Letter pubs.acs.org/NanoLett
Quantitative Thermometry of Nanoscale Hot Spots Fabian Menges,*,†,‡ Heike Riel,† Andreas Stemmer,‡ and Bernd Gotsmann† †
IBM Research - Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland Nanotechnology Group, ETH Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland
‡
S Supporting Information *
ABSTRACT: A method is described to quantify thermal conductance and temperature distributions with nanoscale resolution using scanning thermal microscopy. In the first step, the thermal resistance of the tip−surface contact is measured for each point of a surface. In the second step, the local temperature is determined from the difference between the measured heat flux for heat sources switched on and off. The method is demonstrated using self-heating of silicon nanowires. While a homogeneous nanowire shows a bell-shaped temperature profile, a nanowire diode exhibits a hot spot centered near the junction between two doped segments. KEYWORDS: Scanning thermal microscopy, nanowire, self-heating, nanoscale hot spots, quantitative thermometry
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interest.12,13 Since the heat flow between two materials in contact depends on many parameters, such as the thermal boundary resistance, a straightforward interpretation of measurement signals becomes complicated. As a consequence, thermometry using conventional SThM relies on rescaling the sensor signal to the temperature of the surface using either experimental data of the surface temperature determined from different methods with lower resolution (such as Raman spectroscopy)14,15 or modeling and reference measurements with known material and surface temperature.16,17 Another proposed method determines the tip temperature at zero heat flow.18 However, with increasing lateral resolution this method gets more challenging and is less suitable for temperature mapping. For the case of a metallic sample surface, temperature measurements with nanoscale resolution were demonstrated using point contact thermocouples.19 All these restrictions have limited the implementation of high-resolution thermometry in nanoscale science and technology. Here, we demonstrate how a scanning thermal microscopy (SThM) technique can be used to quantify temperature distributions down to the nanometer range giving examples from self-heating of nanowire devices. Our home-built experimental setup has been described before.11,13 In brief, the heater sensor we use is a resistive silicon heater, a low n-doped (5 × 1017 at/cm3) silicon conductor embedded in a highly doped silicon cantilever. The thermal resistance of the heat path from the heater along the cantilever is typically 2 × 105 K/W. A sharp silicon tip with tip radius of typically 5 nm is fabricated to sit on the heater and to
uantifying temperatures at the nanoscale is a great challenge and a key issue in many technologies. One prominent example is that of self-heating in integrated electronics where power dissipation on the scale of individual transistors has become a limiting factor.1 Nanometer-sized hot spots of up to hundreds of degrees Celsius are thought to influence device performance and reliability.2,3 Characterizing these local temperature variations enables the study of heat transfer and generation, as they provide insights into the underlying thermophysical processes. Self-heating of nanodevices, however, is not the only motivation for the interest in nanoscale thermometry. The capability to study the temperature and thermal conductivity distributions in nanosystems holds great promise for the development of future energy conversion and computing devices.4 It provides a platform for fundamental discoveries in the field of electron−phonon interactions, as they are relevant for the development of low power electronics and efficient thermoelectric energy harvesting systems. The importance of understanding nanoscale temperature distributions, however, is not paralleled with the availability of sensitive methods to measure temperatures. Methods relying on sensing infrared photons are mostly limited to lateral resolutions in the micrometer range.5,6 A higher lateral resolution is attained using scanning thermal microscopy (SThM) techniques in which a thermometer is raster scanned across a surface.7−11 Like in classical thermometry, a temperature sensor is brought into mechanical contact with the sample of interest. However, the sensor cannot equilibrate since the nanoscopic contacts have thermal resistances in excess of 107 K/W that are larger than the thermal resistance of the electrical leads of the thermometer (typically below 2 × 105 K/W). Therefore, for high-resolution SThM one has to consider heat flow to or from the temperature sensor to the region of © 2012 American Chemical Society
Received: September 12, 2011 Revised: December 22, 2011 Published: January 3, 2012 596
dx.doi.org/10.1021/nl203169t | Nano Lett. 2012, 12, 596−601
Nano Letters
Letter
Figure 1. Determination of the thermal tip−surface resistance. Schematic of the tip−surface arrangement for the tip being out of contact (a), in contact with the sample at ambient temperature (b), and in contact with the sample at elevated temperature (c). Panel (d) shows the cantilever thermal resistance taken during approaching the cantilever/tip with respect to the sample surface. Here the sample was approached toward the cantilever tip at a heater temperature of 600 °C. The sample position was set to zero at the contact point.
be correlated to the temperature of the heater by assuming that all electrical power dissipated leads to an increase of the heater temperature. Details on the cantilever temperature calibration, its underlying assumptions and limitations, can be found in the Supporting Information. In a second step, we determine the change in heat flux through opening the heat flow channel through the tip into the surface (see Figure 1b). This can most conveniently be done by measuring power and heater temperature during an approach of the tip to the surface. Figure 1d shows the thermal resistance Rth as a function of piezo displacement during the tip sample approach. The change in Rth resulting from contact is ∼730 K/ W. The tip−sample thermal resistance Rts is calculated as
make contact with the sample surface using conventional atomic force microscopy techniques. At ambient conditions, most of the heat is conducted in the silicon cantilever and through the air-gap to the sample surface12,13,20,21 and only a fraction of the heat travels through the tip. Because the conduction through the air gap is strongly distance dependent, the heat loss will be modulated when the tip is scanned and follows the topography of the sample surface. Therefore, quantitative measurements on temperature distribution under ambient conditions are difficult and require some detailed understanding of the conduction through air. For the resolutions attained in our experiments, we did not find it possible to use the recently proposed two-pass method having the tip in and out of contact,22 because it does not fully account for the complex distance and geometry dependence of the heat transfer through the air-gap that becomes problematic for nonplanar and nanoscale structures. Therefore, the scanning thermal microscope is operated in high vacuum (
