|NDT.net June 2006 Vol. 11 No.6|
On the optical and thermal properties of porous siliconJ. Meena Devi1 (firstname.lastname@example.org),M. Jeyachandran2, K. Ramachandran1
1School of Physics, Madurai Kamaraj University, Madurai-625021.
2Central Electrochemical Research Institute, Karaikudi-630 006.
AbstractThis paper discusses the properties of porous silicon prepared by electrochemical etching using photoluminescence and photoacoustic spectroscopy at room temperature. The experimental results obtained are compared with other reported works.
Introduction:The discovery of strong visible photoluminescence at room temperature in 1990 from porous silicon  has opened the way to worldwide intensive studies on its optical and transport properties and to the numerous technological applications of porous silicon in microsystems such as insulator structures, gas and biochemical sensors, optical devices and so on. The two most widely discussed mechanisms underlying the visible luminescence are quantum confinement model and the surface model. In recent years, a promising application of porous silicon (PS) as new silicon based thermal insulator in thermal effect microsystems has also received much interest, because of its low thermal conductivity . Usually, the PS samples are produced by anodic etching of crystalline silicon wafer in hydrofluoric solution. It was found that the optical and thermal properties of PS strongly depend on the physical parameters of PS films which are strongly dependent upon the fabrication controlling parameters such as electrolyte composition, current density, etching time, etc., as well as on the type of substrate used.
PS samples are made by a porous layer over a crystalline substrate. In order to determine the thermal conductivity by conventional techniques, it is necessary to separate the contribution of porous layer from the crystalline substrate. Moreover, conventional techniques are intrusive and require a sample preparation procedure which hardly applies to PS. The photoacoustic (PA) technique has proved to be powerful for investigating the optical, electronic, and thermal properties of materials as a non contact and non-destructive method by measuring the non-radioactive de-excitation processes that follow optical absorption. This technique takes advantage of no need to remove a silicon substrate from a porous silicon film. In the present work we investigate the photoluminescence and photoacoustic spectrum of porous silicon and we determine the thermal conductivity of PS films from the effective thermal conductivity by using a two layer model.
Experimental Procedure:PS layers were formed on (100)-oriented silicon substrates (thickness: 450µm) by electrochemical anodic etching in a solution of hydrofluoric acid, water and ethanol taken in the ratio 1:1:2. A platinum foil was used as the electrode. Etching time was 10 min. Two samples were prepared with current density 20mA/cm2 (PS-1) and 40 mA/cm2 (PS-2) and the atomic force microscopy (AFM) was performed at ambient air and room temperature using Shimadzu SPM 9500-2J scanning probe microscope. AFM pictures are shown in Figure: 1 and 2. Porosity of the two samples PS- and PS-2 was measured to be 35% and 45% respectively using a Hitachi S450 scanning electron microscope and the SEM images are shown in Figure: 3 and 4. PS layer thickness of two samples was found to be 23.8 and 26.2 µm by measuring the weight change of each silicon wafer after removing the PS layer. Photoluminescence spectrum (Figure: 5) of PS is recorded using Perkin Elmer LS55 luminescence spectrometer at room temperature. Photoacoustic measurements are carried out using the PA setup consisting of 400W Xenon lamp, monochromator (Jobin Yvon Triax 180) electromechanical chopper (PAR 650), lockin amplifier (Perkin Elmer 7225 DSP) and PA cell made up of stainless steel containing microphone and sample at room temperature. At constant chopping frequency of 40Hz, PA spectrum of PS (Figure: 6) is obtained as a function of energy of the illuminating light to observe the energy band structure. Then photoacoustic amplitude and phase of PS (Figure: 7 and 8) are recorded as a function of chopping frequency to determine the thermal conductivity. Chopping frequency is varied from 10 Hz to 100 Hz when the PS sample is placed in the PA cell (in the absence of monochromator).
Results and discussion:
Another possible explanation is that the multiple peaks  can also be due to variation in size of the crystallites and emission would have come from a statistical average of the crystallites. Xun Wang et al.  have reported that multiple peak structures they observed reflect the discontinuous distribution of the dimensions and energy gaps of Si nanostructures in PS samples.
Hence the double peak luminescence observed in the present work may be related to natural surface oxidation of PS in air and non uniformity in distribution and size of pores in addition to quantum confinement effect resulting from size reduction of silicon crystallites.
PL intensity of PS-2 has been enhanced by a factor of 2.6 on comparing it with PS-1. This shows that PL intensity is related with anodizing current density. Kim et al.  have noticed the increase in the PL intensity when they raised the current density from 10 to 100 mA/cm2 and they have reported that increase of PL intensity is likely by the increase in the total volume of the nanocrystallites on the surface of PS. Masato Ohmukai et al.  have investigated the relation between anodization conditions and photoluminescent characteristics and they have said that the PL intensity is affected directly by the current density and so as current density is large or as anodization time is large more luminescing porous silicon is obtained.
At low frequencies (up to 700HZ)  the thermal diffusion length in PS is apparently larger than the layer thickness. As a result, a PA signal is produced by light absorption followed by heating of both the porous layer and the backing crystalline substrate. At higher frequencies, the PA signal is determined by the porous layer alone because in this case thermal diffusion length is of the same order as layer thickness. In the present work PA spectrum is recorded at constant chopping frequency of 40Hz and so the PA signal comes both from porous layer and crystalline substrate.
Several spectral features are seen in the PA spectrum (Figure: 6) of porous silicon. This demonstrates the complicated energy structure of PS due to the band gap widening as a result of quantum confinement effect. The energy positions are given in the Table 1 and they are found in a range of energy 1.88<E<2.25eV. Within that range, we find 2.00 and 2.13 as the PL energies, which are observed in our PA spectrum as 2.01 2.13 eV respectively. Thus our PA and PL measurements on the PS samples reproduce the energies, even though they are complex compared to c-Si. Similar to PL intensity , PA intensity is also enhanced with increase in current density.
The PA energies from the present work are 1.88, 1.93, 2.01, 2.10 and 2.25 eV . This result is compared with PA energies of Ferreira et al.  (Table 1) found in a range of energy 1.60<E<2.14 eV. Our result is consistent with PA energy values obtained by Ferreira et al.  and the variation observed may be explained by the difference in the sample preparation.
aeff = fcl2 (m2/sec) (1)
where l is the thickness of the sample. The characteristic frequency is defined as the frequency at which the sample goes from thermally thick to thermally thin region and where we can observe distinct change in slope in the Figure: 7. From the equation (1) by assuming the PS/Si two layer sample as a homogeneous sample effectively, we determined the effective thermal diffusivities of samples PS-1 and PS-2 to be 9.3x10-6m2/sec and 7.7x 10-6m2/sec respectively. These values agree with those reported by Qing Shen and Tara Toyoda . The differences of the thermal diffusivity of the two samples were mostly due to difference in the porosity. The effective thermal diffusivity became smaller as the porosity of the PS layer became larger. Then effective thermal conductivity (keff) can be determined by the following relation
keff= aeff r c (m2/sec) (2)
where r is the density and c is the specific heat capacity.
In order to calculate the thermal conductivity of the PS film from the effective thermal conductivity, we consider the two layer model  consisting of a PS film (layer 1) of thickness l1 and of Si substrate (layer 1) of thickness l2, both having the same cross section. The two-layer sample was assumed as a effectively homogeneous one with a thickness of l=l1+l2 . From the analogy between the thermal and electrical resistances widely used in heat transfer problems, the effective thermal resistance Reff of this series two-layer system may be written as
where k1 is the thermal conductivity of PS film and k2 is the thermal conductivity of silicon substrate. From equation (4) thermal conductivity of PS layer of samples PS-1 and PS-2 are evaluated to be 0.91 and 0.81 W/mK respectively and they are given in Table: 2 along with other reported values. Error in the present measurement is around 2%.
Shen and Toyodo  have applied photoacoustic technique to study the thermal properties of porous silicon and they have shown that thermal conductivity decreases greatly up to 0.20W/mK when the porosity is larger than 52% and is almost three orders of the amplitude lower than that of crystalline silicon. Berini et al.  have employed photoacoustic technique to measure thermal conductivity of three porous silicon samples as a function of porosity and thickness and they found k to be decreasing for increasing porosity and is two or three orders of magnitude less than that for crystalline silicon. In the present work also thermal conductivity of PS film decreases with increase in porosity and the magnitude is around two orders less than that of crystalline silicon. The above result demonstrates, thermal conductivity of porous silicon layer depends on the porosity and it is lowered when the porosity is increased. Thermal conductivity of bulk silicon is directly proportional to the mean free path of the phonons. In porous silicon, mean free path of the phonons is limited by the mean size of the silicon crystallites  resulting in the reduction of thermal conductivity.
Gesle et al.  have determined the thermal conductivity of electrochemically prepared PS layers over a temperature range 35-320K using a dynamic 3w technique. Within the measured temperature range the thermal conductivity of porous silicon increases monotonically with temperature and they have described the temperature behavior of the thermal conductivity of PS with simple model for heat conduction in PS based on the phonon diffusion model. Thermal conductivity decreases dramatically with increasing porosity for all temperatures studied.
Conclusion:The optical properties of porous silicon prepared by electrochemical etching are studied by photoluminescence and photoacoustic spectroscopy. The PL shows double peaks in the red region which may correspond to natural surface oxidation of PS in air and non uniformity in distribution and size of pores in addition to quantum confinement effect resulting from size reduction of silicon crystallites. The PA spectrum shows peak in the range of energy 1.88>E>2.25eV indicating that the energy structure of PS is complex due to the band gap widening as a result of quantum confinement effect. Thermal conductivity of PS layer measured from photoacoustic technique is well two orders below the crystalline silicon and it decreases with increasing porosity in agreement with other existing studies.