Structural, Optical, and Thermophysical Properties of Mesoporous

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Structural, Optical and Thermo-physical Properties of Mesoporous Silicon Layers: Influence of Substrate Characteristics Amer Melhem, Domingos De Sousa Meneses, Caroline Andreazza-Vignolle, Thomas Defforge, Gaël Gautier, Audrey Sauldubois, and Nadjib Semmar J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 23 Mar 2017 Downloaded from http://pubs.acs.org on March 23, 2017

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The Journal of Physical Chemistry

Structural, Optical and Thermo-physical Properties of Mesoporous Silicon Layers: Influence of Substrate Characteristics Amer Melhem,1* Domingos De Sousa Meneses,2 Caroline Andreazza-Vignolle,3 Thomas Defforge,4 Gaël Gautier,4 A. Sauldubois,5 Nadjib Semmar1 1

GREMI-UMR 7344-CNRS-University of Orleans, F-45067, France

2

CEMHTI-UPR 3079-CNRS-University of Orleans, F-45071, France

3

ICMN-UMR 7374 -CNRS-University of Orleans, F-45071, France

4

Université François Rabelais de Tours, CNRS, CEA, INSA-CVL, GREMAN UMR 7347,

Tours, France 5

CME – University of Orleans, F-45067, France

*Corresponding author: [email protected]

1

ACS Paragon Plus Environment


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ABSTRACT: In this paper, the structural, optical and thermal properties of n-type (100), p-type (100) and (111) mesoporous silicon (MePSi) are reported. The mesoporous silicon was prepared by an electrochemical process from bulk silicon wafer. Depending on the etching depth, analyses show that the porosity of p-type (111) increased by 32 to 40% compared to p (100) which, in turn, increased by 22 to 48% compared to n-type (100). The structure morphology and the abundance of Si-Ox and Si-Hy also depended heavily on the type and crystal orientation of MePSi. The thermal properties of the MePSi layers such as thermal conductivity (κ), volumetric heat capacity (ρCp) and thermal contact resistance (Rth) were determined using the pulsed photothermal method. The thermal conductivity of bulk silicon dropped sharply after etching, decreasing by more than twenty-fold in the case of n-type (100) and by over forty-five fold for p-type (100) and (111). According to the percolation model depending on both porosity and phonon confinement, the drop in thermal conductivity was mainly due to the nanostructure formation after etching. Thermal investigations showed that the volumetric heat capacity (ρCp) followed the barycentric model which depends mainly on the porosity. The thermal contact resistances of MePSi layers were estimated to be in the range of 1x10-8 to 1x10-7 K⋅m2⋅W-1.

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1.

INTRODUCTION

Porous silicon (PSi) thin films can be produced by electrochemical etching (or anodization) of crystalline Si wafer in a fluoride ion containing electrolyte. PSi can roughly be represented as a network of disordered pores vertically interconnected through the Si substrate.1 However, diverse porous layer morphologies can be achieved by varying the etching parameters, especially the Si wafer characteristics. Indeed, the pore size can be classified as a function of the wafer doping level. Macropores (pore size > 50 nm according to IUPAC classification)2,3 and/or micropores (< 2 nm) are synthesized in low-doped Si (< 1018 cm-3) whereas mesopores (pore size between 2 and 50 nm) are etched in highly-doped material (>1018 cm-3)4. Although mesopores can be obtained in both highly-doped n- and p-type Si; slight differences may be distinguished between the two resulting MePSi layers. For instance, n-type Si electrochemical etching leads to a much lower porosity MePSi layer than that of p-type Si for a given anodization current density and electrolyte composition.5,6 These differences are imputed to the width of the space charge region (SCR) during the anodization phase. Highly doped n-type Si present a significantly larger SCR compared to p-type Si with similar doping level.7,8 These differences are far from negligible for the material properties at the macroscopic scale and are a prime parameter to consider when choosing the wafer characteristics for a given application. Thanks to the unique combination of high specific surface area (induced by the small average pore size) and acceptable mechanical stability, MePSi has been applied in many domains such as energy storage,9,10 drug delivery11 or microelectronics12. In microelectronics, MePSi is a promising candidate for the electrical insulation of AC-switch peripheries13 or in radio frequency devices14. However, the electrical property of MePSi is not the only parameter to consider when assessing the performances of a device; its thermal conductivity is 3



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also very important to determine the heat dissipation and thus limit self-heating-induced device damage.15 Characterizations performed in a previous study on MePSi etched from ntype Si demonstrated that the thermal conductivity decreased from 8 to 5 W⋅m-1⋅K-1 with increasing thickness of the MePSi layer.16 The significant decrease in thermal conductivity compared to the pristine crystalline silicon reference (120-150 W⋅m-1⋅K-1)17,18 was attributed to the combination of the porosity and the surface chemistry (presence of SiO and SiH bonds). In the present study, the thermal and structural properties of MePSi layers etched from p-type substrates with different crystalline orientations were determined and compared to those obtained from n-type (phosphorus-doped) Si reported in a previous publication.16 The porous framework was observed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM), allowing the evaluation of pore orientation and density. Fourier transform infrared spectroscopy (FTIR) was employed to determine the thickness, the average porosity and the surface chemistry of the MePSi films. Lastly, the thermal properties of MePSi such as thermal conductivity, volumetric heat capacity and thermal contact resistance were determined by the pulsed PhotoThermal method (PPT) which is a fast infrared pyrometry technique using a nanosecond UV laser beam as the heating source.

2.

EXPERIMENTAL A. MePSi Layer Formation. MePSi layers were prepared through electrochemical

etching of 6-inch p-type (boron-doped) Si wafers with a resistivity of 15-25 mΩ⋅⋅cm and a crystal orientation (100) or (111). The wafers were immersed in a hydrofluoric acid (HF 15 wt.%) – acetic acid (10 wt.%) electrolyte and subjected to anodic oxidation. The MePSi layer etching conditions and characteristics are summarized in Table 1.

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Table 1. Silicon p-type Substrate Characteristics Expected and Measured MePSi Layer Thickness from Infrared Analysis Etching Expected IR- thickness IR- porosity duration (s) thickness (µm) (µm) (%) P1 10 0.2 0.238 58±2 P2 30 1 0.810 64±2 (111) P3 360 10 9.75 64±2 P4 2100 50 53.6 67.5±2 P5 5 0.2 0.235 41.5±2 P6 24 1 0.745 45.5±2 (100) P7 330 10 10.2 48.5±2 P8 1800 50 52.6 50±2 MePSi layers with different thicknesses were produced while controlling the etching duration. The anodic current density was fixed at 30 mA/cm². After anodization, the porous layers were first carefully rinsed by deionized water in order to completely remove toxic waste from the pores, then dried and finally cut in 1 x 1 cm² pieces. Sample

Crystal orientation

B. Optical Characterization. Mid-infrared reflectance spectra were acquired on the sets of MePSi layers using a Bruker Hyperion 3000 microscope coupled to a Vertex 80v Fourier transform spectrometer. The measurements were performed with an aperture of about 150x150 µm2, an instrumental resolution of 4 cm-1 and the internal reference of the microscope (gold mirror). The acquisition and detection of reference and sample fluxes were made with a 15x Cassegrain objective and an MCT detector, respectively. The thickness (), porosity () and dielectric function ( ) of the etched layers were estimated by fitting the reflectance spectra with an optical model involving a thin film on a thick substrate.19 The small diameter size of the porous channels, by comparison to infrared wavelengths, allows material homogenization and thus the application of an effective medium theory to reproduce the optical response of the layers. A version applicable to materials including randomly distributed cylindrical pores perpendicular to the surface of the layer was chosen to take the columnar structure of the porosity of the investigated samples20 into account: −

1 −

= +

1 +

5



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where is the dielectric function of the matrix composing the layer. An extended Drude term21 was included in the dielectric function models to reproduce the contribution to susceptibility of free electrons or holes present in the doped silicon substrates. Causal Gaussian terms22 were also added to the dielectric function model of the layer matrix to deal with the absorption bands induced by Si-O and Si-H bonds. Morphological studies in terms of pore size distribution, shape and density of pores were performed using Scanning Electron Microscopy (on cross sections and plane views) on a Hitachi S4500 FEG-microscope and Transmission Electron Microscopy (on cross sections) on an FEI-CM20 operating at 200kV. Measurements were done on several sets of images in order to obtain statistical measurements. C. Thermophysical Characterization. The thermal characterization of MePSi layers was carried out using the PPT. As reported in previous work,16,17 the main principle of this method (figure 1) consists in heating the sample by a pulsed KrF laser beam (λ= 248 nm, pulse time of 27 ns and fluence of 100 mJ/cm2). The thermal emission from the front (porous) side of the sample surface, imputed to the laser heating, is measured by a rapid IR detector (HgCdTe photodiode by Kolmar technologies, KMPV series). Finally thanks to a calibration protocol, the evolution of the surface temperature is plotted as detailed in ref.16,23 After acquisition of the surface temperature curve versus time, identification under Comsol Multiphysics® is necessary to determine the thermal properties of the sample such as the thermal diffusivity (i.e. thermal conductivity), the heat capacity and the density. It is important to note that a thin film of titanium (200 nm) was deposited by PVD on the MePSi layer. The titanium layer absorbs the incident UV laser photons, creating a uniform heating source at the MePSi surface. Due to the presence of a metal transducer on the 6


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mesoporous surface, the thermal contact resistance was also evaluated using the previous identification step.

Figure 1. Schematic representation of the Pulsed PhotoThermal method (PPT).

3.

RESULTS AND DISCUSSION D. p-type MePSi Structural Characterization. Figure 2 reports the reflectance

spectra of MePSi samples obtained from p-type (111) and (100) oriented Si wafers for thicknesses ranging from 200 nm to 50 µm. The comparison between the spectra of (100) and (111) p-type samples having similar etching thicknesses shows significant differences in periodicity and amplitude of modulation of the interference pattern. Since the optical responses of the parent wafers are the same, the observed differences are a clear indication that the resulting porous structure of the layers is dependent on the crystal orientation during the etching phase. The fits of the experimental data, also reported on Figure 2, allowed the extraction of textural information (Table 1). The thicknesses of the layers estimated with the optimization procedure were close to those targeted during the elaboration phase and the values obtained 7



for the porosity were clearly dependent upon layer thickness and crystal orientation. An increase in porosity with the rise in the layer thickness and a higher porosity for layers elaborated on wafers with (111) orientation are observed. These behaviors were anticipated for this kind of material.6,24

0.3

Experiment Model

111 p-type

0.2

0.3

53.6 µm

0.2 0.1

0.0

0.0 0.3

9.75 µm

Reflectance

0.2 0.1 0.0 0.3

810 nm

0.0 0.3

0.1

0.1

0.0

0.0

745 nm

0.3 238 nm

0.2

0.1 0.0 500

10.2 µm

0.1

0.2

0.3

52.6 µm

0.2

0.2

0.2

Experiment Model

100 p-type

0.1 0.3

Reflectance

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235 nm

0.1

1000

1500

2000 -1 Wavenumber (cm )

2500

0.0 500

1000

1500

2000 -1 Wavenumber (cm )

2500

Figure 2. Layer thickness dependence of the reflectance spectra of p-type MePSi samples with (111) and (100) crystal orientation of the Si wafers and their fits.

These results were confirmed by Scanning Electron Microscopy. In the case of (100) oriented wafers, the pore mean diameter (determined from plane view images) increased from 7 nm to 10 nm for samples P5 to P8 respectively. Finally, this density reached 6x103 pores/µm2 for the P8 sample. The surface porosity was estimated at 45% ± 5% for the latter sample. In comparison to n-type samples, the p-type sample surface roughness and the pore density were higher (Figure 3). Cross section views indicated that the pores are columnar 8


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perpendicularly to the surface and branch laterally like pine needles when etching (100) silicon wafers (figure 4). In the case of (111) p-type samples, the pores are meandering and globally oriented in the direction of holes generated during etching. This might explain the significantly higher porosity observed in (111)-oriented wafers (cf. Table 1).

Figure 3. SEM plane view images of (100) and (111) p-type and (100) n-type MePSi samples. For the two samples the etching depth was 10 µm. (scale bar = 300 nm).

9



Figure 4. SEM cross-section views of (100) and (111) p-type and (100) n-type MePSi samples. (scale bar = 300 nm).

111 p-type 1.5 53.6 µm 1.0 0.5 0.0 1.5 9.75 µm 1.0 0.5 0.0 810 nm 1.5 1.0 0.5 0.0 238 nm 1.5 1.0 0.5 0.0 500 1000 2000 2200 -1 Wavenumber (cm )

0.4 0.2 0.0 0.4 0.2 0.0 0.4 0.2 0.0 0.4 0.2 0.0 2400

Imaginary dielectric function

Imaginary dielectric function

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100 p-type 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.0 500 1000

0.4 52.6 µm

0.2 0.0 0.4

10.2 µm

0.2 0.0 0.4

745 nm

0.2 0.0 0.4

235 nm

0.2 2000

2200

0.0 2400

-1

Wavenumber (cm )

Figure 5. Thickness dependence of the imaginary part of the effective dielectric function of ptype MePSi layers elaborated with Si wafers having (111) and (100) crystal orientations.

As shown in Figure 5, the imaginary parts of the effective dielectric functions showed only minor changes from sample to sample whatever the thickness and crystal orientation. The positions of the main absorption bands observed in the spectra are in good agreement with those reported in the literature.25-27 Those linked to SiH bending and SiH2 wagging vibrations were located at 626 ± 3 cm-1 and 662 ± 3 cm-1, respectively. The scissors bending component of SiH2 had a wavenumber of 909 ± 3 cm-1 and high frequency contributions due to stretching motions were located at 2085 ± 4 cm-1 (SiH), 2114 ± 4 cm-1 (SiH2) and 10


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2139 ± 4 cm-1. Due to the partial oxidation of the porous layers, there were two supplementary absorption bands linked to silicon hydrogen stretching in oxidized configurations: a first one at 2195 ± 5 cm-1 (O2SiH2) and a second at 2250 ± 5 cm-1 (O3SiH). The level of oxidation of the layers which is directly linked to the intensity of the absorption band at around 1060 cm-1 originating from SiO stretching motions did not show any specific trend. The only noticeable fact is that the thinnest layers (200 nm) were more oxidized. 111 p-type

100 p-type 53.6 µm 9.75 µm 810 nm 238 nm

4.5 4.0 3.5 3.0 2.5 500

1000

1500

2000

2500

6.0 Real dielectric function

5.0 Real dielectric function

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


52.6 µm 10.2 µm 745 nm 235 nm

5.5 5.0 4.5 4.0 3.5 500

1000

-1

Wavenumber (cm )

1500

2000

2500

-1

Wavenumber (cm )

Figure 6. Thickness dependence of the real part of the effective dielectric function of p-type MePSi layers elaborated with Si wafers having (111) and (100) crystal orientations. As shown in Figure 6, the real parts of the dielectric functions drastically evolved with thickness and crystal orientation. The dependences are a direct consequence of the evolution of the porosity inside the layers. The increase of porosity with etching duration, i.e. layer thickness, leads to a reduction of the average density of highly polarizable Si-Si covalent bonds. As a consequence, this induces a weakening of the strength of the absorption bands due to the electronic transitions that contribute to the dielectric function at high frequencies (visible, UV spectral range). In the infrared range, this contribution almost exclusively impacts the real part of the dielectric function of the layer. So the diminution of the dispersive 11



part in spectral regions where the imaginary part nearly vanishes is directly linked to the increase of porosity as shown by the results extracted from the effective medium analysis. A comparison of the imaginary parts of the effective dielectric functions of n-type (studied in ref.16) and p-type MePSi samples is reported on figure 7. P-type layers had similar absorption components whatever their crystal orientation and differed strongly from the response of n-type MePSi. The n-type sample was far more oxidized as indicated by the stronger SiO stretching component around 1060 cm-1 and contained fewer Si-H bonds. These differences in oxidation level could be imputed to the tendency of highly doped n-type Si to be easily oxidized in air (compared to highly doped p-type).28 Moreover, the high specific surface area of MePSi can accentuate this difference. Etching depth:10 µm

1.5 Imaginary dielectric function

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100 p-type 111 p-type 100 n-type

1.2 0.9 0.6 0.3 0.0 500

1000

1500 2000 -1 Wavenumber (cm )

2500

Figure 7. Comparison of the imaginary parts of the effective dielectric functions of n-type (N100) and p-type (P-100, P-111) MePSi layers having a thickness of around 10 µm.

12


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E. MePSi 100 p-type Thermal Properties.

(a)

Etching depth of 100 p-type 0.2 µm 1 µm 10 µm 50 µm

250 200 150 100

900

700 600 500

50

400

0

300

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Etching depth of 100 p-type 0.2 µm 1 µm 10 µm 50 µm

(b)

800 Temperature (K)

300 Detector ouput voltage (mV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.5

0.0

Times (µs)

0.5

1.0

1.5

2.0

2.5

3.0

Time (µs)

Figure 8. (a) Output voltage of IR detector and (b) the surface temperature versus time for (100) p-type samples.

Figure 8a shows the raw signal of IR radiation emitted by p-type (100) samples in terms of output voltage of the IR detector following a laser pulse. The evolution of the sample surface temperature is given in figure 8b. The extraction of the temperature through IR radiation requires an additional calibration step as detailed in several papers.16,17,23 Knowing the evolution of the surface temperature after a laser pulse, the final step in the determination of thermal properties is identification by means of numerical simulation under Comsol Multiphysics®.16 We created a multilayer model in Comsol that represents the substrate and the thin layers (MePSI and titanium). Then, the heating parameters, the substrate properties, the titanium layer properties and the experimental data were entered in the model. Comsol then solves the heat equation while varying the thermal properties of the MePSi thin layer in order to fit the simulation curve of surface temperature by the experimental one. Figure 9 shows the experimental and simulation curves of the surface temperature versus time for all (100) p-type samples (P5-P8) during the first few microseconds following a laser pulse. It can be seen that the simulation curve is in good agreement with the experimental one 13



in the case of 0.2 and 1 µm of etching depth. However, this is not the case for 10 and 50 µm of etching depth, namely in the first hundred nanoseconds. Keeping in mind that in those first nanoseconds the thermal wave mainly propagates within the Ti transducer, the remaining part of the curve fits the experimental one well. This part is much more representative of thermal wave propagation inside the MePSi layers. 900

700 600 500 400

700 600 500 400 300

300 200 0.01

0.1

200 0.01

1

0.1

900

900

100 p-type, etching depth : 10 µm Comsol Experimental

700 600 500 400

100 p-type, etching depth : 50 µm Comsol Experimental

800 Temperature (K)

800

1

Times (µs)

Times (µs)

700 600 500 400 300

300 200 0.01

100 p-type, etching depth: 1 µm Comsol Experimental

800 Temperature (K)

Temperature (K)

900

100 p-type, etching depth : 0.2 µm Comsol Experimental

800

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.1

1

200 0.01

Times (µs)

0.1

1

Times (µs)

Figure 9. Experimental and simulation curves of surface temperature versus time for (100) ptype substrates.

Table 2 summarizes the thermal characteristics of MePSi found by identification under Comsol Multiphysics®. Compared to single crystalline Si, a significant decrease in thermal conductivity can be observed, from a few hundred W⋅m-1⋅K-1 to a few W⋅m-1⋅K-1 for MePSi. Also, the thermal conductivity decreased slightly with the MePSi thickness with the exception 14


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of sample (P5) (0.2 µm of etching depth) where the thermal conductivity showed the lowest value. As mentioned in the previous section, the thinnest sample was more oxidized. This observation performed by FTIR measurements could explain this low thermal conductivity value. There was also an increase, overall, of thermal contact resistance and a decrease of volumetric heat capacity (ρCp) with the increase in etching depth. As demonstrated in previous work,16 the ρCp values extracted from the simulation are consistent with the barycenter ones which were calculated using the porosity rate model,17 highlighting the consistency of the two approaches.

Table 2. Thermal Properties of MePSi Obtained from the Anodization of p-type (100)-oriented Si Wafers Thermal Thermal contact Barycentric model Expected ρ.Cp conductivity resistance for the ρCp Sample thickness -3 -1 (J⋅m ⋅K ) (µm) (W⋅m-1⋅K-1) (K⋅m2⋅W-1) (J⋅m-3⋅K-1) P5

0.2

1.7 ± 0.1

(1 ± 0.5)x10-8

(0.96 ± 0.2)x106

(0.95 ± 0.05)x106

P6

1

3.1 ± 0.1

(4 ± 1)x10-8

(0.9 ± 0.1)x106

(0.89 ± 0.05)x106

P7

10

2.9 ± 0.1

(9 ± 1.5)x10-8

(0.85 ± 0.12)x106

(0.84 ± 0.05)x106

P8

50

2.7 ± 0.2

(6.5 ± 2)x10-8

(0.82 ± 0.08)x106

(0.82 ± 0.05)x106

15



F. Thermal Properties Comparison.

100 n-type 100 p-type

100 n-type experimental value 100 n-type percolation model Percolation model with dc=14 nm

100 p-type experimental value 100 p-type percolation model Percolation model with dc=10 nm

-1

8

(b) -1

9

Thermal conductivity (W.m .K )

-1

(a)

-1

I. MePSi 100 p-type Vs100 n-type.

Thermal conductivity (W.m .K )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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7 6

10

5 4 3 2 1 0

10

20

30

Etching depth (µm)

40

50

1 24

28

32

36

40

Porosity rate (%)

44 40 42 44 46 48 50 Porosity rate (%)

Figure 10. (a) Thermal conductivity evolution for n and p- type MePSi substrate versus etching depth. (b) Thermal conductivity comparison between experimental value, percolation model and corrected percolation model for nano-crystallite mean diameter (dc) for both substrates versus porosity.

Figure 10a shows the evolution of thermal conductivity versus etching depth for the MePSi p- and n-type in the same (100) orientation. It can be seen that the thermal conductivity in the case of n-type MePSi was at least two times greater than the p-type one for similar etching depths. This difference in thermal conductivity between the two types cannot be explained only by the difference in porosity of the MePSi layers. We have plotted in figure 10b the thermal conductivity determined by the percolation model29 for two cases. The first one (black squares for n-type and red squares for p-type) concerns situations where the size of the crystallites is greater than the phonon mean free path in monocrystalline Si (ΛSi=43 nm )29,30. In this case, the thermal conductivity depends only on the porosity according to the formula: 16


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= (1 − ) where P is the porosity rate. In the second case, the phonon mean free path is greater than the size of crystallites (black circles for n-type and red circles for p-type) (Figure 10b) and evaluation of the thermal conductivity requires knowing both the size of the crystallites and the phonon mean free path: =

(1 − ) 4 1+ 3 !

(b)

(a)

Figure 11. TEM cross-section showing columnar pores with some branches (a) and zoom (b) on one MePSi column. On these images pores are light and the silicon columns are dark.

Average values for the crystallite diameter (dc) were deduced from the TEM cross section images obtained for different MePSi layers (Figure 11). They were around 14 nm and 10 nm for n-type and p-type, respectively.

17



As shown on Figure 11b, the porosity is not the only parameter explaining the drop in thermal conductivity. Taking into account the size of crystallites in the percolation model with dc < ΛSi leads to far better fits of the experimental data for p- and n-types. This shows that the nanostructuration of c-Si due to electrochemical etching is the major contributor to the drop in thermal conductivity by preventing the diffusion of phonons through the structure. The volumetric heat capacity depends mainly on the porosity as shown in Figure 12a where the experimental values fit quite nicely with the barycentric model in the case of p-type and less in the case of n-type. According to the barycentric model, the volumetric heat capacity of MePSi is related to the porosity by the following equation:

"#$% = "#$% (1 − ) + "#$%'( with the porosity. The extracted values for the volumetric heat capacity are larger for n-type MePSi (Figure 12b). This is logical as the porosity of p-type samples is much higher than that of the n-type

100 n-type experimental value 100 p-type experimental value Barycentric model

1.8 1.6 1.4 1.2 1.0 0.8 0.6 25

30

35

40

45

50

-1

(a)

2.0

-3

-1 -3

6 2.2 x10

Volumetric heat capacity (J.m .K )

for the same etching depth.

Volumetric heat capacity (J.m .K )

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2.2 2.0

x106

(b)


1.8 1.6 1.4 1.2 1.0 0.8 0.6 0

10

Porosity rate (%)

20

30

40

50

Etching depth (µm)

Figure 12. Volumetric heat capacity comparison between experimental values and barycentric model for the two substrates versus (a) porosity (b) Etching depth.

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For thermal contact resistance which depends on the surface morphology of materials, Figure 13 shows that, overall, the thermal contact resistance of 100 p-type MePSi layers was higher than that of the n-type MePSi layers. This is consistent with the surface SEM observation (Figure 3) where the surface roughness of the 100 p-type samples is greater and

-1

-8 12 x10

2

the pore density is higher than that of the 100 n-type samples.

10

Thermal contact resisitance (m .K.W )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



8 6 4 2 0 0

10

20

30

40

50

Etching depth (µm)

Figure 13. Thermal contact resistance versus etching depth for both n- and p-type (100)oriented substrates.

19



II. MePSi 100 p-type vs 111 p-type. As shown in the previous section, the use of an isotropic model for thermal conductivity was enough to identify the thermophysical properties of MePSi 100 p-type and 100 n-type samples. In contrast, applying the same numerical procedure under Comsol Multiphysics did not allow the reproduction of the measured thermal response of MePSi 111 p-type samples with realistic values of the model parameters (results not shown). The failure of the thermal transfer model is no doubt due to the more complex and highly irregular structure of the MePSi 111 p-type layers. Since the classic model does not apply, we restrict our discussion in the following to a comparison of the temporal

900 800

Etching depth: 1 µm 100 p-type 111 p-type

700

Etching depth : 50 µm 100 p-type 111 p-type

600 500 400

300

Normalized Temperature

dependence of the surface temperature of MePSi 111 and 100 p-types (Figure 14).

Temperature (K)

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1.1 1 0.9 0.8 0.7


0.6 0.5 0.4 0.3

0.1

1

0.1

Time(µs)

1 Time(µs)

Figure 14. Measured and normalized temperatures of the sample surface for 100 and 111 p-type (1 and 50 µm etching depths).

Figure 14 plots the evolution of the thermal response of samples with 1 µm etching depth (P2, P6) and 50 µm etching depth (P4, P8). First, we notice that whatever the etching depth, the surface temperature of MePSi 100 p-type layers decrease faster than that of the 111 ptype. This means that heat spreads more rapidly through 100 p-type layers compared to the 111 p-type ones and consequently that the thermal diffusivity ) ** of 100 p-type samples is 20


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greater than that of )

(111 p-type samples). Optical and structural characterizations have shown that the MePSi 111 p-type layers are much more porous than the 100 p-type ones. So, according to the barycentric model, the "#$ value of 111 p-type is smaller than that of the 100 p-type. Moreover, since thermal diffusivity depends on the thermal conductivity and the volumetric heat capacity according to the following relationship: )=

+ ,-.

,

we can conclude that the thermal conductivity of the MePSi 111 p-type layers is smaller than that of 100 p-type ones. The fact that a direct identification of the thermal properties of 111 p-type layers was not possible with a homogenized isotropic value of the thermal conductivity may be related to the more anisotropic structure of the 111 p-type samples. Taking anisotropy of the conductivity into account in the identification step involves solving the thermal heat transfer problem with a 2D thermophysical model (in plane and in depth thermal conductivity). This will be done in upcoming work.

4.

CONCLUSIONS

The structural and optical characterization by SEM and FTIR of several sets of MePSi layers produced with varying etching parameters and Si wafer characteristics confirmed that diverse porous layer morphologies can be achieved. For similar etching conditions, the crystal orientation of the Si wafer and the type of doping have a drastic impact on the porosity and the abundance of Si-Ox and Si-Hy defects. These differences are far from negligible for the material properties at the macroscopic scale. The thermal characterization of the MePSi layers carried out using the PPT evidences different kinds of heat transfer behavior within the layers. The thermal response of samples produced from Si wafers with (100) crystal orientation can 21



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be simulated with a model involving a homogenized isotropic value for the thermal conductivity of the layer. The percolation model including both porosity and phonon confinement explains the results identified for the thermal conductivity of the layers built with this wafer orientation. A barycentric model is also able to reproduce the evolution of the volumetric heat capacity of MePSi. Layers built from Si with (111) crystal orientation behave differently. Their thermal response cannot be reproduced with a homogenized isotropic value of thermal conductivity. The more complex microstructure evidenced by SEM indicates that anisotropy may play a significant role in thermal transfer. In all cases, there is a drastic drop of thermal conductivity from 120-150 W⋅m-1⋅K-1 of pristine silicon to 1-10 W⋅m-1⋅K-1 after etching. These low thermal conductivities are leading to many applications as heat flux waveguide in µ-sensors technology31 and new thermoelectric materials (films and flexible membranes) for µTEG.

Acknowledgments The authors are very grateful to the French regional office “Region Centre” for supporting the scientific project “PoreuxTherm”.

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(31) Ziouche, K.; Godts, P.; Bougrioua, Z.; Sion, C.; Lasri, T.; Leclercq, D. Quasimonolithic heat flux microsensor based on porous silicon boxes. Sens. Actuators, A 2010, 164, 35-40.

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TABLE OF CONTENTS IMAGE

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Structural, Optical, and Thermophysical Properties of Mesoporous

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