Scanning thermal microscopy (SThM) enables thermal conductivity (λ) measurements with a lateral resolution down to a few tens of nanometers. The present work investigates ways to improve SThM images recorded with resistive probes. Probes based on resistance thermometry act both as a thermometer and as a Joule heated nanoscale heat source. The influence of amplitude and frequency of the applied heating voltage on the SThM image quality was systematically studied. To connect the investigated heating parameters to the temperature change at the apex of the SThM probe, electrical–thermal finite element simulations were performed. Image quality was assessed according to three criteria. The first criterion was the thermal contrast (thermal resolution) between materials of different λ’s. To convert measured SThM signals (in mV) into thermal resolution (in Wm−1 K−1), reference measurements were performed by time-domain thermoreflectance, and an implicit calibration method was employed. The second criterion was the distortion of the thermal image by topography. To illustrate the image distortion, the standard deviation of the thermal trace-minus-retrace profile was taken, which could be reduced nearly ten times by changing the heating parameters of the used SThM setup. The third criterion was the spatial resolution of the thermal images. To assess the spatial resolution, gradients in the thermal signal at interfaces between materials were extracted from profiles through thermal images.

High-resolution images of thermal conductivity (λ) and temperature distributions are possible by scanning thermal microscopy (SThM), a variant of scanning probe microscopy (SPM).1,2 Owing to a spatial resolution down to a few tens of nanometers, SThM has become an integral part of the experimental landscape in submicron heat transfer studies. For instance, accurate thermal characterization at the nanoscale helps to understand failure mechanisms (reliability and lifetime) in micro- or nanoelectronic devices and study the impact of nanometer-scale heat transfer on engineered systems.1 

SThM is commonly performed using SPM in which the probe holder is modified to support a thermal probe. For most probes, topography information is captured simultaneously with the thermal information. Various types of thermal probes exist; common sensing mechanisms are Seebeck thermovoltage,3,4 fluorescence,5 thermal expansion,6 or variation in electrical resistance.7,8 Thermal probes that are based on resistance thermometry are, in particular, metallic probes7–10 and doped silicon probes.11 For measurements of λ, resistive thermal probes are heated electrically by DC or AC. The hot tip apex acts as a heat source, exciting the sample and, at the same time, allows measuring the tip temperature in contact with the sample due to the temperature dependency of its electrical resistance. The tip temperature depends on the applied heating power and the heat transfer from the tip to the sample, which depends upon other parameters on the local λ of the sample.12,13

Exciting the probe with AC results in an improved signal-to-noise ratio (SNR) since lock-in detection is possible.1 It was shown that AC modulated methods have better baseline stability and apply lower thermal perturbation to the sample, resulting in higher sensitivity, stability, and resolution than DC methods.12,14

Amplitude and frequency of the applied AC heating voltage can influence the SThM image quality. In general, higher probe temperatures lead to a better signal-to-noise ratio and are thus expected to improve the thermal contrast between materials of different λ’s in the SThM image (also called thermal resolution). However, it may also damage samples sensitive to temperature or burn out of the SThM probe. An increase in thermal contrast was studied for different probe temperatures.15 The optimal probe temperature depends on the investigated sample: For thermal measurements on silicon dioxide (SiO2) on top of a bulk silicon substrate, saturation of the thermal contrast at higher probe temperatures was found, in contrast to measurements on steps of different heights of a hexagonal boron nitride (h-BN) sample. However, the thermal contrast was discussed only in terms of the temperature-dependent voltage drop at the SThM probe; hence, no correlation to the actual thermal resolution (in Wm1K1) was provided. Most works on SThM focus on qualitative measurements, as calibration procedures between measured voltage and λ, are quite elaborate, see Refs. 1, 2, 13, and 16. It is noteworthy that the actual resolution always depends on the investigated sample, and as stated in Ref. 1, most available SThM techniques and probes are more sensitive to materials with λ lower than a few Wm1K1. The λ sensitivity depends on the type of the used probe, and for a given probe-type, it is strongly dependent on the actual shape of the probe.17 

Another criterion for SThM image quality is the convolution of the thermal image with topographical surface roughness. Sample roughness can result in misinterpretation of the measured λ of a material, because size and shape of topographical features significantly impact the measured thermal signal. So-called topographical artefacts lead to inaccurate results in the thermal image, as the probe–sample contact area and therefore the thermal exchange resistance between probe and sample is no longer constant, as typically assumed by heat transfer models.18 Topography artefacts can be so strong that they even obscure local thermal conductivity variations.19 In addition, on thermally homogeneous samples with higher surface roughness, pseudo-contrast in the thermal image was observed due to variations of the contact area between the tip and sample, causing a modified heat flow.20 Many groups working with SThM tackle the distortion problem by post-processing the thermal image by modeling the heat transfer between probe and sample, thus taking the change in contact area into account. As described by Zhang et al.,2 one challenge for modeling the heat transfer between the SThM probe and sample is that the original diffusive heat transport equation (Fourier heat equation) cannot be used anymore, because due to the small dimension of the tip–sample contact region, the constriction resistance is modified by ballistic transport effects.21 Nevertheless, in Ref. 22, an approach for fast calculations of the heat transfer between the SThM probe and the sample was developed by reducing the problem to Poisson's equation solution. Martinek et al.19 used methods, such as neural network analysis and three-dimensional (3D) finite element modeling, to take into account topography influence. These approaches aim to estimate and eventually correct the topography artefacts arising from probe–sample geometry variations during the scan. The elimination of topographical artefacts through post-processing requires knowledge of the probe response to a wide range of features of differing sizes and shapes, which makes modeling and/or training of neural networks time and resource consuming.17 Therefore, reducing topographical artefacts already during scanning would be desirable. Shi et al.23 made SThM measurements of carbon nanotubes using thermocouple probes, applying different heating voltages to the sample—not probe—to eliminate the topography influence and verify that the thermal contrast was not caused by topography-induced artefacts. Metzke et al.15 observed so-called super elevations of the thermal signals at vertical steps, which they identified as indicators of the topography influences on the thermal signal. With higher probe temperatures, these elevations became more pronounced. For nanoscale mapping of temperature, Menges et al.18 presented a method that permitted the elimination of tip–sample contact-related artefacts, by simultaneously probing a time-dependent and a time-averaged heat flux signal. Ho et al.24 developed a technique incorporating double lock-in amplification to minimize temperature drift and artefacts due to the probe–sample contact area. The works of Menges et al.18 and Ho et al.24 both aimed at minimizing artefacts in nanoscale maps of temperature.

A third criterion of the image quality is the spatial resolution of the thermal image (also called thermal–spatial resolution). Even for topography free samples, signal steps at interfaces between two materials do not exhibit an instantaneous transition. The spatial resolution of an SThM image is limited by the tip radius, which also constricts the amount of heat transferred between the tip and the sample.2 The depth information is estimated to be at most a few times the range of the radius of the probe–sample contact.25,26 In Ref. 17, an estimate of the thermal–spatial resolution was extracted from fits to line traces over the transition region between different materials. They showed that spatial resolution depends more on the probe, comparing two types of resistive probes, KNT nanoprobe and Micrometric Wollaston wire probe. Besides the dimensions of the contact zone between the tip and the sample, also the frequency of the heat source modulation has influence on the sample’s interacting volume out of which thermal information is acquired.27 

In the present work, a systematic study on the influence of the amplitude and frequency of the heating voltage applied to the SThM probe on the image quality was performed. Image quality was assessed according to (i) the thermal contrast, (ii) distortion of the thermal signal by sample topography, and (iii) the thermal–spatial resolution. An implicit calibration method was applied, to convert measured voltage into λ values, connecting the probe's heating parameters to the resolution of λ. Electrical–thermal finite element (FE) simulations were performed to calculate the temperature change at the apex of the SThM probe in dependence on the probe's heating parameters.

An SPM based SThM (BRR 2770, Semilab) was applied. All SThM measurements were done inside a scanning electron microscope (SEM) (Crossbeam 340, Zeiss) under vacuum at <10−6 mbar to prevent heat convection via the surrounding atmosphere or a water meniscus.28 The SThM measurements were performed in a contact mode. The resistive SThM probe was heated by applying an AC voltage with frequency ω. The probe acts as a nanoscale heat source with temperature oscillation ΔT; the change in the temperature ΔT of the probe is connected to λ of the sample via

(1)

with P being the amplitude of the heat power deposited in the sample per unit length and C being a frequency-independent term; for details see Refs. 16 and 29. The temperature oscillation ΔT is measured by integrating the probe as part of a Wheatstone Bridge: the resistance change accompanying ΔT is captured by the Wheatstone Bridge as a voltage variation and amplified by a lock-in amplifier (LIA).24 In detail, the 3ω component of the output voltage at the Wheatstone bridge is measured, which is independent of the overall temperature of the probe and sample.16 Thus, the LIA voltage signal contains information on the sample's thermal conductivity. In the following, the voltage signal is referred to as thermal signal.

SThM images were recorded on the cross section of a thin layer stack (AlCu, W, Ti/TiN, BPSG/SiO2, SixNy on a Si substrate, see Sec. II C for details on the sample). The scan area comprised part of the Si substrate, followed by the thin layers with λ between about 1 and 300Wm1K1. See Fig. 1. Sample preparation included cleaving of the sample and subsequent smoothing of the cross section by ion slicing (IM4000+, Hitachi).

FIG. 1.

(a) 5 × 1 μm2 SThM image, recorded at 350 mV, 2409 Hz heating voltage on the cross section of a thin layer stack. Higher voltage signals correspond to lower λ values. (b) Profiles through the SThM image, trace, and retrace. Direction of the trace profile is shown in (a) by the blue arrow. The color-shaded backgrounds schematically mark parts of the profile corresponding to the different layers. (c) SEM images of the SThM probe during scanning, with different magnifications. To visualize the scan area, the SPM is tilted at an angle of 44° (an angle of 0° is perpendicular, 90° is parallel to the SEM electron beam). The rectangle with the green (dashed) line in the lower-left panel marks the scan area.

FIG. 1.

(a) 5 × 1 μm2 SThM image, recorded at 350 mV, 2409 Hz heating voltage on the cross section of a thin layer stack. Higher voltage signals correspond to lower λ values. (b) Profiles through the SThM image, trace, and retrace. Direction of the trace profile is shown in (a) by the blue arrow. The color-shaded backgrounds schematically mark parts of the profile corresponding to the different layers. (c) SEM images of the SThM probe during scanning, with different magnifications. To visualize the scan area, the SPM is tilted at an angle of 44° (an angle of 0° is perpendicular, 90° is parallel to the SEM electron beam). The rectangle with the green (dashed) line in the lower-left panel marks the scan area.

Close modal

SThM scans at different heating amplitudes were subsequently performed on one sample position, area A, scans at different frequencies on area B. Both A and B are at the edge of the sample cross section, see Fig. 1(b), roughly at the center of the region smoothed by ion slicing. Area A and B are a few μm apart, as the probe was retracted and newly adjusted after scanning on area A. Due to the high uniformity of the investigated sample, area A and B are expected to have the same (thermal) properties. Scan areas were set to 5 × 1 μm2. The scan speed was set to 0.9 μm/s, with 512 points per line, and 64 lines per image. This gives a time of 10.85 ms the probe stayed at one scan point, and the filter time of the LIA accordingly was set to 10.49 ms. Topography and thermal images were recorded simultaneously, in trace and retrace.

Profile lines were extracted from the topography and thermal images using the open-source SPM analysis software Gwyddion (Version 2.56).30 Exemplary profile lines are shown in Fig. 1(b). The profiles were automatically divided into curve-sections corresponding to the different materials. The criteria of the extraction and assignment are described in detail in the supplementary material. The TiN/Ti layer and a thin thermal oxide layer terminating the Si substrate were thermally not resolvable. To each of the extracted curve-sections, the corresponding thermal signal was assigned according to the following criteria:

  • For Si and AlCu, the mean of the respective curve-sections was taken as the thermal signal.

  • To assign the thermal signal to the BPSG/SiO2 and SixNy layer, the corresponding curve-sections were fitted with the sigmoidal function
    (2)
    modeling a curve centered around x0 with slope p that crosses over between two asymptotic values A1 and A2. The values A1 and A2 were taken to calculate the thermal signal. A sketch of the sigmoidal function and an overview of the results of fittings are given in the supplementary material. To allow fitting with the sigmoidal function, the BPSG/SiO2 curve-section was divided at the maximum, and both the ascending (left) and descending (right) part of the curve were fitted. The thermal signal of the BPSG/SiO2 layer was calculated as the mean of the higher asymptotic values A2 of both fits and a third value defined as the maximum of the whole profile minus half the noise. As noise, the standard deviation of the Si curve-section was defined. For SixNy, the thermal signal was taken as the mean of (i) the asymptotic A2 value from the fit on the SixNy-Si curve-section and (ii) the A1 value (lower asymptotic value) from the fit of the descending (right) part of the BPSG/SiO2-SixNy curve-section.
  • W: The thermal trace signal showed elevations and depression at the beginning and end of the layer. See Fig. 1. The relative flat part of the curve-section between was defined as the thermal signal for W. The retrace profiles and profiles recorded at heating amplitudes <300 mV showed no flattening of the curve between elevation and depression; therefore, no definite value for the thermal signal could be assigned to the W layer.

The resistive SThM probe KNT-SThM-2an from Kelvin Nanotechnology was used.31 This probe consists of a Si3N4 cantilever with resistive tip coating of 5 nm NiCr and 40 nm Pd, see Fig. 2, lower part, for an SEM image of the apex of the probe. As stated in Ref. 2, the effective sample range of the probe is 1200Wm1K1. The total resistance of the whole probe is given with 275–425 Ω (typ. 350 Ω). As current max. 2.5 mA is recommended.31 This limits the applied heating amplitude to about 800 mV. In the simulation, not the whole probe (350 Ω) was simulated, but the front part of the cantilever including the tip, assuming to have a resistance of 100 Ω. See Fig. 3. This assumption determines the magnitude of the dissipated power.

FIG. 2.

SThM probe. SEM image of the bottom side of the probe (lower part of the image). Black arrows indicate the length of the Pd wire, which is connected to Au electrodes for heating. The corresponding meshed FE model to simulate the probe temperature is plotted in the upper part of the image (note that the mesh used for the simulations, after mesh convergence studies, is actually four times finer, the coarse version is shown for visualization). Inset: Larger view on the probe, image taken from Ref. 31.

FIG. 2.

SThM probe. SEM image of the bottom side of the probe (lower part of the image). Black arrows indicate the length of the Pd wire, which is connected to Au electrodes for heating. The corresponding meshed FE model to simulate the probe temperature is plotted in the upper part of the image (note that the mesh used for the simulations, after mesh convergence studies, is actually four times finer, the coarse version is shown for visualization). Inset: Larger view on the probe, image taken from Ref. 31.

Close modal
FIG. 3.

(a) Thermal transient FE simulation, showing the dynamic behavior of the SThM tip. The simulation was validated to the experimentally measured voltage transient, refer to Ref. 29. (b) Temperature distribution of the shown cantilever region, to which 100 mV DC heating voltage is applied. The maximum temperature at the tip apex under these conditions was found to be 154.9 °C. (c) FE simulated transient temperature response for an AC voltage of 100 mV at the cantilever with 314 Hz (black solid line) and 6028 Hz (red solid line). The ambient (20 °C) and the 100 mV DC voltage temperature values are shown as references using dashed lines.

FIG. 3.

(a) Thermal transient FE simulation, showing the dynamic behavior of the SThM tip. The simulation was validated to the experimentally measured voltage transient, refer to Ref. 29. (b) Temperature distribution of the shown cantilever region, to which 100 mV DC heating voltage is applied. The maximum temperature at the tip apex under these conditions was found to be 154.9 °C. (c) FE simulated transient temperature response for an AC voltage of 100 mV at the cantilever with 314 Hz (black solid line) and 6028 Hz (red solid line). The ambient (20 °C) and the 100 mV DC voltage temperature values are shown as references using dashed lines.

Close modal

In the SThM measurement, the heating voltage applied to the SThM probe was varied between 100 and 350 mV, and the frequency was set to 2409 Hz. Higher voltages were not evaluated to avoid damage of the SThM probe. For amplitudes higher than 350 mV, scanning often became unstable, presumably due to temperature-induced cantilever bending.

For the variation of the frequency, the heating voltage was set to 300 mV. The frequency was randomly varied within one order of magnitude, from about 300 Hz to 3 kHz. The first and last scans were performed at the same frequency to track influences of changes in the probe status. In addition, one frequency (6 kHz) above the cut-off frequency of the probe was analyzed. The upper cut-off frequency of about 3300 Hz for the applied AC heating frequency is given by the thermal time constant of the probe of 300 μs.2 The upper frequency limit depends on how fast the SThM probe can follow the applied AC heating voltage, shown by electrical–thermal simulations below. More details on the cut-off frequencies of the applied KNT-SThM probes can be found in previous works.28,29

To estimate the heating characteristics of the tip of the SThM probe for the different heating amplitudes, transient electrical–thermal FE modeling was carried out using Ansys® Academic Research Mechanical, Release 18.1.

Convective heat transport was neglected, as the experiments were performed in vacuum. Using the Stefan Boltzmann law, radiation loss was estimated to be negligible in the temperature regime up to 500 °C, in comparison to the conductive heat transport. As boundary condition in the electric domain, an effective RMS voltage was applied to the probe via the Au electrodes. In the thermal domain, a constant temperature of 20 °C at the cantilever holder was assumed. To model the SThM probe, its dimensions were measured out of SEM images, see Fig. 2. The material parameters were taken from the literature32–36 except the values for the Pd electrode, whose electrical and thermal transport properties are strongly modified because its thickness is in the order of the mean free path of the electrons. Electrical resistivity is known to become size dependent for very thin layers. The reason is that the electron transport leaves the purely diffusive regime and becomes more ballistic for thin layers. When the layer thickness is in the order of the mean free path of the electrons or below, the electrical resistivity is strongly influenced by boundary scattering.37 Therefore, the value of the Pd electrical resistivity was adjusted to obtain the electrical resistance of 100 Ω for the front part of the cantilever. The electrical resistivities are 0.22×107Ωm for Au36 and 2.24×107Ωm for Pd.32 The heat capacities for Si3N4, Au, and Pd are 800, 129, and 245Jkg1K1, and the mass densities are 3100, 19 300, and 12020kgm3, respectively. The assumed λ are 100Wm1K1 for the Au electrodes (thickness of 150 nm)34 and 71.8Wm1K1 for Pd at the cantilever tip apex (thickness of 45 nm).32 The λ value of Si3N4 (thickness: 350 nm) varies between 1 to 43Wm1K1 in the literature.33,38 For the adjustment, the thermal transient of the probe was simulated and validated to experimental results found in the previous work.29 The thermal transient was measured as a response to a step voltage applied to the SThM probe [see Fig. 3(a)]. The comparison between experiments and simulation showed a significant influence of the thermal conductivity of Si3N4 on the thermal transient. The best match was achieved for a thermal conductivity of 20Wm1K1.

The stationary simulation of the probe's temperature field was performed at an applied voltage difference of 100 mV DC, applied as a boundary condition at the electrodes, as shown in Fig. 3(b). This corresponds to 350 mV operating voltage due to the relation in resistance (350 Ω to 100 Ω) between the whole setup and the front part considered in the simulation. The base where the cantilever is attached to the rest of the system was set to 20 °C. For the DC heating steady state, a maximum temperature Tmax of 154.9 °C at the tip apex was found, see Fig. 3(b).

To consider the dynamic behaviour, FE simulations were made with an AC voltage, see Fig. 3(c). The simulations were done for the minimum and maximum frequencies used in the experiment: 314 and 6028 Hz. The simulations showed the effect of thermal inertia, taken into account that the cantilever cannot follow the power dissipation modulation induced by the AC heating. As illustrated in Fig. 3(c), the change in temperature at the tip apex, after arriving at a sinusoidal steady-state, was 90% at 314 Hz and 57% at 6028 Hz compared to the maximum temperature rise in the DC steady-state case.

All the FE simulations are conducted for an SThM probe without contact with the sample. The temperature modification for a tip getting in contact with a sample is provided as follows. For a voltage drop of 100 mV at the front part of the cantilever, the heating power is P = U2/R = 0.1 mW. Its thermal resistance is defined as Rth,cantilever = (Tmax−Tambient)/P = (154.9−20)/0.1 × 10−3 = 1.35 K/μW. The heat path resistance from the tip into the sample consists of a series connection of the sample thermal resistance (nanoscale heat source constriction resistance) and the tip sample contact resistance. The constriction resistance can be computed by adding the diffusive and the ballistic contributions Rth,constriction = 1/(2λD) + 8Λ/(3πλD2) = 0.3 K/μW (see the supplement of Ref. 39, where the assumptions are λ = 150.7 W m−1 K−1 for the thermal conductivity of Si (see Table I), Λ = 500 nm for the phonon mean free path40 and a constriction diameter of D = 100 nm. The contact resistance was reported for the SThM probe from the Kelvin Nanoprobe to be in the order of Rth,contact ∼ 4 K/μW.41 This results in a typical tip–sample resistance of Rth,tip-sample = Rth,contact + Rth,constriction = 4.3 K/μW. The total thermal resistance, as a parallel connection of the heat path over the tip through the cantilever to its base and the tip to the sample, is Rth,cantilever · Rth,tip-sample/(Rth,cantilever + Rth,tip-sample) ∼ 1 K/μW. As a result, the temperature difference would be a factor of 1.35 smaller in contact in comparison to the simulation result shown in Fig. 3(b), corresponding to a maximum temperature of ∼120 °C when the tip is in contact with the sample. It should be noted that these estimations are only shown for providing guidance regarding the SThM probe's condition.

TABLE I.

TDTR analysis of λ and literature values for the thin layers of the investigated sample. All values and measurements at room temperature.

LayerλTDTR (Wm−1 K−1)λliterat. (Wm−1 K−1)
AlCu 241 ± 5 Bulk Al: 248 ± 657  
BPSG 0.9 ± 0.2 1.2 ± 0.147  
SiO2 0.8 ± 0.1 0.7 to 1.158  
SixNy 17 ± 11 0.7 to 1.3,59 3.3,60 12 ± 248a 
Si (100) 150.7 ± 0.4 148 to 15649,50,61 
LayerλTDTR (Wm−1 K−1)λliterat. (Wm−1 K−1)
AlCu 241 ± 5 Bulk Al: 248 ± 657  
BPSG 0.9 ± 0.2 1.2 ± 0.147  
SiO2 0.8 ± 0.1 0.7 to 1.158  
SixNy 17 ± 11 0.7 to 1.3,59 3.3,60 12 ± 248a 
Si (100) 150.7 ± 0.4 148 to 15649,50,61 
a

In dependence on the preparation process.

The sample under investigation was a multi-layered system of thin layers relevant in modern wafer technologies, with AlCu on top, followed by W, TiN/Ti, BPSG, SiO2, and SixNy on a Si substrate. BPSG and SiO2 were thermally indistinguishable with the SThM and were treated as one layer (BPSG/SiO2). The TiN/Ti layer and a thin thermal oxide layer terminating the Si substrate were thermally not resolvable, see also supplementary material.

A merged topography and thermal image of the sample cross section is shown in Fig. 4(a), recorded with SThM at 350 mV, 2409 Hz heating voltage. Different slopes of the layers in the topography profile are due to different ablation rates of materials of different hardness during ion slicing. The ion sliced region showed slopes of about 0.2° for the AlCu layer, 2.5° for W, and −1.7° for BPSG, all values with reference to the Si-substrate where the slope was set to 0°. See Fig. 4(b). At x = 1.8 μm (close to the BPSG/SiO2–SixNy interface), a small bump is visible, which is probably caused by the change of the ablation rate and/or re-deposition at the interface during the ion slicing process. Sample root mean square roughness calculated from topography scans on the sample cross section amounted to 0.5 ± 0.2 nm on Si and SiN, 1.0 ± 0.2 nm on BPSG/SiO2, 1.1 ± 0.2 nm on W, and 1.3 ± 0.2 nm on AlCu.

FIG. 4.

(a) Merged topography and thermal image (350 mV, 2409 Hz) of the sample cross section. (b) Topography profile. Different slopes of the layers are due to different ablation rates of the materials during surface polishing by ion slicing. Polishing also results in rills due to the so-called curtaining effect, primarily visible in (a) at the AlCu layer.

FIG. 4.

(a) Merged topography and thermal image (350 mV, 2409 Hz) of the sample cross section. (b) Topography profile. Different slopes of the layers are due to different ablation rates of the materials during surface polishing by ion slicing. Polishing also results in rills due to the so-called curtaining effect, primarily visible in (a) at the AlCu layer.

Close modal

Figure 5 shows an SEM image of the sample cross section and gives information on the elemental distribution of the sample, measured with energy-dispersive x-ray spectroscopy (EDX).

FIG. 5.

SEM image of the investigated sample (a) recorded with an ESB detector (Zeiss), (b) with a Ultim Extreme Detector (Oxford Instruments), (c) corresponding elemental distribution (EDX).

FIG. 5.

SEM image of the investigated sample (a) recorded with an ESB detector (Zeiss), (b) with a Ultim Extreme Detector (Oxford Instruments), (c) corresponding elemental distribution (EDX).

Close modal

To obtain reference λ values for the implicit calibration method described in Sec. III A, the sample was thermally characterized by time domain thermoreflectance (TDTR).42,43 Measurements were done with the PicoTR and NanoTR (Netzsch), detailed information on the measurement method can be found in the Conference Proceeding44 and in Refs. 29 and 45. TDTR is an optical pump–probe beam method to measure thermophysical properties of sub-micrometer thin films. The method utilizes temperature-induced changes in the reflectance of the surface of the sample to derive the thermal properties of layer systems. In contrast to SThM measurements, TDTR measures on the sample surface, not on the cross section. The pump beam heats the sample, and by recording the thermal transient with the probe beam, information on the heat transport through the layered structure is gained. To extract the λ values of the individual layers from the measured cooling curve, knowledge on sample characteristics like layer thickness, their specific heat and density is required. In the present work, layer thicknesses required for the TDTR analysis were measured out of SEM images of the sample cross section, values for specific heat and density were taken out of the literature.46–51 In Table I, the results of the TDTR measurements are shown. The measurement uncertainties result from the uncertainty calculation according to Ref. 52. The experimental noise and the uncertainties of the used model parameters (thermal conductivity, layer thickness, and volumetric heat capacity) are considered.

Thermal images recorded at different heating parameters of the SThM probe are shown in Fig. 6. To compare thermal signals recorded at different settings of the heating amplitude and frequency, the difference in the thermal signal between layer and Si-substrate was defined as ΔVlayer. It is to note that the BPSG/SiO2 layer had the highest ΔVlayer because its thermal conductivity was most different from the reference Si layer. To compare the signal-to-noise ratio (SNR), the standard deviation of the Si baseline was defined as noise ΔVnoise for all layers. This is reasonable because one major source for variation in noise within one scan area can be attributed to variation in the roughness of the surface. On the present sample, the variation in roughness of the different layers was <1 nm, as shown in Sec. II C. The noise level can be estimated for all layers from the data for Si. In general, unwanted modification (noise) in the thermal signal during scanning in vacuum on thermally homogeneous samples can, among others, be attributed to changes in the contact area between the probe and sample, or noise of the Wheatstone Bridge setup (like thermal noise of the resistors).53 

FIG. 6.

Thermal images (5 × 1 μm2) recorded at different heating amplitudes as denoted in the insets at 2409 Hz heating frequency. A clear improvement of the thermal contrast with increasing heating amplitude was observed.

FIG. 6.

Thermal images (5 × 1 μm2) recorded at different heating amplitudes as denoted in the insets at 2409 Hz heating frequency. A clear improvement of the thermal contrast with increasing heating amplitude was observed.

Close modal

For all layers, a general trend of increased ΔVlayer with increased heating voltage was observed, according to Eq. (1). See Fig. 7(a). For the variation of the heating amplitude, the frequency was set to 2409 Hz. For the W layer, only in the trace signal at 350 mV, it was possible to unambiguously locate the corresponding thermal signal, as described in Sec. II A. The deviation of the trace and retrace signal for ΔVSixNy is likely caused by topography's influence on the thermal signal and will be discussed in Sec. III B.

FIG. 7.

Thermal contrast dependent on heating amplitude. (a) ΔVlayer for different settings of the heating amplitude at 2409 Hz heating frequency. For all materials, ΔVlayer increases at higher amplitudes. (b) SNR dependent on the heating amplitude. The dashed lines serve as a guide for the eye.

FIG. 7.

Thermal contrast dependent on heating amplitude. (a) ΔVlayer for different settings of the heating amplitude at 2409 Hz heating frequency. For all materials, ΔVlayer increases at higher amplitudes. (b) SNR dependent on the heating amplitude. The dashed lines serve as a guide for the eye.

Close modal

Characterization of the signal-to-noise ratio (SNR), Fig. 7(b), showed an about ten times better SNR for measurements taken with 350 mV than with 100 mV for all materials: For the AlCu layer, the SNR increased about 13 (trace)/15 (retrace) times, for SixNy about 14 (trace)/9 (retrace) times, for the BPSG/SiO2 layer 7 (trace)/11 (retrace) times.

The deviation in SNR between trace and retrace measurement at 350 mV visible for AlCu and BPSG/SiO2 is due to the higher noise level of the trace measurement. The higher noise level in trace was probably caused by this being the first measurement on area A. To evaluate if the SThM tip scanning in contact caused any change in surface topography, the roughness of the scanned area was calculated from the topography images simultaneously recorded with the thermal images. Here, the roughness of the whole scan area was calculated. For scans on area A, a decrease in surface roughness of the overall scan area after the first scan from 4.5 to 3.9 nm was observed. For scans on area B, the roughness did not change noticeably (variation in roughness <0.1 nm). The sample surface probably contained residual material from the ion slicing process and/or a thin contamination layer, which was removed after the first scan. As the sample was briefly exposed to air between polishing in the ion slicer and installation in the SThM-SEM, the formation of a thin oxide layer cannot be excluded. It is to note that the probe was heated >1 h before the start of the first scan to ensure that a periodic stationary state was established.

Keeping the heating voltage at 300 mV and increasing the frequency from about 300 Hz to 6 kHz decreased the thermal signal by a factor of ten. See Fig. 8(a). The decrease in thermal signal is caused by the lower tip temperature at higher heating frequencies, given by the thermal inertia of the probe as shown by the simulation results in Fig. 3(c). The decrease is also reflected in the correlation between thermal signal (proportional to ΔT) and heating frequency (ω) given in Eq. (1).

FIG. 8.

Thermal contrast in dependence on the heating frequency at 300 mV. (a) ΔVlayer for different settings of the heating frequency. Colored dashed lines are fits to the curves. For all materials, ΔVlayer decreases at higher heating frequency. (b) SNR ratio in dependence on the applied heating frequency (colored points). Colored dashed lines show calculated SNR values, for calculations see the main text. The dashed black lines serve as a guide for the eye.

FIG. 8.

Thermal contrast in dependence on the heating frequency at 300 mV. (a) ΔVlayer for different settings of the heating frequency. Colored dashed lines are fits to the curves. For all materials, ΔVlayer decreases at higher heating frequency. (b) SNR ratio in dependence on the applied heating frequency (colored points). Colored dashed lines show calculated SNR values, for calculations see the main text. The dashed black lines serve as a guide for the eye.

Close modal

The SNR decreased only by a factor of about two. See Fig. 8(b). The reason is presumably the lower noise at higher frequencies due to enhanced integration per measuring point. To visualize the relation between SNR and frequency, the SNR was calculated for all frequencies between 100 Hz and 6 kHz (in steps of 100 Hz), based on the measured data points of the trace signal. This was done according to the following procedure: Considering the relation between thermal signal and frequency given in Eq. (1), measured data points were fitted by a logarithm function of the form

(3)

From the fit parameters a and b, Vlayer-calc was calculated. ΔVlayer-calc, defined by Vlayer-calcVSi-calc, is depicted as the colored dashed lines in Fig. 8(a).

A noise value noisecalc for all frequencies ω was calculated using the formula

(4)

with ωi indexing the n = 6 frequencies of the heating voltage, stdωi being the corresponding measured standard deviation of the Si baseline, and t being the measurement time per scan point of 10.85 ms. The SNR ratios were calculated for all layers by dividing the corresponding ΔVlayer-calc by noisecalc; see colored dashed lines in Fig. 8(b). From these curves, the frequencies of the maximum SNR can be estimated, with about 1100 Hz for BPSG/SIO2, 1000 Hz for SixNy, 1400 Hz for AlCu, and 1700 Hz for W (all calculations done for trace signals).

The measured noise levels ΔVnoise (in mV) were converted into thermal conductivity values Δλ (thermal resolution, in Wm1K1). Therefore, an implicit calibration method was applied, as described in Ref. 54. The method is based on finding the fit function that best describes the relation between the measured voltage and thermal conductivity values. A fit function of the form

(5)

was applied, with a, b, and c being the parameters to be fit. To obtain the fitting parameters, ΔVlayer of at least three reference layers and their corresponding λ values have to be known. In this work, Si, SixNy, SiO2, and AlCu were taken as reference layers. Reference values for λ were taken from TDTR measurements. Figure 9 shows the curve fitting exemplarily for SThM measurements at 350 mV, 2409 Hz heating voltage.

FIG. 9.

Converting measured voltage into λ values by implicit calibration, exemplarily shown for thermal signals (voltage signals) recorded at 350 mV, 2409 Hz heating voltage. The y axis shows ΔVlayer, defined as the difference in voltage signal between layer and Si substrate. The x axis gives the corresponding λ values. Curve fitting as described in the inset is applied to find the form of the equation that describes the relation between voltage and λ.

FIG. 9.

Converting measured voltage into λ values by implicit calibration, exemplarily shown for thermal signals (voltage signals) recorded at 350 mV, 2409 Hz heating voltage. The y axis shows ΔVlayer, defined as the difference in voltage signal between layer and Si substrate. The x axis gives the corresponding λ values. Curve fitting as described in the inset is applied to find the form of the equation that describes the relation between voltage and λ.

Close modal

The relation between ΔVnoise (the standard deviation of the Si baseline measured at the respective heating parameters) and Δλ is given by

(5a)

considering that for the Si-baseline the thermal difference signal ΔVSi was defined as zero. The theoretical thermal resolution Δλ then can be stated as

(5b)

however, the accuracy of conversion of voltage values to thermal conductivity was comparatively low with an uncertainty of about ±10[Wm1K1], thus the actual measurement accuracy amounted to >10%. Table II gives a summary of the noise level and the corresponding Δλ values calculated from the fit parameters for all settings of the heating voltage. The highest measurement accuracy of <10% was achieved at 1323 Hz heating frequency, 300 mV heating voltage.

TABLE II.

Conversion of the measured voltage signal into thermal conductivity, at heating voltage of amplitude A and frequency ω. The uncertainty is quantified (i) using the conversion of the measured voltage noise levels ΔVnoise into thermal conductivity noise Δλ and (ii) by propagation of the uncertainties of the fit parameters [a, b, and c from Eq. (5)] as Δλfit. The last column shows the fitted thermal conductivity λSi together with the larger of the two prementioned errors.

A (mV)ω (Hz)ΔVnoise (mV)Δλ (Wm−1 K−1)λSi (W m−1 K−1)
350 2409 0.52 4.6 132.8 ± 9.8 
200 2409 0.55 6.5 132.9 ± 9.2 
100 2409 3.3 53.0 137.4 ± 75.4 
300 314 0.27 3.5 135.6 ± 20.7 
300 703 0.23 2.9 121.3 ± 13.8 
300 1323 0.09 1.8 121.4 ± 8.1 
300 2409 0.21 2.1 122.2 ± 11.8 
300 3012 0.1 2.6 117.9 ± 7.3 
300 6028 0.06 5.0 112.8 ± 2.6 
A (mV)ω (Hz)ΔVnoise (mV)Δλ (Wm−1 K−1)λSi (W m−1 K−1)
350 2409 0.52 4.6 132.8 ± 9.8 
200 2409 0.55 6.5 132.9 ± 9.2 
100 2409 3.3 53.0 137.4 ± 75.4 
300 314 0.27 3.5 135.6 ± 20.7 
300 703 0.23 2.9 121.3 ± 13.8 
300 1323 0.09 1.8 121.4 ± 8.1 
300 2409 0.21 2.1 122.2 ± 11.8 
300 3012 0.1 2.6 117.9 ± 7.3 
300 6028 0.06 5.0 112.8 ± 2.6 

ΔVlayer values were taken from the trace profiles. SiO2, Si, and AlCu showed good agreement between trace and retrace signal. For ΔVSixNy extracted from the retrace profile, the fit did not converge (within 400 iterations). This could be an indicator that the thermal information for SixNy contained in the retrace profile was distorted by topography artefacts. Values for SixNy from the literature and comparative TDTR measurements indicated a thermal conductivity of SixNy of <20 Wm−1 K−1 (Ref. 33), which was in agreement with the λ value of about 20 Wm−1 K−1 calculated with the implicit calibration method from the measured ΔVSixNy from the trace profile (at 350 mV, 2409 Hz).

A joint representation of both the thermal and topography signal in trace and retrace is shown in Fig. 10(a). The alignment procedure of the profiles is described in the supplementary material. In parts with stronger topographical features, a visible deviation between thermal trace and retrace signal occurred, indicating the distortion of the thermal signal by topography (also called topography artefacts).

FIG. 10.

(a) Profiles extracted from simultaneously recorded topography (right-hand axes) and thermal (left-hand axes) images, trace and retrace. Recorded at 350 mV, 2409 Hz heating voltage. The color-shaded backgrounds schematically mark parts of the profile corresponding to the different layers. In (b), the thermal trace image (5 × 1 μm2) is shown. The blue line shows the profile through the image, and the black square gives the profile thickness.

FIG. 10.

(a) Profiles extracted from simultaneously recorded topography (right-hand axes) and thermal (left-hand axes) images, trace and retrace. Recorded at 350 mV, 2409 Hz heating voltage. The color-shaded backgrounds schematically mark parts of the profile corresponding to the different layers. In (b), the thermal trace image (5 × 1 μm2) is shown. The blue line shows the profile through the image, and the black square gives the profile thickness.

Close modal

As can be seen in Fig. 10(a), for the BPSG/SiO2 layer (highlighted in light blue), the lateral position of the maximum thermal signal was shifted against each other for trace and retrace scanning. This can be explained as the position of the contact between the tip and the sample is not necessarily the same for scanning in trace and retrace. Such anisotropic behavior was also observed in Ref. 17, where SThM scans with a similar probe-type had been performed. There, the behavior was explained by the anisotropic tip of SThM-KNT probes. The anisotropy is caused by the geometric structure of the probe. The resistive element for thermal measurements is not freestanding but deposited on the bottom side of the SiN cantilever, see Fig. 2.

At the SixNy layer [Fig. 10(a), orange highlighted region], the thermal curves showed visible deviation between trace and retrace, presumably due to different contacts between the tip and probe due to topographical features [see the bump in the topography profile at about x = 1.6 μm in Fig. 10(a)]. The different contact resulted in a different heat flow from the probe to sample, causing the observed difference in thermal signal.

The thermal trace signal of the W layer [greenish region in Fig. 10(a)] showed substantial distortion of the thermal signal at both interfaces, getting more pronounced at lower heating amplitudes (not shown here). It has to be noted that there is a Ti/TiN layer between W and BPSG/SiO2, which was not thermally resolvable, but appeared in the topography profile as a small bump left of the minimum marking the W–BPSG/SiO2 interface. The slope of the surface changed at both W interfaces (change of −2.3° at the beginning and +4.2° at the end of the W layer, see Fig. 4). This change presumably resulted in a decreased, respectively, increased tip–sample contact at the beginning and end of the layer. Besides topography, there might be several other relevant reasons for a changed signal close to interfaces: First, close to the interface, the volume of heat transport lies within the two materials on both sides of the interface. Second, interface scattering sets in when the probe is exciting close to the interface, reducing λ. Third, the interface could, in principle, also increase λ locally by channeling phonons like a waveguide by interface phonon modes.55 

Figure 11 shows the thermal trace and retrace profile aligned to each other for different settings of the heating amplitude. To illustrate the influence of the probe's heating parameter on the distortion of the thermal image, the aligned thermal trace and retrace profiles were subtracted from each other. From the resulting trace-minus-retrace (t-m-r) profiles the standard deviation (std) and positive and negative maximum values (+max. and −max.) were calculated. In areas with minimal distortion of the thermal signal, like on the Si substrate, these values are close to zero.

FIG. 11.

Aligned thermal trace and retrace profiles for different heating amplitudes [(a) 350 mV, (b) 200 mV, (c) 100 mV)] at a fixed heating frequency of 2409 Hz. Deviations between trace and retrace profiles are larger at lower heating amplitudes and most pronounced at interfaces between layers.

FIG. 11.

Aligned thermal trace and retrace profiles for different heating amplitudes [(a) 350 mV, (b) 200 mV, (c) 100 mV)] at a fixed heating frequency of 2409 Hz. Deviations between trace and retrace profiles are larger at lower heating amplitudes and most pronounced at interfaces between layers.

Close modal

In Fig. 12(a), the corresponding t-m-r profiles are depicted together with the topography profile. Figure 12(b) shows the t-m-r profiles for different settings of the heating frequency. Three positions were identified where the thermal signal was most disturbed by topography. First, at the W–(Ti/TiN–) BPSG/SiO2 interface [Fig. 12(a) at x = 0.6 μm, Fig. 12(b) at x = 1.1 μm] where the topographical slope changed from +2.5° to −1.7° the t-m-r profile had a −max. of −6 mV. Values given here are for 350 mV, 2409 Hz. Second, a +max. of about 7 mV occurred at the ∼1 nm high bump at the SixNy layer [Fig. 12(a)] at x = 1.2 μm, Fig. 12(b) at x = 1.6 μm. The third position, where the thermal signal was substantially distorted by topography, was at the interface between AlCu and W [Fig. 12(a) at x = 0.1 μm, Fig. 12(b) at x = 0.7 μm] where the slope changed from +0.2° to +2.5°. Table III summarizes std and ±max values of the t-m-r profiles for the different settings of the heating voltage. In regions that appeared flat in the topography image, like the Si substrate, trace and retrace of the thermal signal showed an alignment.

FIG. 12.

Influence of the heating parameters of the probe on topography artefacts in thermal images. Thermal trace and retrace profiles are subtracted from each other and depicted together with the topography profile (black line) for (a) different heating amplitudes at a fixed heating frequency of 2409 Hz and (b) different heating frequencies at a fixed heating amplitude of 350 mV. The number in brackets in the inset of (b) denote the order in which the measurements were performed, starting and ending with 2409 Hz.

FIG. 12.

Influence of the heating parameters of the probe on topography artefacts in thermal images. Thermal trace and retrace profiles are subtracted from each other and depicted together with the topography profile (black line) for (a) different heating amplitudes at a fixed heating frequency of 2409 Hz and (b) different heating frequencies at a fixed heating amplitude of 350 mV. The number in brackets in the inset of (b) denote the order in which the measurements were performed, starting and ending with 2409 Hz.

Close modal
TABLE III.

Trace-minus-retrace (t-m-r) thermal profiles for different heating voltage settings with amplitude A and frequency ω. Standard deviation (std), and positive and negative maximum of the t-m-r profiles were calculated. In addition, the std of the t-m-r profiles of the Si baseline was calculated [“SThM (Si) std”]. “Area No.” indicates the scan area (A or B) and the order of measurement. Parameters of the first scans on area A and B are of contrasting color.

A (mV)f
(Hz)
SThM
std (mV)
SThM
+ max (mV)
SThM
− max (mV)
SThM (Si) std (mV)Area No.
350 2409 1.7 7.3 −6.0 0.24 A1 
200 2409 1.4 6.4 −4.4 0.86 A3 
100 2409 5.6 14.0 −13.3 6.1 A2 
300 314 2.2 6.4 −7.6 0.37 B5 
300 703 1.3 6.1 −4.5 0.22 B4 
300 1323 0.9 2.7 −4.4 0.11 B6 
300 2409 1.8 7.3 −6.6 0.34 B1 
300 2409 0.6 1.7 −2.4 0.10 B7 
300 3012 0.6 2.2 −2.9 0.16 B2 
300 6028 0.3 0.7 −1.2 0.07 B3 
A (mV)f
(Hz)
SThM
std (mV)
SThM
+ max (mV)
SThM
− max (mV)
SThM (Si) std (mV)Area No.
350 2409 1.7 7.3 −6.0 0.24 A1 
200 2409 1.4 6.4 −4.4 0.86 A3 
100 2409 5.6 14.0 −13.3 6.1 A2 
300 314 2.2 6.4 −7.6 0.37 B5 
300 703 1.3 6.1 −4.5 0.22 B4 
300 1323 0.9 2.7 −4.4 0.11 B6 
300 2409 1.8 7.3 −6.6 0.34 B1 
300 2409 0.6 1.7 −2.4 0.10 B7 
300 3012 0.6 2.2 −2.9 0.16 B2 
300 6028 0.3 0.7 −1.2 0.07 B3 

It can be seen that topography artefacts appeared mostly at interfaces between layers, where the slope of the surface changed, and at sharp features. Another explanation for the difference between thermal trace and retrace signal at interfaces is that the cantilever tip carries a bit of sample material and therefore changes its characteristic slightly when scanning on another material. This could have a significant effect when scanning over layers of different hardness.

Area A and B are expected to have the same (thermal) properties due to the investigated layers' high uniformity and the small distance (some μm) between the scan areas. Therefore, values measured on A and B were compared to each other. Scans A1 and B1 were excluded from the following discussion due to the changed surface condition after the first scan in contact mode (discussed in Sec. III A).

Increasing the amplitude from 100 to 200 mV decreased the ±max values of the t-m-r profile by a factor of 2 and 3, respectively, the std decreased by a factor of 4. The std of the Si baseline decreased by a factor of 7. Increasing the amplitude from 200 to 300 mV (at 2409 Hz) decreased the ±max. values by a factor of about 4 and 2, respectively, the std by a factor of 2.3, and the std of Si by a factor of 8.6.

Increasing the frequency from 314 to 2409 Hz improved the alignment between trace and retrace. The ±max values of the t-m-r profile decreased by a factor of about 4 and 3, respectively, the std decreased by a factor of 3.6. The std of the Si baseline decreased by a factor of 3.7. Further increase in frequency to 3012 Hz did not lead to a further reduction of the std on Si and ±max even increased slightly. Increasing the frequency over the cut-off frequency to 6028 Hz apparently improved the alignment; however, this is to be contributed to the decreasing sensitivity of the probe to the sample thermal properties after the cut-off frequency has been exceeded.

It is to note that a reduction of scan speed always results in a decrease in topography artefacts. This is because of the improved feedback control, which results in a more constant mechanical contact between tip and sample. However, scan speed in SThM images is already very low. With the settings chosen in this work, a 5 × 1 μm2 scan with 512 points per line took about 6 min.

A higher thermal–spatial resolution is characterized by more confined transition regions. Estimates of the thermal–spatial resolution were extracted from fits to the thermal profiles over the transition regions between different materials. For the fitting, the sigmoidal function described in Eq. (2) was applied. More confined transition regions lead to a higher slope p, and the width of the layers in the thermal image corresponds more to the actual layer width (within the limits of the spatial resolution of the SThM tip).

The interfaces SixNy–Si-substrate, BPSG/SiO2–SixNy, and W–BPSG/SiO2 were studied. The part of the thermal profile corresponding to the BPSG/SiO2 layer [bluish region in Fig. 10(a)] was divided at the maximum and both the ascending (from the W–BPSG/SiO2 interface to the maximum) and the descending (from the maximum to the BPSG/SiO2–SixNy interface) part of the curve were fitted. The distance between the x0 values of the ascending (x0−a) and the descending (x0−d) curve was used to estimate the width of the BPSG/SiO2 layer in the thermal image. Figure 13 shows values for the slope p at the different heating amplitudes and frequencies, Fig. 14 for the width of the BPSG/SiO2 layer.

FIG. 13.

Slope of the thermal profiles over the transition regions between different materials, for (a) different heating amplitudes, (b) different heating frequencies. Slopes measured from trace profiles are depicted as full symbols, from retrace profiles as empty symbols. Error bars in (b) are based on the deviation between measurements at 2409 Hz taken at the beginning and end of the frequency variation.

FIG. 13.

Slope of the thermal profiles over the transition regions between different materials, for (a) different heating amplitudes, (b) different heating frequencies. Slopes measured from trace profiles are depicted as full symbols, from retrace profiles as empty symbols. Error bars in (b) are based on the deviation between measurements at 2409 Hz taken at the beginning and end of the frequency variation.

Close modal
FIG. 14.

Width of the BPSG/SiO2 layer in the thermal profiles for (a) different heating amplitudes, (b) different heating frequencies. Widths measured from trace profiles are depicted as full symbols, from retrace profiles as empty symbols. Error bars in (b) are based on the deviation between measurements at 2409 Hz taken at the beginning and end of the frequency variation.

FIG. 14.

Width of the BPSG/SiO2 layer in the thermal profiles for (a) different heating amplitudes, (b) different heating frequencies. Widths measured from trace profiles are depicted as full symbols, from retrace profiles as empty symbols. Error bars in (b) are based on the deviation between measurements at 2409 Hz taken at the beginning and end of the frequency variation.

Close modal

For the variation of the heating amplitude, Fig. 13(a), no systematic change of p was observed. Thermal profiles could not be evaluated for a heating amplitude 100 mV due to too much noise in the thermal image. Interestingly, at the SixNy - Si interface, p was about 3 times higher in the retrace than the trace profile for all heating voltage settings. The difference is presumably caused by the already discussed anisotropy of the SThM tip and the influence of surface topography on the SThM signal. For a variation of frequency, p at the SixNy–Si interface did not change notably in trace; however, for the retrace profile p increased from about −22 ± 10 at about 300 Hz to −44 ± 10 at about 6 kHz. See Fig. 13(b). In other words, the transition region between Si and SixNy decreased from about 160 ± 20 nm to about 80 ± 20 nm.

No tendency of the increase was observed at the other interfaces. Supposing any relation between thermal–spatial resolution and frequency of the heating voltage existed, it is very likely hidden by topography artefacts in the thermal image, which are most pronounced at the interfaces.

The actual width of the BPSG/SiO2 layer amounted to 480 ± 15 nm, as measured from SEM and topographical SPM images. The width of the layer in the thermal image amounted to about 400 nm (trace) and 410 nm (retrace), at 300 mV, 2409 Hz. No systematic change of thermal layer width with heating frequency or amplitude was observed. Figure 13 shows that at the W–BPSG/SiO2 interface the retrace, and for the BPSG/SiO2−SixNy interface, the trace profile exhibited a higher slope. Taking x0−a of the W−BPSG/SiO2 curve from the retrace and x0−d of the BPSG/SiO2–SixNy curve from the trace profile increased the width of the thermal BPSG/SiO2 layer to about 430 nm, which is a deviation of about 10% from the actual layer width.

To study the dependence between differences in λ at interfaces and thermal–spatial resolution, the slope of the interfaces SixNy–Si, BPSG/SiO2–SixNy, and W–BPSG/SiO2 was compared. Values measured at 300 mV, 2409 Hz were analyzed. As shown in Sec. II B, at these heating parameters influence of topography artefacts was minimal. However, differences between the slope measured in trace and retrace were still significant. As can be seen from Table IV, no relation between differences in λ at interfaces and thermal resolution was observed.

TABLE IV.

Thermal resolution at interfaces in dependence on differences in λλ). Measured at 300 mV, 2409 Hz.

InterfaceΔλ
(Wm−1 K−1)
p
trace
p
retrace
W–BPSG/SiO2 160 ± 10 11.5 15 
SixNy–Si 130 ± 10 −15 −32 
BPSG/SiO2–SixNy 20 ± 10 −13.5 −6.5 
InterfaceΔλ
(Wm−1 K−1)
p
trace
p
retrace
W–BPSG/SiO2 160 ± 10 11.5 15 
SixNy–Si 130 ± 10 −15 −32 
BPSG/SiO2–SixNy 20 ± 10 −13.5 −6.5 

This showed that for studies on the thermal–spatial resolution, different sample preparation methods are necessary to minimize the influence of topography at interfaces. One option would be sample polishing by focused ion beam; however, attention has to be paid to possible surface contamination with gallium ions.

The influence of the heating parameters of the SThM probe on the image quality was studied in terms of thermal contrast between materials of different λ’s, distortion of the thermal image by topographical artefacts, and spatial resolution in the thermal image. To convert values measured by SThM (in mV) into thermal resolution, λ of reference layers were measured with TDTR and an implicit calibration method was employed. SThM images were recorded on the cross section of a thin layer stack consisting of materials relevant in modern wafer technologies. It was shown that both the amplitude and frequency of the AC heating voltage had an influence on thermal contrast. The measurements taken with 350 mV showed a ten times higher SNR compared to the measurements taken with 100 mV for all materials. At heating frequencies between 1000 and 1700 Hz, the highest SNR was observed. This frequency range provided the best relation between decreased thermal signal and lower noise at higher frequencies. Electrical–thermal finite element simulations were applied to model the temperature at the apex of the SThM probe, giving a temperature of about 155 °C at the SThM tip for an applied of 350 mV DC. The simulation considering the dynamic case, when AC voltage was applied to the probe, showed that the magnitude of the temperature oscillation at the SThM tip nearly approached the DC response at ∼300 Hz heating frequency. For a frequency of ∼6000 Hz AC, the temperature oscillation was reduced by a factor of ∼2.

By aligning topography and thermal images, the influence of size and shape of topographical features on the thermal image was illustrated. Thermal properties at interfaces between different materials are often the focus of interest but, particularly at interfaces, sample preparation often results in an uneven topography, as shown in this work. The standard deviation (std) of the thermal trace-minus-retrace profile was taken to illustrate the image distortion. It was shown that both the heating amplitude and the frequency affected the distortions in the thermal image. By changing the settings of the probe's heating parameters, distortion could be reduced by a factor of about 10. Diminishing the influence of topography artefacts already during scanning by careful selection of the heating parameters is a recommended addition to the post-processing of thermal images. Another way to achieve more reliable thermal imaging with less distortion due to topography artefacts would be to combine aligned trace and retrace images as described in the work of Ren et al.56 Image segments next to more prominent topographical features show, depending on the orientation of the feature, a more reliable signal in trace or retrace. This could be seen from the different gradients in the thermal signal at interfaces in trace and retrace, like the BPSG/SiO2 layer.

The width of the transition regions between materials was studied to illustrate the thermal–spatial resolution in dependence on heating amplitude and frequency. The influence of topography at interfaces between materials made evaluation difficult, only at the SixNy–Si interface a decrease of the transition region from about 160 ± 20 nm to about 80 ± 20 nm for a frequency increase from 300 Hz to about 6 kHz was observed.

All authors contributed equally to this work.

See the supplementary material for the extraction of thermal signals from the SThM images and details on the correct assignment of the thermal signal to the individual layers. Furthermore, the alignment between thermal and topography and trace and retrace profiles is described.

This study was supported by Power2Power, a European co-funded innovation project on Semiconductor Industry. The project receives grants from the European H2020 research and innovation program, ECSEL Joint Undertaking, and National Funding Authorities from eight involved countries under Grant Agreement No. 826417. The participating countries are Austria, Finland, and Germany, including the Free States of Saxony and Thuringia, Hungary, the Netherlands, Slovakia, Spain, and Switzerland.

The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center “Integrated Computational Material, Process and Product Engineering (IC-MPPE)” (Project No. 859480). This program is supported by the Austrian Federal Ministries for Climate Action, Environment, Energy, Mobility, Innovation and Technology (BMK) and for Digital and Economic Affairs (BMDW), represented by the Austrian research funding association (FFG), and the federal states of Styria, Upper Austria, and Tyrol.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material