistance of this cantilever was
105 K/W and the noise-limited resolution was 6.9 pm/Hz1/2 , while the resolution of a
similar cantilever without the isolation layer was 58.0 pm/Hz1/2 .
Tip wear and fouling are key limitations for AFM imaging. Figure 6(f) shows a heated
cantilever fabricated entirely from doped diamond, having a resistive heater at the tip.41
This cantilever had a low thermal time constant of 0.45 µs, which was due to the high
thermal conductivity of diamond, and was also very resistant to tip wear and fouling. Figure 6(g) shows a silicon heated cantilever with an ultra-nanocrystalline diamond (UNCD)–
coated tip that was exceptionally resistant to wear and fouling.91
In general, heated AFM cantilever tips are not well suited for electrical and electrothermal microscopy, since the tip voltage is coupled to the cantilever temperature. However,
there are promising opportunities of novel electrothermal measurements such as variable
temperature Kelvin probe microscopy or scanning gate microscopy.92,93 In response to
this need, heated cantilevers have been proposed that have integrated electrical elements.
Figure 6(h) shows an electrothermal cantilever with an integrated heater and an n-p-n backto-back diode whose tip temperature and voltage can be independently controlled.94 The
diode breakdown voltage was 10 V when the cantilever free end was around 175◦ C. A
similar cantilever with a platinum electrode over a resistive heating element has been developed for thermoelectric voltage measurement at the tip.16 Another cantilever with a
Schottky diode at the cantilever free end allowed the decoupling of tip temperature and tip
voltage.95
Microcantilevers with large heater areas, or hotplates, have small temperature gradients and large capture areas that make them attractive tools for performing biochemical
experiments with increased sensitivity. A 15 m × 150 µm rectangular heater was used as
a thermal displacement sensor to align a 2D AFM cantilever array, and it had a 10 µm dynamic range while having a resolution less than 1 nm.86 A microcantilever with a 100 µm
× 100 µm hotplate was developed for chemical, biological, and biochemical applications
such as temperature interrogation of biochemical binding to cantilevers, calorimetry, and
triggering chemical reactions.84 Temperature uniformity of 2–4 % was achieved over a
temperature range of 25–200◦ C. Similar hotplate cantilevers replaced optical deflection
sensing by integrating piezoresistors to the cantilever base, thus improving scalability and
enabling thermogravimetric and biochemical applications.85,96
3.3 Thermal Cantilever Actuation
A microheater can be used to engineer thermal stresses in single- or bimaterial structures
to achieve in-plane or out-of-plane actuation. A bent beam heated at the fixed ends was
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used to achieve 5 µm of rectilinear in-plane actuation.97 A related design for microscale
tweezers used thermomechanical expansion to grip and manipulate micron-sized objects.98
Periodic excitation of an integrated heater caused silicon heated cantilevers to oscillate due
to thermomechanical expansion.99 The cantilever oscillations had an amplitude of 484 nm
at an actuation frequency of 29.4 kHz, which was sufficient to perform topography mapping in intermittent contact mode. Differences in thermomechanical expansion of different materials can also be exploited for actuation. Gold/silicon nitride bimorph cantilevers
can individually actuate cantilevers to improve the scalability of dip pen nanolithography
(DPN).100
Heated cantilevers can be actuated using methods that do not involve self-heating.
Lorentz forces generated by the flow of alternating current through a U-shaped heated
cantilever in the presence of a magnetic field can be used to oscillate a cantilever, thereby
enabling intermittent contact topography mapping and local thermal analysis.15 Heated
cantilevers have been operated in intermittent contact using electrostatic actuation via large
capacitive platforms integrated into the cantilevers.69
3.4 Cantilever Characterization and Calibration
All applications of heated cantilevers require an understanding of the cantilever mechanical, electrical, and thermal characteristics. Detailed characterization also enables quantitative fundamental measurements. Typical silicon heated cantilevers have spring constants
ranging from 0.01 to 10 N/m, and resonant frequencies ranging from 50 to 300 kHz and
are calibrated using the thermal noise method.34,35,69 Raman microspectroscopy enables
cantilever temperature characterization with spatial and temperature resolutions of 1 µm
and 3◦ C.34,52 The electrical resistivity of the cantilever heater depends on temperature and
is used for temperature calibration. The cantilever response near the thermal runaway is
stabilized via an electrical “burn-in” process that also allows long-term storage of such
cantilevers.52 The thermal transient response of heated cantilevers is given by the thermal
time constant, which is measured from the pulse response and is on the order of 0.1–
100 µs.34,35,40,65 Although heated cantilevers are typically used in ambient air, they have
been operated in a variety of environments.14,51,56−58
The way that the cantilever is heated can affect experimental precision and accuracy.
Heated cantilevers are typically heated in an open loop with either a constant (DC) or alternating (AC) bias voltage or current through the cantilever heating circuit. Compared to
the AC mode of operation, the DC mode enables simpler experimental set up and interpretation of measurements while the noise and drift in the thermal signal are larger.62,72
Besides a high signal-to-noise ratio, an important benefit of the AC mode is the ability to
study frequency-dependent electric and thermal phenomena.9,53,68,82 Cantilevers can be
operated via feedback schemes wherein a parameter such as the cantilever power supply or
the cantilever resistance is held constant. This technique enables substantial improvements
in sensitivity, resolution, drift correction, and transient response.88,101,102
An understanding of the mechanical and electrothermal dynamics of heated cantilevers
can help improve high-speed electrothermal cantilever operation.61 The frequency dependence of heater dynamics such as sensitivity, noise, resolution, and bandwidth can be
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understood by using a systems approach that involves decoupling and then linking the
cantilever thermal and electrical response in a linearized model.103 The bandwidth of
data storage heated cantilevers was found to be 100 kHz using this approach. The cantilever mechanics can also be integrated into the aforementioned cantilever electrothermal
model.102
3.5 Arrays of Heated Cantilevers
Arrays of AFM cantilevers can have higher throughput than single AFM cantilevers. Figure 7(a) shows one of the first cantilever arrays that had integrated piezoresistive sensors.104
Heated AFM cantilevers are attractive for arrays, since they can be individually addressed
through independent electrical connections.
Figure 7(b) shows a 2D array of 1024 silicon cantilevers with integrated heater thermometers developed for thermomechanical data storage.83,105 The cantilevers were operated in parallel via time-multiplexed electronics that addressed cantilevers row by row.39
Schottky diodes were integrated in series with each cantilever to reduce the cross talk
between cantilevers.37 The array chip thermal expansion was reduced by aligning the cantilevers in a 2D grid.39,83 This thermal expansion was compensated by heating the chip
using embedded heater elements coupled with temperature sensors on each side of the
chip. Engaging the array onto the surface was simplified by performing position feedback
on dedicated approach sensor cantilevers at the corners of the array chip and not on each
cantilever in the array. In other words, certain cantilevers in the array were optimized for
purposes besides data storage in order to maximize array bandwidth.33 Tip wear and loading force on the sample were reduced by using low-stiffness cantilevers. Thermal constrictions around the heaters allowed for a small cantilever thermal time constant.83 Increased
packaging density of the cantilever array was achieved by bonding the cantilever array chip
to a second wafer already containing the electrical interconnects.83,106
Figure 7(c) shows a cantilever array developed with both piezoresistive and heaterthermometer sensors integrated into each cantilever. Electrical cross talk between the two
sensors on each cantilever was minimized by doping the leg regions differentially such that
a diode was formed between the leads of two sensors. The noise-limited resolution of the
heater sensor was 0.46 nm/Hz1/2 while that of the piezoresistive sensor was 3.4 nm/Hz1/2 .
These were among the first active cantilever arrays integrated into a commercial AFM.107
Figure 7(d) shows an array of cantilevers with integrated heaters that was integrated into a
commercial AFM using an architecture of custom electrical and mechanical adapters that
could be scaled to arrays of different sizes, and sensor or actuator configurations.108
Figure 7(e) shows an array of 1024 thermal cantilevers having integrated aluminum nitride actuators and metal-metal junction tips. The cantilevers could either be used to sense
temperature or as nanoheaters for data storage purposes.109 Figure 7(f) shows an array
of thermal cantilevers with microbolometers integrated at the tips for thermal topography
imaging.110 The compliant cantilevers had a dynamic range of 7 µm, obviating an actuation mechanism for the array, thus allowing the imaging of delicate biological samples
and surfaces with very tall features Fig. 7(g) shows an array with gold/silicon nitride thermal bimorph cantilevers used to actuate the cantilevers toward the surface for performing
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FIG. 7: Cantilever arrays with thermal elements. (a) Array of piezoresistor embedded cantilevers.104 (b) IBM Millipede with 1024 heated cantilevers.37 (c) Array of cantilevers with embedded piezoresistors and heater-thermometers.107 (d) Array of heated
cantilevers.108 (e) Array of 1024 thermocouple cantilevers.109 (f) Array of highly compliant cantilevers with microbolometers at the tips.110 (g) Array of cantilevers actuated
via thermal bimorph.100 (h) Array of bimaterial cantilevers for sensing heat flow using a
combination of piezoresistive and heater sensors.111
DPN.100 Heaters integrated into cantilever arrays have also been used to actuate the cantilevers. The thermal bimorph actuation method is suitable for low cantilever actuation
frequencies, small cantilever footprint, large deflection, and low voltage of operation. Figure 7(h) shows a microcantilever array designed to sense heat flows from infrared sources,
for applications such as microcalorimetry and mass detection.111 The deflection of each
bimorph cantilever that was sensed by an integrated piezoresistor was an input for a microheater at the cantilever base. The cantilever irradiation was measured from the heat
supplied by the heater to compensate the cantilever deflection.
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3.6 Related Cantilever-Based Thermometry Techniques
The development of heated AFM cantilever technology has been informed by related developments in bimaterial cantilever temperature sensors and SThM.10,112−118 Bimaterial
cantilevers have measured a variety of behaviors including chemical reaction energies
with a resolution of around 1 Pj,116 light with a power resolution of 40 pW,119 near-field
radiation,114,120 and thermal conductivity of polyethylene nanofibers.115 To improve the
sensitivity of a bimaterial cantilever, a thermal constriction was implemented in a bimaterial cantilever by using thin, long, and narrow isolation legs between the heated region
and the cantilever base.112,113 Analysis of bimaterial cantilevers also led to experimental
values for cantilever conductance of 7.91 µW/K25 and an air heat transfer coefficient of
3400 Wm−2 K−1 ,26 which are fundamental to understanding cantilever temperature distribution.
SThM measures local temperature or thermal properties of a sample with a sharp tip.
At first, the scanning tunneling microscope (STM) measured the temperature-dependent
tunneling voltage between the STM tip and the sample.1,121 Subsequent studies utilized
AFM cantilever–based sensors such as an AFM cantilever with an integrated thermocouple junction2,10,24,26,28,117,122−125 or a resistive element,75,79−82,126,127 although several
SThM schemes employed a regular AFM cantilever.74,76 In order to improve the spatial
and temporal resolution, the sensor size was scaled down to below 100 nm75,125 and the
sensing region was thermally isolated.54,123,125 Sensor fabrication and characterization
became cost efficient due to the development of batch fabrication methods.26,28,122,125
Fundamental understanding of cantilever heat transfer has led to improved sensor design
and measurement techniques.54,123,125
4. APPLICATIONS
The key applications that drove early research on heated microcantilevers were thermal
microscopy,2 data storage,3 and materials analysis.8,128 This research generated improved
fundamental understanding of heat transfer from the cantilever as well as advancements
in the design, fabrication, and use of heated AFM cantilevers. This research enabled new
applications for these cantilevers.
4.1 Data Storage
A heated AFM cantilever enables a nanomechanical data storage concept, in which the
heated AFM cantilever tip can melt small indentation data bits into a thin polymer film.83
Large arrays of individually addressable heated tips enable high data throughput.33,47,69
Figure 8(a) shows a schematic of the array named the Millipede due to the thousands
of cantilevers.37,39,106 The array is scanned in contact with a thin polymer film. When
the tip is hot, it sinks into the film and forms an indentation that serves as a data bit. A
warm cantilever can be used to read the data indentations by measuring the heat transfer
between the cantilever and the surface.4,47 Figure 8(b) shows an image of the Millipede
array. Figures 8(c) and 8(d) show some examples of data bits written with the Millipede.
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FIG. 8: (a) A graphic representation of the Millipede device writing data bits on a soft
polymer surface.37 (b) Optical picture of the Millipede array in its packaging.37 (c,d) Data
bits written with the Millipede.4
Over a period of several years, a series of publications reported significant improvements in data storage performance, as well as increases in cantilever and systems complexity. The original heated cantilever design concept had two doped silicon legs and a
doped heater at the tip.83 The same heater could be used to write and read indents.4,47
Heat transfer simulations showed that a smaller heater allowed for increased writing speed
by reducing the heating time, while a larger heat transfer increased read sensitivity.33,47 To
maximize both speed and sensitivity, a separate thermal readback sensor was introduced
to operate hotter than the tip with read sensitivities of 1 × 10−4 nm−1 . The writing heater
at the tip was reduced in size, leading to a thermal time constant of ∼1 µs. A capacitive
platform enabled electrostatic cantilever actuation by applying a bias between substrate and
cantilever, making it possible to mechanically actuate the cantilever.129 As device complexity increased, so did the interconnect architecture and packaging complexity.106 The data
rate and data density of thermomechanical data storage increased significantly over time.
The data density is limited by the size of each data bit, which is governed by the heated
tip sharpness as well as the mechanical properties and thickness of the polymer substrate.4
Data writing speed is determined by the heated cantilever thermal pulse time, and reading
speed is determined by the speed of the x − y scanner stage. Early demonstrations of the
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Millipede reached 65 Gbit/in2 data densities at 10 Mbits/s readback rates.130 As the heater
thermal time constant, polymer chemistry,131 and scanning stage improved,129,132 heated
tips achieved a data density of 1 Tbit/in2 at a single tip data rate of 10 Mbps.133
4.2 Measurements with Heated Tips
Heated AFM tips have been used to measure the nanometer-scale thermal, mechanical,
and electrical properties of materials. The cantilever heater temperature is controlled in
order to set the temperature of the tip-substrate interface, and the material response is then
measured. The spatial resolution of heated tip measurements is governed by the contact
between tip and sample, as well as the sample thermal properties.
A heated tip can measure the thermal conductivity and heat capacity of a surface with
nanometer-scale resolution. Qualitative measurements of heat transfer between micro–
heater-thermometers and samples have been made for a variety of tips and substrates.2,18,25,134,135 Thermal conductivity calculations require a thermal resistor network
model and knowledge of the cantilever dissipated heat and heater temperature. Tracking
heat dissipation and heater temperature while scanning a surface provided nanometer-scale
thermal conductivity for a variety of substrates.2,8,25,78 Transient heat transfer measurements of thermal diffusivity were performed by applying a periodic bias to the cantilever.78
Nanometer-scale objects embedded below a surface were detected with a heated tip by
measuring changes in heater power dissipation.78
Cantilever heater power dissipation is sensitive to the distance between heater and
substrate, allowing heated tips to measure surface topography. The first nanotopography
measurement was a nondestructive SPM technique employing a 100 nm sharp heated
thermocouple tip, which measured heat flow between the tip and substrate with 100 nm
resolution.1 Heated AFM cantilevers were used for thermal topography imaging in both
DC53 and AC89 operation. Thermal imaging with heated cantilevers obtained simultaneous thermal and topographical images of biased electronic devices and interconnects using
a wire thermocouple tip.24 Thermocouple junction tips fabricated with silicon oxide and
silicon nitride had lower thermal conductivity than silicon tips, which reduced heat dissipation at the thermocouple junction and improved spatial resolution to 50 nm.30 Heated tips
with low–thermal conductivity polyimide cantilever beams achieved a 2.3 mK temperature
sensitivity because the cantilever beam conducted less heat away from the tip.136 Operating a heated silicon AFM tip with a closed-loop temperature control scheme increased
topography sensitivity 100-fold over previous work to 4.68 mV/nm.88
Heated cantilever tips can detect the local phase change in materials. A heated tip detects the glass transition temperature by measuring a change in heater-sample distance or
dissipated power when the tip melts the surface and sinks into it. A Wollaston wire tip can
measure the onset of melting in a variety of polymers by measuring changes in heat flow
due to changes in material phase.8 The spatial resolution is about 10 µm, depending on
the material properties. Glass transition, melting, recrystallization, and thermal decomposition temperatures were measured for a number of polymers within material volumes of a
few cubic micrometers. Soft polyimide cantilevers with integrated thin film metal resistors
were developed to improve spatial resolution and soft sample compatibility, and were used
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to measure glass transition temperatures in photoresists.25 Silicon heated cantilevers were
used for glass transition measurements because silicon cantilevers have the sharpest tips for
high resolution, and they have high resonant frequency for dynamic measurements. Glass
transition temperatures were measured using nanometer-scale thermal analysis (nano-TA),
where a heated cantilever could measure temperature-dependant material softening and
glass transition with about 50 nm spatial resolution.9,137,138 Thermal analysis with heated
tips has been used to measure the nanometer-scale spatial distribution of phases, components, and contaminants in polymers, pharmaceuticals, foods, and biological and electronic
materials.139
Applying external oscillations to a heated AFM tip while performing nano-TA provides additional substrate mechanical behaviors.9,140,141 This technique can measure elastic moduli, damping factors, and thermal expansion coefficients with lower noise than conventional nano-TA for zeptoliter material volumes.73,142 Heated cantilevers were recently
oscillated by Lorentz forces to perform local mechanical property analysis.15
Heated AFM cantilever tips can measure transport in low-dimensional electronic nanostructures.125 A tip with a thin film metal thermistor measured local temperature along a
Joule-heated graphene nanoribbon (GNR), and to measure hotspots in defective GNRs.143
A thermocouple tip was used to measure the topography and local temperature of a 350
nm–wide resistively heated gold line, and showed that tip conduction is much more important than air conduction for submicron heated regions.44 Local thermal and electric fields
from a heated tip were used to study transport in single-wall carbon nanotube field-effect
transistors (CNTFETs) in both contact and tapping modes.93
A tip-sample temperature gradient results in a thermoelectric potential that can be used
to determine tip and sample Seebeck coefficients. Local temperature-dependent contact
potential measurements on a gold substrate were used to estimate a Seebeck coefficient of
–4.30 mV/K between tip and sample.92 Knowledge of the tip-sample Seebeck coefficient
can be used to calibrate the tip temperature while in contact with conducting surfaces.74 A
three-legged electrothermal cantilever with independent control of tip bias and heater temperature was used to measure the thermoelectric voltage at a point contact.94 In a similar
measurement, a metal wire tip measured the thermal conductivity and Seebeck coefficient
of thin films.144 Temperature increase was measured via changing resistance of the tip as
a function of input power, and the Seebeck voltage was measured across the tip and a thin
Au strip deposited below the film. The measurements were performed for porous films of
Bi2 Te3 and Bi2 Se3 , which are thermoelectric materials. SThM was also used to measure
electric conduction and thermoelectric voltage in individual NaCo2 O4 nanofibers using a
doped silicon thermal cantilever.145
Heat transfer modeling can help to resolve materials properties from the measured
temperature and heat flows. A key challenge is to accurately distinguish tip-sample heat
flux from the large flux from the heater to its surroundings. Tip-sample contact resistance
is another heat transfer modeling component difficult to estimate. A dual cantilever device
was used to measure the tip-sample heat flux with one cantilever as a local heater and a
second cantilever as a thermometer.146 Another experiment isolated heat flux to the air
by comparing the temperature of a tip with thin film heater just before and during surface
contact.54 A noncontact local thermal conductivity technique was developed to eliminate
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the need to model contact resistance.42 A three-legged electrothermal cantilever measured
surface temperature under the tip, and it was found that a contact resistance of 108 K/W
should be used in tip-sample heat transfer models.94
4.3 Measurements with Heated Cantilevers
A number of analytical measurement techniques use the cantilever heater and not the
tip, such as calorimetry or thermogravimetry. Heated cantilevers can perform thermogravimetry on nanogram-sized samples. The first thermogravimetry device was a heated
cantilever with an integrated piezoresistor used to measure cantilever vibration.128 The
cantilever measured the dehydration temperature of copper sulfate pentahydrate by monitoring the shift in resonance frequency on a heating the device.128 Resistively heated cantilevers were designed and fabricated with large heaters and uniform temperature distributions for more accurate thermogravimetric analysis.147 A microcantilever hotplate with
an integrated piezoresistor strain gauge achieved 1–3 ng resolution by compensating for
temperature-induced strain.96 Microcantilever hotplates are capable of thermogravimetry
with 10 K/s heating rates and nanogram resolution.85,96
Heated cantilevers can perform calorimetry by monitoring cantilever temperature during chemical reactions. A heated piezeoresistive cantilever detected the presence of explosive materials on the cantilever by inducing deflagration.148 An array of single-crystal
silicon microhotplates was developed for differential scanning calorimetry.149 The hotplate had a very high heating efficiency of 36.7 K/mW with a time constant of 1 ms. A
microhotplate with a heat capacity of 50 nJ/K was developed to measure reaction rates
of platinum-catalyzed combustion of hydrogen in air.150 Recently, a polysilicon-based advanced microcalorimetric membrane was developed to measure reaction heats of propane
oxidation in air.151
Microhotplates can measure thermal transport in small samples such as individual nanotubes or micro-/nanofibers. A microfabricated suspended device with platinum thin film
heater-thermometers supplied heat to measure thermal transport in individual multiwall
carbon nanotubes.152 The measured thermal conductivity of 3000 W/m K exceeded previous estimations by two orders of magnitude. In another experiment, a thermal cantilever
captured the temperature response at one end of glass nanofibers subjected to pulse heating
at the opposite end to calculate thermal diffusivity.153
A microcantilever heat source can induce fluid flow. Measurements of fluid motion near
a heated cantilever using particle image velocimetry (PIV) showed fluid convection around
a heated cantilever.51 On liquid surfaces, large temperature gradients induced by thermal cantilevers have been shown to induce flow velocities approaching 3000 µm/s.154,155
Microfluidic actuation of water and oil achieved by the Marangoni effect were used to
generate toroidal and doublet flow patterns. The use of programmable arrays to perform
has demonstrated the scalability and viability of this alternate method for fluidic manipulation on a featureless substrate.156,157 Microcantilevers with integrated resistive heaterthermometers have also been used as a metrology tool to investigate convective heat flow
in microscale jet flows.158,159 By modulating the heating and cooling of the microheater,
a full boiling curve for the hydrocarbon microjets was constructed.
311
4.4 Nanofabrication Using Heated Tips
Heated AFM tips can fabricate a wide variety of nanostructures by mechanically or chemically modifying surfaces, depositing material onto surfaces, or providing temperature required for material growth. A wide variety of materials have been patterned with heated
AFM cantilever tips, including organics, metals, nanoparticles, biomaterial, carbon nanotubes, and graphene.
A variety of heated tips were used to form pits into a polymer surface.3,160−162 Figure 9(a) shows data bits written in a polycarbonate substrate spaced less than 200 nm apart
with a patterning time of 5 ms per bit.22 More recently, thermal lithography focused on
more complicated geometries for mask formation, and employed solid state heater tips
to maximize spatial resolution.163,164 Figure 9(b) shows a fractal pattern consisting of
774,000 pixels written in 12 s with a heated tip at 2 µs per pixel.165 This patterning speed
was achieved by electrostatically forcing the hot tip into contact for 1–10 µs and by eliminating the need for conventional AFM laser feedback.
Heated tip nanolithography based on nanometer-scale thermochemical reactions is
known as thermochemical nanolithography (TCNL). The first demonstration of TCNL
selectively cross linked nanometer-scale patterns in photoresist.166 Semiconducting nanostructures were patterned in diazide-dyine thin films by thermally inducing cycloaddition.167
Figure 9(c) shows electroluminescent poly p-phenylene vinylene (PPV) nanosctructures
created by local heating of a sulfonium salt precursor film.71,168 Local heating with a
heated tip reduced graphene oxide to produce conducting graphene nanoribbons, shown in
Fig. 9(d).6 Scanning a hot tip on a sol-gel precursor film converted the film into crystalline
ferroelectric nanostructures on a variety of electronic-compatible substrates.169 Heated tips
formed 3D patterns in thin films that undergo thermal sublimation.7,170 Figure 9(e) shows
a 10 × 20 µm nanopattern of the world written using a thermal tip heated to 700◦ C.171
TCNL has also been used to chemically modify the surface properties of films. A heated
tip converted a hydrophobic surface to a hydrophilic surface by inducing a reversible chemical change at the surface of the film.172,173 Heat from a thermal tip deprotected a surface
by removing an amine group, and multiple biomolecules subsequently functionalized the
exposed regions, shown in Fig. 9(f).174 Heated tips formed patterns on block copolymer
films that allowed for bioconjugation.175,176 In all cases, it was shown that features on the
order of 100 nm were produced with TCNL.
Thermal cantilevers can deposit material from the tip to the substrate.72,177−182 Thermal dip pen nanolithography (tDPN) uses a heated cantilever tip to deposit inks that are
solid at room temperature by melting the ink and transferring it to the substrate. Thermal dip pen nanolithography has advantages over conventional dip pen nanolithography
(DPN),183 where a water-soluble ink diffuses from the tip to substrate through a water
meniscus at the tip. In tDPN, polymer only transfers when the tip is hot, making it possible
for an unheated tip to measure written feature topography without depositing ink. A heated
tip can deposit many thermoplastic polymers and does not require a meniscus to mediate transport. The rate of ink flow can be controlled by changing the tip temperature.72
Thermal cantilevers first deposited octadecylphosphonic acid (OPA) molecules on mica.72
The ink did not transfer to the surface until the heater temperature exceeded 100◦ C, and
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313
FIG. 9: Nanopatterns and nanostructures created using a heated tip. (a) Early work on thermomechanical data bit writing on polycarbonate.22 (b) A fractal pattern thermally written
at a rate of 2 µs/pixel and read at 0.75 mm/s.165 (c) Nanopatterning of an organic semiconducting polymer poly (p-phenylene vinylene).71 (d) A heated tip forms graphene nanoribbons on graphene oxide by thermal reduction.6 (e) A 3D topographical map of the world.171
(f) Functionalized nanopatterns created by selectively deprotecting amines and exposing to
thiols, maleimides, aldehydes, or biotins.174 (g) Deposition of a poly(3-dodecylthiophene2,5-diyl) semiconducting polymer between two metal electrodes.180 (h) Nanosoldering indium deposited between two electrodes using thermal dip pen nanolithography.177 (i) Patterning of polymer nanostructures with aligned iron oxide nanoparticles.181
the rate of transfer increased with increasing temperature. Molecular-level patterning control can be achieved with tDPN. Poly(3-dodecylthiophene) (PDDT), a semiconducting
polymer, was deposited one monolayer at a time, lying flat against the surface.178 The
heated tip deposited the polymer between gold electrodes in order to enable the electronic
properties measurements on the semiconducting polymer, shown in Fig. 9(g).180 Poly(Nisopropylacrylamide) (PNIPAAm) was patterned onto a surface and reversibly bonded to
proteins by inducing a hydrophobic-hydrophilic phase transition.179 Thermal tips have patterned low–melting point metal indium between two electrodes to make electrical contact,
shown in Fig. 9(h).177
Nanoparticles 2–10 nm in diameter that are magnetic, semiconducting, fluorescent, and
metallic can be mixed into polymer ink and thermally deposited onto surfaces, shown in
Fig. 9(i).181 In some cases, the particles align in a single row of particles at the center of a
wide line of polymer, attributed to high shear on the polymer induced by the speed of the
tip. Gold nanoparticles mixed into semiconducting polymer dope the material and raise its
conductivity.
Graphene nanoribbons were fabricated using tDPN.182 The heated tip deposited polymer on top of a graphene sheet between two electrodes. Xenon difluoride gas converted
exposed regions to insulating flourographene. The polymer on top of the resulting nanoribbon reduced edge defects and prevented the graphene nanoribbon from absorbing contaminants.
Heated cantilevers directly grew carbon nanotubes (CNTs) onto the heater region.184,185
A heated cantilever was placed into a chemical vapor deposition chamber and heated to
314
800◦ C for 15 min while reactive gases flowed through the chamber.184 The chamber was
unheated during the experiment, and CNTs grew only on the cantilever heater. Heated cantilevers also grew CNTs while immersed in solution.185 Heated cantilever growth provides
a high-throughput, array-scalable technique for synthesizing nanomaterials.
5. CHALLENGES AND OPPORTUNITIES FOR HEATED AFM
CANTILEVERS
There have been significant advances in the design, characterization, and application of
heated AFM cantilevers. These advances have led to new applications that have had both
research success and commercial success. Heated AFM cantilevers have also enabled new
ways to measure and exploit nanometer-scale heat flows. These advances in both fundamentals and applications present exciting opportunities and challenges.
The key fundamental opportunity for a heated AFM tip is to investigate nanometerscale heat flows. A heated AFM cantilever tip can form a nanometer-scale hotspot on
a substrate, which for some substrates may produce subcontinuum heat flows. The very
steep temperature gradient can also produce thermoelectric effects. The key fundamental
challenge is to measure heat flow through the tip and to assess the temperature at the tipsample interface. Quantitative comparisons between experimental observations and theory are needed. The simulations must account for the macroscopic heat flows from the
cantilever as well as the microscopic heat flows through the tip and substrate. The key
experimental challenge is to understand heat flows at the nanometer-scale interface between the heated tip and a substrate.
The key applied opportunity for heated AFM cantilevers is for materials characterization. While many publications have shown heated AFM tips used to investigate polymers,
only a little work has been published on the investigation of biological samples.142 Heated
AFM cantilevers work well in water and buffer solutions,57,58 which could enable integration into microfluidic systems and perhaps in vitro experiments. While heated AFM
cantilevers and cantilever tips have been used for calorimetry and thermogravimetry, there
is a need for further research to make these measurements quantitative and useful in the analytical chemistry laboratory. This work could include heated AFM tip measurements for
temperature-dependent dynamic mechanical analysis or rheometry at the nanometer scale.
While there is significant interest in materials for energy applications, only a little work
has been done to use heated AFM tips to characterize energy materials. Heated AFM cantilever tips could be used to characterize thermoelectric186 or pyroelectric169,187 materials
at the nanometer scale. Heated AFM tips could also be used to characterize temperaturedependent transport processes in energy storage systems.188
An important trend in AFM technology is the combination of nanometer-scale tips
with optical beams.189,190 Heated tips could be combined with infrared191,192 or Raman spectroscopy190 for novel thermochemical measurements. Nanometer-scale chemical
measurements are a significant opportunity for scanning probes in general, and the ability to control local temperature offers an orthogonal probe of material behavior. Another
important trend in AFM technology is the deepening understanding of cantilever mechanical dynamics and how the cantilever dynamics can be exploited for new applications.193
315
There are opportunities for novel operating concepts that couple cantilever electrothermal
dynamics with cantilever mechanical behavior.
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chapter 10 heated atomic force microscope cantilevers and their

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