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PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014

Approximate Analysis of Optical Properties for ZnO Rough Surfaces

S. Daliento, P. Guerriero, M. Addonizio, A. Antonaia

Abstract - TCO (Transparent Conductive Oxides) layers often exhibit very rough surfaces and their optical properties, can not be described by one dimensional analytical models and numerical approaches must be adopted. However, computational time becomes, often, too large. In this paper we propose an automated procedure, based on the interaction between MATLAB and the Sentaurus TCAD environment which finds, in a generic rough surface, the smallest area characterized by the same statistical features of the whole surface so that full 3D analysis can be performed.

I. INTRODUCTION

Transparent and Conductive Oxides (TCO) are often exploited as anti reflective coatings in optoelectronic devices. To this end they exhibit very rough surfaces; therefore, conventional one dimensional models are unreliable to effectively describe their behavior. Many commercial software packages allow full three dimensional capability for accurate numerical simulations of arbitrarily shaped surfaces. They operate on a discretized mesh which reproduces the shape of the real surface. A common drawback of this approach is that the number of grid points required to describe the surface is too large, leading to unpractical computational time. A second problem depends on the unreliability of geometry models for modeling light propagation when roughness induces diffraction effects.

In this paper we propose an automated procedure, based on the interaction between MATLAB and Sentaurus TCAD [1,2], which finds, in a generic surface, the smallest area characterized by the same statistical features (average roughness, standard deviation and so on) of the whole surface; thus, a reduced device, with same optical properties of the real one, can be defined and analyzed. The same procedure looks for the existence of a two dimensional section where statistical parameters are conserved as well, so that, in some cases, the analysis can be reduced to a two dimensional one. The availability of this procedure allowed us to check the limits of light propagation models for a given structure, and leads us to define whether exact solution of Maxwell equations are needed to take into account diffraction phenomena.

Many samples were specifically fabricated by varying

deposition parameters to obtain different surface roughness (from smooth to very rough). Comparison between experiments and simulations, the latter performed by importing real device geometries, proved the reliability of our approach.

The paper is organized as follows. In Section II the MATLAB code which evaluates statistical parameters and looks for the minimal surface is described. In Section III the procedure is applied to experimental samples made by CVD deposited ZnO thin film [3,4]. Conclusions are drawn in Section IV.

II. PROCESSING OF THE IMAGES

As previously mentioned layers analyzed in this paper were ZnO thin films. Fig.1 shows an example among the AFM (Atomic Force Microscopy) images gained for our samples. As can be seen pyramidal shapes are randomatic distributed over the surface thus assuring antireflective behavior. As first step of the processing the image of Fig.1 has been loaded in the MATLAB environment. A GUI (Graphical User Interface) interface, shown in Fig.2, has been built for a friendly use. The GUI allows commands input and results visualization; as an example, in the upper right corner of Fig.2 we can see the image of Fig.1 reproduced as MATLAB plot.

Fig. 1. AFM image of a CVD deposited thin film layer

S.Daliento and P.Guerriero are with the Department of Electrical Engineering and Information Technology, University of Naples, Via Claidio 21, Naples, Italy, E-mail: daliento@unina.it

M.Addonizio and A.Antonaia are with the ENEA research center, località Granatello, Portici, Italy, E-mail: marialuisa.addonizio@unina.it

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Fig. 2. Picture of the MATLAB GUI interface

The MATLAB code underlying the GUI has three main features, it evaluates statistical roughness parameter of the whole image; looks for the smallest surface with same parameters; automatically generates the Sentaurus input file for numerical analysis.Statistical parameters have been evaluated according to the definition of effective roughness height given in [5]

( )L

rms r x dxL

20

1 (1)

Where r is the difference between the profile eight and its mean value and L is the size of the sample.

The parameter given in (1) has been iteratively evaluated by considering decreasing portions of the total

Fig. 3 Sentaurus mesh for the cross section of an AFM image

Fig.4 Three dimensional Sentaurus mesh for an AFM image

area by means of a successive halving criterion. The algorithm stops when the smallest area which holds the starting value of the effective roughness is found. Then the algorithm verifies that different portions having the area just defined exhibit same parameters. Once a reduced surface is chosen (it is shown in the lower corner of Fig.2) the effective roughness is evaluated along a finite set of transversal cross sections (the step of the scan is adjustable from the GUI).

If the effective roughness for the cross section is the same already valuated for the reduced surface, the subsequent numerical analysis is performed in a two-dimensional reference system, otherwise, full three-dimensional analysis is performed. The procedure ends after automatically generating the input code for the Sentaurus environment. As an example Fig.3 shows an image of the two-dimensional grid generated by Sentaurus after receiving the input from MATLAB, while Fig.4 shows the analogous for a 3D case.

Once statistical parameters have been determined a further simplification, which can be eventually adopted, consists in the substitution of the real surface with an equivalent surface formed only by regular pyramids.

Fig. 5 Sentaurus structure with non uniform (left) and uniform (right) pyramids.

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Fig. 6 Transmittances evaluated for structures with different surface shape but same effective roughness.

Geometries of the pyramids should be chosen so as to have same statistical parameters of the real surface. The reliability of this simplification is evidenced in Fig.5 and Fig.6. The structure in the left side of Fig.5 has pyramids with different heights while the structure in the right side has uniform pyramids but their heights are chosen to have same statistical parameters of the non uniform structure. As can be seen in Fig. 6 the transmittances evaluated for the two cases are perfectly coincident.

III. EXPERIMENTS

Aforementioned samples were fabricated according to [3]. They were both optically and electrically characterized, in particular optical properties were defined in terms of transmittance profile. Experimental transmittances were then compared with those evaluated by Sentaurus. This latter makes available three models for describing light propagation and interaction of light with interfaces. The simplest one is the TMM model [6] which only applies to flat surfaces so that it is fully not suitable for our cases. The second model considers light as formed by discrete “rays” and applies geometry laws for reflection and transmission. Usually this method is preferred over others because computational efforts are reduced. However it should be considered that the width of pyramids like those shown in Fig.1 are comparable with the wavelengths in the visible spectrum, hence, diffraction effects can not be neglected. To overcome this problem exact solution of Maxwell equations is required; the special model allowed for this application is termed EMW (Electro Magnetic Wave solver). Ray tracing and EMW have been checked with reference to samples either subjected or not subjected to diffraction effects. As an example Fig.7 shows the comparison between a measured transmittance profile and the corresponding profile evaluated by means of the raytracing method when no diffraction is present.

Experiment2D model

Fig.7 Measured and simulated transmittance profiles in a 2D case.

Notice that a two dimensional approach has been adopted in this case, this means that the automated procedure previously described found a cross section of the real device characterized by same statistical parameters of the three dimensional structure.

Fig.8 reports a case where a 3D analysis has been performed on a structure manifesting diffraction effects. As can be seen the geometry approach (ray-tracing) is not suitable for this case while the EMW model is fully effective.

After these checks, which can be view as a tuning of the Sentaurus environment, the method has been applied to the analysis of aSi:H (Hydrogenated amorphous Silicon) based thin film solar cells characterized by increasing effective roughness of the TCO. In Fig.9 both the structure of the device (left) and the corresponding mesh (right).are shown.

500 1000 1500 20000

20

40

60

80

100

T (%

)

Wavelength (nm)

L900 Ell

ExperimentGeometricalmodelEMW  model

Fig. 8 Comparison between EMW and raytracing models

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Fig. 9 a-Si solar cell structure.

It is worth noting that reliable modeling of electronic devices require accurate setting of a number of parameters like carrier lifetime surface recombination velocity [7-11] and so on. Thus, results summarized in Fig.9 and Fig.10 where it is evident that the increasing of the roughness is beneficial for the device, should be taken as “normalized” results, in the sense that it was not considered that all parameters may change when a different process is performed so that each device should be characterized.

Curren

t[A]

Voltage [V]

Increasing roughness

Fig. 10 IV curves of an aSi solar cell for increasing roughness

In detail, Fig.10 shows that the current supplied by the solar cell increases when the roughness increases. That is because, as shown in Fig.11 the transmittance of the TCO increases as well. Fig. 11 also shows the diffused transmittance, which is a good check of the light scattering occurring at the TCO surface.

III. CONCLUSION

In this paper an automated procedure for analyzing AFM images in the MATLAB environment has been presented. The procedure evaluates statistical parameters which qualifies the roughness of the surface and look for the minimal area holding same parameters with the aim to

simplify Sentaurus three-dimensional simulations. The procedure allowed the comparison of three different models describing light propagation. Examples and experiments showing the limits of the models and the overall reliability of the procedure have been shown.

Fig. 11 Total and diffuse transmittance for increasing roughness

REFERENCES

[1] “MATLAB user’s guide” Mathworks, www.mathworks.it [2] Sentaurus User’s guide [3] M.L. Addonizio, A. Antonaia “Enhanced electrical stability of

LP-MOCVD-deposited ZnO:B layers by means of plasma etching treatment”, Journal of Physical Chemistry, 117 (46).

[4] O. Tari, A. Aronne, M.L. Addonizio, S. Daliento, E. Fanelli, P. Pernice, “Sol-gel synthesis of ZnO transparent and conductive films: A critical approach”, Solar Energy Materials and Solar Cells” 105 , pp. 179-186, (2012)

[5] DIN EN ISO 4287 [6] S.J. Orfanidis "Electromagnetic Waves and Antennas" Rutgers

University NJ, 1999 [7] S. Daliento, O. Tari, L. Lancellotti, “Closed-form analytical

expression for the conductive and dissipative parameters of the MOS-C equivalent circuit” IEEE Transactions on Electron Devices 58 (10), pp. 3643-3646 (2011)

[8] S. Daliento, L. Mele, E. Bobeico, L. Lancellotti, “Analytical modelling and minority current measurements for the determination of the emitter surface recombination velocity in silicon solar cells” Solar Energy Materials and Solar Cells 91 (8) , pp. 707-713 (2007).

[9] S. Daliento, L. Mele, “Approximate closed-form analytical solution for minority carrier transport in opaque heavily doped regions under illuminated conditions”, IEEETransactions on Electron Devices, 53 (11) , pp. 2837-2839 (2006)

[10] S. Bellone, G.D. Licciardo, S. Daliento, L. Mele, “Experimental measurements of majority and minority carrier lifetime profile in SI epilayers by the use of an improved OCVD method” IEEE Electron Device Letters, 26 (7) , pp. 501-503(2005)

[11] A. Cutolo, S. Daliento, A. Sanseverino, G.F. Vitale, L. Zeni, “An optical technique to measure the bulk lifetime and the surface recombination velocity in silicon samples based on a laser diode probe system”, Solid-State Electronics 42 (6) , pp. 1035-1038 (1998)