Scanning joule expansion microscopy
Thermal measurements at the nanometer scale are of both academic and industrial interest, particularly in regards to nanomaterials and modern integrated circuits.
AC or pulsed electrical signal is applied to the sample creating Joule heating and resulting in periodic thermal expansion.
Since AFM has feedback controller with a bandwidth, for example 20 kHz (different AFM may have different bandwidths), the signal below 20 kHz is captured and processed by the feedback controller which then adjusts the z-piezo to image surface topography.
Joule heating frequency is kept well above 20 kHz to avoid feedback response and to separate topological and thermal effects.
Usually expansion signals approximately 0.1 Angstroms start to be detected, although the resolution of SJEM highly depends on the whole system (cantilever, sample surface, etc.).
By comparison, Scanning Thermal Microscopy (SThM) has coaxial thermocouple at the end of sharp metal tip.
The quality and resolution of the images are very dependent on the nature of the thermal contact between tip and the sample; hence it is quite difficult to control in a reproducible way.
[3] Scanning Joule Expansion Microscopy, however, has the potential of achieving similar to AFM resolution of 1~10 nm.
In practice, however, the spatial resolution is limited to the size of the liquid film bridge between the tip and the sample, which is typically about 20 nm.
Scanning Joule Expansion Microscopy has been used to measure the local heat dissipation of an in-plane gate (IPG) transistor to study hot spots in semiconductor devices,[4] and thin-film alloy like cobalt-nickel silicide.
[5] Signal obtained by the AFM (and captured by lock-in amplifier) are actually representations of the cantilever deflection at a specific frequency.
For sinusoidal heating, the wavelength of the acoustic wave in air with speed of 340 m/s is about several millimeters, which is much larger than the length of cantilever.
Typically, piezoelectric expansion is linearly dependent on applied voltage and a simple subtraction can be used to correct for this effect.
Electrostatic force does not depend on the frequency of the applied AC signal, therefore allowing for a simple method to differentiate and account for this contribution.
More importantly, after coating, the signal only depends on the temperature, independent of the expansion coefficient of different materials, allowing for SJEM to be used for a wide array of samples.
In addition, expansion signal increases monotonically with the thickness of coating polymer, while the resolution will decrease due to greater thermal diffusion.
In order to extract accurate temperatures, additional modeling taking into account thermal expansion and cantilever bending is necessary.
In such software, the appropriate differential equations for electrical, thermal and mechanical expansion are chosen and proper boundary conditions are set.
Miniaturization of modern integrated circuits has led to hugely increased current densities and therefore, self-heating.
In addition, these large, highly localized temperature fluctuations cause repeated stress gradients on the vias, ultimately leading to device failure.
Traditional thermometry techniques use electrical characterization to determine resistivity and estimate the average temperature along an interconnect.
However, this method is not able to characterize local temperature rises which may be significantly higher near vias due to their extremely high aspect ratios.
Optical methods are diffraction limited to resolutions greater than 1 um, far larger than most modern vias feature sizes.
SJEM has been used to do in situ thermal mapping of these devices with lateral resolution in the sub-0.1 um range.
SJEM has been used to extract thermal conductivities of constrictions in different thicknesses of thin metallic films.
In particular, SJEM can be directly used for characterization of band gap distributions in nanotube transistors, nanowires, and graphene nanomeshes and nanoribbons.
Near the edges where large height differences or material mismatches exist, artifact expansion signals are usually detected.
In addition, at a large step, loss of contact between the tip and the sample could result in an artifact in the image.
Finally, interactions between the tip and electric field can occur when large gate biases are applied to the substrate.
The contribution from these artifacts can be reduced by applying thicker polymer coatings or operating at a lower gate bias to decrease electric field.
