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International Journal of the Physical Sciences Vol. 5(5), pp. 465-469, May 2010Available online at http://www.academicjournals.org/IJPSISSN 1992 - 1950 2010 Academic Journals

Full Length Research Paper

Effects of thin film thickness on emittance, reflectanceand transmittance of nano scale multilayers

S. A. A. Oloomi*1, A. Saboonchi1 and A. Sedaghat1

1Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, I.R., Iran.

Accepted 19 April, 2010

Knowledge of the radiative properties of multilayer consisting of silicon and related materials, such assilicon dioxide (SiO2), silicon nitride (Si3N4) and gold (Au) with different thicknesses is required formany microsystem applications. This paper describes the study of the effects of thin film thickness on

radiative properties of nano scale multilayer. The results showed that silicon dioxide and silicon nitridecoating act as anti reflector and these coatings reduce reflectance toward bare silicon. If thickness ofnon metal coating increases, reflectance of multilayer decreases and transmittance increases. Gold thinfilm coating increases reflectance. The reflectance of multilayer coated with gold increases byincreasing the thickness of coating. This study will benefit and enhance the value of nano coatingtechnology in the semiconductor industries, particularly in the development of micro electromechanicaland nano electromechanical devices.

Key words: Nano scale multi layer, thin films, thickness, metal coating, non metal coating, radiative properties.

INTRODUCTION

Optical techniques and radiative processes playimportant roles in current industrial and daily life.Examples are advanced lighting and display, materialsand surface characterization, real time processmonitoring and control, laser manufacturing, rapidthermal processing (RTP), communication, data storageand reading, radiation detection, biomedical imaging andtreatment, ground and space solar energy utilization,direct energy conversion, etc. Optical and thermalradiative properties are fundamental physical propertiesthat describe the interaction between electromagneticwaves and matter from deep ultraviolet to far-infraredspectral regions. In fact, optical property measurements

and analysis offer powerful tools to understand thephysics of solids and other materials. However, opticaland radiative properties depend on a large number ofvariables; modeling of radiative properties of nano scalemultilayer is a convenient way to analyze the observedresults.

Silicon dioxide (SiO2) layer coated on lightly doped

*Corresponding author. E-mail: amiroloomi@me.iut.ac.ir. Tel:989133593179.

silicon substrate has higher reflectance than siliconnitride (Si3N4) coating for visible wavelengths. In thesewavelengths the reflectance increases as thetemperature increases due to decreasing emittance; butin infrared wavelengths, the reflectance andtransmittance decrease as the temperature increases(Oloomi et al., 2009a).

The reflectance and transmittance of thick siliconsubstrate with 700 m thickness and coated by silicondioxide thin film with 300 nm thickness were alreadycalculated by (Lee et al., 2005) with incoherenformulation. In this paper, the effects of film thickness onradiative properties of nano scale multilayer are

considered. The film coating consists of multi-layerstructure of metal and non metal thin film coatings withvarying thickness from 0 - 200 nm. This work usesincoherent formulation for calculating the radiativeproperties of semiconductor materials related to therecent technological advancements that are playing avital role in the integrated-circuit manufacturingoptoelectronics and radiative energy conversion devicesLightly doped silicon is used and the empiricaexpressions for the optical constants of lightly dopedsilicon are employed. Silicon dioxide and silicon nitrideare used as non metal thin film coatings and gold is used

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466 Int. J. Phys. Sci.

3

2

d

d

1Nd

Figure 1. Schematic of thin-film coatings on both sides of a thick silicon.

as metal thin film coating.

MODELING

Incoherent formulation

When the thickness of silicon substrate is much greater than thecoherent length and the considered wavelength falls in the semitransparent region of silicon, interferences in the substrate aregenerally not observable. In this case, the incoherent formulation orgeometric optics should be used to predict the radiative propertiesof the silicon substrate. Two ways to get around this problem are touse the fringe-averaged radiative properties and to treat thin-filmcoatings as coherent but the substrate as incoherent (Zhang et al.,

2003). Figure 1 shows the geometry of the silicon wafer with multithin-film coatings on both sides. Note that t is the transmittance ofthe multilayer structure at the top surface (air-coatings-silicon) for

rays incident from air. Similarly, bs is for the multilayer structure atthe bottom surface for rays incident from the substrate. On the other

hand, ts and b are for rays incident from silicon.The absorption of silicon can be taken into consideration by

introducing the internal transmittance

)cos

4exp(

s

ssi

dk

= (1)

Here, sk is the extinction coefficient of silicon, sd is the thickness

and s is the angle of refraction. The radiative properties of thesilicon wafer with thin-film coatings such as reflectance ,transmittance and emittance in the semi transparent regioncan be expressed as (Timans, 1996):

bstsi

bstita

2

22

1+=

(2)

bstsi

bti

21

=

(3)

=1(4)

Optical constants

The optical constants, including the refractive index (n) and theextinction coefficient (), of a material are complicated functions othe wavelength and temperature. We need optical constants omaterials for calculating the radiative properties of nano scalemultilayers.

The Jellison and Modine (J-M) expression of optical constants osilicon for a wavelength between 0.4 m and 0.84 m is given in(Jellison et al., 1994):

TnTnJM )()(),( 0 += (5)

220 )/24.1(648.3

3.97565.4

+=n (6

22

34

)/24.1(648.3

10394.510864.1)(

+=

(7)

Li developed a functional relation, for optical constants of siliconthat covers the wavelength region between 1.2 m and 14 m (Li1980):

2

)()()(),(

TTgTTn

rL += (8)

++=TT

r

3100268.1631.11)(

31026 101347.8100384.1 TT

(9)

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Oloomi et al. 467

Figure 2. A comparison of the calculated results (left side) with results of (Lee et al., 2005) (right side).

284 103835.7108011.40204.1)( TTTg ++= (10)

=TT

64 10526.810786.1exp()( )10363.110685.4 31229 TT +

(11)

The J-M expression is used in this study to calculate the opticalconstants of silicon for the wavelength region from 0.5 m to 0.84m but Lis expression is employed for wavelengths above 1.2 m.For a wavelength range of 0.84 m to 1.2 m, we use a weightedaverage based on the extrapolation of the two expressions.

84.02.1

)84.0()2.1(

+=

LJMAVG

nnn

(12)

The optical constants of silicon dioxide, silicon nitride and gold aremainly based on the data collected in Palik (1998).

RESULTS AND DISCUSSION

Figure 2 compares the reflectance and transmittance ofthick silicon substrate with 700 m thickness and coatedby silicon dioxide thin film with 300 nm thickness in two

different coating cases and two different temperatureswith the results in (Lee et al., 2005). The electromagnetic

waves are incident at = 0. The calculated results are ingood agreement with results in (Lee et al., 2005)Because the refractive index of silicon dioxide (around1.45) is smaller than that of silicon, the reflectance with acoating is always lower than that of bare silicon for nonmetal thin film coatings (Figure 2). The oscillation in thereflectance is due to interference in the silicon dioxidecoating. The free spectral range is determined

by 12 )2(/ = ffdn , where is the separation

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468 Int. J. Phys. Sci.

Figure 3. Radiative properties of silicon sub layer coated with silcon dioxide coating on both sides.

Figure 4. Radiative properties of silicon sub layer coated with silcon nitride coating on both sides.

between adjacent interference maxima and nfand dfarethe refractive index and thickness of the thin film. The

spectral separation increases toward longerwavelengths. As the film thickness increases, the freespectral range decreases, resulting in more oscillationswith the thicker silicon dioxide film. Therefore oscillationsincreased toward longer wavelengths. Interferences inthe substrate are generally not observable in the

incoherent formulation. This is the major differencebetween coherent and incoherent formulations (Oloomi etal., 2009b). The silicon sub layer thickness is 500 m andlayers temperature is 25C. Radiative properties of nanoscale multilayer such as reflectance, transmittance andemittance are shown in Figures 3 to 5 for different thinfilm coatings. These properties are compared inwavelength of 1.55 m. Thickness of thin film coatingchanged from 0 to 200 nm for silicon dioxide coating,silicon nitride coating and gold coating. Silicon dioxideand nitride coatings are used as metal thin film coatingsand gold coating used as non metal thin film coating.

The results in Figures 3 to 5 show that the emittance inthis wave length and at room temperature is negligibleTherefore SiO2 and Si3N4 layer can be considered as agood anti reflector layer because they reduce reflectancetoward silicon surface. Meanwhile, thin gold layeincreases reflectance. It is shown that for non metal thinfilm coating, the reflectance decreases as the thicknessincreases, because of increasing transmittance, but fometal thin film coating, transmittance decreases as thethickness increases, because of increasing reflectanceFrom the Figures 3 and 4, it was concluded thatincreasing the thickness of thin film coating up to 100 nmhas no important effect on the radiative properties omultilayer for non metal coatings.

Figures 3 and 4 show that increase of non metal thinfilm coatings thickness greater than 100 nm causesincrease of transmittance and decrease of reflectancerapidly. Reflectance increases and transmittance decree-ses rapidly till thickness of gold thin layer reaches to 60nm and then the properties remain constant (Figure 5).

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Oloomi et al. 469

Figure 5. Radiative properties of silicon sub layer coated with gold coating on both sides.

From the results, it was observed that the reflectancedecreases 97% by increasing the thickness of siliconnitride layer to 200 nm. The reflectance changed from0.469 to 0.198 by increasing thickness of silicon dioxidelayer to 200 nm (Figures 3 and 4). It was also observedthat increasing thickness of gold layer to 60 nm causesincrease in the reflectance from 0.469 to 0.972 (Figure 5).From the results, it may be concluded that industrialrequirements are supported by selecting coatingsmaterial and thickness.

REFERENCES

Jellison GE, Modine FA (1994). Optical Functions of Silicon at ElevatedTemperatures, J. Appi. Phys. 76: 3758-3761.Lee BJ, Zhang ZM (2005). Modeling Radiative Properties of Silicon with

Coatings and Comparison with Reflectance Measurements, J.Thermophys. Heat Transfer 19: 558-565.

Li HH (1980). Refractive Index of Silicon and Germanium and ItsWavelength and Temperature Derivatives, J. Phys. Chern. Ref. Data,9: 561-658.

Oloomi SAA, Sabounchi A, Sedaghat A (2009a). Parametric Study o

Nanoscale Radiative Properties of Thin Film Coatings, Nano TrendsJ. Nanotechnol. Appl. 7: 1-7.

Oloomi SAA, Sabounchi A, Sedaghat A (2009b). Modeling ThermaRadiative Properties of Nanoscale Multilayer with IncoherenFormulation, World Academy of Science, Eng. Technol. 37: 922-928.

Palik ED (1998). Silicon Dioxide (SiO2), Silicon Nitride (Si3N4) and Gold(Au), Handbook of Optical Constants of Solids, San Diego, CA.

Timans PJ (1996). The thermal radiative properties of semiconductorsAdvances in Rapid Thermal and Integrated Processing, AcademicPublishers, Dordrecht, Netherlands, 35-102.

Zhang ZM, Fu CJ, Zhu QZ (2003). Optical and Thermal RadiativeProperties of Semiconductors Related to Micro/Nanotechnology, AdvHeat Transfer 37: 179-296.