A universal method for thermal conductivity measurements on micro-/nano-films with and without substrates using micro-Raman spectroscopy

doi:10.1016/j.tsep.2017.06.009

Thermal Science and Engineering Progress

Volume 3, September 2017, Pages 95-101

https://doi.org/10.1016/j.tsep.2017.06.009 Get rights and content

Abstract

The ability to measure intrinsic thermal conductivity via a non-contact, non-destructive process is extremely attractive. Micro-Raman spectroscopy has been demonstrated to enable effective non-contact thermometry with further work providing a non-destructive estimation of values for thermal conductivity on suitable materials. However significant limitations remain for nano- and micro-films. Materials that do not meet dimensional requirements for thickness or that are in-situ on a substrate or supporting structure present significant challenges using existing approaches. For such samples, representative measurements must be obtained using alternative methods that can compromise samples and/or require relative complexity in experimental design and analysis. Here an analytical model is shown allowing thermal conductivity to be measured free of such limitations via a straightforward approach using micro-Raman spectroscopy. Results are then obtained experimentally and values compared with those obtained using a complimentary technique demonstrating an improved accuracy over existing micro-Raman approaches. Furthermore, this model enables the effect of any substrate or supporting structure on measured values to be quantified and estimations for thermal conductivity of the sample itself to then be calculated where an influence is determined. Current estimations determining the threshold of substrate influence are shown to be insufficient and the importance of obtaining values of thermal conductivity for samples themselves under such conditions is demonstrated.

Introduction

The measurement of intrinsic thermal conductivity is crucial for many applications where performance is linked directly to this fundamental property. Accurate measurement via a straightforward, non-destructive approach offers significant benefits but is not without challenges.

Micro-Raman spectroscopy has been demonstrated to provide effective non-contact thermometry, drawing on a temperature dependence of the obtained Raman peak shift [1], [2], [3], [4], [5]. Such an approach has been enhanced further by the demonstration of non-destructive extraction of thermal conductivity, taking advantage of the localised heating effect of a laser [6], [7], [8], [9]. However limitations in the practical application of such measurement techniques remain – particularly for nano-film / thin-film materials and associated microsystems.

Where samples do not meet restrictive dimensional criteria or are in contact with a substrate or supporting structure, difficulties in isolating sample thermal conductivity from what is an experimentally measured apparent thermal conductivity can often be encountered. In many cases a representative solution for the properties of the sample itself cannot be obtained.

An approach to micro-Raman thermal conductivity measurement has been previously presented [10]. This approach requires the sample thickness to be at least an order of magnitude greater than the laser diameter in order to eliminate any substrate effect from measured thermal conductivity creating a practical barrier for many applications using thinner materials. A solution was offered to this limitation for sub-micrometer samples where sample isolation cannot be assumed [11]. This solution, following an approach by Dryden et al. [12], also requires specific sample/substrate conditions to be met. Such conditions treat the sample as a thin coating where ratio of sample thickness to laser spot radius approaches zero providing an equation dominated by substrate thermal conductivity. Such an approach also requires that substrate thermal conductivity be much greater than that of the sample. While alternative equations can be derived via the original work [12], [13] to allow for conditions where i) a sample has high thermal conductivity relative to the substrate or ii) is of sufficient dimension to be considered a thick coating i.e. sample thickness more than twice the laser radius; the results obtained by such thin and thick coating approximations can differ significantly even as coating thicknesses converge. This creates uncertainty in approach and a difficulty in achieving solutions for a range of material thicknesses and conditions.

The use of a free standing geometry to remove any substrate effect has been successfully demonstrated on materials including silicon and graphene [8], [9], [14], [15], [16]. By suspending a sample over a hole – for the case of samples with no fixed substrate – or removing an area of substrate to produce a free standing section of sample, direct measurement of thermal conductivity via micro-Raman spectroscopy can be undertaken. Although effective in removing the contribution of the substrate to any measured value of thermal conductivity, such approaches present practical restrictions.

Currently such limitations reduce the opportunities for the measurement of thermal conductivity via a micro-Raman spectroscopy based approach, leaving alternative methods that may compromise samples via metallic deposition and/or require relative complexity in experimental design or analysis [17], [18], [19], [20], [21].

In this work we present a theoretical model addressing these current limitations. Firstly, an updated approach allowing a more accurate estimation of thermal conductivity via micro-Raman data is given; and this improved accuracy is further demonstrated experimentally. Secondly, a thermal restriction parameter is then developed allowing a numerical solution for sample thermal conductivity itself to be isolated if a substrate or supporting structure influence is present. Limitations based upon relative layer properties and associated effects are avoided.

Using this model, thermal conductivity can be readily and universally obtained for samples where measurement difficulties are presently encountered, while a more rigorous interrogation can also be undertaken for samples where measurement via a micro-Raman approach remains more straightforward. Results can be obtained even as the ratio of sample thickness to laser radius is varied across a wide range.

Sample thermal conductivity can therefore be directly evaluated for a wide variety of material properties and dimensions via an approach that is both straightforward and non-destructive. The contribution of any substrate or support structure to experimentally measured thermal conductivity can also be understood allowing for the isolation of sample thermal conductivity on dual layer components and systems.

Section snippets

Measurement of thermal conductivity

The application of micro-Raman thermometry and subsequent extraction of thermal conductivity draws upon the temperature dependence of an obtained Raman peak shift. By varying input laser power - and thus heat flux – a relative peak shift and associated temperature change can be induced and recorded providing sufficient laser power is available to produce a surface temperature rise. Combining these effects allows a Raman measured thermal conductivity to be obtained for both sample and any

Experimental

In order to evaluate the accuracy of solutions provided by our model, micro-crystalline silicon samples containing two alternative dopant species were manufactured and thermal conductivity measured.

A 1 μm thick micro-crystalline silicon film was applied onto glass substrates (∼1 mm thick, $k$ = 1.025 W m⁻¹ K⁻¹) via plasma enhanced chemical vapour deposition using an analogous approach as in reference [27]. P-type samples containing boron were characterised post-manufacture and found to have a

Model accuracy

While the experimental aspects of micro-Raman thermometry and measurement of thermal conductivity are consistent with previous work, the approach presented in this model to derive thermal conductivity from these measurements is new. Typically approaches follow previous work by reference [10] utilising an equation for the calculation of thermal conductivity originally given by reference [28]. Expressed in common terms this can be given as $T = \frac{2 P}{π (2 a) k}$

This equation, originally presented for thermal

Conclusion

Here an analytical model was demonstrated allowing thermal conductivity to be measured for micro- and nano-films using micro-Raman spectroscopy via a straightforward approach free of limitations imposed by the presence of a supporting substrate. Results from the model were also compared with previous approaches, showing improved agreement with experimental data in the scientific literature. Further validation was carried out by experimental measurements obtained using our own micro-Raman

Acknowledgement

NMW acknowledges The Royal Society of Edinburgh for financial support through the JM Lessells Postgraduate Scholarship in Engineering.

References (31)

T. Kociniewski et al.
Temperature mapping by μ-Raman spectroscopy over cross-section area of power diode in forward biased conditions
Microelectron. Reliab.
(2015)
H. Wang et al.
Analysis of the 3-omega method for thermal conductivity measurement
Int. J. Heat Mass Transfer
(2009)
J.A. Greenwood
Constriction resistance of a plated solid
Int. J. Heat Mass Transfer
(2015)
M. Bauer et al.
Temperature-depending Raman line-shift of silicon carbide
J. Raman Spectrosc.
(2009)
S. Khachadorian et al.
The morphology of silicon nanowire samples: a Raman study
Physica Status Solidi (b)
(2009)
D.S. Moore et al.
Raman temperature measurement
J. Phys: Conf. Ser.
(2014)
J.R. Serrano et al.
Micro-Raman thermometry of thermal flexure actuators
J. Micromech. Microeng.
(2006)
M. Li et al.
Parallel measurement of conductive and convective thermal transport of micro/nanowires based on Raman mapping
Appl. Phys. Lett.
(2015)
A. Ould-Abbas et al.
Study of Thermal Conductivity of Porous Silicon Using the Micro-Raman Method
Open J. Phys. Chem.
(2012)
E. Chávez-Ángel et al.
Reduction of the thermal conductivity in free-standing silicon nano-membranes investigated by non-invasive Raman thermometry
APL Mater.
(2014)

C. Shanshan et al.

Thermal conductivity measurements of suspended graphene with and without wrinkles by micro-Raman mapping

Nanotechnology

(2012)

S. Périchon et al.

Measurement of porous silicon thermal conductivity by micro-Raman scattering

J. Appl. Phys.

(1999)

S. Huang et al.

Thermal conductivity measurement of submicrometer-scale silicon dioxide films by an extended micro-Raman method

Microsyst. Technol.

(2009)

J.R. Dryden

The effect of a surface coating on the constriction resistance of a spot on an infinite half-plane

J. Heat Transfer

(1983)

J.R. Dryden et al.

The effect of coatings on the steady-state and short time constriction resistance for an arbitrary axisymmetric flux

J. Heat Transfer

(1985)

Cited by (12)

A novel heat transfer characterization method for a thermal management scheme of 3D-IC chips
2024, Measurement: Journal of the International Measurement Confederation
A novel surface-modified silicon-based thermal management technology has been proposed for 3D IC architecture in this study. 2 × 2 cm² double sides polished silicon chips’ surface with micro-fin (MF) and micro-pin fin (MPF) structures have been achieved by applying silicon microfabrication technology of deep reactive ion etching, which is applicable to the interlayer of 3D IC packaging technology. By integrating a mini wind tunnel with Raman spectrometer, the transient thermal property measurement system is originally designed to evaluate the cooling capability of the surface-modified silicon interlayer. Finite Element Analysis was involved to confirm this view by taking fluid dynamics and heat transfer into account. The sample with 100 × 100 µm² MPF structure expresses the appropriate exponential decay time constant τ (with unit of 1), which is 4.71 and 8.53 under cooling and heating measurement conditions, respectively. This also proved that the combination of Raman thermometry with forced gas flow could be a relevant measurement tool for transient thermal property.
Effective thermal contact conductance of encased silicon ball from molecular dynamics simulations
2024, Solid State Communications
The heat dissipation performance of point-contact structures in many micro/nano-devices is critical. In this study, the effects of the normal load and diameter of the silicon ball on the effective thermal contact conductance (G_eff) of the encased silicon ball between two silicon plates were studied by using the non-equilibrium molecular dynamics method. The results show that increasing the normal load increases the real contact area between the silicon ball and silicon plate, and thus improves the transmission channel and the density of states of low-frequency phonons, resulting in the observation that the G_eff increases with increasing normal load. It is also found that the G_eff is not sensitive to the diameter of the silicon ball from 2.66 to 4.16 nm at low normal load due to the competition between the enhanced interfacial thermal conductance across the contact region and the reduced internal thermal conductance of the silicon ball. The variation of G_eff in the encased silicon ball structure with the external load and diameter has important guidance for the packaging and thermal design of micro/nano-devices.
Thermoelectric properties of silicon and recycled silicon sawing waste
2019, Journal of Materiomics
Citation Excerpt :
In comparison to the measurement of thermal conductivity of Si nanowires that can be realized through suspending the wires with micro-fabricated microstructures [93,132], measurements of thermal conductivity of Si nanolayers require different techniques such as Raman spectroscopy [152,153], time-domain thermoreflectance (TDTR) [154], frequency-domain thermoreflectance (FDTR) [155], and thermal transient grating (TTG) [156]. Similar to the results in Si nanowire, the thermal conductivity of Si nanolayer/film/membrane follows a general trend: the thinner the layer, the lower the thermal conductivity and the higher the zT [157–160]. Single-crystalline Si shows room-temperature thermal conductivities of 75 W m−1 K−1, 22 W m−1 K−1, and 9 W m−1 K−1 at layer thickness of 74 nm, 20 nm, and 9 nm, respectively [161–163].
Large-scale-applicable thermoelectric materials should be both self-sustaining, in order to survive long-term duty cycles, and nonpolluting. Among all classes of known thermoelectric materials, these criteria reduce the available candidate pool, leaving silicon as one of the remaining options. Here we first review the thermoelectric properties of various silicon-related materials with respect to their morphologies and microstructures. We then report the thermoelectric properties of silicon sawing wastes recycled from silicon wafer manufacturing. We obtain a high power factor of ∼32 μW cm⁻¹ K⁻² at 1273 K with 6% phosphorus substitution in the Si crystal, a value comparable to that of phosphorus-doped silicon-germanium alloys. Our work suggests the large-scale thermoelectric applicability of recycled silicon that would otherwise contribute to the millions of tons of industrial waste produced by the semiconductor industry.
Evaluation of heat conduction in a laser irradiated tooth with the three-phase-lag bio-heat transfer model
2018, Thermal Science and Engineering Progress
Citation Excerpt :
The laser application is accompanied with thermal science in micro scale and low radiation time. Wight et al. analysed the thermal conductivity measurements on thin layers [3]. The laser can be considered to be a form of light amplifier – it provides for the enhancement of particular properties of light energy.
In this study, a dental short pulse laser with a Gaussian beam profile was applied normally to the top surface of a mineral organ i.e. the human tooth for a root canal therapy. A numerical method of finite difference is adopted to solve the time-dependent heat transfer equation. The real boundary conditions of thermal insulation on the sharp segment of the root canal and periodic heat flux on the top boundary of the tooth were applied. The comparison of a three-phase-lag (TPL) bio-heat transfer model with other heat transfer studies has shown that this new bio-heat model (TPL) could accurately predict the thermal behaviour of a non-homogeneous structure such as the human tooth. It was observed that decreasing of the pulse time, increasing of the pulse number and laser spot radius are the logical approaches for dental pulp ablation in comparison with increasing of laser intensity or increment of continuous irradiation time. Based on the results of this investigation, an optimum dental laser with heat flux of 5 W/cm² that could make adequate temperature increments in the range of 5 °C to 8 °C inside the dental pulp after 30 s is suggested. The time of each pulse was 0.1 s, and eight times were iterated in the first ten seconds of treatment time while the laser radius was 3 mm.
Revealing Low Thermal Conductivity of Germanium Tin Semiconductor at Room Temperature
2024, Advanced Materials Interfaces
A Novel Heat Transfer Characterization Method for a Thermal Management Scheme of 3d-Ic Chips
2023, SSRN

View all citing articles on Scopus

View full text

A universal method for thermal conductivity measurements on micro-/nano-films with and without substrates using micro-Raman spectroscopy

Abstract

Introduction

Section snippets

Measurement of thermal conductivity

Experimental

Model accuracy

Conclusion

Acknowledgement

Microelectron. Reliab.

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Temperature-depending Raman line-shift of silicon carbide

J. Raman Spectrosc.

The morphology of silicon nanowire samples: a Raman study

Physica Status Solidi (b)

Raman temperature measurement

J. Phys: Conf. Ser.

Micro-Raman thermometry of thermal flexure actuators

J. Micromech. Microeng.

Parallel measurement of conductive and convective thermal transport of micro/nanowires based on Raman mapping

Appl. Phys. Lett.

Study of Thermal Conductivity of Porous Silicon Using the Micro-Raman Method

Open J. Phys. Chem.

Reduction of the thermal conductivity in free-standing silicon nano-membranes investigated by non-invasive Raman thermometry

APL Mater.

Thermal conductivity measurements of suspended graphene with and without wrinkles by micro-Raman mapping

Nanotechnology

Measurement of porous silicon thermal conductivity by micro-Raman scattering

J. Appl. Phys.

Thermal conductivity measurement of submicrometer-scale silicon dioxide films by an extended micro-Raman method

Microsyst. Technol.

The effect of a surface coating on the constriction resistance of a spot on an infinite half-plane

J. Heat Transfer

The effect of coatings on the steady-state and short time constriction resistance for an arbitrary axisymmetric flux

J. Heat Transfer