$$\mathbf{I}(\mathbf{P}, \mathbf{A}) = \mathbf{I}\_0 \left[ \sin^2 \mathbf{P} \sin^2 \mathbf{A} + \tan^2 \mathbf{W} \cos^2 \mathbf{P} \cos^2 \mathbf{A} + \frac{1}{2} \tan \Psi \; \cos \mathbf{A} \; \sin 2\mathbf{P} \sin 2\mathbf{A} \right] \tag{1}$$

By considering the polarizer and analyzer separately, Chao [4] improved Steel's [5] intensity ratio technique to align the polarizer and analyzer to the incident plane. For alignment, the following intensity ratios A and B are defined:

$$\mathbf{A}(\alpha, \beta) = \frac{\mathbf{I}(45^{\circ} + \alpha, \beta)}{\mathbf{I}(45^{\circ} + \alpha, 90^{\circ} + \beta)}\tag{2}$$

$$\mathbf{B}(\alpha, \beta) = \frac{\mathbf{I}(-45^{\circ} + \alpha, \beta)}{\mathbf{I}(-45^{\circ} + \alpha, 90^{\circ} + \beta)}\tag{3}$$

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 43

Figure 1. Schematic setup of PSA ellipsometry: A: analyzer, S, light source; P, polarizer; D, detector.

In addition to the azimuth angle of P and A, the small angle deviation α and β from the incident plane, respectively, are considered. These intensity ratios are expanded to the firstorder approximation around their respective scales, and expressed as follows:

$$\mathbf{A}(\mathfrak{a}, \mathfrak{B}) \cong \tan^2 \psi - 2 \left[ 2 \tan^2 \Psi \text{ \(\alpha - \sec^2 \Psi \tan \Psi \cos \Lambda \) \right] \tag{4}$$

$$\mathcal{B}(\alpha, \beta) \cong \tan^2 \Psi + 2 \left[ 2 \tan^2 \Psi \text{ } \alpha - \sec^2 \Psi \text{ } \tan \Psi \text{ } \cos \Lambda \text{ } \beta \right] \tag{5}$$

These two equations intersect with each other when

establish the plane of incident by aligning the azimuth angle of polarizer and analyzer to the plane of incident, both of which are the fundamental components of ellipsometer. Collins [2] and Chao [3] applied the null technique and the intensity ratio technique to locate the azimuth zeros of polarizer (P) and analyzer (A) with respect to the plane of incident, respectively. Both methods are complicated and time consuming. Due to the development of symbolic computer program Mathematica, one can analytically obtain the zeros of polarizer and analyzer with respect to the incident plane. In this chapter, the azimuth zeros of P and A to the incident plane will be located by an intensity ratio method. By rotating the analyzer, a three-intensity measurement technique will be applied to measure the ellipsometric parameters. According to the theoretical models, one can deduce the optical parameters from the measured ellipsometric parameters. Since only three intensities are needed to be measured, the imaging ellipsometry can be established. By using the following models: (a) the film thickness of flat and curved surface; (b) the refractive indices of homogeneous and nonhomogeneous bulk medium; (c) focused beam for surface plasmon resonance (SPR) phenomena, one can prove that this

The photoelastic modulator (PEM) will be introduced in the polarizer-sample-analyzer (PSA) ellipsometric system for an in situ/real-time ellipsometry. The in situ alignment technique of the optical axis of PEM is essential for establishing a real-time ellipsometry. Here, the real-time measurements of the ellipsometric parameters under etching and thermal heating processes will be presented. In addition to real time, one can also use the post-flight technique to analyze

The PSA ellipsometry setup is shown in Figure 1. Before inserting the PEM, one can setup the PSA ellipsometry for three-intensity measurement. For aligning the azimuth angles of P and A with respect to the incident plane, one can setup the PSA configuration in the interested incident angle (typical 70� in IC industry). The measured reflected intensity is expressed in

Ψ cos 2

By considering the polarizer and analyzer separately, Chao [4] improved Steel's [5] intensity ratio technique to align the polarizer and analyzer to the incident plane. For alignment, the

A α; β ¼ I 45� þ α, β

B α; β ¼ I �45� þ α, β

P cos 2

A þ 1

2 tan Ψ cosΔ sin 2P sin 2A

I 45� þ α, 90� þ β (2)

I �45� þ α, 90� þ β (3)

(1)

simple imaging ellipsometry has many different applications.

42 Ellipsometry - Principles and Techniques for Materials Characterization

the ellipsometric parameters, Ψ, Δ, and azimuth angles of P and A:

A þ tan 2

P sin 2

following intensity ratios A and B are defined:

the digital waveform of an anisotropic medium.

2. The alignment in PSA ellipsometry

I Pð Þ¼ ; A I0 sin 2

$$2\tan^2\Psi \text{ } \alpha - \sec^2\Psi \text{ } \tan\Psi \text{ } \cos\Delta \text{ } \beta = 0\tag{6}$$

so the deviation of α and β can be easily obtained for the opposite of cosΔ. Two incident angles [3], and fixed incident angle by two samples and two wavelengths [6] are proposed to align the azimuth angles of polarizer and analyzer. These complicated processes can be substituted by an analytical measurement technique [7]. In polar coordinates, if the incident light is Ep=Es, the reflected intensity is distributed in an elliptical form [5] as shown in Figure 2, which can be formulated as

$$\mathbf{I(A)} = \mathbf{L}\cos^2(\mathbf{A} - \boldsymbol{\Theta}) + \mathbf{T}\sin^2(\mathbf{A} - \boldsymbol{\Theta})\tag{7}$$

where L and T are the magnitudes of the maximum and minimum intensities, respectively, and θ is the azimuth of maximum intensity. Since there are only three unknowns, one can measure three intensities to deduce the three parameters. Eq. (7) can also be written as follows:

$$\mathbf{I(A)} = \mathbf{B(1 + C\cos 2A + D\sin 2A)}\tag{8}$$

where the parameters B, C, and D can be written in terms of L, T, and θ, that is, B = 0.5(L+T), C = (L�T)cos2θ/(L+T), and D = (L�T)sin2θ/(L+T). It is easy to prove that parameters B, C, and D can be measured by three intensities measured at A = 0�, 60�, and 120�;

Figure 2. Intensity distribution in polar coordinates at various azimuth angles of analyzer.

$$\mathbf{B} = \frac{1}{3} [\mathbf{I}(\mathbf{0}^\circ) + \mathbf{I}(\mathbf{60}^\circ) + \mathbf{I}(\mathbf{120}^\circ)] \tag{9}$$

$$\mathbf{C} = \mathbf{2} - [\mathbf{I}(60^\circ) + \mathbf{I}(120^\circ)]/\mathbf{B} \tag{10}$$

$$\mathbf{D} = \frac{1}{\mathbf{B}\sqrt{3}}[\mathbf{I}(60^\circ) - \mathbf{I}(120^\circ)] \tag{11}$$

So, tan2θ = D⁄C; L = B+DB/sin2θ and T = 2B�L. By comparing the expansion of Eq. (1), one can obtain the following relationships:

$$\tan 2\theta = \frac{\cos \Delta \quad \sin 2\mathbf{P} \cdot \sin 2\Psi}{\cos 2\mathbf{P} - \cos 2\Psi} \tag{12}$$

$$
\tan^2 \Psi = \frac{1+\mathcal{C}}{1-\mathcal{C}} \tan^2 \mathcal{P} \tag{13}
$$

$$\frac{\left(\mathbf{L} - \mathbf{T}\right)^2}{4\mathbf{L}\mathbf{T}}\sin^2 2\theta = \cot^2 \Lambda \tag{14}$$

when there is no deviation in the azimuth angles of polarizer and analyzer. Even there are deviations α and β for P and A, respectively, one can substitute those errors in the previous relations and obtain the analytical results, that is

$$\sin 2\alpha = \frac{1 - \sqrt{\frac{(1 + \mathcal{C}\_1)(1 - \mathcal{C}\_2)}{(1 - \mathcal{C}\_1)(1 + \mathcal{C}\_2)}}}{1 + \sqrt{\frac{(1 + \mathcal{C}\_1)(1 - \mathcal{C}\_2)}{(1 - \mathcal{C}\_1)(1 + \mathcal{C}\_2)}}}\tag{15}$$

$$\tan\Psi = 4\sqrt{\frac{1-\sqrt{\frac{(1+\mathcal{C}\_1)(1-\mathcal{C}\_2)}{(1-\mathcal{C}\_1)(1+\mathcal{C}\_2)}}}{1+\sqrt{\frac{(1+\mathcal{C}\_1)(1-\mathcal{C}\_2)}{(1-\mathcal{C}\_1)(1+\mathcal{C}\_2)}}}}\tag{16}$$

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 45

$$\beta = \frac{1}{4} \left( \tan^{-1} \frac{\mathbf{D}\_1}{\mathbf{C}\_1} - \tan^{-1} \frac{\mathbf{D}\_2}{\mathbf{C}\_2} \right) \tag{17}$$

where subscripts 1 and 2 indicate the three-intensity measurement obtained at P = 45� and �45�, respectively. After correction, the value Δ can be obtained by substituting the corrected value into the appropriate relation. The most important aspect of this technique is the concept of direct determination, in contrast to locating the minimum intensity in the null ellipsometry, which not only requires a sensitivity detector but also requires a polarizer with a high extinction ratio. This intensity ratio technique only needs a minimum amount of data to deduce the deviations and ellipsometric parameters simultaneously. If the detector is a high-dynamic range detector, the precision of this three-intensity measurement technique will be compatible to the commercial ellipsometer. Moreover, a complicated alignment process is not required in the simple PSA ellipsometry.

#### 3. Three-intensity measurements technique in PSA ellipsometry

The analytical alignment technique provides a simple and accurate alignment technique in ellipsometry. Since only three-intensity measurements are required, one can use chargecoupled device (CCD) as a detector for imaging ellipsometry.

#### 3.1. Film thickness of SiO2/Si thin film

B ¼ 1

Figure 2. Intensity distribution in polar coordinates at various azimuth angles of analyzer.

44 Ellipsometry - Principles and Techniques for Materials Characterization

obtain the following relationships:

relations and obtain the analytical results, that is

D ¼ 1 B ffiffiffi 3

tan 2

ð Þ L � T 2 4LT sin 2

sin 2α ¼ 1 �

tan Ψ ¼ 4

So, tan2θ = D⁄C; L = B+DB/sin2θ and T = 2B�L. By comparing the expansion of Eq. (1), one can

tan 2θ ¼ cosΔ sin 2P sin 2Ψ

Ψ ¼ 1 þ C

when there is no deviation in the azimuth angles of polarizer and analyzer. Even there are deviations α and β for P and A, respectively, one can substitute those errors in the previous

q

q

q

1 þ

1 �

vuuuut

1 þ

1 � C tan 2

2θ ¼ cot 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ 1þC1 ð Þ 1�C2 ð Þ 1�C1 ð Þ 1þC2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ 1þC1 ð Þ 1�C2 ð Þ 1�C1 ð Þ 1þC2

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ 1þC1 ð Þ 1�C2 ð Þ 1�C1 ð Þ 1þC2

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ 1þC1 ð Þ 1�C2 ð Þ 1�C1 ð Þ 1þC2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3 I 0� ð Þþ I 60� ð Þþ I 120� ½ � ð Þ (9)

p I 60� ð Þ� I 120� ½ � ð Þ (11)

cos 2P � cos 2Ψ (12)

q (15)

P (13)

Δ (14)

(16)

C ¼ 2 � I 60� ð Þþ I 120� ½ � ð Þ =B (10)

In the beginning, the azimuth angles of polarizer and analyzer are aligned to the incident plane by the Brewster angle of a nonabsorbent as the reference zero. After the rough alignment, the azimuth angle of polarizer is set at 45� and �45�, respectively, for analyzer to be at three angles, that is, 0�, 60�, and 120�, and the corresponding three-intensity measurements. One can choose an appropriate incident angle (typical 70�) for ellipsometric measurements. Using the relations in the last section, one can calculate Ψ, Δ, α, and β from three-intensity measurements. According to the definition of ellipsometric parameters to Fresnel reflection coefficient [1], one can deduce the film thickness of thin film (SiO2/Si thin film) through computer program. The primary objective is to compare the ellipsometric parameters measured with rough alignment to the analytically corrected values. Just as expected, the system errors are clearly observable in the deduced values of Ψ and Δ, measured at P = 45� and �45� separately, as shown in Figure 3. After readjusting the azimuth angles of polarizer and analyzer, one can observe the flat distribution of Ψ and Δ measured at P = 45� and �45�. The corrected ellipsometric parameters of the results deviated from each other by less than 0.01�, as shown in Tables 1 and 2. The corrected values are used for film thickness deduction. It is known that a rotating polarizer ellipsometry can deviate the incident angle [8]; the incident angle for thickness deduction is 69.94� instead of 70�.

#### 3.2. Imaging ellipsometry

In the PSA ellipsometry, one can add a beam expander and use CCD as a detector, such as shown in Figure 4. This imaging ellipsometry can measure the refractive index of a flat bulk

Figure 3. Ellipsometric measurements of PSA ellipsometry for a SiO2 film on a Si substrate: (a) ψ and (b) Δ measured after a rough alignment (filled squares) at P = 45and 45, where α = 0.9980.011 and β = 1.2330.005 and after readjusted (filled circles) at P = 45 and 45, where α = 0.0150.009 and β = 0.0060.003.

medium, curved surface, and film thickness on a curved surface. Moreover, the SPR phenomena will be presented by a focused light beam.

#### 3.2.1. Refractive index of flat surface of a bulk medium

Since there is no multiple reflection on a bulk medium, the refractive index of a bulk medium can be easily obtained by the ellipsometric parameter from the following relationship, let ρ = tanΨ eiΔ, then

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 47

Table 1. Optimized ellipsometric measurements of PSA ellipsometry for a SiO2 film on a Si substrate after rough alignment.

Table 2. Optimized ellipsometric measurements of PSA ellipsometry for a SiO2 film on a Si substrate after readjusting azimuth angles of polarizer and analyzer.

medium, curved surface, and film thickness on a curved surface. Moreover, the SPR phenom-

Figure 3. Ellipsometric measurements of PSA ellipsometry for a SiO2 film on a Si substrate: (a) ψ and (b) Δ measured after a rough alignment (filled squares) at P = 45and 45, where α = 0.9980.011 and β = 1.2330.005 and after readjusted

Since there is no multiple reflection on a bulk medium, the refractive index of a bulk medium can be easily obtained by the ellipsometric parameter from the following relationship, let ρ =

ena will be presented by a focused light beam.

tanΨ eiΔ, then

3.2.1. Refractive index of flat surface of a bulk medium

46 Ellipsometry - Principles and Techniques for Materials Characterization

(filled circles) at P = 45 and 45, where α = 0.0150.009 and β = 0.0060.003.

Figure 4. Schematic setup of the PSA imaging ellipsometer: Laser; P, polarizer; A, analyzer; S, sample; Expander, beam expander, and CCD camera. The elliptically distributed intensity on the right is under various azimuth angles of A in the polar coordinates.

$$\mathbf{n}\_1 = \mathbf{n}\_0 \tan \Theta\_i \left[ 1 - \frac{4\rho}{\left(1 + \rho\right)^2} \sin^2 \Theta\_i \right]^{\frac{1}{2}} \tag{18}$$

where n1, n0 are the refractive indices of bulk medium and incident medium, respectively. θι is the incident angle.

The graded index structure has been widely used in fiber communication, in technologies such as the graded index fiber, and the gradient-index (GRIN) lens. The knowledge of the refractive index profile (RIP) of this graded index structure is important not only to assess its performance in optical devices but also to control the quality of products [9]. Since it is very important to measure the RIP of a gradient index material, the nondestructive measurement using imaging ellipsometry is suggested. The well-known material BK7 glass can be used to evaluate this imaging ellipsometry, such as shown in Figure 5. Since glass is nonabsorbent, the refractive index can be obtained by Ψ. In addition, the RIP of a gradient index fiber can be measured; its surface property can also be examined by α, such as shown in Figure 6, which will be proved that it is the direction of surface's normal.

#### 3.2.2. The curved surface

Surface topography is a topic of great interest to science, technology, and industry. Both the contact stylus-based instruments [10] and noncontact optical instruments [11] can be used to measure and characterize the topography of a surface. By performing the ellipsometric measurements at two azimuth angles of the polarizer that differ by 90�, one can determine the azimuth deviation (α) of polarizer with respect to the incident plan by the three-intensity technique of PSA ellipsometry. After adjusting the deviation, one can prove that the azimuth

Figure 5. Imaging ellipsometric study of a BK7 glass: n = 1.520�0.003.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 49

n1 ¼ n0 tan θi 1 � 4ρ

will be proved that it is the direction of surface's normal.

48 Ellipsometry - Principles and Techniques for Materials Characterization

Figure 5. Imaging ellipsometric study of a BK7 glass: n = 1.520�0.003.

the incident angle.

3.2.2. The curved surface

where n1, n0 are the refractive indices of bulk medium and incident medium, respectively. θι is

The graded index structure has been widely used in fiber communication, in technologies such as the graded index fiber, and the gradient-index (GRIN) lens. The knowledge of the refractive index profile (RIP) of this graded index structure is important not only to assess its performance in optical devices but also to control the quality of products [9]. Since it is very important to measure the RIP of a gradient index material, the nondestructive measurement using imaging ellipsometry is suggested. The well-known material BK7 glass can be used to evaluate this imaging ellipsometry, such as shown in Figure 5. Since glass is nonabsorbent, the refractive index can be obtained by Ψ. In addition, the RIP of a gradient index fiber can be measured; its surface property can also be examined by α, such as shown in Figure 6, which

Surface topography is a topic of great interest to science, technology, and industry. Both the contact stylus-based instruments [10] and noncontact optical instruments [11] can be used to measure and characterize the topography of a surface. By performing the ellipsometric measurements at two azimuth angles of the polarizer that differ by 90�, one can determine the azimuth deviation (α) of polarizer with respect to the incident plan by the three-intensity technique of PSA ellipsometry. After adjusting the deviation, one can prove that the azimuth

1 þ ρ � �2 sin 2

" #1

θi

2

(18)

Figure 6. Imaging ellipsometric study of a flat GRIN lens: (a) azimuth deviation (α) of the surface. (b) Measured refractive index profile (\*: x-axis, ○: y-axis, solid line: RIP provided by NSG).

deviation of polarizer measured by this imaging ellipsometry can be used to measure the surface's normal; thus, it can be used to measure the surface topography of a lens. In the beginning, the alcohol surface is regarded as a flat surface for calibration; then one can tilt an SiO2/Si sample for investigating its effect to the azimuth deviation of polarizer. In the previous section, the refractive index profile of a GRIN lens has been obtained. Here, one can use the same technique to measure the RIP of the diluted alcohol, such as shown in Figure 7. Since both the GRIN lens and diluted alcohol have flat surfaces, their azimuth deviations are near to zero. Tilting a plate confirms that α can be used to measure the normal line of the surface, such as shown in Figure 8. After understanding the meaning of α, one can measure the refractive index of a BK7 plano-convex lens and its surface's normal, such as shown in Figure 9. This can be flattened by correcting the α, as shown in Figure 10. Furthermore, one can rotate the tilted SiO2/Si to investigate the three-direction cosines of the surface's normal. From the top view of a tilted plane, such as shown in Figure 11b, one can identify the surface's normal deviated by the tilted angle Θ with components α, and Δθ along x- and y-axes, respectively. The measured deviation α is the surface's normal projected on x-axis, which is perpendicular to the intersection of incident plane and sample surface. Δθ is the deviation of the incident angle caused by the tilting and can be deduced from the three-direction cosines. Three positions are examined, Table 3; all these results can be used to deduce the thickness of the thin film SiO2 on silicon substrate [12]. For simplicity, one shall use a cylindrical lens and set it up as in Figure 12, then examine the thickness of its coating by the three-intensity measurements technique, the

Figure 7. Imaging ellipsometric study of water and diluted alcohol: (a) azimuth deviation (α) of the diluted alcohol surface, (b) azimuth deviation (α) of the water surface, (c) refractive index profile of diluted alcohol n = 1.373 0.002, and (d) refractive index profile of water n = 1.333 0.002.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 51

Figure 8. Imaging ellipsometric study of azimuth deviation of polarizer (a) caused by the tilting of a SiO2 thin film on Si substrate. The thin film is tilted from 2 to 2 with step 1.

measured Ψ and Δ are shown in Figure 13. In this configuration, the measured α is zero at the vertex of the cylinder. The corrected Ψ and Δ are flat which can be used to deduct the thickness of the coating. In conclusion, this three-intensity measurement technique can perform a measurement on thin film coating of a curved and titled surface with high precision.

#### 3.2.3. Focused beam and surface plasmon resonance

deviation of polarizer measured by this imaging ellipsometry can be used to measure the surface's normal; thus, it can be used to measure the surface topography of a lens. In the beginning, the alcohol surface is regarded as a flat surface for calibration; then one can tilt an SiO2/Si sample for investigating its effect to the azimuth deviation of polarizer. In the previous section, the refractive index profile of a GRIN lens has been obtained. Here, one can use the same technique to measure the RIP of the diluted alcohol, such as shown in Figure 7. Since both the GRIN lens and diluted alcohol have flat surfaces, their azimuth deviations are near to zero. Tilting a plate confirms that α can be used to measure the normal line of the surface, such as shown in Figure 8. After understanding the meaning of α, one can measure the refractive index of a BK7 plano-convex lens and its surface's normal, such as shown in Figure 9. This can be flattened by correcting the α, as shown in Figure 10. Furthermore, one can rotate the tilted SiO2/Si to investigate the three-direction cosines of the surface's normal. From the top view of a tilted plane, such as shown in Figure 11b, one can identify the surface's normal deviated by the tilted angle Θ with components α, and Δθ along x- and y-axes, respectively. The measured deviation α is the surface's normal projected on x-axis, which is perpendicular to the intersection of incident plane and sample surface. Δθ is the deviation of the incident angle caused by the tilting and can be deduced from the three-direction cosines. Three positions are examined, Table 3; all these results can be used to deduce the thickness of the thin film SiO2 on silicon substrate [12]. For simplicity, one shall use a cylindrical lens and set it up as in Figure 12, then examine the thickness of its coating by the three-intensity measurements technique, the

50 Ellipsometry - Principles and Techniques for Materials Characterization

Figure 7. Imaging ellipsometric study of water and diluted alcohol: (a) azimuth deviation (α) of the diluted alcohol surface, (b) azimuth deviation (α) of the water surface, (c) refractive index profile of diluted alcohol n = 1.373 0.002, and

(d) refractive index profile of water n = 1.333 0.002.

In conventional ellipsometry, the light beam has to be collimated carefully to avoid the polarization errors. In the last section, we show that one can perform the ellipsometric measurement of a curved surface. Since the three-direction cosines have been well understood, one can measure a convergent/ divergent beam without any restriction [13]. Using a focused beam in the PSA imaging ellipsometry, one can perform the ellipsometric measurement under the surface plasmon resonance (SPR) condition and observe the resonance phenomena.

Figure 9. Imaging ellipsometric study of the radius of curvature of the BK7 plano-convex lens: (a) the magnitude of the azimuth deviation (α) of the surface and (b) the derived and measured α of the lens at the center and the edge (dashed line: derived from the radius measured by the Zygo phase-shift interferometer, solid line: measured by the imaging ellipsometric technique).

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 53

Figure 10. Imaging ellipsometric study of the RIP of the BK7 plano-convex lens: (a) the deduced RIP by considering the incident angle at 70 and (b) the deduced RIP by substituting its corresponding incident angles.

Figure 9. Imaging ellipsometric study of the radius of curvature of the BK7 plano-convex lens: (a) the magnitude of the azimuth deviation (α) of the surface and (b) the derived and measured α of the lens at the center and the edge (dashed line: derived from the radius measured by the Zygo phase-shift interferometer, solid line: measured by the imaging

ellipsometric technique).

52 Ellipsometry - Principles and Techniques for Materials Characterization

Figure 11. Schematic configuration of a tilted sample: (a) side view and (b) top view that indicates the motion of its surface normal: Θ, the tilted angle by spacer; Δθ, the component that contributes to the incident angle variation; α, the component measured in the deviation of the polarizer.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 55

a θ, the incident angle; Θ, the tilted angle; the relationship of the three-direction cosine is cos2 Θ = 1[sin2 Δα+ sin2 Δθ].

Table 3. Ellipsometric measurements of tilted and untilted samples.

Figure 11. Schematic configuration of a tilted sample: (a) side view and (b) top view that indicates the motion of its surface normal: Θ, the tilted angle by spacer; Δθ, the component that contributes to the incident angle variation; α, the

component measured in the deviation of the polarizer.

54 Ellipsometry - Principles and Techniques for Materials Characterization

Figure 12. Deviation angle of the surface normal across the vertex of a cylindrical lens: open circles, measured α across the vertex of the lens; solid line, its best linear fit.

A cylindrical lens is used to produce a fan-shaped beam for multiple incident angles configuration. This can simplify the analysis to be a two-dimensional case. The three-intensity measurement technique can measure the ellipsometric parameters against each incidence angle but do not have to calibrate the azimuth errors of polarizer and analyzer. As a result of multiple incident angles approach, the whole Ψ curve around the SPR region can be obtained without rotating the sensor chip. The basic setup of the SPR sensor chip is in Kretchmann's configuration, such as shown in Figure 14. The beam can be expanded by a beam expander, then focused it on the base of a prism/biosensor around the resonance incident angle (air: 44). One can measure the three intensities when P is at 45 and 45, respectively. The measured intensities

Figure 13. Ellipsometric parameters and thickness profile of the cylindrical lens: (a) Ψ and (b) Δ measured when P = 45; (c) Ψ and (d) Δ measured when P = 45; (e) Ψ and (f) Δ after correction. Film thickness is 1004.3 nm.

can be converted into ellipsometric parameters Ψ and Δ. Since the SPR phenomenon is more clearly observable by Ψ, we would like to present it by the distribution of Ψ versus the incident angle. The sensor chip is in Au/air (Figure 15) assembly. The solid line in the figure represents the theoretical value. This result can be used for calibration before other measurements.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 57

Figure 14. The schematic setup of SPR for imaging ellipsometry.

Figure 15. The distribution of Ψ versus incident angle of the sensor chip in air (circles are the measured value; solid line is the theoretical value).

#### 4. PEM ellipsometry

can be converted into ellipsometric parameters Ψ and Δ. Since the SPR phenomenon is more clearly observable by Ψ, we would like to present it by the distribution of Ψ versus the incident angle. The sensor chip is in Au/air (Figure 15) assembly. The solid line in the figure represents the theoretical value. This result can be used for calibration before other measurements.

Figure 13. Ellipsometric parameters and thickness profile of the cylindrical lens: (a) Ψ and (b) Δ measured when P = 45;

(c) Ψ and (d) Δ measured when P = 45; (e) Ψ and (f) Δ after correction. Film thickness is 1004.3 nm.

56 Ellipsometry - Principles and Techniques for Materials Characterization

In PSA ellipsometry, one has to rotate both polarizer and analyzer in order to measure the ellipsometric parameters. These rotations do cause the incident angle to deviate from the setup and slow down the speed of measurements. In the beginning of 1990, the real-time/in situ ellipsometric system has started to develop. By inserting a PEM in the PSA ellipsometry, one can construct an ellipsometry without any mechanical motion and thus substantially increase the speed of measurement. A photoelastic modulator (PEM) is a device that utilizes the photoelastic effect to modulate the phase retardation in a harmonic form [14]. For accurately measuring the ellipsometric parameters with high precision, one has to align the strain axis of PEM to the incident plane and calibrate its modulation amplitude. Since the incident plane has been well aligned in the PSA ellipsometry, one can easily align the strain axis to the incident plane by null and then determine its axis directly through the measurements of two DC intensities when the azimuths of the analyzer are separated by 45�. Regarding the modulation amplitude of PEM, although one can use the waveform of its half-wave in an oscilloscope to calibrate the modulation amplitude, it is usually very hard to visualize the flat shape of the waveform while its modulation amplitude is at half-wave. Recently, there is great progress in the data acquisition (DAQ) system with multi-functions. In this chapter, we perform the two options of the DAQ system for aligning the strain axis and calibrating the modulation amplitude of PEM in the ellipsometry: (1) lock-in amplifiers and (2) digitized oscilloscope. Since the digitized waveform can be stored for analyzing, the system errors of PEM controller can be inspected.

#### 4.1. Alignment of the strain axis of PEM

The basic setup of the PEM ellipsometer is shown in Figure 16. If the azimuth angle of the initial linear polarized light is set at 45�, and the strain axis of PEM deviates from the incident plane by θ, the measured intensity can be simplified as

$$\mathbf{I(A)} = \mathbf{I\_0} \left[ \mathbf{L} \sin^2 \mathbf{A} + \mathbf{M} \cos^2 \mathbf{A} \cdot \tan^2 \Psi + \mathbf{N} \sin \mathbf{A} \cdot \cos \mathbf{A} \right] \tag{19}$$

where

$$\mathbf{L} = 0.5[1 + \cos \Delta\_{\mathbf{P}} + (1 - \cos \Delta\_{\mathbf{P}})(1 - \sin \Delta\_{\mathbf{P}})] \tag{20}$$

$$\mathbf{M} = 0.5[1 + \cos \Delta\_{\mathbf{P}} + (1 - \cos \Delta\_{\mathbf{P}})(1 + \sin 4\Theta)] \tag{21}$$

$$\mathbf{N} = 0.5[1 + \cos \Delta\_{\mathbf{P}} - (1 - \cos \Delta\_{\mathbf{P}}) \cos 4\theta] \tan \Psi \, \cos \Delta - \sin \Delta\_{\mathbf{P}} \, \cos 2\theta \, \tan \Psi \, \sin \Delta \tag{22}$$

The modulation amplitude Δp of PEM is modulated as δ0cos(ωt). By setting the azimuth angle of analyzer at 0�, the measured intensity can be expressed as

Figure 16. Schematic setup of PEM ellipsometer.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 59

$$\mathbf{I}(0^\circ) = 0.5\mathbf{I}\_0 \tan^2 \Psi \ [2 + (1 - \cos \Delta\_\mathbf{P}) \sin 4\Theta] \tag{23}$$

then the intensity can be Fourier expanded by its harmonic function

intensities when the azimuths of the analyzer are separated by 45�. Regarding the modulation amplitude of PEM, although one can use the waveform of its half-wave in an oscilloscope to calibrate the modulation amplitude, it is usually very hard to visualize the flat shape of the waveform while its modulation amplitude is at half-wave. Recently, there is great progress in the data acquisition (DAQ) system with multi-functions. In this chapter, we perform the two options of the DAQ system for aligning the strain axis and calibrating the modulation amplitude of PEM in the ellipsometry: (1) lock-in amplifiers and (2) digitized oscilloscope. Since the digitized waveform can be stored for analyzing, the system errors of PEM controller can be inspected.

The basic setup of the PEM ellipsometer is shown in Figure 16. If the azimuth angle of the initial linear polarized light is set at 45�, and the strain axis of PEM deviates from the incident

A tan 2

N ¼ 0:5 1½ � þ cosΔP � ð Þ 1 � cos ΔP cos 4θ tan Ψ cosΔ � sinΔP cos 2θ tan Ψ sinΔ (22)

The modulation amplitude Δp of PEM is modulated as δ0cos(ωt).  Alignment of the strain axis of PEM

Figure 16. Schematic setup of PEM ellipsometer.

where

plane by θ, the measured intensity can be simplified as I Að Þ¼ I0 L sin 2

58 Ellipsometry - Principles and Techniques for Materials Characterization

of analyzer at 0�, the measured intensity can be expressed as

$$\cos \Delta\_{\rm P} = \mathbf{J}\_0(\delta\_0) - 2\mathbf{J}\_2(\delta\_2) \cos 2\omega t \dots \tag{24}$$

By taking the zero-order Bessel function J(δ0) at its zero point, that is, δ0 =0.383λ, we can simplify the DC component of its intensity as

$$\mathrm{I}\_{dc}(0^\circ) = 0.5 \mathrm{I}\_0 \tan^2 \Psi \,\, [2 + \sin 4\Theta] \,\, \tag{25}$$

From this equation, the strain axis of PEM deviates from zero by θ�, which can be measured by the DC component of the intensity. Taking two Idc at θ0 and θ0+45�, one can obtain θ0 through the following relation:

$$\sin 4\Theta\_0 = 2 \frac{\mathbf{I}\_{\rm dc}(0^\circ)\_{\theta = \theta\_0} - \mathbf{I}\_{\rm dc}(0^\circ)\_{\theta = \theta\_0 + 45^\circ}}{\mathbf{I}\_{\rm dc}(0^\circ)\_{\theta = \theta\_0} + \mathbf{I}\_{\rm dc}(0^\circ)\_{\theta = \theta\_0 + 45^\circ}} \tag{26}$$

A typical result after rough alignment is shown in Figure 17. According to the intensity ratio of Eq. (26), one can easily prove that the deviation of azimuth δθo resulting from those intensity fluctuations is

Figure 17. DC intensity distribution of the PEM ellipsometer. The azimuth angle of A is at 0� versus the azimuthal angle of the strain axis of PEM. \*The experimental data and the solid line show the intensity distribution when the strain axis of PEM is at 0.2764�0.0003�.

$$
\delta\Theta\_0 = \frac{\tan 4\Theta\_0}{4\tan^2 \Psi} \frac{\delta\Gamma}{\Gamma} \tag{27}
$$

The intensity fluctuation can be large at θ0 = 22.5�, which is far away from the roughly aligned value. By readjusting the θ0 to zero, one can obtain a well-aligned PEM ellipsometry.

#### 4.2. Calibration of the modulation amplitude of PEM

According to the last section, the strain axis of PEM can be well aligned to the incident plane, θ is zero, and the azimuth of polarizer is at 45�, Eq. (19), can be simplified as

$$\mathbf{I(A)} = 0.5\mathbf{I\_0} \left[ \sin^2 \mathbf{A} + \tan^2 \Psi \cdot \cos^2 \mathbf{A} - \tan \Psi \cdot \sin 2\mathbf{A} \; (\cos \Delta \; \cos \Delta \mathbf{p} + \sin \Delta \; \sin \Delta \mathbf{p}) \right] \tag{28}$$

Since the Fourier expansions of the harmonic functions are

$$\sin \Delta\_{\rm P} = \mathcal{Z}\mathbf{J}\_1(\delta\_0)\sin \omega \mathbf{t} + \mathcal{Z}\mathbf{J}\_3(\delta\_0)\sin \mathbf{3}\omega \mathbf{t} + \dots \tag{29}$$

$$\cos \Delta\_{\rm P} = \mathfrak{Z}\_0(\mathfrak{d}\_0) + \mathfrak{Z}\_2(\mathfrak{d}\_0)\sin 2\omega t + \mathfrak{Z}\_4(\mathfrak{d}\_0)\cos 4\omega t + \dots \tag{30}$$

One can prove the following relation for the measurement of Ψ and Δ:

$$\sin 2\Psi = \frac{\sqrt{\left(\frac{\mathbf{l}\_{\text{lf}} \left(45^{\circ}\right)}{\mathbf{l}\_{\text{f}} \left(30\right)}\right)^{2} + \left(\frac{\mathbf{l}\_{\text{f}} \left(45^{\circ}\right)}{\mathbf{l}\_{\text{f}} \left(30\right)}\right)^{2}}{\mathbf{l}\_{\text{dc}} \left(45^{\circ}\right) + \mathbf{l}\_{\text{dc}} \left(-45^{\circ}\right)}\tag{31}$$

$$\tan \Delta = \frac{\mathbf{I}\_{1f}(45^\circ)\mathbf{I}\_2(\delta\_0)}{\mathbf{I}\_{2f}(45^\circ)\mathbf{I}\_1(\delta\_0)}\tag{32}$$

It is very interesting to notice that the even/odd harmonics are related by the similar physical parameters except the orders of its Bessel function. So,

$$\frac{\mathbf{I}\_{1f}}{\mathbf{I}\_{3f}} = \frac{\mathbf{J}\_1(\mathfrak{S}\_0)}{\mathbf{J}\_3(\mathfrak{S}\_0)}\tag{33}$$

$$\frac{\mathbf{I}\_{2f}}{\mathbf{I}\_{4f}} = \frac{\mathbf{J}\_2(\mathfrak{d}\_0)}{\mathbf{J}\_4(\mathfrak{d}\_0)}\tag{34}$$

The modulation amplitude δ0 can be measured by the intensity ratio of even/odd harmonics. In the operation menu of PEM [15], the value δ0 can be calibrated by the oscilloscope waveform of a half-wave, that is, δ0 = 0.5, such as shown in Figure 18. However, when one is constructing a new element in a system, some defects are expected. Since one can measure the modulation amplitude by the even/odd intensity ratios, one can calibrate the modulation amplitude and compare it with the digitized oscilloscope waveform obtained from DAQ system, such as shown in Figure 19. The system errors, azimuth angle, and modulation amplitude can be corrected after the alignment and calibration in order to establish an accurate PEM ellipsometer.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 61

Figure 18. The oscilloscope waveforms when the modulation amplitude of PEM is a half-wave [15].

δθ0 ¼ tan 4θ0 4 tan 2Ψ

The intensity fluctuation can be large at θ0 = 22.5�, which is far away from the roughly aligned

According to the last section, the strain axis of PEM can be well aligned to the incident plane, θ

value. By readjusting the θ0 to zero, one can obtain a well-aligned PEM ellipsometry.

is zero, and the azimuth of polarizer is at 45�, Eq. (19), can be simplified as

Ψ cos 2

One can prove the following relation for the measurement of Ψ and Δ:

sin 2Ψ ¼

Since the Fourier expansions of the harmonic functions are

parameters except the orders of its Bessel function. So,

4.2. Calibration of the modulation amplitude of PEM

60 Ellipsometry - Principles and Techniques for Materials Characterization

A þ tan 2

I Að Þ¼ 0:5I0 sin 2

δI

� � (28)

A � tan Ψ sin 2A cos ð Þ Δ cosΔP þ sin Δ sinΔP

sinΔP ¼ 2J1ð Þ δ0 sin ωt þ 2J3ð Þ δ0 sin 3ωt þ … (29)

cosΔP ¼ 2J0ð Þþ δ0 2J2ð Þ δ0 sin 2ωt þ 2J4ð Þ δ0 cos 4ωt þ … (30)

þ I2f 45� ð Þ J2ð Þ δ0

Idc 45� ð Þþ Idc �45� ð Þ (31)

(32)

(33)

(34)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �2 r

I1f 45� ð Þ J1ð Þ δ0 � �2

tan Δ ¼ I1f 45� ð ÞJ2ð Þ δ0 I2f 45� ð ÞJ1ð Þ δ0

It is very interesting to notice that the even/odd harmonics are related by the similar physical

¼ J1ð Þ δ0 J3ð Þ δ0

¼ J2ð Þ δ0 J4ð Þ δ0

The modulation amplitude δ0 can be measured by the intensity ratio of even/odd harmonics. In the operation menu of PEM [15], the value δ0 can be calibrated by the oscilloscope waveform of a half-wave, that is, δ0 = 0.5, such as shown in Figure 18. However, when one is constructing a new element in a system, some defects are expected. Since one can measure the modulation amplitude by the even/odd intensity ratios, one can calibrate the modulation amplitude and compare it with the digitized oscilloscope waveform obtained from DAQ system, such as shown in Figure 19. The system errors, azimuth angle, and modulation amplitude can be corrected

I1f I3f

I2f I4f

after the alignment and calibration in order to establish an accurate PEM ellipsometer.

I (27)

Figure 19. Recorded digitized oscilloscope waveform when the modulation amplitude of PEM has been claimed as halfwave: left—before calibration and right—after calibration.

#### 4.3. Applications

For monitoring the physical processes, plasma etching [16], deposition [17], thermal heating [18], and photo-induced [19], one has to establish the in situ alignment technique for PEM ellipsometry. A DAQ card is an analog-to-digital converter. In the PEM ellipsometry, the multifunction DAQ (typical PCI-6111) can be used as two lock-in amplifiers for real-time measurement (10 sets/s), and post-flight analysis, that is, analyze the reflected waveform of the digital oscilloscope specification of the DAQ system, so the data rate can reach 25,000 sets/s. With the help of a stroboscope to modulate the light source, one can lock the wave at four specific phases to measure the ellipsometric parameters of the testing sample. By using CCD as the detector, an imaging ellipsometry can also be established in the PEM ellipsometry. The followings are examples for the applications of PEM ellipsometry.

#### 4.3.1. Plasma etching

For monitoring the etching process, a plasma-etching chamber can install a PEM ellipsometer to monitor the etching process, such as the schematic setup shown in Figure 20. A thick wafer is used to extract the etched thickness under etching, which can be monitored by the PEM ellipsometry to avoid over-etch. After calibrating the modulation amplitude, one can etch the film to the targeted thickness by monitoring the behavior of Ψ and Δ with the theoretical predication in real time. For example, we target a thick SiO2 on polysilicon started from around 500 nm to be etched to 30 nm. The measured value with the theoretical value, such as

Figure 20. Schematic setup of the IPC etcher.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 63

Figure 21. Distributions of Ψ for film etched from 500-nm thickness of SiO2 on silicon substrate (a) before calibration and (b) after calibration: (dotted line) theoretical value; (solid line) measured value fc [16].

in Figure 21a, the histogram of Ψ before correction, and Figure 21b, the histogram of Ψ after correction (fc, the correction factor from the measurement of modulation amplitude), can be compared. In the corrected curve, we observed the behavior of etching: the sharp rising of Ψ in the end cycle, around 70 nm. In the end, we can control the etching process: the etching stopped at the thickness of the film to be close to 30 nm within 0.2 nm, such as shown in Figure 22.

#### 4.3.2. Thermal heating

4.3. Applications

4.3.1. Plasma etching

Figure 20. Schematic setup of the IPC etcher.

For monitoring the physical processes, plasma etching [16], deposition [17], thermal heating [18], and photo-induced [19], one has to establish the in situ alignment technique for PEM ellipsometry. A DAQ card is an analog-to-digital converter. In the PEM ellipsometry, the multifunction DAQ (typical PCI-6111) can be used as two lock-in amplifiers for real-time measurement (10 sets/s), and post-flight analysis, that is, analyze the reflected waveform of the digital oscilloscope specification of the DAQ system, so the data rate can reach 25,000 sets/s. With the help of a stroboscope to modulate the light source, one can lock the wave at four specific phases to measure the ellipsometric parameters of the testing sample. By using CCD as the detector, an imaging ellipsometry can also be established in the PEM ellipsometry. The follow-

For monitoring the etching process, a plasma-etching chamber can install a PEM ellipsometer to monitor the etching process, such as the schematic setup shown in Figure 20. A thick wafer is used to extract the etched thickness under etching, which can be monitored by the PEM ellipsometry to avoid over-etch. After calibrating the modulation amplitude, one can etch the film to the targeted thickness by monitoring the behavior of Ψ and Δ with the theoretical predication in real time. For example, we target a thick SiO2 on polysilicon started from around 500 nm to be etched to 30 nm. The measured value with the theoretical value, such as

ings are examples for the applications of PEM ellipsometry.

62 Ellipsometry - Principles and Techniques for Materials Characterization

The perovskite materials are attractive because they exhibit extremely high piezoelectric coefficients and a wide region of controlled dielectric constants when the compositions are near the morphotropic phase boundary (MPB) [20]. In previous studies, doping Ru into complex oxides can enhance the photorefractive effect in the red and near-infrared spectral regions [21]. In addition, using Ru as a dopant in various inorganic crystals can considerably improve their response time and photoconductivity [22]. Therefore, Ru-doped perovskites can be considered as practical material for optical memories. In the process of storage, the temperature of the surroundings can fluctuate due to laser irradiation, heat dissipation, and so on. However, for

Figure 22. The histogram of an etching of SiO2/Si, the target of the process was 30 nm.

optical storage, the refractive index of the perovskite material must be stable under the working temperature. It will be interesting to measure their refractive indices during heating in order to understand what would be the most favorable working temperature for optical storage. One can setup the PEM ellipsometry as shown in Figure 23 to monitor the refractive index of perovskite material under heating. In the thermally isolated chamber, the samples can be heated from room temperature to 200C by the thermoelectric cooler (TE cooler), which operates based on the Peltier effect, so it can be used as heater when the electric current is

Figure 23. Schematic setup of the PEM ellipsometer for measuring the variation in the refractive index during the heating process: probe beam: HeNe laser (632.8 nm); P: polarizer; PEM: photoelastic modulator; S: sample; θ: incident angle.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 65

Figure 24. Refractive indices of (a) pure 0.9PZN-0.1PT and (b) Ru-doped 0.9PZN-0.1PT against temperature during heating: T: tetragonal; C: cubic.

inversely applied. The TE cooler is small but highly reliable. The sample can be sandwiched between two TE coolers to maintain uniformity of temperature of the sample. A k-type thermocouple was attached to the surface of the sample to monitor the temperature. The voltage produced by the thermocouple can be acquired by one of the channels of the same data acquisition system. The voltage is then converted to the required temperature scale according to the NIST ITS-90 Thermocouple Database. In this way, both the temperature and the ellipsometric parameters can be simultaneously monitored. According to the study by Chuang et al. [18], the ellipsometric parameters of pure and Ru-doped 0.9PZN–0.1PT were measured by PEM ellipsometry with a sampling rate of 10 sets/s. The refractive indices were converted from the measured Ψ and Δ, such as shown in Figures 24a and b. From the results of the experiment, one can conclude that when Ru is used as a dopant in 0.9PZN–0.1PT, the Curie region is broadened and shifted closer to room temperature. Therefore, the PEM ellipsometry can be used to analyze the behavior of material under heating.

#### 4.3.3. Photo-induced effect

optical storage, the refractive index of the perovskite material must be stable under the working temperature. It will be interesting to measure their refractive indices during heating in order to understand what would be the most favorable working temperature for optical storage. One can setup the PEM ellipsometry as shown in Figure 23 to monitor the refractive index of perovskite material under heating. In the thermally isolated chamber, the samples can be heated from room temperature to 200C by the thermoelectric cooler (TE cooler), which operates based on the Peltier effect, so it can be used as heater when the electric current is

Figure 23. Schematic setup of the PEM ellipsometer for measuring the variation in the refractive index during the heating process: probe beam: HeNe laser (632.8 nm); P: polarizer; PEM: photoelastic modulator; S: sample; θ: incident angle.

Figure 22. The histogram of an etching of SiO2/Si, the target of the process was 30 nm.

64 Ellipsometry - Principles and Techniques for Materials Characterization

Holographic data storage has been considered to be a promising data storage technology because it provides high storage density and fast readout rate. One of the fundamental issues for this technique to be successful is the availability of thick recording materials. Recently, research involving organic photopolymers has become of interest because of the flexibility for fabrication. Photopolymers exhibit a photorefractive effect, and the photo-induced changes in the refractive index can be used to record the holographic interference pattern in order to form phase grating. Based on this idea, many new photopolymers have been synthesized and studied. The photo-induced refractive index variation and photo-induced birefringence are two of the most often used mechanisms for producing the necessary changes in refractive

Figure 25. Histogram of measured refractive index during heating: (a) pure PMMA: the 488-nm laser was turned on at the 200th second and then turned off at the 500th second. The average refractive index is 1.4930.003; (b) PQ-doped PMMA: the 488-nm laser was turned on at the 23rd second and turned off at the 3623rd second; the refractive changes from 1.497 to 1.487. It is exposed to 488 nm (Ar/Kr tunable laser) with total exposure energy density of 68.4 J/cm2 .

indices for holographic recording. Thus, various methods have been proposed for investigating these two effects in different photopolymers for further improving the properties of the recording materials. The refractive indices of the photopolymers have been measured by an Abbe refractometer and a prism coupler, but the variation of the refractive index is commonly extracted from the diffraction formula by measuring the diffraction efficiency of a recorded grating [23]. Since the PEM ellipsometry can measure the refractive index during exposure, one can compare the photorefractive effect of photopolymers under irradiation. The PEM ellipsometry was used to measure the pure and doped PMMA, such as shown in Figures 25a and b. From these two measurements, one can conclude that the holographic recording in PQdoped PMMA was mainly due to the change in the refractive index. The change in the refractive index is produced by molecular structure changes of the PQ molecules. This in situ/real time can observe the structure change under irradiation.

#### 4.3.4. Post-flight analysis

Since most data acquisition systems are multi-function systems, if the PEM ellipsometry employs its function of lock-in amplifier to measure dc, 1f, and 2f signals for deducing the ellipsometric parameters, one can only obtain a data rate of 10 sets/s. In Section 4.2, the DAQ system has been used as digital oscilloscope for calibrating the modulation amplitude of PEM. The waveform obtained from the digital oscilloscope can be stored for post-flight analysis. The ellipsometric parameters can be obtained by fast Fourier transform of the stored waveform. In this case, the PEM ellipsometry can reach the speed limit of PEM, since Hinds PEM90 operated at an oscillating frequency around 50 kHz, so its data rate can reach 25,000 sets/s, for example, if one wishes to measure the response time of twisted nematic liquid crystals. It is known that the response time of twisted nematic liquid crystals (TN-LC) is in the millisecond regime, the transmitted PEM-DAQ ellipsometry can be used to analyze the variation of its ellipsometric parameters under a square wave. Figure 26 shows the histogram of the ellipsometric parameters of a TN-LC cell applying a 5-Hz square wave with a step voltage of 5 V. From the graph, one can measure the rising time and fall time of the TN-LC, which are 7.5 and 19 ms, respectively.

The Development of Three-Intensity Measurement in PSA Ellipsometry and Photoelastic Modulation Ellipsometry http://dx.doi.org/10.5772/intechopen.70086 67

Figure 26. Histograms of measured ellipsometric parameters for the twisted nematic liquid crystal cell (transmission ellipsometry, λ = 632.8 nm). A square wave of 5 Hz and strength 5 V was applied.

indices for holographic recording. Thus, various methods have been proposed for investigating these two effects in different photopolymers for further improving the properties of the recording materials. The refractive indices of the photopolymers have been measured by an Abbe refractometer and a prism coupler, but the variation of the refractive index is commonly extracted from the diffraction formula by measuring the diffraction efficiency of a recorded grating [23]. Since the PEM ellipsometry can measure the refractive index during exposure, one can compare the photorefractive effect of photopolymers under irradiation. The PEM ellipsometry was used to measure the pure and doped PMMA, such as shown in Figures 25a and b. From these two measurements, one can conclude that the holographic recording in PQdoped PMMA was mainly due to the change in the refractive index. The change in the refractive index is produced by molecular structure changes of the PQ molecules. This in situ/real

.

Figure 25. Histogram of measured refractive index during heating: (a) pure PMMA: the 488-nm laser was turned on at the 200th second and then turned off at the 500th second. The average refractive index is 1.4930.003; (b) PQ-doped PMMA: the 488-nm laser was turned on at the 23rd second and turned off at the 3623rd second; the refractive changes from 1.497 to 1.487. It is exposed to 488 nm (Ar/Kr tunable laser) with total exposure energy density of 68.4 J/cm2

Since most data acquisition systems are multi-function systems, if the PEM ellipsometry employs its function of lock-in amplifier to measure dc, 1f, and 2f signals for deducing the ellipsometric parameters, one can only obtain a data rate of 10 sets/s. In Section 4.2, the DAQ system has been used as digital oscilloscope for calibrating the modulation amplitude of PEM. The waveform obtained from the digital oscilloscope can be stored for post-flight analysis. The ellipsometric parameters can be obtained by fast Fourier transform of the stored waveform. In this case, the PEM ellipsometry can reach the speed limit of PEM, since Hinds PEM90 operated at an oscillating frequency around 50 kHz, so its data rate can reach 25,000 sets/s, for example, if one wishes to measure the response time of twisted nematic liquid crystals. It is known that the response time of twisted nematic liquid crystals (TN-LC) is in the millisecond regime, the transmitted PEM-DAQ ellipsometry can be used to analyze the variation of its ellipsometric parameters under a square wave. Figure 26 shows the histogram of the ellipsometric parameters of a TN-LC cell applying a 5-Hz square wave with a step voltage of 5 V. From the graph, one can measure the rising time and fall time of the TN-LC, which are 7.5 and 19 ms, respectively.

time can observe the structure change under irradiation.

66 Ellipsometry - Principles and Techniques for Materials Characterization

4.3.4. Post-flight analysis

The generalized ellipsometry (GE) has been developed to measure the refractive indices of anisotropic crystals [24]. In GE, at least three polarization states have to be used for extracting the physical parameters of anisotropic crystals. Using a fixed polarizer and PEM, one can generate various polarization states (200/cycle, Hinds90) because of the harmonic oscillation property of PEM. Two modulators of generalized ellipsometry [25] have been developed to measure the anisotropic medium. Due to the development of inverse problem in optics, Chuang et al. [26] implemented the program of Hodgkinson (BTF tool box) to simulate the reflected intensity profile. This profile can be analyzed and compared with the digitized waveform obtained from DAQ system of PEM ellipsometer. In his study, he found a distinguished characteristic in the reflected waveform for different complex refractive indices. Instead of using the Fourier transform on the waveform, he analyzed the reflected/transmitted waveform to extract the physical parameters. In the same reference, he proved that two incident angles are required to extract the complex refractive indices and the orientation of its optical axis of the anisotropic crystal. First, he concentrated his analysis on the reflected waveform at the incident angle of 70. According to the Fresnel reflection coefficient of a uniaxial crystal, one can graph the normalized reflected intensity waveform as Figure 27a. The asymmetric distribution provides the information of absorbing or nonadsorbing materials. Assume kave = 0.5(ke+ko) and Δk=keko are the averaged and difference between the extinction of ordinary and extraordinary coefficients, respectively, and nave = 0.5(ne+no) and Δn = neno are the averaged and difference between ordinary and extraordinary refractive indices, respectively. Using Figures 27b and c, one can conclude that the value of averaged extinction coefficient and difference can be estimated from the height (H) of the dip by the parametric

Figure 27. Estimation for complex refractive index (θi=70): (a) the normalized reflected intensity profile; (b) the parametric equations of the dip depth (H) versus the averaged extinction coefficient (kave); and (c) the parametric equations of the minimum intensity (Imin) versus the averaged refractive indices (nave).

Table 4. The parametric equations of dip height H for estimating the extinction coefficients obtained by simulated reflected waveform when θι at 70�.

Table 5. The parametric equations of Imin for estimating the refractive coefficient obtained by simulated reflected waveform when θι at 70�.

equations (Table 4). The averaged refractive index can be estimated by the minimum intensity Imin of the waveform, which is linearly related to the average refractive index (Table 5). It is known that the genetic algorithm is the mechanism of nature evolution and is considered as the optimal solution in the complex multidimensional search spaces. The parametric equations really can narrow down the searching region in genetic algorithm. Since the genetic algorithm [27] has been applied in ellipsometry, one can simulate the waveform and find the characteristic property to narrow down the searching region, then to search the complex refractive indices and the orientation of optical axis. Using two optimized incident angles, Chuang et al. [26] extracted the no and ne of quartz crystal to be 1.543 and 1.552, respectively. In addition, the orientation of its optical axes was also measured from the same

Figure 28. Measured reflected intensity profiles of quartz at incident angles of 65� (o) and 70� (●). All these measured values are compared with the calculated values (-). Only 1/5 data points in each cycle are displayed.

Figure 27. Estimation for complex refractive index (θi=70): (a) the normalized reflected intensity profile; (b) the parametric equations of the dip depth (H) versus the averaged extinction coefficient (kave); and (c) the parametric equations of

the minimum intensity (Imin) versus the averaged refractive indices (nave).

68 Ellipsometry - Principles and Techniques for Materials Characterization

waveform. Figure 28 shows the comparison between simulated waveform by using the extracted physical parameters (refractive indexes, orientation of optical axis) and measured values. This work presents the powerfulness of the post-flight analysis technique; one only has to use one cycle (20 μs of Hinds PEM 90) of the reflected intensity signals to extract all the optical parameters.

#### 5. Future prospects

The three-intensity measurements technique in PSA ellipsometry can be easily constructed into the imaging ellipsometry. In this system, the rotation of polarizer and analyzer not only slows down the measuring speed but also causes the incident beam to deviate from its setting. This is the reason for establishing the PEM ellipsometry. However, the modulation frequency of PEM is very high (most PEM operates in 50 kHz), and one must use fast response detector for PEM ellipsometry. The operation of CCD camera is a time-consuming process in comparing with the modulation frequency of PEM. The PEM imaging ellipsometry can only be established by employing the modulated laser diode as pulse for strobe illumination [28] at four specific phases. In this technique, one has to calibrate the initial phase for synchronizing the four specific phases to perform ellipsometric measurements. Again, with the help of symbolic computer program, Mathematica, Tsai [29] de-associated the initial phase by extra strobe measurement. This PEM stroboscopic imaging ellipsometry can measure a moving sample dynamically, such as the motion of dropping oil on SiO2 film. The speed of measurement can be improved by using high-power light source to reduce the exposure time and high-speed DAQ system to match the data transfer of CCD.

For further developing the ellipsometry, one can use the liquid crystal variable retarder to replace PEM. It is interesting to notice [30] a three-intensity measurements technique in ellipsometry by varying the phase retardation of liquid crystal instead of varying the polarization by rotating any part of the system. In addition to a liquid crystal variable retarder, a quarter wave plate has been introduced to form an ellipsometer without any mechanical motion. The in situ calibration of the liquid crystal variable retarder has to be performed. Just like the three-intensity measurement in PSA ellipsometry, one can install a liquid crystal variable retarder by varying three phases to form an imaging ellipsometry. Polarizer and quarter wave plate can be formed as polarization generator, liquid crystal variable retarder and analyzer can be packed as polarization analyzer. Since all these components are lightweight with low cost, one can construct a compact and portable system for imaging ellipsometric measurements. The only disadvantage of liquid crystal variable retarder is its stability in temperature. For accurate measurement, one has to use a temperature controller. We await the improvement of the liquid crystal variable retarder for the establishment.

#### Acknowledgements

All these works were accomplished by my students under the grants of National Science Council in Taiwan.

### Author details

Yu-Faye Chao

waveform. Figure 28 shows the comparison between simulated waveform by using the extracted physical parameters (refractive indexes, orientation of optical axis) and measured values. This work presents the powerfulness of the post-flight analysis technique; one only has to use one cycle (20 μs of Hinds PEM 90) of the reflected intensity signals to extract all the

The three-intensity measurements technique in PSA ellipsometry can be easily constructed into the imaging ellipsometry. In this system, the rotation of polarizer and analyzer not only slows down the measuring speed but also causes the incident beam to deviate from its setting. This is the reason for establishing the PEM ellipsometry. However, the modulation frequency of PEM is very high (most PEM operates in 50 kHz), and one must use fast response detector for PEM ellipsometry. The operation of CCD camera is a time-consuming process in comparing with the modulation frequency of PEM. The PEM imaging ellipsometry can only be established by employing the modulated laser diode as pulse for strobe illumination [28] at four specific phases. In this technique, one has to calibrate the initial phase for synchronizing the four specific phases to perform ellipsometric measurements. Again, with the help of symbolic computer program, Mathematica, Tsai [29] de-associated the initial phase by extra strobe measurement. This PEM stroboscopic imaging ellipsometry can measure a moving sample dynamically, such as the motion of dropping oil on SiO2 film. The speed of measurement can be improved by using high-power light source to reduce the exposure time and high-speed

For further developing the ellipsometry, one can use the liquid crystal variable retarder to replace PEM. It is interesting to notice [30] a three-intensity measurements technique in ellipsometry by varying the phase retardation of liquid crystal instead of varying the polarization by rotating any part of the system. In addition to a liquid crystal variable retarder, a quarter wave plate has been introduced to form an ellipsometer without any mechanical motion. The in situ calibration of the liquid crystal variable retarder has to be performed. Just like the three-intensity measurement in PSA ellipsometry, one can install a liquid crystal variable retarder by varying three phases to form an imaging ellipsometry. Polarizer and quarter wave plate can be formed as polarization generator, liquid crystal variable retarder and analyzer can be packed as polarization analyzer. Since all these components are lightweight with low cost, one can construct a compact and portable system for imaging ellipsometric measurements. The only disadvantage of liquid crystal variable retarder is its stability in temperature. For accurate measurement, one has to use a temperature controller. We await the improvement of the liquid crystal variable retarder for the establishment.

All these works were accomplished by my students under the grants of National Science

optical parameters.

5. Future prospects

Acknowledgements

Council in Taiwan.

DAQ system to match the data transfer of CCD.

70 Ellipsometry - Principles and Techniques for Materials Characterization

Address all correspondence to<EMAIL_ADDRESS>
Department of Photonics, National Chiao Tung University, Taiwan, ROC

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[13] Han CY, Du CY, Chen YR, Chao YF. Developing a phase and intensity measurement technique with multiple incident angles under surface plasmon resonance condition.

[14] Jasperson SN, Schnatterly SE. An improved method for high reflectivity ellipsometry based on a new polarization modulation technique. Review of Scientific Instruments.

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[16] Wang MW, Chao YF, Leou KC, Tsai FH, Lin TL, Chen SS, et al. Calibrations of phase modulation amplitude of photoelastic modulator. Japanese Journal of Applied Physics.

[17] Collins RW. In situ ellipsometry of thin-film deposition: Implications for amorphous and microcrystalline Si growth. Journal of Vacuum Science & Technology. B. Microelectronics

[18] Chuang CI, Marinova V, Lin SH, Chao YF. Phase-modulated ellipsometry for probing the temperature-induced phase transition in ruthenium-doped lead zinc niobate-lead titanate single crystal. Thin Solid Films. 2011;519:2867-2869. DOI: 10.1016/j.tsf.2010.12.085

[19] Chuang CI, Hsiao YN, Lin SH, Chao YF. Real-time measurement of photo-induced effects in 9,10-phenanthrenequinone-doped poly(methyl methacrylate) photopolymer by phasemodulated ellipsometry. Optical Communication. 2010;283:3279-3283. DOI: 10.1016/j.

[20] Liu W, Ren X. Large piezoelectric effect in Pb-free ceramics. Physical Review Letters.

[21] Lin CH, Huang CY, Chang JY. Increasing the conductivity of photorefractive BaTiO3 single crystals by doping Ru. Applied Surface Science. 2003;208–209:340-344. DOI:

[22] Rakitina L, Gospodinov M, Briat B. Photorefractive and photochromic properties of Ru doped Sr0:61Ba0:39Nb2O6 crystal. Optical Communication. 2002;213:373-378. DOI:

[23] Robinson TG, DeCorby RG, McMullin JN, Haugen CJ, Kasap SO, Tonchev D. Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films.

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72 Ellipsometry - Principles and Techniques for Materials Characterization

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Intensity-Modulation.pdf

optcom.2010.04.036

10.1016/S0169-4332(02)01393-4

10.1016/S0030-4018(02)02124-7

64.000128

**Provisional chapter**

## **Multilayer Polarizer at the Energy of 50–1000 eV**

**Multilayer Polarizer at the Energy of 50–1000 eV**

DOI: 10.5772/intechopen.70088

#### Jingtao Zhu and Mingqi Cui Jingtao Zhu and Mingqi Cui Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70088

#### **Abstract**

Accurate evaluation of polarization states of the radiation is necessary for polarization-sensitive studies, which requires polarization optical elements, such as polarizer, analyzer, and phase retarder. In extreme ultraviolet (EUV) and soft X-ray region, the closeness of the real part of the refractive index to unity, coupled with high absorption, makes the realization of polarizers such as birefringence and dichroic polarizers impossible. Periodical multilayers are commonly used in polarization study working at the quasi-Brewster angle. To expand narrow spectral bandwidths of periodic multilayers, aperiodic and lateral gradual multilayer polarizers including reflective analyzers and transmission phase retarders are utilized. In this chapter, we demonstrate a series of periodic, aperiodic, and lateral gradual broadband multilayer polarizers with the material combinations of Mo/Si, Mo/Y, Mo/B4 C, Cr/C, Cr/Sc, Cr/Ti, Cr/V, WSi2 /Si, W/B4 C, etc. Different multilayer polarizers correspond to different energy ranges, covering 50–1000 eV totally, including "water window" and the L absorption edges of Fe, Co, and Ni. Polarization measurements are performed at BESSY II, Diamond Light Source, National Synchrotron Radiation Laboratory in Hefei and Beijing Synchrotron Radiation Facility. Some of the polarizers we have developed are applied to the polarization measurements of BESSY II UE56/1-PGM and Beamline 3W1B of Beijing Synchrotron Radiation Facility.

**Keywords:** polarization, extreme ultraviolet (EUV), soft X-ray, multilayer thin film, synchrotron radiation beamline

#### **1. Introduction**

For polarization-sensitive studies, such as circular dichroism spectroscopy, spin-polarized photoelectron spectroscopy, and spectroscopic ellipsometry [1–4], accurate evaluation of the polarization state of the radiation is clearly crucial. Traditionally, in the visible and ultraviolet regions of the spectrum, birefringence and dichroic polarizers are used. But, in the soft X-ray region and extreme ultraviolet regions, collectively known as the EUV, the closeness of the

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

(real part of the) refractive index, coupled with high absorption, makes the realization of these kinds of polarizers impossible. As the one-dimension artificial crystal, multilayer can be utilized as polarizers and phase retarders in EUV and soft X-ray regions for its interference structures, which are based on Bragg diffraction theory [5, 6]. Periodical multilayers are commonly used in polarization study when they work at the quasi-Brewster angle. But the narrow spectral bandwidth of Bragg peak cannot fulfill the need of broadband spectrum applications. In order to expand the narrow spectral bandwidth of the periodic multilayer, the aperiodic multilayer polarizer including reflective analyzer and transmission phase retarder is utilized [7–10]. Complete polarization analysis has been performed by this new developed polarization system [11]. However, with the energy increasing, especially for the "water window" energy range, which is essential to biology researches, the aperiodic multilayer is no longer suitable because the period thicknesses in such energy region are ultra-thin (typically less than 1.0 nm). In this case, a lateral gradual multilayer is utilized and demonstrated with different material combinations. We also design and fabricate different types of multilayer polarizers at the energy range from 50 to 1000 eV covering the L absorption edges of metal magnetic materials Fe, Co, and Ni and also including the important energy range "water window." Measurements of the multilayer polarizers are performed at BESSY II, Diamond Light Source, Beijing Synchrotron Radiation Facility, and National Synchrotron Radiation Laboratory.

#### **2. Design**

The design of multilayer for polarization analysis requires determining the following parameters: materials combination, incident angle, and layer thickness distribution. The best material combination for multilayer is to form smooth and abrupt interface with low absorption and high optical contrast. The imperfections of interface as well as the absorption will influence the reflectivity of the multilayer. The absorption will be enhanced at a specific energy during the interaction between materials and incident light. To minimize the absorption, we choose material with the absorption edge slightly smaller than the working energy as the spacing layer. To maximize the interference in the structure of multilayer, the one with high optical contrast to the spacing layer is selected as the absorption layer. Here, we design periodical multilayer polarizers with different material combinations at the energy range from 50 to 1000 eV. **Table 1** shows the typical material combinations at different working energies.

Taking Mo/Y multilayer as an example, the calculated s-reflectivity, p-reflectivity, and *R*s */R*p with the optimized parameters are shown in **Figure 1**. *Y*-axis is in log to make all curves clear. The corresponding parameters are shown in **Table 2**, where, *D* represents the period thickness, *N* for bilayer numbers, and *γ* for the ratio of spacing layer thickness to period thickness. From **Figure 1**, we can see that the bandwidth is quite narrow. Such polarizers are effective over a very small wavelength range and close to the Brewster angle (approximately 45° for EUV and soft X-ray radiation); the narrowband wavelength and angular properties may be disadvantages for some studies. In order to overcome this, Yanagihara et al. [12] developed the

**Table 1.** Typical material combinations for different energy ranges.

(real part of the) refractive index, coupled with high absorption, makes the realization of these kinds of polarizers impossible. As the one-dimension artificial crystal, multilayer can be utilized as polarizers and phase retarders in EUV and soft X-ray regions for its interference structures, which are based on Bragg diffraction theory [5, 6]. Periodical multilayers are commonly used in polarization study when they work at the quasi-Brewster angle. But the narrow spectral bandwidth of Bragg peak cannot fulfill the need of broadband spectrum applications. In order to expand the narrow spectral bandwidth of the periodic multilayer, the aperiodic multilayer polarizer including reflective analyzer and transmission phase retarder is utilized [7–10]. Complete polarization analysis has been performed by this new developed polarization system [11]. However, with the energy increasing, especially for the "water window" energy range, which is essential to biology researches, the aperiodic multilayer is no longer suitable because the period thicknesses in such energy region are ultra-thin (typically less than 1.0 nm). In this case, a lateral gradual multilayer is utilized and demonstrated with different material combinations. We also design and fabricate different types of multilayer polarizers at the energy range from 50 to 1000 eV covering the L absorption edges of metal magnetic materials Fe, Co, and Ni and also including the important energy range "water window." Measurements of the multilayer polarizers are performed at BESSY II, Diamond Light Source, Beijing Synchrotron Radiation Facility, and National Synchrotron Radiation

76 Ellipsometry - Principles and Techniques for Materials Characterization

The design of multilayer for polarization analysis requires determining the following parameters: materials combination, incident angle, and layer thickness distribution. The best material combination for multilayer is to form smooth and abrupt interface with low absorption and high optical contrast. The imperfections of interface as well as the absorption will influence the reflectivity of the multilayer. The absorption will be enhanced at a specific energy during the interaction between materials and incident light. To minimize the absorption, we choose material with the absorption edge slightly smaller than the working energy as the spacing layer. To maximize the interference in the structure of multilayer, the one with high optical contrast to the spacing layer is selected as the absorption layer. Here, we design periodical multilayer polarizers with different material combinations at the energy range from 50 to 1000 eV. **Table 1** shows the typical material combinations at different working energies.

Taking Mo/Y multilayer as an example, the calculated s-reflectivity, p-reflectivity, and *R*s

with the optimized parameters are shown in **Figure 1**. *Y*-axis is in log to make all curves clear. The corresponding parameters are shown in **Table 2**, where, *D* represents the period thickness, *N* for bilayer numbers, and *γ* for the ratio of spacing layer thickness to period thickness. From **Figure 1**, we can see that the bandwidth is quite narrow. Such polarizers are effective over a very small wavelength range and close to the Brewster angle (approximately 45° for EUV and soft X-ray radiation); the narrowband wavelength and angular properties may be disadvantages for some studies. In order to overcome this, Yanagihara et al. [12] developed the

*/R*p

Laboratory.

**2. Design**

**Figure 1.** *R*s , *R*p, and *R*s /*R*p for Mo/Y periodic multilayers.

**Table 2.** Parameters of Mo/Y periodic multilayers.

double-multilayer polarizer, which, however, requires a complicated experimental arrangement and degrades the throughput. By rotating and translating the multilayer polarizers, an s-reflectivity of >4% in the wavelength range of 8–15 nm has been achieved. Also, Kortright et al. [13] have constructed a continuously tunable, laterally graded multilayer-based polarimeter working over a wide energy range. Using a series of translatable laterally gradual multilayers, the polarization state of the beam can be determined over the range of 1.6–25 nm.

To simplify the use of broadband polarizers, the design and performances of aperiodic broadband multilayer polarizers are described here.

At the quasi-Brewster angle, the ratio of the s- to p-reflectivity reaches the largest, where the reflective analyzer can be obtained. Since the complex refractive indices of all materials are very close to unity in EUV and soft X-ray ranges, the quasi-Brewster is close to 45°. The polarization degree *P* of beam reflected from a multilayer is determined by usual manner,

$$P = \frac{R\_\ast - R\_p}{R\_\ast + R\_p} \tag{1}$$

where *R*s and *R*p are the reflectivities for s- and p-polarized radiation, respectively. In the design of a reflective multilayer analyzer, the optimization of layer thickness distribution is achieved by minimizing the merit function (MF) [14],

$$\text{MF} = \frac{1}{m} \sum\_{\neq 1}^{m} \left[ 1 - P\left(\lambda\_{\rangle}\right) \right]^2 \tag{2}$$

where the summation is over a selection of discrete wavelengths in the desired range. The layer thickness distribution is considered as independent variable. During the recursive optimization, only randomly selected layer thickness changes that decrease MF are retained, finally leading to an optimized layer thickness distribution that provides a minimum value of MF.

For the wide angular multilayer analyzer, the optimization is achieved by minimizing the following merit function (MF)

$$\text{MF} = \frac{1}{m} \sum\_{j=1}^{m} \left( 1 - P\left(\theta\_j\right) \right)^2 \tag{3}$$

where the summation is over a selection of discrete angles in the desired range.

The phases of the transmitted s (Φs ) and p (Φp) electromagnetic fields can be calculated following the formalism of Vidal and Vincent [15], in which the phase shift ΔΦ = Φs − Φp is evaluated as a function of the wavelength, the grazing angle, the optical constants of the materials, the number of layers, and their thicknesses. Initially, the published criteria for selecting material and the number of bi-layer were used to satisfy both the maximum phase shift and the transmission intensity [16]. Then, the grazing angle was set in the region between the Bragg peak and the total reflection [17], at which the phase shift is maximum. The numerical optimization method was based on the minimization of the usual merit function (MF)

double-multilayer polarizer, which, however, requires a complicated experimental arrangement and degrades the throughput. By rotating and translating the multilayer polarizers, an s-reflectivity of >4% in the wavelength range of 8–15 nm has been achieved. Also, Kortright et al. [13] have constructed a continuously tunable, laterally graded multilayer-based polarimeter working over a wide energy range. Using a series of translatable laterally gradual multilayers, the polarization state of the beam can be determined over the range of 1.6–25 nm. To simplify the use of broadband polarizers, the design and performances of aperiodic broad-

At the quasi-Brewster angle, the ratio of the s- to p-reflectivity reaches the largest, where the reflective analyzer can be obtained. Since the complex refractive indices of all materials are very close to unity in EUV and soft X-ray ranges, the quasi-Brewster is close to 45°. The polar-

*R*s + *R*p

design of a reflective multilayer analyzer, the optimization of layer thickness distribution is

where the summation is over a selection of discrete wavelengths in the desired range. The layer thickness distribution is considered as independent variable. During the recursive optimization, only randomly selected layer thickness changes that decrease MF are retained, finally leading to an optimized layer thickness distribution that provides a mini-

For the wide angular multilayer analyzer, the optimization is achieved by minimizing the

following the formalism of Vidal and Vincent [15], in which the phase shift ΔΦ = Φs − Φp is evaluated as a function of the wavelength, the grazing angle, the optical constants of the materials, the number of layers, and their thicknesses. Initially, the published criteria for selecting material and the number of bi-layer were used to satisfy both the maximum phase shift and the transmission intensity [16]. Then, the grazing angle was set in the region between the Bragg peak and the total reflection [17], at which the phase shift

*m* ∑ *j*=1 *m*

where the summation is over a selection of discrete angles in the desired range.

*m* ∑ *j*=1 *m*

and *R*p are the reflectivities for s- and p-polarized radiation, respectively. In the

[1 − *P*(*λj*)]

(1 − *P*(*θj*))

2

) and p (Φp) electromagnetic fields can be calculated

2

(1)

(2)

(3)

ization degree *P* of beam reflected from a multilayer is determined by usual manner,

band multilayer polarizers are described here.

78 Ellipsometry - Principles and Techniques for Materials Characterization

*P* = *R*s − *R* \_\_\_\_\_p

achieved by minimizing the merit function (MF) [14],

MF = \_\_1

MF = \_\_1

The phases of the transmitted s (Φs

where *R*s

mum value of MF.

following merit function (MF)

$$MF = \left(\frac{1}{n}\sum\_{j=1}^{n} \left(\Phi\_0 - \Delta\Phi(\lambda\_j)\right)^2\right)^{1/2} \tag{4}$$

where ΔΦ(*λj* ) is the calculated phase retardation at wavelength *λj* and Φ0 is the desired phase shift.

By using the above scheme, we have designed a series of aperiodic multilayers such as Mo/Y [7], Mo/Be, Ni/C, and Mo/Si [8, 9], which can be utilized as broadband reflection analyzer and transmission phase retarder [10]. The broad angular Mo/Si multilayer analyzer is described in detail as an example, which the layer thicknesses oscillate from 3 to 11 nm, a range that is feasible to manufacture using direct current (DC) magnetron sputtering machine. The calculated mean s-reflectivity in the 45–49° range at working wavelength of 13 nm is 64.99 ± 0.18% and the degree of polarization is up to 99.12 ± 0.71%.

However, with the increasing energy, especially in the "water window" energy range, period thicknesses are decreasing to around 1.0 nm. It is difficult for magnetron sputtering to deposit such thin layer accounting interface roughness and diffusion. In this case, a lateral gradual multilayer structure is utilized to fulfill the Bragg condition either for varying energy or varying incident angle. Each periodic thickness of the lateral gradual multilayer varies in the horizontal direction corresponding to different energy, so that the energy bandwidth can be broadened to a respectively large range.

We design a series of lateral gradual multilayer polarizers with the material combinations of Mo/Si, Mo/Y, Mo/B4 C, Cr/C, Cr/Sc, Cr/Ti, Cr/V, W/Si, WSi2 /Si, and W/B4 C, which the minimum lateral gradual reaches 0.01 nm/mm with the total length of 70 mm.

As an example, the designed parameters of WSi2 /Si multilayer polarizer are given in **Table 3**. The working energy range is 430–760 eV. The calculated s- and p-reflectivities at every 5 mm are shown in **Figure 2**.

**Table 3.** Designed parameters of WSi2 /Si lateral gradual multilayer.

**Figure 2.** The calculated s- and p-reflectivities of WSi2 /Si lateral gradual multilayer.

#### **3. Fabrication**

The multilayer polarizers were deposited using a calibrated ultrahigh vacuum direct current (DC) magnetron sputtering system. They were deposited onto P(100) silicon wafer substrates at room temperature. Mask and speed control system were utilized in the fabrication of lateral gradual multilayers to control the lateral growth. The deposited multilayers were measured, for quality control, using a grazing incident angle X-ray reflectometry (XRR).

As an example, **Figure 3** shows the XRR curves for Mo/Si lateral gradual multilayer. Bragg peaks move evenly at different positions of the multilayer, which suggests a great homogeneity in lateral gradual variation. The appearances of all the fifth-order Bragg peaks prove the stability of fabrication technique.

The XRR result for W/B4 C lateral gradual multilayer with 150 layers is shown in **Figure 4**. The measured period thicknesses at the positions of every 5 mm (every 2 mm at beginning) are given in **Table 4**. As a result, period thicknesses of W/B4 C lateral gradual multilayer vary from 1.75 to 0.95 nm, and the multilayer covers the L absorption edges of Fe, Co, and Ni (600–900 eV) at quasi-Brewster angle, which is essential to the researches on magnetic materials.

**Figure 3.** XRR results for Mo/Si lateral gradual multilayer at different positions (translations are set in *Y*-axis to make all the curves clear).

**Figure 4.** XRR results for W/B4 C lateral gradual multilayer at different positions.

**3. Fabrication**

stability of fabrication technique.

**Figure 2.** The calculated s- and p-reflectivities of WSi2

80 Ellipsometry - Principles and Techniques for Materials Characterization

The XRR result for W/B4

materials.

The multilayer polarizers were deposited using a calibrated ultrahigh vacuum direct current (DC) magnetron sputtering system. They were deposited onto P(100) silicon wafer substrates at room temperature. Mask and speed control system were utilized in the fabrication of lateral gradual multilayers to control the lateral growth. The deposited multilayers were measured,

/Si lateral gradual multilayer.

As an example, **Figure 3** shows the XRR curves for Mo/Si lateral gradual multilayer. Bragg peaks move evenly at different positions of the multilayer, which suggests a great homogeneity in lateral gradual variation. The appearances of all the fifth-order Bragg peaks prove the

The measured period thicknesses at the positions of every 5 mm (every 2 mm at beginning)

vary from 1.75 to 0.95 nm, and the multilayer covers the L absorption edges of Fe, Co, and Ni (600–900 eV) at quasi-Brewster angle, which is essential to the researches on magnetic

C lateral gradual multilayer with 150 layers is shown in **Figure 4**.

C lateral gradual multilayer

for quality control, using a grazing incident angle X-ray reflectometry (XRR).

are given in **Table 4**. As a result, period thicknesses of W/B4

**Table 4.** Measured periods of W/B4 C lateral gradual multilayer at different positions.

### **4. Characterization and applications in synchrotron radiation measurement**

The performances of Mo/Y and Mo/Si aperiodic multilayers have been evaluated using the high precision polarimeter on beamline UE56/1-PGM at BESSY II. The details can be found in our previous articles [7–11].

Taking as an example, measured mean s-reflectivities of Mo/Si transmission phase retarders with the bandwidth of 2.0 nm are 10.4% at 47° and the corresponding polarization efficiency is up to 98.9%, which is nearly four times of the periodic one. The analyzer also exhibits high s-reflectivity over the angular range of 10° at the fixed wavelength.

The polarization performance of Mo/Si transmission phase retarders is evaluated with broadband analyzer. A transmittance ratio *T*p/*T*s of 5–23 from 12.5 to 13.2 nm is achieved and a constant phase shift of 50° at wavelength of 13.8–15.5 nm with the relative transmittance is 0.8–1.2.

Using this broadband Mo/Si polarizing system, the polarization of BESSY II UE56/1-PGM at 13.1 nm has been determined for the first time to our knowledge. As a result, the light of monochromatic radiation is nearly completely circularly, where the Stokes parameter is |S3| ≥ 0.94, and the linear polarization is the largest with −0.96 for in-plane radiation [11].

A flexible soft X-ray multilayer polarimeter has been designed and built on beamline I06 at diamond Light Source. This allows polarization measurements using multilayers with unprecedented reproducibility and accuracy. The polarimeter with its pinhole assemblies and hexapod is easy to align to a beamline. More detailed description about this polarimeter can be seen in Ref. [18].

Experiments to characterize polarization properties of broadband lateral gradual multilayers have been performed. The designed energy range is from 434 to 764 eV at quasi-Brewster angle for WSi2 /Si lateral gradual multilayer. The measurements are performed at every 2.5 mm along the horizontal direction. The corresponding multilayer periods are from 1.18 to 2.03 nm. The highest s-reflectivity reaches 2% in the wide energy range of 434–764 eV, i.e., a 330 eVbroadband polarizer has been achieved.

The optical properties of Mo/Si and Mo/Y lateral gradual multilayer are evaluated at NSRL in Hefei. The designed parameters are shown in **Tables 5** and **6**.

Reflectivities at different position of both Mo/Si and Mo/Y lateral gradual multilayer are measured at metrology station of NSRL in Hefei. As shown in **Figures 5** and **6**, the highest reflectivity of Mo/Si multilayer is more than 50% and obtained at the wavelength of 14.4 nm (86 eV). Mo/Y multilayer achieves the highest reflectivity of 32% at the wavelength of 13 nm (95 eV). The Bragg peaks of both multilayers distribute homogeneously in the energy-space at different positions, which shows a great stability in the gradient control during fabrication along the horizontal direction.

**Table 5.** Designed parameters of Mo/Si lateral gradual multilayer.

**4. Characterization and applications in synchrotron radiation**

s-reflectivity over the angular range of 10° at the fixed wavelength.

The performances of Mo/Y and Mo/Si aperiodic multilayers have been evaluated using the high precision polarimeter on beamline UE56/1-PGM at BESSY II. The details can be found in

C lateral gradual multilayer at different positions.

Position (mm) 08 10 15 20 25 30 35 40 45 50 55 60 65 *D* (nm) 1.75 1.73 1.63 1.56 1.48 1.40 1.34 1.28 1.22 1.17 1.13 1.08 0.95 Energy at 45° (eV) 501 507 538 562 592 626 654 685 719 749 776 812 923

Taking as an example, measured mean s-reflectivities of Mo/Si transmission phase retarders with the bandwidth of 2.0 nm are 10.4% at 47° and the corresponding polarization efficiency is up to 98.9%, which is nearly four times of the periodic one. The analyzer also exhibits high

The polarization performance of Mo/Si transmission phase retarders is evaluated with broad-

constant phase shift of 50° at wavelength of 13.8–15.5 nm with the relative transmittance is

Using this broadband Mo/Si polarizing system, the polarization of BESSY II UE56/1-PGM at 13.1 nm has been determined for the first time to our knowledge. As a result, the light of monochromatic radiation is nearly completely circularly, where the Stokes parameter is |S3|

A flexible soft X-ray multilayer polarimeter has been designed and built on beamline I06 at diamond Light Source. This allows polarization measurements using multilayers with unprecedented reproducibility and accuracy. The polarimeter with its pinhole assemblies and hexapod is easy to align to a beamline. More detailed description about this polarimeter can

Experiments to characterize polarization properties of broadband lateral gradual multilayers have been performed. The designed energy range is from 434 to 764 eV at quasi-Brewster

along the horizontal direction. The corresponding multilayer periods are from 1.18 to 2.03 nm. The highest s-reflectivity reaches 2% in the wide energy range of 434–764 eV, i.e., a 330 eV-

The optical properties of Mo/Si and Mo/Y lateral gradual multilayer are evaluated at NSRL in

/Si lateral gradual multilayer. The measurements are performed at every 2.5 mm

≥ 0.94, and the linear polarization is the largest with −0.96 for in-plane radiation [11].

of 5–23 from 12.5 to 13.2 nm is achieved and a

**measurement**

0.8–1.2.

be seen in Ref. [18].

angle for WSi2

our previous articles [7–11].

**Table 4.** Measured periods of W/B4

82 Ellipsometry - Principles and Techniques for Materials Characterization

band analyzer. A transmittance ratio *T*p/*T*s

broadband polarizer has been achieved.

Hefei. The designed parameters are shown in **Tables 5** and **6**.

**Table 6.** Designed parameters of Mo/Y lateral gradual multilayer.

**Figure 5.** Reflectivities of Mo/Si lateral gradual multilayer at different positions.

**Figure 6.** Reflectivities of Mo/Y lateral gradual multilayer at different positions.

### **5. Polarimeter in Beijing Synchrotron Radiation Facility (BSRF) and application**

A compact high precision eight-axis automatism and two-axis manual soft-ray polarimeter has been designed, constructed, and installed in 3W1B at the Beijing Synchrotron Radiation Facility (BSRF). The beamline is a windowless full ultra-high vacuum (UHV) soft X-ray beamline utilizing a permanent-magnet wiggler source. It supplies focusing monochromatic soft X-rays. The photon energy region is from 50 to 1600 eV. There are four operational modes in this polarimeter device, which are double-reflection, double-transmission, front-reflection-behind-transmission, and front-transmission-behind-reflection. The schematic diagrams of four modes are shown in **Figure 7**. The chamber of the polarimeter links to the beamline by UHV ferrofluidics feedthrough on the upstream. It can be rotated around the axis of the incident beam. The chamber is supported on gimbals and installed in a rigid bench which can move in three dimensions. The schematic diagram and the photo of the polarimeter are shown in **Figures 8** and **9** [19].

The polarization properties of Mo/Y, Mo/B4 C, and W/B4 C lateral gradual multilayer have been characterized by this polarimeter. Results are shown in **Figure 10**.

Mo/B4 C lateral gradual multilayer polarizer is used to measure the polarization characteristics of the beamline 3W1B at BSRF. The measured parameters are given in **Table 7**. A highest s-reflectivity of 12% is achieved at the energy of 188 eV. **Figure 11** shows the measured reflectivities, where, p-reflectivities are not low enough comparing to s-reflectivities. That suggests the beam coming out from 3W1B is not completely linear polarized, which coincides with the result shown in **Table 7** that the average degree of polarization is around 72% for the beamline 3W1B.

**Figure 7.** Schematic diagrams of four operational modes in polarimeter: (a) double-reflection; (b) double-transmission; (c) front-reflection-behind-transmission; (d) front-transmission-behind-reflection.

**5. Polarimeter in Beijing Synchrotron Radiation Facility (BSRF) and**

A compact high precision eight-axis automatism and two-axis manual soft-ray polarimeter has been designed, constructed, and installed in 3W1B at the Beijing Synchrotron Radiation Facility (BSRF). The beamline is a windowless full ultra-high vacuum (UHV) soft X-ray beamline utilizing a permanent-magnet wiggler source. It supplies focusing monochromatic soft X-rays. The photon energy region is from 50 to 1600 eV. There are four operational modes in this polarimeter device, which are double-reflection, double-transmission, front-reflection-behind-transmission, and front-transmission-behind-reflection. The schematic diagrams of four modes are shown in **Figure 7**. The chamber of the polarimeter links to the beamline by UHV ferrofluidics feedthrough on the upstream. It can be rotated around the axis of the incident beam. The chamber is supported on gimbals and installed in a rigid bench which can move in three dimensions. The schematic diagram and the photo of the polarimeter are shown in **Figures 8** and **9** [19].

C, and W/B4

C lateral gradual multilayer polarizer is used to measure the polarization characteristics of the beamline 3W1B at BSRF. The measured parameters are given in **Table 7**. A highest s-reflectivity of 12% is achieved at the energy of 188 eV. **Figure 11** shows the measured reflectivities, where, p-reflectivities are not low enough comparing to s-reflectivities. That suggests the beam coming out from 3W1B is not completely linear polarized, which coincides with the result shown in **Table 7** that the average degree of polarization is around 72% for the beamline 3W1B.

C lateral gradual multilayer have been

**application**

Mo/B4

The polarization properties of Mo/Y, Mo/B4

characterized by this polarimeter. Results are shown in **Figure 10**.

**Figure 6.** Reflectivities of Mo/Y lateral gradual multilayer at different positions.

84 Ellipsometry - Principles and Techniques for Materials Characterization

**Figure 8.** Schematic diagram of the polarimeter at BSRF: (1) chamber; (2) azimuthal angle of polarizer; (3) collimator translation x-y stage; (4) I0 detector; (5) polarizer; (6) moving rocker; (7) sample stage; (8) rotational stage to change azimuth angle of analyzer; (9) analyzer; and (10) main detector.

**Figure 9.** Photo of the polarimeter device.

To obtain complete liner polarization at 3W1B, two twins-born Cr/C multilayers are used as polarizer and analyzer at the energy of 206 eV. Both Cr/C multilayers have the exactly same optical characteristic with bi-layer number of 100 and period thickness of 4.318 nm. Using the double-reflection mode of the soft X-ray polarimeter, a nearly complete linear polarized beam is achieved. The schematic diagram is the same as shown in **Figure 7(a)**. Both multilayers are set at their quasi-Brewster angles. As a result, the degree of linear polarization is raised from 0.585 to 0.995 after polarized by Cr/C multilayer at 206 eV. The detailed results of the polarization optimization at other energies are shown in **Table 8** [20].

**Figure 10.** S-reflectivity as a function of energy: (a) Mo/Y; (b) Mo/B4 C; (c) W/B4 C.

**Table 7.** Measured parameters of Mo/B4 C lateral gradual multilayer at different positions.

To obtain complete liner polarization at 3W1B, two twins-born Cr/C multilayers are used as polarizer and analyzer at the energy of 206 eV. Both Cr/C multilayers have the exactly same optical characteristic with bi-layer number of 100 and period thickness of 4.318 nm. Using the double-reflection mode of the soft X-ray polarimeter, a nearly complete linear polarized beam is achieved. The schematic diagram is the same as shown in **Figure 7(a)**. Both multilayers are set at their quasi-Brewster angles. As a result, the degree of linear polarization is raised from 0.585 to 0.995 after polarized by Cr/C multilayer at 206 eV. The detailed results of the polariza-

C; (c) W/B4

C.

tion optimization at other energies are shown in **Table 8** [20].

**Figure 10.** S-reflectivity as a function of energy: (a) Mo/Y; (b) Mo/B4

**Figure 9.** Photo of the polarimeter device.

86 Ellipsometry - Principles and Techniques for Materials Characterization

**Figure 11.** S-reflectivities and p-reflectivities at different energies of the beamline 3W1B.

**Table 8.** Measurement results of linear polarization at different energies.

#### **6. Conclusion**

The multilayers can be utilized in EUV and soft X-ray polarization applications. A series of multilayers with periodic and aperiodic thicknesses are designed to broaden the bandwidth. Measurements are performed at BESSY-II, Diamond and Beijing Synchrotron Radiation Facility. For Mo/Y aperiodic multilayer, polarization efficiency is up to 20% over a 90–120 eV (10.5–13.5 nm) energy range. Mo/Si broadband transmission phase retarder is also realized. Combination using the polarimeter, complete polarization characteristics of the synchrotron radiation beam is performed. The results show that broadband aperiodic multilayer greatly simplifies polarization experiments. For further development of multilayer polarizers in soft X-ray region, especially the "water window" range, a series of lateral gradual multilayers are utilized. The performance of WSi2 /Si lateral gradual multilayer polarizer is evaluated at diamond light source, which, as a result, covers the energy range of 434–764 eV. In addition, polarization measurements of Mo/Si, Mo/Y, Mo/B4 C, W/B4 C, and other lateral gradual multilayers have been performed at Beijing Synchrotron Radiation Facility and National Synchrotron Radiation Laboratory in Hefei. These researches create some novel experimental methods, such as soft X-ray magnetic circular dichroism, element resolution Faraday effect, and Kerr effect measurements, which provide the powerful tools for biology, medicine, information, material science, etc.

#### **Acknowledgements**

The authors are indebted to Dr. Igor V. Kozhevnikov for useful discussions. Special thanks are due to Dr. Franz. Schäfers, Dr. Hongchang Wang, Matthew Hand, Hongjun Zhou, Tonglin Huo, and Dr. Lijuan Sun for their kind assistance during the measurement at BESSY, Diamond, NSRL, and BSRF. The authors are grateful to Dr. Alan Michette, Dr.Keith Powell, Dr. Slawka Pfauntsch, Dr. Sawhney Kawal, and Prof. Zhanshan Wang for their great support during this work. The author would also like to thank Miao Li, Shengming Zhu, Bin Ji, Jinwen Chen, and Jiayi Zhang for the participations during multilayer design, fabrication, and measurement processes. This work was supported by the National Natural Science Foundation of China (contract numbers 11375131 and U1432244), by the Royal Society—NSFC International Exchanges funding (reference IE141043 and<PHONE_NUMBER>1), and by the Fundamental Research Funds for Central Universities.

#### **Author details**

Jingtao Zhu1 \* and Mingqi Cui2

\*Address all correspondence to<EMAIL_ADDRESS>
1 MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai, China

2 Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

#### **References**

**6. Conclusion**

of WSi2

Mo/Si, Mo/Y, Mo/B4

**Acknowledgements**

**Author details**

of Sciences, Beijing, China

\* and Mingqi Cui2

\*Address all correspondence to<EMAIL_ADDRESS>
and Engineering, Tongji University, Shanghai, China

Jingtao Zhu1

C, W/B4

88 Ellipsometry - Principles and Techniques for Materials Characterization

powerful tools for biology, medicine, information, material science, etc.

The multilayers can be utilized in EUV and soft X-ray polarization applications. A series of multilayers with periodic and aperiodic thicknesses are designed to broaden the bandwidth. Measurements are performed at BESSY-II, Diamond and Beijing Synchrotron Radiation Facility. For Mo/Y aperiodic multilayer, polarization efficiency is up to 20% over a 90–120 eV (10.5–13.5 nm) energy range. Mo/Si broadband transmission phase retarder is also realized. Combination using the polarimeter, complete polarization characteristics of the synchrotron radiation beam is performed. The results show that broadband aperiodic multilayer greatly simplifies polarization experiments. For further development of multilayer polarizers in soft X-ray region, especially the "water window" range, a series of lateral gradual multilayers are utilized. The performance

/Si lateral gradual multilayer polarizer is evaluated at diamond light source, which,

C, and other lateral gradual multilayers have been performed at

as a result, covers the energy range of 434–764 eV. In addition, polarization measurements of

Beijing Synchrotron Radiation Facility and National Synchrotron Radiation Laboratory in Hefei. These researches create some novel experimental methods, such as soft X-ray magnetic circular dichroism, element resolution Faraday effect, and Kerr effect measurements, which provide the

The authors are indebted to Dr. Igor V. Kozhevnikov for useful discussions. Special thanks are due to Dr. Franz. Schäfers, Dr. Hongchang Wang, Matthew Hand, Hongjun Zhou, Tonglin Huo, and Dr. Lijuan Sun for their kind assistance during the measurement at BESSY, Diamond, NSRL, and BSRF. The authors are grateful to Dr. Alan Michette, Dr.Keith Powell, Dr. Slawka Pfauntsch, Dr. Sawhney Kawal, and Prof. Zhanshan Wang for their great support during this work. The author would also like to thank Miao Li, Shengming Zhu, Bin Ji, Jinwen Chen, and Jiayi Zhang for the participations during multilayer design, fabrication, and measurement processes. This work was supported by the National Natural Science Foundation of China (contract numbers 11375131 and U1432244), by the Royal Society—NSFC International Exchanges funding (reference IE141043

1 MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science

2 Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy

and<PHONE_NUMBER>1), and by the Fundamental Research Funds for Central Universities.

**Provisional chapter**

#### **Spectroscopic Ellipsometry Study of Organic-Inorganic Halide: FAPbIxBr3−x Perovskite Thin Films by Two-Step Method Spectroscopic Ellipsometry Study of Organic-Inorganic Halide: FAPbI x Br3−x Perovskite Thin Films by Two-Step Method**

DOI: 10.5772/intechopen.70281

#### Hajime Shirai Hajime Shirai

[16] Kim DE, Lee SM, Jeon I. Transmission characteristics of multilayer structure in the soft x-ray spectral region and its application to the design of quarter-wave plates at 13 and 4.4 nm. Journal of Vacuum Science & Technology A Vacuum Surfaces & Films.

[17] Kortright JB. Polarization properties of multilayers in the EUV and soft x ray. Proceedings of SPIE—The International Society for Optical Engineering. 1994;**2010**:160-167

[18] Wang H, Dhesi SS, Maccherozzi F, et al. High-precision soft x-ray polarimeter at Diamond Light Source. Review of Scientific Instruments. 2011;**82**(12):123301

[19] Sun L, Cui M, Zhu J, et al. Multilayer-based soft X-ray polarimeter at the Beijing

[20] Cui M, Sun L, Zhu J, et al. The soft X-ray polarimeter and applications at BSRF. Nuclear

Synchrotron Radiation Facility. Chinese Physics C. 2013;**37**(7):83-87

1999;**17**(2):398-402

Techniques. 2010;**1234**(1):641-644

90 Ellipsometry - Principles and Techniques for Materials Characterization

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70281

#### **Abstract**

Spectroscopic ellipsometry (SE) was used to investigate the role of isopropyl alcohol (IPA) solvent in the synthesis of organic-lead-halide perovskite CH(NH2 ) 2 PbIx Br3−x [FAPbIx Br3−x] thin films including the effect of I/Br composition ratio by the two-step reaction of an amorphous (a-)PbIx Br2−x layer and FAIx Br1−x solution diluted in IPA. An optical dispersion model was developed to extract the complex refractive index *N* (=*n* + i*k*), optical transition, and film thickness of FAPbIx Br3−x perovskites by SE analysis at different I/Br composition ratio as a function of immersion time in a solution of FAIx Br1−x diluted in IPA. SE combined with X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM) revealed that Br incorporation into films promoted the densification of FAPbIx Br3−x perovskite network along with increased film thickness and volume fraction of void. IPA promoted film crystallization of a-PbIx Br2−x accompanied by the formation of surface roughness, grain boundaries, and voids, followed by enhanced diffusion of FAIx Br1−x into the grain boundaries/voids in the mesoporous crystallized PbIx Br2−x network. These processes contribute synergistically to the growth of the perovskite structure.

**Keywords:** ellipsometry, organic-lead-halide perovskite, two-step reaction, role of isopropyl alcohol (IPA) solvent, growth mechanism

#### **1. Introduction**

In recent years, organic-inorganic halide perovskite solar cells have significantly attracted much interest as high-efficiency solar cell material due to their high absorption coefficient, ambipolar carrier transport, and long-carrier diffusion lengths, which have resulted in power conversion efficiencies (PCEs) as high as 20.1% [1–3]. Methylammonium [(CH3 NH3 )+ ; MA] lead triiodide (MAPbI3 ), which is used in the most efficient perovskite solar cells, has a bandgap (*E*g ) of around 1.57 eV [4, 5], a very sharp absorption edge [6], and an impressively

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

low difference between the open-circuit voltage (*V*oc) and its bandgap potential (*E*g /*q*) [6–8]. However, the instability of MAPbI3 with respect to humidity, temperature, and light soaking is a serious problem hindering long-term reliability of the photovoltaic performance. Therefore, the formamidinium [(NH2 )2 CH+ ; FA] lead triiodine (FAPbI3 ) perovskite, where the ionic radius of the A-site FA+ ion (253 pm) is larger than that of MA+ (217 pm), has recently been extensively studied due to better-phase stabilization and higher photovoltaic performance over other systems such as MAPbI3 , and better stability for air storage with an extension of the optical absorption edge to the infrared region up to around 840 nm [5]. More recently, interest has extended to the FAPbIx Br3−x and Cs0.2FA0.8PbIx Br3−x perovskite, which has even higher stability against humidity as well as temperature. A bandgap is also tunable from 1.43 to 2.35 eV by substitutional doping of bromide ions to iodine sites [9].

In addition, various methods for the fabrication of perovskite thin films have been extensively studied, such as a one-step solution process [10], sequential two-step reaction [11, 12], and vacuum deposition [13]. Although an efficient PCE of around 20% has been achieved using uniform and dense perovskite layers prepared by a one-step solution process [14, 15], this involves complex procedures such as precise control of the composition ratio in the precursor solution and the rate of evaporation to adjust the composition ratio of the perovskite film. An alternative approach is a two-step deposition method using porous PbX2 (X = I, Cl, Br) films and organic halide solutions such as MAX and FAX diluted in 2-isopropanol alcohol [IPA; (CH3 )2 COH] solvent on an electron transport layer such as mesoporous TiO2 or ZnO, which results in better coverage and uniformity than the one-step process. However, the film morphology of the porous PbX2 in the two-step deposition method has a strong effect on the chemical reactivity with the alkyl amine halide, which in turn determines the film homogeneity and crystallinity of the resultant perovskite thin films. To control the morphology of PbX2 films, solvent vapor treatment [16], and additives such as hydriodic acid [17], dimethyl sulfoxide (DMSO), and *N*-methyl-2-pyrrolidone [18] have been tested. For example, Miyadera et al. reported that the rate of perovskite formation from polycrystalline PbI2 on mesoporous TiO2 was approximately one order of magnitude faster than that of well-oriented dense PbI2 on glass [19]. In addition, the type of solvent is sensitive to the morphology of PbI2 . *N,N*-Dimethylformamide (DMF; CH3 NCHO) is generally used to promote the crystallization of PbI2 . The use of DMSO or cumene hydroperoxide (CHP; C6 H5 C(CH3 )2 OOH), which has lower vapor pressures than DMF, has been reported to suppress the rapid crystallization and to form an amorphous structure that reacts preferentially with MAI diluted in IPA solvent, resulting in a slower rate of crystallization of MAPbI3 and a more homogeneous film structure [20, 21]. However, the role of the polar IPA solvent in the synthesis of FAPbIx Br3−x perovskites is still not clear because the reaction rate is very fast. Thus, to understand the effect of Br incorporation on the fine structure and the growth mechanism of perovskites by a two-step method from PbIx Br2−x film and FAIx Br1−x solution diluted in IPA solvent, a slower reaction rate is preferable from amorphous (a-)PbIx Br2−x rather than from mesoporous crystalline PbX2 by immersion in FAX/IPA solution at lower temperatures.

In this chapter, we present the role of the IPA solvent in the synthesis of FAPbIx Br3−x perovskites including the effect of Br incorporation in the films by a two-step solution process using spectroscopic ellipsometry (SE) as well as X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM) observation.

#### **2. Experimental section**

low difference between the open-circuit voltage (*V*oc) and its bandgap potential (*E*g

)2 CH+

1.43 to 2.35 eV by substitutional doping of bromide ions to iodine sites [9].

film. An alternative approach is a two-step deposition method using porous PbX2

et al. reported that the rate of perovskite formation from polycrystalline PbI2

. The use of DMSO or cumene hydroperoxide (CHP; C6

Br2−x film and FAIx

In this chapter, we present the role of the IPA solvent in the synthesis of FAPbIx

spectroscopy (FTIR), and scanning electron microscopy (SEM) observation.

by immersion in FAX/IPA solution at lower temperatures.

vent, resulting in a slower rate of crystallization of MAPbI3

reaction rate is preferable from amorphous (a-)PbIx

ing is a serious problem hindering long-term reliability of the photovoltaic performance.

been extensively studied due to better-phase stabilization and higher photovoltaic perfor-

sion of the optical absorption edge to the infrared region up to around 840 nm [5]. More

even higher stability against humidity as well as temperature. A bandgap is also tunable from

In addition, various methods for the fabrication of perovskite thin films have been extensively studied, such as a one-step solution process [10], sequential two-step reaction [11, 12], and vacuum deposition [13]. Although an efficient PCE of around 20% has been achieved using uniform and dense perovskite layers prepared by a one-step solution process [14, 15], this involves complex procedures such as precise control of the composition ratio in the precursor solution and the rate of evaporation to adjust the composition ratio of the perovskite

Br) films and organic halide solutions such as MAX and FAX diluted in 2-isopropanol alcohol

which results in better coverage and uniformity than the one-step process. However, the film

chemical reactivity with the alkyl amine halide, which in turn determines the film homogeneity and crystallinity of the resultant perovskite thin films. To control the morphology of PbX2 films, solvent vapor treatment [16], and additives such as hydriodic acid [17], dimethyl sulfoxide (DMSO), and *N*-methyl-2-pyrrolidone [18] have been tested. For example, Miyadera

was approximately one order of magnitude faster than that of well-oriented dense

on glass [19]. In addition, the type of solvent is sensitive to the morphology of PbI2

lower vapor pressures than DMF, has been reported to suppress the rapid crystallization and to form an amorphous structure that reacts preferentially with MAI diluted in IPA sol-

perovskites is still not clear because the reaction rate is very fast. Thus, to understand the effect of Br incorporation on the fine structure and the growth mechanism of perovskites by

including the effect of Br incorporation in the films by a two-step solution process using spectroscopic ellipsometry (SE) as well as X-ray diffraction (XRD), Fourier-transform infrared

structure [20, 21]. However, the role of the polar IPA solvent in the synthesis of FAPbIx

COH] solvent on an electron transport layer such as mesoporous TiO2

ion (253 pm) is larger than that of MA+

with respect to humidity, temperature, and light soak-

in the two-step deposition method has a strong effect on the

NCHO) is generally used to promote the crystallization

H5 C(CH3 )2

, and better stability for air storage with an exten-

; FA] lead triiodine (FAPbI3

Br3−x and Cs0.2FA0.8PbIx

However, the instability of MAPbI3

Therefore, the formamidinium [(NH2

mance over other systems such as MAPbI3

92 Ellipsometry - Principles and Techniques for Materials Characterization

recently, interest has extended to the FAPbIx

ionic radius of the A-site FA+

[IPA; (CH3

rous TiO2

PbI2

of PbI2

talline PbX2

)2

morphology of the porous PbX2

*N,N*-Dimethylformamide (DMF; CH3

a two-step method from PbIx

/*q*) [6–8].

(X = I, Cl,

or ZnO,

on mesopo-

OOH), which has

Br3−x perovskites

and a more homogeneous film

Br1−x solution diluted in IPA solvent, a slower

Br2−x rather than from mesoporous crys-

.

Br3−x

) perovskite, where the

(217 pm), has recently

Br3−x perovskite, which has

A-PbIx Br2−x thin films with a film thickness of around 150 nm were prepared on glass by spin coating a mixture of FAIx Br1−x and PbIx Br2−x powder (PbI2 :PbBr2 = 3:1 and 3:2 molar ratio) in a DMF/CHP (95:5, v/v) cosolvent at 3000 rpm for 30 s. A-PbIx Br2−x films prepared using the DMF/ CHP cosolvent promoted the growth of perovskite structure after immersion in FAIx Br1−x/ IPA solution, whereas no reaction to form the perovskite occurred in a-PbIx Br2−x films prepared from 100 vol% DFM solvent. Thus, a-PbIx Br2−x fabricated with DMF/CHP cosolvent was used as a precursor to promote the formation of perovskite structure. A-PbIx Br2−x films were immersed in a solution of FAIx Br1−x (FAI:FABr = 3:1 molar ratio) in IPA solvent for various times (*t* im) at 25°C. Finally, the FAPbIx Br3−x films were rinsed with IPA to remove the residual solution and contaminants from the film surface.

The refractive index *n* and extinction coefficient *k* of the corresponding FAPbIx Br3−x films were determined using a phase-modulated spectroscopic ellipsometer (UVISEL, Horiba Jobin Yvon). The ellipsometric angles, Ψ and Δ, which determine the complex reflection coefficient ratio, *ρ* = tanΨ *ei*Δ , were also measured for 71 points in the range of 1.5–5.0 eV (0.05 eV step) with an integration time of 200 ms at each photon energy. The angle of incidence, *θ*i , of the probe light was 70°. The measured values for the *n* and *k* spectra, denoted by <*n*> and <*k*>, include information regarding the surface roughness, voids, and bulk inhomogeneity of the perovskite film and the PbIx Br2−x precursor. The bulk component of optical constants for the perovskite films, *n* and *k*, and the volume fractions of perovskite and voids (*f* perov, *f* void) were determined using a modified amorphous model based on the Forouhi-Bloomer (FB) model described in Eq. (1), combined with the Bruggeman effective medium approximation (EMA) [22, 23]:

$$n(\omega \mid \text{\(\omega \; )}=\frac{B \cdot (\omega - \omega\_{\\_j}) + \text{C}}{(\omega - \omega\_{\\_j})^2 + \text{\(\(\omega \; \)}^2 + \text{C}\_j^2} \tag{1}$$

$$k(\omega \mid) = \begin{cases} \frac{A\_{\circ} \cdot E\_{\circ} \cdot (\omega - \omega\_{\circ})^2}{(\omega - \omega\_{\circ})^2 + \Gamma^2} & \text{for } \omega > \omega\_{\circ} \\ 0 & \text{for } \omega \ge \omega\_{\circ} \end{cases} \tag{2}$$

where

$$\begin{aligned} B &= \frac{A\_{\dot{\gamma}}}{\Gamma\_{\dot{\gamma}}} \cdot [\Gamma\_{\dot{\gamma}}^2 - (\omega\_{\dot{\gamma}} - \omega\_{\dot{\gamma}})^2] \\ C &= 2 \cdot A\_{\dot{\gamma}} \cdot \Gamma\_{\dot{\gamma}} \cdot (\omega\_{\dot{\gamma}} - \omega\_{\dot{\gamma}}) \end{aligned} \tag{3}$$

The quantities *Aj* , *Γ*0 , *ωj* , and *ωg* represent the resonance amplitude, the oscillator-broadening parameter, the resonance energy, and the Tauc optical gap, respectively. Spectral fitting was performed using the optical constant for bulk FAPbIx Br3−x perovskite described in Eq. (1), and *f* perov, *f* void, and each film thickness *di* (*i* = 1, 2, 3), as variables. A probable structure was determined using the optical model by minimization of the standard deviation *χ*2 between the measured and calculated ellipsometric error parameters using a linear regression method as follows [24]:

$$\chi^2 = \frac{1}{2N - M} \sum\_{i=1}^{N} \left[ \left( \tan \Psi\_i^c - \tan \Psi\_i^m \right)^2 - \left( \cos \Delta\_i^c - \cos \Delta\_i^m \right)^2 \right] \tag{4}$$

where the superscripts *c* and *m* represent the calculated and measured values, and *N* and *M* are the numbers of the measured and calculated wavelengths, respectively.

The fine structures of the a-PbIx Br2−x and perovskite FAPbIx Br3−x thin films were also evaluated using X-ray diffraction (Bruker D8 ADVANCE ECO) with the diffractometer in Bragg-Brentano mode using Cu Kα radiation with a Lynxeye XE detector, Fourier-transform infrared spectroscopy (Shimadzu spectrometer, IRTracer-100), field emission scanning electron microscopy (FESEM; S4800, Hitachi High Technologies, Japan) with energy-dispersive X-ray spectroscopy (EDX) (Bruker XFlash 5030/Quantax 400), and atomic force microscopy (AFM; NanonavieII/ SPI-3800, Hitachi High-Tech Science, Japan) to support the results of the SE analysis.

#### **3. Results and discussion**