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Spin-coating and ellipsometry investigation of thin polymer films - - PDF document
Spin-coating and ellipsometry investigation of thin polymer films - - PDF document
X-Ray and Neutron Science International Student Summer Programme at ILL/ESRF Spin-coating and ellipsometry investigation of thin polymer films Report Albert Prause supervised by Aljo sa Hafner Berlin, October 29, 2017 Report
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Report Introduction 1 Introduction Thin polymer films play an important role for industrial applications and scientific re-
- search. They are used in microelectronics for chip production or organic semiconductors
as well as optical coatings for lenses, mirrors or glasses.[1] Thereby the film thickness of the layer is one major parameter to adjust physical properties and interactions. Addi- tionally well defined polymer layers are necessary for fundamental research, for example in the investigation of long-range van der Waals forces associated with stabilization and destabilization of surrounding layer.[2] For this, the controllability and reproducibility
- f the polymer layer are essential for the desired application.
Preparation of the films can be done using different methods like spin, dip, flow or spray-coating or grafting methods. Especially spin-coating is widely used. It is a simple and cheap method for depositing polymers on solid substrates. Additionally spin-coating exhibits very good reproducibility and homogeneity in thickness.[1,3,4] The prediction of spin-coated layer thicknesses is a challenging task. Likewise theo- retical description of the spin-coating process involves mass transport phenomena and fluid dynamics whereby it becomes rapidly complex. For that reason the prediction
- f layer thickness is based on empirical models with experimental data as the basis.
Although these models have experimental data as underlying basis. In addition spin- coating has several parameters which influence the resulting layer thickness. The main parameters are the polymer concentration cg, the angular velocity ω, solution viscosity η and evaporation rate of solvent e. In order to obtain the scaling behavior, many studies investigate the dependence of the layer thickness on these parameters.[4,5] In this work the main aspect was the investigation of the layer thickness as a function
- f concentration for different molecular weights of hydrogenated polystyrene (h-PS).
We used four different molecular weights to cover almost three orders of magnitude. Secondly, we studied the reproducibility and homogeneity of the deposited layer and finally, the influence of viscosity was studied in dependence on the layer thickness in order to verify our experiments with the literature. The films were prepared by spin-coating and the thickness of the polymer film was measured via ellipsometry. 1
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Report Chemicals and methods 2 Chemicals and methods 2.1 Chemicals The used polymer was h-PS with four different molecular weights Mn (2.8, 21, 432, 1690 kg mol−1) which correspondingly cover almost three orders of magnitude and a low polydispersity (Mw/Mn between 1.04 and 1.07)a. For the preparation of polymer solutions toluene (99 %) was used as solvent. The substrates were silicon wafer (Si), cut along the (100) crystal plane, of different sizes and thicknesses. Cleaning of wafers was performed with MilliQ water (resistance >18 MΩ cm), ethanol, acetone and chloroform. 2.2 Preparation 2.2.1 Cleaning of wafers Every wafer was cleaned with a multi-step procedure: (i) 15 min sonication in mild DECON90/water solution, (ii) 15 min sonication in ethanol, (iii) 15 min sonication in acetone, (iv) 15 min sonication in chloroform, (v) 15 min sonication in water. After the cleaning procedure the wafers were inspected and, if necessary, cleaned again from step (iii). Afterwards, they were dried with filtered nitrogen flow and stored in a plastic dish. Before spin-coating the wafer, the thickness of the SiO2 layer on top was determined by ellipsometry. 2.2.2 Spin-coating Uniform films can be produced via spin-coating by spreading a fluid on a horizontal rotating substrate. Commonly the deposition is done under static conditions or with a low angular velocity. After deposition the substrate is accelerated to high angular
- velocities. During rotation the deposited liquid is thinned by ejecting excess liquid and
evaporation of the solvent.[1] Therefore, the polymer has to be in liquid form. This is achieved by solubilising the polymer in an organic solvent. Preparation of polymer films was performed by spin-coating from solution of h-PS in
- toluene. At first the desired amount of polymer was dissolved in appropriate amount of
toluene to get the desired concentration and mixed for a minimum of 72 h. The error
- f preparation of polymer solutions was investigated by weighing the vials directly
after preparation and before using the solution for spin-coating. Also independently
aMw/Mn for h-PS with 432 kg mol−1 was not available.
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Report Chemicals and methods prepared solutions were used to figure out how accurate one can prepare a specific concentration. For spin-coating, we used a two step programme where the first step was set to 500 rpm angular velocity for 2 s. The second step was set to 3000 rpm for 50 s. During all preparations the spin-coating programme was hold constant. The spin-coating was performed with the described programme in two runs. The first run was carried out only with toluene and shortly afterward the second run with the desired polymer solution. Thereby the wafer was wet fully with solution either toluene
- r polymer solution.
The thickness of the resulting polymer layer was evaluated by ellipsometry. 2.3 Ellipsometry The reflection of light on thin films involves a phase and amplitude shift between parallel and perpendicular polarization. This shift depends mainly on the thickness and the refractive index of the layer which is widely used to determine the thickness
- f the layer. To determine the phase shift one uses an ellipsometer. Hereby elliptically
polarized light is introduced via a polarizer and a compensator, e.g. a λ/4 wave plate. The specific polarized light reflects on the film and passes through an analyzer. The resulting intensity of the reflected light is measured. Thereof the phase shift between parallel and perpendicular polarization can be counted back. With these information the film thickness and the refractive index can be calculated via Fresnel theory.[6,7] Ellipsometry measurements were performed on a variable angle phase modulation ellip- someter by Beaglehole Instruments. The instrument uses a He-Ne laser (λ = 633 nm). For every measurement an angle scan between 35 ◦ and 73 ◦ in 2 ◦ steps was performed. The data evaluation was done with the instrument software in Igor Pro 6 (WaveMet- rics). For evaluation a multi-layer model was created with the layer sequence Si, SiO2, h-PS and air. The refractive indices of the materials for the used wavelength were included into the software (nSi = 3.882, nSiO2 = 1.457, nh-PS = 1.588 and nair = 1). The thickness of SiO2 was fixed to the previously measured value which was obtained without the polymer film. With this parameters the evaluation of the h-PS film thick- nesses was performed whereby the initial value for the h-PS film had to be in the proper range. Error and homogeneity estimation of the layer thickness were conducted via measuring different spots on the same wafer. Furthermore independently spin-coated wafers with the same polymer concentration were measured. Also the instrumental accuracy was taken into consideration which is in the range of 1 Å.[8] 3
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Report Results 3 Results 3.1 Layer thickness of spin-coated films 3.1.1 Influence of concentration and molecular weight The prepared polymer films were measured with ellipsometry to determine the layer thickness of the deposited polymer. Table 3.1 shows the measured film thickness for a given polymer concentration and molecular weight.
Table 3.1: Overview of layer thicknesses of polymer films for the given concentration and molecular weight. The uncertainty of d is between 2.5 and 1 % and for cg below 0.5 %.
Mn / kg mol−1 cg / g L−1 d / Å Mn / kg mol−1 cg / g L−1 d / Å 2.8 1.04 38 432 1.30 46 2.78 102 2.69 102 3.99 148 3.82 154 9.55 354 9.55 446 20.72 750 19.23 1061 27.54 1061 25.62 1595 37.29 1442 37.90 2847 21 1.30 50 1690 0.95 38 2.78 109 2.69 134 3.73 147 4.16 230 10.37 417 10.77 880 19.76 845 19.23 2328 29.64 1289 28.24 4731 37.90 1732 37.99 9386 In figure 3.1 the layer thickness is plotted versus the polymer concentration for all used molecular weights. The trend for measured thicknesses is linear for low molecular weights Mn (2.8 and 21 kg mol−1). For higher Mn the divergence from a linear trend increases drastically, see figure 3.1(a). Figure 3.1(b) focuses on the low concentration regime where the trend in thickness is for all molecular weights the same. Only the highest Mn with 1690 kg mol−1 diverges very quickly. 4
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Report Results
5 10 15 20 25 30 35 40 2000 4000 6000 8000 10000 200 400 600 800 1000 5 10 100 1000 30 10 100 3
(b) d / nm d / Å cg / g L-1
h-PS (2.8 kg mol-1), h-PS (21 kg mol-1), h-PS (432 kg mol-1), h-PS (1690 kg mol-1)
(a) d / nm d / Å cg / g L-1
Figure 3.1: Layer thickness d of h-PS films on Si versus the initial polymer concentration. Each color indicates the molecular weight of the polymer. In (a) one can see the plot in linear scaling
- ver the whole concentration range. Part (b) shows a detailed view on the low concentration
regime in logarithmic scale of the thickness. The size of the symbols reflects a conservative error estimation of the data points.
3.1.2 Homogeneity of polymer film The deposited polymer film was investigated with respect to the homogeneity of the
- layer. Therefore larger wafers were spin-coated and measured in different points based
- n an underlying grid.
In figure 3.2 the measured layer thickness and the corresponding positions on the wafer are displayed. Part 3.2(a) shows a very thin layer where the deviation in thickness is in the range of accuracy of ellipsometry (davg = 52 Å, Mn = 21 kg mol−1, cg = 1.3 g L−1). The polymer film in fig. 3.2(b) shows larger deviations in absolute values but the relative deviation is in the between 1 and 2 % (davg = 440 Å, Mn = 21 kg mol−1, cg = 10.4 g L−1). Additionally the increase in layer thickness to the edges of the wafer is observable. The sample in figure 3.2(c) has less increase in thickness toward the edges but depicts one artifact (x ≈ 4 cm) which could be related to dust. Overall the deviation of the layer thickness is less than 1% (davg = 1721 Å, Mn = 21 kg mol−1, cg = 37.8 g L−1). The last wafer, fig. 3.2(d) shows a dome like polymer layer with thickest film in the middle and a thinning toward the edges. This effect can be attributed to the high viscosity of the used polymer solution (davg = 4730 Å, Mn = 1690 kg mol−1, cg = 28.2 g L−1). Nevertheless the relative deviation of the layer thickness is under 1.5%. 5
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Report Results
1 2 3 4 5 6 40 50 60
x / cm d / Å
4 5 6 1 2 3 4 5 6
y / cm d / Å
1 2 3 4 5 6 420 440 460
x / cm d / Å
4 2 4 4 4 6 1 2 3 4 5 6
y / cm d / Å
1 2 3 4 5 6 1680 1720 1760
(d) (c) (b)
x / cm d / Å
(a)
1 6 8 1 7 2 1 7 6 1 2 3 4 5 6
y / cm d / Å
1 2 3 4 5 6 4600 4700 4800 4900
x / cm d / Å
4 6 4 7 4 8 4 9 1 2 3 4 5 6
y / cm d / Å
Figure 3.2: Film homogeneity of different layer thicknesses. The layer were prepared out of h-PS solution (Mn = 21 kg mol−1) with concentrations of 1.3 g L−1 (a), 10.4 g L−1 (b), 37.8 g L−1 (c). In (d) the highest molecular weight of h-PS (Mn = 1690 kg mol−1) with a concentration of 28.2 g L−1 was used. The red points on a wafer indicate the measuring spots.
3.2 Evaluation of scaling with viscosity The viscosity of a polymer solution combines the molecular weight and the polymer concentration and so it is an important parameter in spin-coating. Especially for higher concentrations and/or molecular weights a non-linear behavior of viscosity as a function of concentration is obtained. Three regimes can be defined: (i) the non- entanglement region where the chains aren’t interacting with each other, (ii) transition region with slightly entangled chains and (iii) region with entangled chains overlapping each other.[5,9] The thickness of spin-coated layer d is directly proportional to η1/3.[5] The viscosity is taken into account to eliminate inherent effects due to change in concentration or molecular weight. 6
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Report Results Estimation of viscosity The viscosity for each polymer concentration and molecu- lar weight was calculated from reported data of Weissberg et al. (1951)[10] and Kniewske and Kulicke (1983)[11]. Therefore the viscosity η of a polymer in solution can be related to its concentration cg through ηsp cg = [η]ek1[η]cg with ηsp = η − η0 η0 , (1) where ηsp is the specific viscosity of the polymer solution, η0 the solvent viscosity, [η] the intrinsic viscosity of the polymer and k1 an experimental parameter. Additionally, the Mark-Houwink equation, [η] = KM a
w, relates the mass averaged molecular weight
Mw with the intrinsic viscosity [η] of the polymer, too. For this K and a are solvent- polymer pair dependent parameters.[10] The intrinsic viscosity for each molecular weight was taken from literature data if data existed for a polymer with similar molecular weight and polydispersity. Otherwise [η] was calculated with published values of K and a for h-PS in toluene.[11] The parameter k1 was determined from reported data[10] based on equation 1. With the estimated k1 values a scaling law between Mn and k1 was created. For our purpose k1 = b · M −0.66
n
+ c (2) was a good compromise between the error in b and c and the weighting of Mn. This means that with an exponent lower than −0.66 the error would rise for b and c and with values between −0.66 and 0 the weighting of Mn would decrease. For positive exponents one did not get a linear trend. Thus, the relation was introduced to linearize
- btained values for k1 and also to estimate k1 for every Mn via a simple function. The
- btained and used values are b = 150(41) g0.66 mol−0.66 and c = 0.195(20).
On the basis of the calculated [η] and k1 values for each of the four used polymers it is possible to estimate the viscosity for every concentration up to 40 g L−1 (based on the data range of underlying viscosity data). Consideration of viscosity The calculated viscosity of all polymer concentrations and molecular weights are displayed in figure 3.3. For the two polymers with lower molecular weight the trend in viscosity is linear over the observed concentration range. As opposed to this the viscosity of polymers with higher molecular weight diverges already below a concentration of 5 g L−1 from a linear trend. This can be attributed to the increasing entanglement of polymer chains.[9] 7
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Report Results
5 10 15 20 25 30 35 40 1 10 100 1 10 100
- / mPa s
- / mPa s
cg / g L-1
h-PS (2.8 kg mol-1) h-PS (21 kg mol-1) h-PS (432 kg mol-1) h-PS (1690 kg mol-1)
Figure 3.3: Estimated viscosity for the used concentrations and molecular weights (toluene viscosity = black dashed line).
In figure 3.4 the thickness is plotted versus the concentration cg times the viscosity η to the power 1/3. The obtained linear trend for all used molecular weights indicates the importance of the solution viscosity.
1 10 100 100 1000 10000 20 10 100 1000 2 h-PS (2.8 kg mol-1) h-PS (21 kg mol-1) h-PS (432 kg mol-1) h-PS (1690 kg mol-1)
d / nm d / Å cg
⋅ 1/3 / (mPa s)1/3 g L-1Figure 3.4: Layer thickness d versus viscosity η to the power 1/3. Linear regression of all data points was applied (d = 43.83(14) Å g−1 L (mPa s)−1/3 · cg · η1/3; black dashed line).
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Report Discussion 4 Discussion The deposited layer thickness via spin-coating depends on the used concentration and molecular weight of the polymer. For higher concentrations and higher molecular weights a non-linear trend was observed. The main reason for this behavior can be found in the viscosity of polymer solutions.[5] Its effect can also be seen in the mea- surements of the film homogeneity, especially for high molecular weights and concen-
- trations. The dome (fig. 3.2) formation is an artifact caused by high solution viscosity
(η ≈ 43 mPa s) as a result of entanglement of polymer chains. The reason for the non-linear increase of viscosity is caused by the entanglement of polymer chains in solution.[9] Furthermore this influence was proofed with estimated viscosities, see figure 3.4, where a linear trend was obtained over the observed concentra- tion range for all used molecular weights. Through this linear scaling with d ∼ cg · η1/3 it is possible to obtain the same layer thickness for different molecular weights by adjusting the concentration of the polymer. Additionally it opens the possibility to estimate any layer thickness by calculating or measuring the viscosity of the solution. This way it becomes easy to prepare a specific layer thickness using the spin-coating procedure. 5 Conclusion In this work the preparation of h-PS films on Si was studied. The resulting thick- ness with a fixed spin-coating programme was determined for different polymer con- centrations and molecular weights. Thereby two kind of trends were observed: For low molecular weights (Mn of 2.8 and 21 kg mol−1) a linear trend was obtained over the investigated concentrations range; For high molecular weights (Mn of 432 and 1690 kg mol−1) a fast deviation from the non-linear behavior was observed. Further- more the reproducibility and homogeneity of the prepared films were estimated. The deviation of thickness was below 3 %. The error in concentration was estimated as a conservative value below 0.5 %. Accordingly we can confirm the high reproducibility and homogeneity of spin-coated films. Furthermore we could unify the trend between the four used molecular weights of h-PS to a linear trend. By estimating and applying the solution viscosity for each spin- coated solution we obtained a linear function (see figure 3.4) for the four polymers with respect to the well-known relation of d ∼ cg · η1/3. 9
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Report References References [1]
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