Mapping Temperature Using Transmission Kikuchi Diffraction

Abstract

Electronic devices are engineered at increasingly smaller length scales; new metrologies to understand nanoscale thermodynamics are needed. Temperature and pressure are fundamental thermodynamic quantities whose nanoscale measurement is challenging as physical contact inevitably perturbs the system. Here we demonstrate Kikuchi diffraction thermometry (KDTh), a non-contact scanning electron microscope (SEM) technique capable of mapping nanoscale temperatures and pressures. KDTh detects local volumetric lattice changes in crystalline samples by precisely fitting Kikuchi patterns. Temperature changes are deduced using the coefficient of thermal expansion (CTE). We map lattice parameters and temperatures on Joule-heated graphite by rastering a 5.5-nm electron probe across the sample. Our parameter precision is ~0.01% and our temperature sensitivity is 2.2 K/$\sqrt{Hz}$. KDTh offers advanced sensitivity by fitting the entire Kikuchi pattern, even beyond the precision measured in transmission electron microscopy. KDTh can operate in both transmission (transmission Kikuchi diffraction, TKD) and reflection (electron backscatter diffraction, EBSD) modes.

Figures (4)

• Figure 1: Strain mapping with TKD. a) Diagram of in-situ biasing setup in the SEM chamber. The sample is attached to the back of the holder, and the electrical connection is established through a ribbon cable (see Supplementary Information "Microchip Design"). The setup utilizes an off-axis TKD detector geometry. The black solid lines and gray dashed lines indicate collection angles for typical TKD and 4D-STEM systems, respectively. b) SEM image of a MoS$_2$ flake collected by forward-scatter detectors. c) A TKD pattern from the middle of the MoS$_2$ flake. A high-symmetry zone axis [0001] is at the bottom of the pattern outside of the collection region. The band highlighted with solid white lines corresponds to the family of lattice plane $(1\bar{1}00)$. The width of the Kikuchi bands varies with strain, with red and blue dashed lines indicating the directions of change that correspond to positive and negative strain respectively. d) Inverse pole figure (IPF) map overlayed with SEM image and IPF (inset) showing (0001) alignment. e) Strain map of the MoS$_2$ flake. f) Normalized cross-correlation coefficient (NCC) plot from two different pixels in e), the position of the max NCC is the best fit lattice parameter.
• Figure 2: Detection of thermal expansion. a) SEM image of a graphite flake connected to three Cr/Au electrodes. Electrode 1 and 2 are used to bias the graphite flake. The white box highlights the region where TKD maps are acquired. b) Strain map of the graphite flake without electrical bias, overlaid on the SEM image. c) Strain maps of the graphite flake at different applied heating powers (see Supplementary Information "Strain Maps" for complete maps). The strain increases with applied power due to thermal expansion. d) Histogram of lattice parameter $c$ measured at different heating powers. All scale bars are 5µm. The color bar applies to both b) and c).
• Figure 3: In-situ temperature mapping while stepping the power. a) A graphite flake connected to three Cr/Au electrodes. Electrodes 1 and 2 are used to bias the graphite flake. MoS$_2$ flakes scattered around the window are ignored in this study. b) Temperature map of the graphite flake while the heating power is varied six times during a TKD scan. The six different temperatures are visually distinguishable. c) Histogram of the measured lattice parameter $c$ for the six different regions in b). The peaks correspond to different heating powers are clearly separated. d) Temperature change as a function of biasing power. A linear relation is observed. e) Row-average temperature plotted with corresponding heating power. f) A summary of temperature measurements done in electron microscopes liu_novel_2006vijayan_situ_2018park_direct_2021brintlinger_electron_2008cremons_direct_2016fritsch_sub-kelvin_2022wu_novel_2012wu_development_2013gnabasik_fast_2025chen_detecting_2022hu_mapping_2018barker_automated_2021mecklenburg_nanoscale_2015cretu_nanometer-level_2023lagos_thermometry_2018kikkawa_optical_2022idrobo_temperature_2018minson_quantitative_2023chen_estimation_2024. The probe size or fiducial size limits the spatial resolution. However, the spatial resolution for temperature mapping is also limited by the phonon mean free path mecklenburg_nanoscale_2015, which is typically a few nanometers or above. Therefore, a probe size below 1 nm does not necessarily mean an improved spatial resolution for temperature mapping. The dashed lines represent relative sensitivity limit for different types of electron guns (see Supplementary Information "Gun Brightness Limited Measurement Sensitivity" section for details).
• Figure 4: Continuous temperature ramp. a) SEM image of a graphite flake in contact with three Cr/Au electrodes. The black rectangle indicates the field of view where TKD mapping is performed. b) A map of lattice parameter $c$ of the graphite flake derived from the TKD map as the heating power varies. The row-average of the lattice parameter tracks the varying heating power, indicating the temperature induced thermal expansion. c) Histogram of b). The two peaks, corresponding to 0 mW and 70 mW, respectively, are separated by $1.86\pm0.02$ pm, which corresponds to a temperature difference of $101\pm1$ K. The dashed lines indicate the fit window around each peak, and the red curves represent fits to a Gaussian distribution. d) Temperature versus heating power. The temperature change induced by Joule heating is $1.5\pm0.1$ K/mW. Black arrows indicate the chronology of the power ramp.