Good Practice Guide Mueller Polarimetry measurements on PV Films. Søren A. Jensen and Poul-Erik Hansen

Transcription

1 Good Practice Guide Mueller Polarimetry measurements on PV Films Søren. ensen and Poul-Erik Hansen une 7

2 Contents ntroduction... 3 Ellipsometry... 3 Müller matrix ormalism... 3 Experimental setup... 4 Müller ellipsometry setup... 4 Sample abrication... 7 Roughness measurement... 7 Modeling o rough surace in ellipsometry... 9 Rayleigh-Rice... Eective medium... Ellipsometry results... Organic solar cell materials... 3 Samples... 3 Measurements... 4 Results... 5 Summary... 7 Reerences... 7

3 ntroduction Ellipsometry Ellipsometry is an optical non-destructive technique or inding the complex valued opto-electronic properties o thin ilms which has been widely applied to thin-ilm photovoltaics. The operating principle o ellipsometry is to shine light with a well-deined polarization onto a ilm or a layered stack o ilms and recording the relected and/or the transmitted light. The polarization ellipse o the light ater interacting with the sample is measured, and inormation on the opto-electronic properties through the complex dielectric unction or reractive index n can be extracted as well as structural inormation such as layer thicknesses. Generally, the ellipsometry measurement provides two parameters, and which are wavelength dependent. These parameters are related to the complex amplitude relection coeicients o the sample by: r p r s = tan ψ e iδ # Here r p and r s are the relection coeicients or light polarized parallel p and perpendicular s to the plane o incidence, respectively. When the ellipsometry experiment is at its simplest, that is when measuring a perectly lat, semi-ininite, uniorm, isotropic and non-magnetic sample, the optical parameters o the sample contained in n=n real +ik can be extracted rom and. n this simple case, describes the light absorption determined by k, and describes the phase change which relates directly to n real. n a spectroscopic ellipsometer, n can thus be determined as a unction o wavelength. normation on the electronic structure o the material, such as the magnitude o the bandgap, can be obtained by analyzing the wavelength dependent, complex valued n. 3 n is known or a given material in the idealized geometry mentioned above, then an ellipsometry measurement o a non-ideal sample can yield inormation o the samples morphological properties such as its surace roughness, alloy composition and void raction. s samples rarely consist o a simple interace, but oten multiple layers that are not perectly lat, a modeling approach is generally used to extract the optical and structural parameters. Müller matrix ormalism Most samples do not ulill the idealized conditions described in connection with and above. For instance, samples can display depolarization, meaning that unpolarized or partially unpolarized light will be 3

4 emitted rom the sample even though the incident light is perectly polarized. Such unpolarized light is best described by the Stokes vector ormalism 4 : S x + y S S = [ ] = x y # S S 3 [ R + L ] Here S is the total light intensity S is the dierence in light intensity between linear polarization in the x and y directions, respectively, S is the dierence between linear polarization at +45 and, and S 3 is the dierence between right-circular polarized, and let-circular polarized light. Using the normalized stokes vector S = we can express partially polarized light as p cos ψ S = [ ] #3 p sin ψ cos Δ p sin ψ sin Δ Where p is the degree o polarization. The transormation o the Stokes vector when the light interacts with an optical element or a sample is described by a 44 matrix known as a Müller matrix. relecting surace o isotropic material with ellipsometric parameters and has the normalized Müller matrix 5 m m N 4 M = N = #4 m 4 m C S 44 S C Where N = cosψ, S = sinψsinδ, C = sinψ cosδ. For anisotropic and depolarizing samples, seven independent parameters must be measured, which can be done by Müller matrix spectroscopy. 4 Experimental setup Müller ellipsometry setup 4

5 5 Figure llustration o Müller polarimeter. The ellipsometry setup employed here is shown in Figure. The ollowing description o the setup can also be ound in 6 : t is a goniometric and spectroscopic scatterometric setup that can be applied in relectometric, generalized ellipsometric and diractometric measurement mode. s radiation sources we use a iber coupled stabilized Xenon lamp Ocean optics, HPX--HP-DUV. The Xenon lamp covers the wavelength range rom 3 to 8 nm. The light rom the iber coupled Xenon lamp is collimated using a microscope objective. The collimated light passes irst through a lens system producing weakly ocused light with a diameter o 4 mm at the position o the sample and then through a polarization state generator PSG made rom a polarizer Newport GT4 ollowed by a photo elastics modulator Hinds nstrument, /FS5. The angle o incidence on the sample may be varied between ±9 by rotating the rotation stage Thorlabs, NR36S equipped with an angular encoder Heidenhain, ER 4C. The detector arm can be scanned over nearly the complete diraction plane ±75 and is equipped with a polarization state analyzer PS, made rom a photo elastic modulator Hinds nstrument, /FS6 and a polarizer Newport GT4, ollowed by a microscope objective Newport, U-7X that ocuses the light into a iber coupled monochromator Spectral products, DK4 with a PMT detector Hamamatsu, R98P. The detected signal is recorded in a digitizer gilent L4534 and analyzed by ast Fourier transormation. The recorded signal rom the Mueller polarimetry may be written as:... cos sin sin cos cos cos sin sin DC t t t t t t t t 5 Where j j j=, are the angular modulation requencies o the Photo Elastic Modulators PEMs and j j=, are phases and

6 6 DC X X X X X X X X DC 6 n these equations n is Bessel unctions o the irst kind o order n=,, and j is the Bessel amplitude. n the experiment we normalize the data in the ollowing way: DC,,,,,,,, 7 n this way we are able to measure nine components o the Muller matrix simultaneously. The rest o the Muller matrix elements may be obtained by rotating the PSG Polarization State Generator and the PS Polarization State nalyzer. This rotation angle is called θ m or the PSG and θ m or the PS. PSG/PS consists o a polarizer and a PEM Photo Elastic Modulator, the angle between the PSG Polarizer and PEM is called θ b and θ b or the PS. Table shows the relation between Müller matrix elements and measured normalized intensities.

7 m b m b,8,8 -m 4 m 4 m 3 m 3 m 43 -m 34 m 33,8 45,5 -m 4 m 4 m 3 -m m 43 m 4 -m 3 -m 4 m 4 m 3 - m 3 m 43 -m 33,8,8 45, 5 45,5 45,5 45,5 9,7 9,7 9,7 9,7 35,35 35,35 35,35 35,35 9,7 35,35,8 45,5 9,7 35,5,8 45,5 9,7 35,35,8 45,5 9,7 35,35 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 -m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m 3 -m -m -m -m -m 3 -m 3 -m 3 -m 3 m m m m Table : Relationship between angular settings o PEMs and polarizers and the Mueller matrix elements picked up by the measured requency components. The red colours show the azimuth angles o the PEMs commonly used or measuring the 5 matrix elements indicated with green colour. m m 3 -m - m 3 m m 3 - m - m 3 - m 3 m 3 - m - m 3 m m 43 -m 4 -m 4 -m 4 -m 4 - m 43 - m 43 - m 43 - m 43 m 4 m 4 m 4 m 4 m 34 - m 4 -m 34 m 4 m 34 - m 4 - m 34 m 4 m 34 - m 4 -m 34 m 4 m 34 - m 4 m 3 -m 3 m m 3 - m - m 33 m 3 m 33 -m 3 m 3 - m - m 3 m Sample abrication The sample was a Cun,GaSe CGS standard absorber layer manuactured by HZB. The CGS layer was deposited on a glass substrate which had previously been coated with a molybdenum contact. No urther layers were deposited on top o the CGS. Roughness measurement The roughness measurements have been perormed with a Sensoar Plu Neox intererence and conocal microscope. The instrument is equipped with the objectives listed in Table. Objective magniication / N Lateral resolution blue light µm Vertical resolution nm Conocal x / N.45.3 < 5x / N.8.7 <3 5x / N.95.5 < ntererometric x / N x / N

8 Table : Overview o the lateral and vertical resolution or the dierent objectives. The roughness measurements have been perormed with the 5x objective. The measurements have been analyzed with the SPP sotware rom mage Metrology using the SPP classical roughness calculation methods. This method calculated the surace roughness without applying any S or L ilter. Figure Conocal microscopy image o CGS ilm let and cross section illustrating the rms roughness and autocorrelation length right. Figure let shows a height plot o the CGS ilm acquired with the conocal microscope equipped with the 5x magniying lens. The right plot in Figure shows a line scan through the height data. n rms value o the heights o roughness irregularities = 68 4 nm was extracted rom the data using the commercial sotware SPP rom mage Metrology. Figure 3 utocorrelation unction o the data in Figure. Figure 3 shows the autocorrelation unction. From this, the autocorrelation length can be ound as the length or which the unction decreases by a actor /e; we ind = 465 nm. 8

9 Modeling o rough surace in ellipsometry The dielectric constant or a non-perect surace is ound by making a model surace that relects the physical properties o the measured surace. The model surace is traditionally described as a substrate and thin ilms. The thin ilm is urther divided into a bulk layer and a roughness/intermixing layer. The optical response rom each bulk layer and roughness/intermixing layer is described by dielectrics unctions. The dielectrics unction and the thickness o the roughness/intermixing and bulk layers are ound by itting the optical model to the measured and parameters as shown in Figure 4. Figure 4: Traditional way o inding the dielectric constants. 9

10 Rayleigh-Rice The complex optical properties o an isotropic rough suraces can be ound using the Rayleigh-Rice ormalism as described by Franta and Ohlídal. 7,8 The Rayleigh-Rice method is dierent rom the traditional approach in the sense that the roughness layer does not have a set o dielectric constants o its own; it has the same dielectric constants as the bulk layer. The roughness is described by surace texture parameters called that can be measured using optical and stylus proilometers. The best choice or a rough interace would be a conocal microscope with a high N objective, since the tip o a stylus proilometer will give a depth depending inluence o one o the parameters called the correlation length. The change in the complex Fresnel relection coeicients or a randomly rough surace characterized by and can be calculated as: r s,p = σ s,p K x, K y wk x n k sin θ, K y dk x dk y #8 Where n is the complex reractive index o the ambient, k = π/λ is the wavenumber o the radiation, θ is the angle o incidence and K x and K y are reciprocal lattice space coordinates. The kernel unctions p,s are given by: p K x, K y = p + b c B 3K + B 6p K y + bc B 6p [K b c + K + bc ] B 3p K + K x K + bc b ck x + bc s K x, K y = s + B 5s K #9 + bc Where b = n k K c = n k K # nd K = K x + K y p = k n n X/D B 3p = k n n sinθ W/D B 6p = k n n cosθ X/D B 6p = n n cos θ W Dk #

11 B 3p = k 3 n n sinθ X/D s = k n n cosθ cosθ r s B 5s = k n cosθ r s With D = n cos θ + n cos θ n sin θ + n n cos θ cos θ X = n n cosθ t p # W = n n n n sinθ t p Here n is the complex reractive index o the material with the rough surace, θ is the transmission angle and r s, r p, t p, t s, are the Fresnel relection and transmission coeicients or lat interace. The normalized power spectral density unction w can be parametrized with the widely used Gaussian unction: wk = ξ 4π e K ξ 4 #3 Eective medium n eective medium theory, the opto-electronic properties o a complex medium such as an alloy, a colloidal solution or a medium with air intrusions, or instance a rough surace, are described by a single homogeneous eective medium. n this ormalism, the complex permittivity ε o the eective medium also called the eective permittivity can be expressed in terms o the permittivities and volume ractions o the individual media making up the eective medium. popular eective medium model to ind the eective permittivity is the Maxwell-Garnett mixing ormula, however, in a two phase system this model is only valid when the volume raction o one phase is signiicantly larger than the other. 9 nstead we apply the Bruggeman ormula which is symmetric with respect to the constituent media. For a two component system with permittivities, and volume ractions,, respectively, the eective permittivity is given by ε = b + 8ε ε + b, b = 4 ε + ε #4 Ellipsometry results the pseudo-permittivity, or equivalently the complex reractive index n, is known, either rom extraction rom measured ε with the Bruggeman ormula 4 or rom direct measurements on a lat homogeneous material, the Rayleigh-Rice ormula 8 can be used to calculate the ratio o the eective complex relection coeicients r p r s = r p + Δr p r s + Δr s, rom which the ellipsometric parameters and

12 can be calculated using. These parameters can in turn be used to calculate the Müller matrix elements N, S and C in 4. From ellipsometric measurements on our samples, we were unable to obtain satisactory values or n using the Bruggeman analysis described above, which threats the roughness as a homogeneous layer with one permittivity. more advanced Bruggeman analysis approach [3] might have been successul, but would require many more variables than the Rayleigh-Rice approach. We considered values or n or various values o the Ga concentration x = [Ga] [Ga] + [n] rom literature, these are plotted in Figure 5. ccording to this data, the reractive index does not change signiicantly with Ga concentration. Figure 5 Real and imaginary dashed line components o the complex reractive index. The n value or x =. is taken rom, the values or x =.,.4, and.75 are taken rom. We used the roughness value o = 68 nm ound rom the conocal microscopy data in Figure as input parameter in 8; in order to determine the correlation length we calculated a library using a range o values with a spacing o 5 nm. n optimal solution rom this library was ound by minimization o the squared sum o errors between the calculated and measured Müller parameters. Figure 6 shows the measured Müller matrix elements as well as N, S, and C parameters ound by calculating a library or a range o values and perorming minimization. The N, S, and C parameters were calculated or the our n values shown in Figure 5, corresponding to dierent x values. The ound values or are 3 nm, 3 nm, 35 nm, and 35 nm or x =.,.,.4, and.75 respectively.

13 Figure 6 Measured Müller matrix elements and best it elements calculated or n values corresponding dierent values o the Ga concentration x. From the comparison in Figure 6 it seems that the Ga value x =. its the data better than the higher values, suggesting that x is closer to than to.. more precise determination o x could possibly be perormed via an optimization algorithm using interpolation o the n values. This however, is computationally very heavy because o the double integral in 8. Organic solar cell materials Samples The eect o O and UV light exposure to organic solar cell materials was investigated. The samples were photoactive P3HT:PCBM layers deposited on glass substrates. Four samples with dierent post deposition treatments were prepared as shown in Table 3. 3

14 Sample preparation label mbient air exposure Beore mounting in chamber Dry % O exposure UV exposure Beore O % O - 6 hrs - ir 7 hrs 6 hrs - Uv+ir 7 hrs 6 hrs 3 hrs Table 3 Treatments to the our samples measured. Measurements During measurements the samples were mounted in an oxygen chamber abricated by NPL. low control unit connected to the chamber made it possible to control the mixture o nitrogen and oxygen gas inside the chamber. The chamber was equipped with a sample holder that made it possible to have up to six samples simultaneously inside the chamber. The chamber was equipped with two large parallel windows that made near normal incident transmission measurement possible. However, o normal incident measurements were very diicult to perorm due to the chamber geometry. Figure 7 shows the Fresnel power relection- and transmission coeicients or an air-glass interace; it is clear that at o normal incidence, the coeicients dier or dierent polarizations. For this reason, only ellipsometry measurements perormed at normal incidence relect the dielectric unction o the material without inluence rom the windows. Figure 7 Calculated Fresnel relection and transmission coeicients or an air-glass interace where the reractive index o glass is assumed to be real with a value o n =.5. Normal incidence transmission measurements were perormed using the Müller polarimetry setup with non-oscillating PEMs whereas the ellipsometry measurements were perormed with oscillating PEMS. n transmission measurements the ellipsometric variable N in 4 is an expression o the signed diattenuation, which is a property o a transmitting material in which the transmittance depends on the 4

15 incident polarization state o light. Change in the N parameter is thus a measure o how the s-polarized and p-polarized transmittance are aected by the sample preparation. The ellipsometric variables S and C are linked to the material retardation. The material retardation is a measure o the phase shit dierence between the two orthogonal polarization states s and p as the light beam passes through the material. The S parameter will be dierent rom zero or material with bireringence. perect polarizer diattenuator will have N=-, S=C=, whereas a perect retarder has N=, atans/c. Results Müller parameters and transmission measured at normal incidence on the samples described in Table 3 are shown in Figure 8 and Figure 9 respectively. The results show that the post-deposition treatments do change the anisotropic Müller matrix elements and that we observe a change in the isotropic Müller matrix elements. The clear change in the diattenuation and retardation igures show that the surace stoichiometry is changed when applying sample preparation ir and UV+ir, whereas % O does not alter the surace stoichiometry. For the isotropic Mueller matrix elements, we also see no change due to % O sample preparation, but change due to UV+ir sample preparation. This shows that it is not enough to characterize the solar cell ater % O sample preparation, since the photoactive layer sample continues to change over a longer timescale. The normal incident transmission measurements also show that the UV+ir sample preparation aects the photoactive layer much more than the % O sample preparation. The polarization dependent response o the photoactive layer should be looked upon as a degradation, since it lowers the eiciency o the interaction with the unpolarised light rom the sun. 5

16 Figure 8 Normal incident Müller polarimetry measurements or dierent sample preparations described in Table 3. Figure 9 Normal incident transmission measurements or dierent sample preparations described in Table 3. O does not alter the diattenuation or retardation o the photoactive layer, but ir and UV light does alter the diattenuation or retardation o the photoactive layer. The photoactive layer is an optical bireringence layer. The incident sunlight onto solar material is unpolarised light. The optimal material or solar cell has high absorption with low diattenuation, high resistance towards environmental gasses and is capable o being mounted in a ixture without altering the optical and electrical properties. We have observed that the glass 6

17 substrate is not bireringent, and the polarization properties o the light are not altered by the substrate. The eiciency o solar cells with glass substrates is thereore not aected by illuminating the solar cell rom the backside or the ront side. The ull cell is aected by O exposure and UV light exposure that lower the almost isotropic absorption o the material. Summary Ellipsometry has proven to be a powerul tool or characterizing both the morphological properties o a sample, e.g. layer thicknesses, surace roughnesses and the composition o a complex medium, as well as the optical properties o the materials. This technique has successully been applied to various photovoltaic samples. We employed Müller polarimetry to study the high eiciency thin ilm PV material Cun,GaSe CGS. These samples were ound to possess very high surace roughness = 68 4 nm, which could be described by the Rayleigh-Rice model in our analysis o the Müller data. The analysis allowed us to obtain a measure o the correlation length which was ound to be in the range o 3 nm. We also used Müller polarimetry to study photoactive P3HT:PCBM ilms which had undergone various treatments with air, O and UV radiation. These ilms were measured in a sample cell with a glass window, which only allowed measurements at normal incidence. The sample treatments were ound to have an eect on the Müller matrix elements, and we ind that the surace stoichiometry is changed when exposing the sample to ir and UV+ir, but not upon % O exposure. Reerences.C. Boccara, C. Pickering, and. Rivory, editors, Proceedings o the First nternational Conerence on Spectroscopic Ellipsometry Elsevier, msterdam, Li, R.W. Collins, M.N. Sestak, P. Koirala, N.. Podraza, S. Marsillac, and.. Rockett, in dv. Charact. Tech. Thin Film Sol. Cells 6, pp H.G. Tompkins and E.. rene, editors, Handbook o Ellipsometry William ndrew Publishing, 5. 4 H. Fujiwara, Spectroscopic Ellipsometry ohn Wiley & Sons, Röseler, nrared Spectroscopic Ellipsometry kademie-verlag, Berlin, P.-E. Hansen, M.H. Madsen,. Lehtolahti, and L. Nielsen, ppl. Sur. Sci D. Franta and. Ohlídal, Opt. Commun. 47, D. Franta and. Ohlídal, Opt. Commun. 48,

18 9 V.. Markel,. Opt. Soc. m. 33, M.. lonso, K. Wakita,. Pascual, M. Garriga, and N. amamoto, Phys. Rev. B 63, 753. M.. lonso, M. Garriga, C.. Durante Rincón, E. Hernández, and M. León, ppl. Phys. Mater. Sci. Process. 74, 659. M.H. Madsen and P.-E. Hansen, Sur. Topogr. Metrol. Prop. 4, D. Lehmann, F. Seidel and D. RT Zahn SpringerPlus 3:8 4. 8