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Materials Research

Print version ISSN 1516-1439On-line version ISSN 1980-5373

Mat. Res. vol.4 no.1 São Carlos Jan. 2001 

Thermal and Optical Properties of Porous Silicon 

A. Ferreira da Silvaa, T. Souza da Silvaa, O. Nakamuraa,
M.M.F. d’Aguiar Netoa, I. Pepea, L. S. Romanb, E. Vejec

aInstituto de Física, Universidade Federal da Bahia,
Campus Universitário de Ondina, 40210-340 Salvador - Ba, Brasil
bDepartamento de Física, Universidade Federal do Paraná,
C.P. 19044, 81531-990 Curitiba - Pr, Brazil
cDepartment of Electric Power Engineering, Technical University of Denmark,
Building 325, DK-2800 Lyngby, Denmark


Received: October 19, 2000; Revised: January 8, 2001


Thermal diffusivity and optical absorption have been investigated for porous silicon, at room temperature, using photoacoustic spectroscopy. The experimental results obtained conform well with the existing studies recently published. The value obtained for thermal diffusivity is 0.045 ± 0.002 cm2/s.The absorption onsets show energy structures, differing from the ordinary semiconductor of bulk type. PACS 51.20.Td; 74.25.Fy; 73.20.Dy; 78.20.Wc; 81.40.Tv

Keywords: thermal properties, optical properties, photoacoustic spectroscopy, porous silicon

1. Introduction

Owing to the wide-ranging of possible technological applications in opto-electronic devices1-27 and biocompatible materials as well28-33, the interest in characterizing porous silicon (PS) has recently increased very much. Porous silicon has been studied intensively since the discovery by Canham1, that even at room temperature PS can emit very bright photoluminescence (PL), in great contrast to crystalline silicon (c-Si). Usually, the PS samples are produced by anodic etching of c-Si wafers in hydrofluoric (HF) solution.

A large amount of investigations is devoted to the PL and absorption measurements of PS1-6,8, but so far there has been a few reports on its thermal properties7,17,18,34,35. In this work we have devoted our attention to obtain, by applying the photoacoustic spectroscopy (PAS), the optical absorption and the thermal diffusivity, which is, as other optical properties, an important physical parameter to be considered in device modeling, specially for power dissipation. The PAS spectra are obtained directly from the heat generated in a sample, due to nonradiative absorption processes36,37. The fact that the PA signal depends on how the heat diffuses through the sample enable us to measure its thermal diffusivity7,17,18,38. The experimental PA setups, consisting of a periodically exciting light source, a photoacoustic cell containing the sample and a microphone are described in details in Refs. 37 and 38 for optical absorption and thermal diffusivity respectively.

2. Experimental

The samples were produced by etching p-type c-Si wafers of crystal orientation (100) and resistivity 1-30 Wcm eletrochemycally in 40% HF: ethanol 1:1. The electrolytic cell as well as the etching procedure are described in Ref. 5. Current densities from 5 mA/cm2 to 25 mA/cm2 were used and in each case, the current density was always kept constant during etching. Etching times were from 60 to 90 min, so that all samples consisted of a fairly thick layer of PS. Scanning force microscopy (SFM) investigation revealed a typical thickness of around 30 mm.

The SFM measurements were performed using a Digital Instrument Nanoscope III running in tapping mode. In this imaging mode, the SFM tip-cantileve oscillates sinusoidally at high frequencies (300 kHz) with amplitude 10-100 nm, so that the tip contacted the surface once during each period. The data were taken in ambient air at room temperature. The samples were stored in air for a long time (>> 1 month), so that surface oxidation had equilibrated. This implies that the surface structure is fairly reproducibly and does not change in time. Scans were made over areas from 500 x 500 nm to 20 x 20 mm with a resolution of 512 x 512 pixels and the scan rate of 1-2 Hz.

3. Results and Discussion

Figure 1 shows a typical SFM image of p-type PS sample produced with 60 min etching time. In Fig. 2 we show the PA spectrum of the same sample used for Fig. 1. Several spectral features are seen, revealing the complex band system originated from the surface roughness as shown in Fig. 1. The PA energies are respectively 1.603 ± 0.048, 1.668 ± 0.050, 1.751 ± 0.052, 1.882 ± 0.056, 2.025 ± 0.086 and 2.143 ± 0.064eV. Such structures have recently been confirmed by PL, photoluminescense excitation (PLE) and photocurrent measurements21,26.




To measure thermal diffusivity, the acoustic signal produced in the gas cavity by the sample is detected by a Sunheiser condensed microphone and analyzed in respect to the modulator reference by a lock-in amplifier38. For the transmission arrangement, corresponding to the rear-side excitation of a thermally thick sample, the thermoacoustic phase contribution is given by the equation38.

where F0 is the initial phase, as is the thermal diffusivity, Ls is the sample thickness (Ls = 530 mm), and f is the chopping frequency. These parameters are determined by a numerical least-squares fitting procedure. In Fig. 3 we show the rear-PA intensity as a function of the chopping frequency f for the PS sample. It is shown that the PA signal intensity S is proportional to f l, for our best set of measurements l = -0.92. Figure 4 shows the chopping frequency dependence of rear-signal phase. The solid curve represents the best fit of the data to Eq. (1). The value obtained for the thermal diffusivity, at room temperature is as = 0.045 ± 0.002 cm2/s. This value may be compared to as = 0.047 cm2/s and as = 0.053 cm2/s recently found7,18 by Cruz-Orea et al.7 and Calderón et al.18, respectively, with open photoacoustic cell method. It is worthwhile to point out that there are some discrepancies between thermal conductivity values in the literature7,17,18,25. Like the thermal diffusivity, the thermal conductivity k is another important parameter to manufacturing devices. The measurement of as allows us to obtain k, once the density r and the specific heat Cv are know. We determine k by the relation k = asrCv. Cruz-Orea7 with a spark-process PS found k = 0.0074 w/cmK and as = 0.047 cm2/s, Calderón et al., with the usual eletrochemical etching process found k = 0.130 ± 0.006 W/cmK and as = 0.053 ± 0.0035 cm2/s respectively. They have used a n-type PS. Amato et al.17, found, for p-type PS the values k = 0.025 W/cmK and k = 0.039 W/cmK respectively for two different samples, while a value of k = 0.312 W/cmK for a n-type PS. Shinoda et al.25, with a thermally induced ultrasonic technique found k = 0.01 W/cmK. We may mention that Amato et al.17, have used forheat capacity a value equal to that of c-Si. Using the heat capacity of c-Si, Cv = 1.67 J/cm3K and of PS from Shinoda et al.25. Cv = 0.7 J/cm3K we found k = 0.075 W/cmK and k = 0.031 W/cmK respectively. The results above confirm the good possibility for thermal insulation given by PS layers in contrast to c-Si, which has higher thermal properties, i.e., as = 0.9 cm2/s and k = 1.67 W/cmK.




In summary, we have obtained through the PAS technique, the complex structure of the band gap energies and the thermal diffusivity of porous silicon. Several absorption features were observed from the PAS spectrum. The positions of these features were found in a range of energy 1.603 ± 0.048 £ E £ 2.143 ± 0.064 eV. The thermal diffusivity result is 0.045 ± 0.002 cm2/s, a value compared to other semiconductors of current technological importance38. The results conform well with the existing studies recently published, recognizing PS as a good material with potential to be used, for instance, thermal insulating layers and structures.




The authors would like to acknowledge the support of the Brazilian National Research Council, CNPq and SEPLANTEC/CADCT (Bahia). LSR acknowledges the financial support of the Göran Gustafsson foundation, and Thin Film Electronics AB, Sweden. EV is very grateful to support from the Danish Natural Science Research Council, the Carlsberg Foundation, Director Ib Henriksens Foundation, and the NOVO Nordic Foundation.


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