INA I N nstitut für anostrukturtechnologie und Analytik Practical training ellipsometry Lab training nanosensorics Supervisor: Uh-Myong Ha Version: December 22, 2014 University of Kassel
Contents 1 Introduction 3 2 Fundamentals 4 2.1 Polarized light................................. 4 2.2 The Ellipsometer principle........................... 7 2.2.1 Measuring bulk materials....................... 8 2.2.2 Measuring thin films.......................... 8 3 Procedure 9 4 Getting the results 11 4.1 Task 1: Calculating n of the glas substrate................. 11 4.2 Task 2: Measuring the silicium wafer samples................ 13 4.3 Checklist for lab report............................ 14 Bibliography 15 2
1 Introduction Ellipsometry is a non-invasive and non destructive measurement method, which enables to obtain refractive index, layer thickness and absorption coefficient of a thin layer. The relative change of polarization of light hitting a sample surface is measured and can give information about the sample properties. The resolution of ellipsometry regarding thickness is very precise and enables measuring thickness < 1 nm and refractive index error from 0.001 to 0.01 [1]. In this lab experiment you should measure one glas substrate and two different silicium wafer samples. In the protocol you should calculate the refractive index based on the incident angle and the angles of polarizer/analyzer and compare it with the determined value via ellipsometer software. 3
2 Fundamentals 2.1 Polarized light Ellipsometry uses the effect that linearized light hitting a surface at an oblique incidence will change its polarization state resulting in most cases in elliptic polarized light (as seen in Figure 2.1.1). Figure 2.1.1: Linear polarized light hitting a sample surface will normally result in reflected light, which is elliptical polarized[1, p. 3]. To create linear polarzied light there are several possibilities. For ellipsometry usually a polarizer will be used, which changes unpolarized light into a well defined linear polarized state. The field vector E of the polarized light can be described as the superposition of two orthogonal waves E x and E y. E = E x sin(ωt k r) + E y sin(ωt k r + ϕ xy ) (2.1.1) ω = Frequency, t = time, k = wavevector, r = local vector and ϕ = phase shift. 4
2 Fundamentals In most cases light will be elliptical polarized and circular (E x = E y ) and linear (if there is no phase shift) polarized light being a special case. Elliptical polarized light can result from a difference between the two orthogonal field vectors and a phase shift. linear elliptical(left) circular(left) elliptical(left) φ xy 0π π 5 π 2 4π 5 linear elliptical(right) circular(right) elliptical(right) φ xy 1π 6π 5 Figure 2.1.2: At a set E x and E y one can change the polarization state of light just by changing the phase shift. It is visible that linear light will be obtained if the phase shift is an integer number [1]. 3π 2 9π 5 5
2 Fundamentals E p ψ E s Figure 2.1.3: The relation between the ellipse and the angle which will be measured within the experiment. is describing the phase difference between s- and p-polarized wave whereas tan(ψ) describes the diagonal of the surrounding box, which is equal to all the possibles ellipses. Having gives us a clear image of the ellipse within this box [1]. Elliptical polarized light can be graphically depicted as seen in Figure 2.1.3. If we look at the polarized state within the ellipsometer we will have to change the subscripts x/y to p/s since the vector fields are either perpendicular (senkrecht s) or within the plane of incidence (parallel p). Here the diagonal/ratio between the both amplitudes of electron vectors E p and E s is depicted by tan(ψ). A box is created, in which all possible ellipses of those vectors can fit in. With the parameter, which depicts the phase difference between the two waves, it is possible to draw the ellipse. Both parameters are used for the calculation of the complex reflectance ratio (ρ) (Equation 2.1.2). ρ = r p r s = tan(ψ)e i (2.1.2) r p/s = reflectance amplitude coefficient 6
2 Fundamentals 2.2 The Ellipsometer principle The light path of a so called PSCA ellipsometer is shown in Figure 2.2.1. As mentioned before unpolarized light (a) from a light source will be linear polarized using a polarizer, resulting in a well defined state (b). This linear polarized light will hit a sample, which will change its polarization state (c). As mentioned before this can result from a phase change which is compensated using the compensator resulting in linear polarized light (d). Furthermore a change of the reflectance amplitude coefficients r s/p can occur, which will result changed orientation and/or length of the electron vector (d). This can be measured using the analyzer (e). Sample Polarizer Compensator Analyzer Source Detector (a) (b) (c) (d) (e) Figure 2.2.1: By using an ellipsometer one can measure the ellipsometric values of ψ and. Those values are related via Fresnel equations to the refractive index of the sample, to the film thickness and the absorption coefficient [1]. 7
2 Fundamentals 2.2.1 Measuring bulk materials To measure the refractive index n of a bulk material the incidence angle of the light source as well the ratio of r s/p has to be known. Based on these parameters it is possible to calculate n by using the Fresnel equations [2]. 2.2.2 Measuring thin films The measurement of thickness d, complex refractive index ñ and the absorption coefficient κ of a thin film is much more complex than the measurement of a bulk material. If you take a look at Figure 2.2.2 you can see that the light path itself is more complex as the reflected light will be reflect several more times within the thin film. All those reflected light parts will summarize to a elliptical polarized state. So to determine ñ an approximation using computer modeling has to be done, which is embedded within the ellipsometer software.... Figure 2.2.2: Lightpath at a thin film. Adding a thin film on top of a bulk material will result in a more complex light path, which will result in a elliptical polarized state. The sum of the reflected light will be measured with ellipsometry. For the determination of n, κ and d computer modeling has to be used [1]. 8
3 Procedure Safety tips: Keep in mind that you are working with a laser, which has the class 3B. So don t look into the laser beam and don t wear reflective stuff like watches or rings. When working on the sample table, keep the laser lid shut! Mind this especially if you are exchanging or moving the sample. Microscope Polarizer Display Analyzer Laser Figure 3.0.1: Setup photo of the ellipsometer Initialization At the beginning of the experiment the ellipsometer and the PC has to be turned on. During the booting process of the PC the ellipsometer has to be calibrated. The display of the ellipsometer should read initialize Analyzer. To initialize analyzer turn the right wheel of the ellipsometer until the display reads initialize Polarizer. Repeat the same process for the analyzer for the left wheel and the ellipsometer is ready. 9
3 Procedure Measuring the glas substrate While the laser lid is shut put the glas substrate on the sample table. Open now the laser shutter and align it so that the laser spot is hitting the substrate. What follows now is the fine alignment of the sample table. To achieve that one has to turn on the microscope light and by looking through the microscope align two crosses until both are overlapping. After the successful alignment the microscope light has to be turned off. Finally check if the reflected laser light hits the photodiode on the analyzer side. During the actual measurement the polarizer and the analyzer has to be aligned so that light intensity shown on the ellipsometer display is minimal. The measurement has to be conducted on the photodiode quadrant Q2 and Q4. A detailed explanation of the measurement process will be conducted during the experiment. For the glas substrate the incident angle of the laser as well the angles of the polarizer and the analyzer has to be noted down (see subsection 2.2.1). Furthermore use the ellipsometer software to calculate n and write it down. Measuring the silicium wafer samples After the measurement of the glas substrate a blank silicium wafer substrate will be measured like the glas substrate. Save the refractive index of the wafer substrate within the ellipsometer software. Following this is the measurement of two different wafer samples. Keep in mind to shut the laser lid during the exchange of the samples. Using the ellipsometer software calculate ñ, κ and d (see subsection 2.2.2). 10
4 Getting the results Within the results part of the lab report the task is to calculate n of the measured glas substrate and compare it with the value of the ellipsometer software. Furthermore you should write down the determined values for n, κ and d of the silicium wafer samples. 4.1 Task 1: Calculating n of the glas substrate Laser α α Photodetector y E P olarizer y E Analyzer n 1 n 2 p x a x s p β P A (a) (b) (c) Figure 4.1.1: (a) Mockup of light path on an ideal surface. (b) shows the linear polarized light at the polarizer (P) which has an angle of p. (c) is the same picture for the Analyzer (A) with the angle a. Note that we assume that for both vectors E P = EA, since there is no absorption [1]. The goal is to use the measured incident angle α, as well as both angles of the polarizer p and the analyzer a to calculate n of a glas substrate (see Figure 4.1.1). To calculate the refractive index of the glas substrate we have make a few assumptions. First we assume that the light which hits the sample and is reflected will be perfectly 11
4 Getting the results linear (as in Figure 4.1.1 (b) and (c)). Additionally we assume there are no absorption effects so that there is no phase transition for the reflection. To simplify the calculation we furthermore assume that n is only real and that the interface is perfect. The change of E after the reflection off the glas substrate can be measured by measuring both angles p and a at the minimum intensity. Based on these assumptions it is possible to derive an equation for n 2 = n glas. Starting with the Fresnel equation for r s and the assumption that the measurement is conducted within air (n 1 = n air = 1) we can conclude (see subsection 2.2.1 for theory). r s = n 1 cos(α) n 2 cos(β) n 1 =1 r s = cos(α) n 2 cos(β) n 1 cos(α) + n 2 cos(β) cos(α) + n 2 cos(β) (4.1.1) Furthermore the change of amplitude along of the reflectance amplitude coefficient r is described by two equations (following Figure 4.1.1 (b)(c)). The angles a and p were measured within the experiment and represent the angle of the analyzer and the polarizer. We make another assumption that r s r x, which is used to replace r s. r x = sin(a) sin(p) = r s r y = cos(a) cos(p) (4.1.2) Using the above equation for r s and Equation 4.1.1 it is possible to transform the equation so you get an expression for n 2 n 2 =... (4.1.3) Equation 4.1.3 includes also cos(β), which we didn t measure. To eliminate cos(β) we use the following equations (Snell Descartes law and Pythagorean theorem). n 1 sin(α) = n 2 sin(β) (4.1.4) sin 2 (β) + cos 2 (β) = 1 (4.1.5) 12
4 Getting the results At the end you should have an equation which should include a square root. Compare the calculated value for n glas with the measured value of n glas. For the discussions part you should explain what creates the difference between the calculated value and the measured value of n glas. Additionally explain what error sources could contribute to the calculated value. 4.2 Task 2: Measuring the silicium wafer samples In this part you should write down the measured refractive index for the silicium substrate. The measured complex refractive index, absorption coefficient and thickness has to be written down. Furthermore explain in this part why you measured a blank silicium substrate at the beginning of second measurement. In the discussion part please make assumptions based on the determined values for thickness and refractive index, which material was used as a thin layer. For further information look at http://refractiveindex.info/ and compare your values. 13
4 Getting the results 4.3 Checklist for lab report Please write down an description of what you did in the experiment within the lab report. What did you measure? Write a measurement protocol and attach orignal measurement protocol. Table 4.3.1: Example measurement protocol Parameter Substrate ψ glas silicium Results Task 1: Derive the equation for the calculation of n glas and comment each step within the protocol. Task 2: What samples did you measure? Why did you measure them? Write down the values for ñ, κ and d calculated by the ellipsometer software. Discussion: For task 1: Write down what could create the difference between the calculated value and the measured value of n glas. For task 2: Considering the determined thickness and refractive index what thin film is on top of the wafer? Write down an conclusion, which entails all the results calculated and measured and compare them in one or two sentences. 14
Bibliography [1] Dr. Thomas Kusserow. Nanosensorics: 05-Ellipsometry: 05-Ellipsometry, 15.12.2014. URL http://te.ina-kassel.de/index.php/nanosensorics_en.html. [2] J.Ph.PIEL. Introduction to ellipsometry, 07.10.2008. URL https://cmi.epfl.ch/ metrology/files/sopra%20ges%205e/introduction%20to%20ellipsometry.pdf. [3] Jesper Jung, Jakob Bork, Tobias Holmgaard, Niels Anker Kortbek. Ellipsometry. PhD thesis, AALBORG UNIVERSITY, Aalborg Øst, 21.12/004. URL http:// homes.nano.aau.dk/kp/ellipsometry/main.pdf. 15