overview of variable angle spectroscopic ellipsometry vase, part 1

Overview of Variable Angle Spectroscopic Ellipsometry (VASE), Part I:

Basic Theory and Typical Applications

John A. Woollam·, Blaine Johs, Craig M. Herzinger, James Hilfiker, Ron Synowicki, and Corey L. Bungay

JA. Woollam Co., Inc., 645 'M' St. #102, Lincoln, NE 68508

ABSTRACT

Variable angle spectroscopic ellipsometry (VASE) is important for metrology in several industries, and is a powerful teclutique for research on new materials and processes. Sophisticated instrumentation and software for VASE data acquisition and analysis is available for the most demanding research applications, while simple to use software enables the use of VASE for routine measurements as well. This article gives a basic introduction to the theory ofellipsometry, references "classic" papers, and shows typical VASE applications. In the following companion paper, more advanced applications are discussed.

Keywords: Ellipsometry, optical properties, spectroscopy, metrology

1. VASE THEORY

1.1. Introduction

The mathematical theory for ellipsometric analysis is based on the Fresnel reflection or transmission equations for polarized light encountering boundaries in planar multilayered materialsl,2. These come fr0I!l solutions to Maxwell's equations3. The ellipsometric measurement is normally expressed in terms of Psi ('¥) and Delta (~):

tan('¥) .eilJ. = p = rp (1) rs

where rp and rs are the complex Fresnel reflection coefficients of the sample for p- (in the plane of incidence) and s- (perpendicular to the plane of incidence) polarized light, illustrated in Figure 1. Spectroscopic Ellipsometry (SE) measures the complex ratio p as a function of wavelength4-ll. Variable Angle Spectroscopic Ellipsometry (VASE) performs the above measurement as a function of both wavelength and angle of incidencel2.

• Correspondence: Email: [email protected]; WWW: www.jawoollam.com; Telephone: 402-477-7501; FAX: 402-477-8214

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Overview of Variable Angle Spectroscopic Ellipsometry (VASE), Part I:

Basic Theory and Typical Applications

John A. Woollam·, Blaine Johs, Craig M. Herzinger, James Hilfiker, Ron Synowicki, and Corey L. Bungay

JA. Woollam Co., Inc., 645 'M' St. #102, Lincoln, NE 68508

ABSTRACT

Variable angle spectroscopic ellipsometry (VASE) is important for metrology in several industries, and is a powerful technique for research on new materials and processes. Sophisticated instrumentation and software for VASE data acquisition and analysis is available for the most demanding research applications, while simple to use software enables the use of VASE for routine measurements as well. This article gives a basic introduction to the theory of ellipsometry, references "classic" papers, and shows typical VASE applications. In the following companion paper, more advanced applications are discussed.

Keywords: Ellipsometry, optical properties, spectroscopy, metrology

1. VASE THEORY

1.1. Introduction

The mathematical theory for ellipsometric analysis is based on the Fresnel reflection or transmission equations for polarized light encountering boundaries in planar multilayered materialsJ

,2. These come froI!l solutions to Maxwell's equations3• The

ellipsometric measurement is normally expressed in terms of Psi ('II) and Delta (A):

'6 rtan('¥) .e' = p = -.!!... (1) rs

where rp and rs are the complex Fresnel reflection coefficients of the sample for p- (in the plane of incidence) and s- (perpendicular to the plane of incidence) polarized light, illustrated in Figure 1. Spectroscopic Ellipsometry (SE) measures the complex ratio p as a function of wavelength4-11. Variable Angle Spectroscopic Ellipsometry (VASE) performs the above measurement as a function ofboth wavelength and angle of incidencel2

•

• Correspondence: Email: [email protected]; WWW: www.jawoollam.com; Telephone: 402-477-7501; FAX: 402-477-8214

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3. elllpticfllly polflr/zed light I

p-plane

4 / Critical Reviews Vol. CR72

1. linearly polarlzed light ... E p:plane

s-plane

Figure h- Interaction ofpolarized light with a sample.

Because ellipsometry measures the ratio of two values it is highly accurate and reproducible, and no reference material is necessary. Because it measures a phase quantity'A' (as well as an amplitude ratio), it is very sensitive even to the presence of very thin films. Use of Spectroscopic Ellipsometry (SE) results in increased sensitivity to multiple film parameters, and as well, eliminates the 'period' problem, associated with interference oscillations in thick films. Another feature of SE is that it measures data at the wavelength of interest, which is ofparticular importance for industrial problems such as development of lithography at new wavelengths. Adding multiple angles to spectroscopic capability (VASE) provides new information because of the different optical path lengths traversed, and it optimizes sensitivity to the unknown parameters.

To illustrate the thin film sensitivity advantage of ellipsometry over traditional reflectivity measurements, consider the following figures. Figure 2 shows the calculated change in reflectance caused by a thickness change of O.lom on a 100m thick Si02 layer on crystalline Silicon. A typical reflectometer system can not accurately measure intensity values to better than 0.1%, and therefore a reflectivity measurement is not very sensitive to small changes in ultra thin film thicknesses. (Reflectance precision may better than 0.10/0, but data accuracy is needed for thickness accuracy.) The ellipsometric sensitivity to a similar change in thin film thickness is shown in Figure 3. As typical ellipsometers can accurately measure 'P and A to better than 0.02° and 0.1° respectively, iUs clear that film thickness changes down to the subAscale can easily be resolved with"this technique.

O.OOOOL-.--------,--.----~====:::c==:;-J

f -0.0002

~ -0.0004

.5

~ -0.0006

" G -0.0008

-O.OO1~==-----'---::400==-~--::600==-~--::600==-----L--:-::1000·

Wavelength (nm)

Figure 2. Calculated change in reflectivity for a O.lnm thickness change on a IOnm Si02 on Silicon sample.

J

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Optical Metrology / 5

0.065.--------,,--......,.---.--~-.....,....-_,_-..,.___,0.10

0.060II> .().OO g.

III~ 0.055 .si'..., -Exp'!'-E75' .().10 ~.

.5'"" 0.050 -_. Exp6·E 75'

?' Ql 0.045 .().20 lr c:: <D.."" ~ 0.040 l) m.().3O

0.035

0.030 '------'_----'-_~_----'-_~_ __'__ _'_____J .().40 200 400 600 800 1000

Wavelength (nm)

Figure 3. Calculated change in ellipsometric parameters 'P and ~ for a O. lnm thickness change on a IOnm Si02 on Silicon sample.

1.2. What Can Be Determined by VASE?

Many desired material parameters can be extracted by VASE analysis, including layer thickness, surface and/or interfacial roughness, and optical constants. The ellipsometric 'l' and ~ data measured on a bulk sample can be directly inverted into the 'pseudooptical' constants of the material, assuming that surface oxide and/or TOughness effects are negligible (this transfonn is given by Equation 2, in which '<I>' is the angle of incidence, and 'p' is the complex ellipsometric ratio defined in Equation 1). In addition, VASE is also sensitive to gradients in material properties vs. depth in the film, optical anisotropy, and any physical parameter that depends on the material optical constants (such as crystallinity, alloy composition, and temperature). A full optical and microstructure analysis of real materials, including multi-layered structures, requires use of regression analysis, as will be explained in a following section.

1.3. Instrumentation Basics

Figure 4 shows the block diagram layout of a rotating analyzer spectroscopic ellipsometer (RAE). Light from an arc lamp passes through a monochromator, and a narrow spectral band of collimated light then passes through a polarizer, reflects at oblique angle off the sample under study, passes through a second, rotating polarizer (analyzer) and enters a detector. The angle of incidence in this ellipsometer is computer controlled, and is generally in the range of 500 to 800

, depending on sample. Other ellipsometer configurations (shown in Figure 5) are the Rotating Polarizer (RPE), Rotating Compensator (RCE), and Polarization Modulation (PME). The predominant configuration in the early history ofellipsometry was the Null Ellipsometer. In recent years, however, the rotating element, or modulation-based ellipsometers have become more popular13

.

I

II


rotBling analyzerand pho\Odode de_ ~ ;

nzer

/colrnating lens

Figure 4. Block diagram ofa rotating analyzer spectroscopic ellipsometer.

Rotating Analyzer Ellipsometer (RAE)r--'--......;..----,_I Polarizer I- ISample 1_

, Analyzer .

(continuously rotating) •

(l)e -

Rotating Polarizer Ellipsometer (RPE)

Polarizer I I I ( . I taUng') - Sample - Analyzercontinuous y ro I----••

5 C/)1:

Rotating Compensator Ellipsometer (RCE) ~ -I Polarizer I Compensator +1 Sam Ie '-I Anal er 1_ CD

(continuously rotating) PI' ~ yz ff :3' Phase Modulation Ellipsometer (PME)

_I Polarizer I-I Modulator I-I Sample I-I Analyzer 1~

Null Ellipsometer (NE)

-I Polarizer I-I Compensator I-I Sample r-I Analyzer 1Figure 5. Block diagram of various ellipsometer configurations.

Each ellipsometer configuration has different features and merits. With null ellipsometers, the azimuth of each optical element is rotated to extinguish beam intensity at the detector. Traditionally null ellipsometry data acquisition is slow, involving manual adjustments. Also, it is difficult to make spectroscopic measurements, thus for years laser sources were used. One positive attribute is that null ellipsometers are accurate, and there are low systematic errors.

Polarization Modulation Ellipsometers can operate at very high modulation rates, 50kHz, and thus have the potential for very rapid data acquisition provided the probe beam is intense enough (e.g. a laser) to achieve a reasonable signal-to-noise figure. In a scanning wavelength spectroscopic configuration acquisition rates are usually limited by the comparative low signal strength ofa broad-band source and by monochromator slewing speed. Because the typical PME modulator is not inherently spectroscopic (e.g. drive voltage adjusted for each wavelength) and the modulation rate is typically very high, PME type systems are not well suited to simultaneous measurements at multiple wavelengths using an array based detector. Overall, spectroscopic PME


systems are difficult to construct and calibrate, require very stable modulators are required for high accuracy, and are noisy when 'f' is near 0° or 45° (depending the particular instrument configuration).

Rotating Polarizer or Rotating Analyzer Ellipsometers (RPE or RAE) can be highly accurate and are easy to construct. However, they are less sensitive to a when a is near 0° or 180°, and secondly, the acquisition speed is theoretically limited by the rotating element (IS-50Hz is typical). However, source intensity typically limits acquisition speed to about 1 second per measurement. The RPE configuration places a static (typically adjustable) polarizer after the sample. It is therefore immune to polarization sensitivity effects in the detector, however, the RPE system is sensitive to residual polarization in the source beam. Because monochromators tend to produce partially polarized light, in the RPE configuration, the monochromator almost always comes after the sample and "white light" (full spectrum of source) illwninates the sample, which sometimes results in solarization of the optical elements and the measurement beam can modify photosensitive samples. Conversely, the RAE system, with its static polarizer before the sample, is not affected by residual source polarization but may require calibration of detector polarization sensitivity for highest accuracy. In the RAE system, the monochromator is almost always before the input polarizer and only one wavelength at a time propagates through the system

The Rotating Compensator Ellipsometer (RCE) configuration has advantages over the previous configurations in that it uses two static polarizers which eliminate sensitivity to both residual source polarization and detector polarization sensitivity. Furthermore, the RCE measures 'f' and a over their full ranges with almost equal accuracy. The primary hurdle to RCE systems is designing the compensating element to be close enough to ideal over an acceptable spectral range. The maximum speed is similar to RPE and RAE style systems, but the RCE configuration is compatible with array based detectors for truly parallel spectroscopic measurement. The RCE configuration is discussed in more detail in the companion paper.

Other optical configurations have been used, but those described above are the main ones used today. Specifications of major instrument types can be obtained from manufacturer's product literature or from published research papers of instruments developed in universities. This is not the place to give details of all the possibilities, however much ellipsometry is now done spectroscopically, sometimes at a fixed angle of incidence, but often at variable angles, with manual or automated control of angle of incidence. The commercially available spectral range covers 150 nm to 33 !olIn, and somewhat wider ranges have been used in academic research. Also, spectroscopy is done using monochromators, diode or CCD arrays, or Fourier transform methods. The other general configuration choice is between in situ (on a process chamber) and ex situ (on table-top). Some instruments can perform intensity transmittance and reflectance measurements, as well as reflection or transmission ellipsometry. Both horizontal and vertical sample orientations are available. For complex anisotropic materials, automated sample rotation stages have been used. Cryostat sample chambers have also been adapted to allow VASE measurements as a function of temperature, typically from 4K to well above room temperature.

,,,., '''·r·'·'' " -----"I·~ -

1

r ..


1.4. Data Analysis Tbeory

Ellipsometry does not directly measure film thicknesses or optical constants, it measures 'I' and!!.. To extract useful information about a sample, it is necessary to perform a model dependent analysis of the ellipsometric 'I' and !!. data. Figure 6 outlines this process.

Model structure: consists of layers of specified thicknessesoptical properties: each layer has optical constants

1 1

!Layer#n

J ;;

Layer #2 ~Layer Thicknesses

Layer #1 Layer Optical Constants

Substrate :~: : ~~~~'::tro~=~~nt ~ • can~IeX dielectric constant

\ \ /' "-\

Model Generated Data ....2-- l Experimental Data use the model structure and L------ f:.~ Fit -" VASE data acqUIred by

optical properties to cak:ulate ,---- compare generated \ ellipsometer system predicted data and experimental data, )

(formulas used in calculation: \ adjust model parameters or any optical data acquired , by spectrophotometer. etcSnelrs law, Fresnel equations,

thin film interference expression) '-. to rrin,mlZ8 difference / \, ,I

~---...-..,."""

Figure 6, Flowchart of VASE Data analysis procedure.

First, data are acquired covering the desired spectral range and angles of incidence. A model for the optical structure of the sample is then constructed. For example, this may include a substrate and a single film on top, or substrate plus film with roughness on top, or more complex multilayer structures. In the example section below, we will show the analysis of quite complex materials systems.

Second, the Fresnel equations along with the assumed model are used to predict the expected 'I' and !!. data for the wavelength and angles of incidence chosen. Figure 7 shows light propagating from the ambient media into a simple system where the material is a bulk solid, or has asingle film on a substrate). Analytic algebraic expressions can be written for predicting 'I' and !!. as functions of optical constants and layer thickness. Optical constants ('n' and 'k') describe how light propagates through a given material. The algebra of calculating 'I' and !!. will not be presented here, but can be found in standard references. 1


Sample Nanna!

Ambic:nl, no

(a)

(b)

Figure 7. (a) Reflection oflight at material interfaces, and (b) multiple reflections within a film, which result in thin fllrn interference effects.

In the case of more complex materials systems, the algebra becomes tedious, and analytical expressions are not usually derived. Rather a matrix multiplication procedure is followed in which each layer and boundary of the structure is represented by a matrix, and a computer is used to do the matrix multiplication, yielding predicted ellipsometric data for a multilayer structure.

The third part of the process described in Figure 6 is to compare the actual measured '¥ and ~ with the predictions of the model based on Fresnel equations, assuming values of the optical constants and thicknesses. While the forward calculation, simulating measurements from a specific model, is straightforward, the inverse problem of determining what the sample parameters were that produced the actual experimental results is a more difficult problem. An obvious, but often tricky, feature of all modelbased data analysis procedures is in picking the model to use and deciding what parameters to try and determine from the analysis. The analysis procedure is usually called data fitting because the adjustable model parameters are varied to find the best fit of the generated data to the actual experimental data. The most common fit parameters are thicknesses and optical constants. In some cases, good optical constants are available in published tables. In other cases ellipsometric analysis can be used to determine both optical constants and thicknesses, as well as other parameters of the system.

Various fitting algorithms have been tried, but by far the most commonly used is the Marquardt-Levenberg algorithm. Again, this will not be described here, as it is quite involved, and is well documented elsewherel4

. The object is to quickly determine the model which exhibits the minimum difference (BEST FIT) between the measured and

10 / Critical Reviews Vol. CRn

calculated '¥ and Ii. values. The (Root) Mean Squared Error (MSE) is used to quantify the difference between the experimental and predicted data. A smaller MSE implies a better model fit to the data. The MSE can be nonnalized by the standard deviations on the experimental data, so noisy points are weighted less heavily. The MSE function commonly used15 is given by Equation 3. Minimizing the MSE (or Fitting the Data) by iterative non-linear regression is illustrated in Figure 10, which shows that convergence for a system with one, or just a few variables is quite rapid.

(3)

Iterative Fit to Experimental Data by varying the Thickness (

110r----.-..,...-......----,r--........--r--..----,-........--, ,-..... -·Initial guess, 1=16oA

: -.....'-~.----·1st iteration, 1=218.4Ai -..... - - 2nd ~eration, 1=237.2A100 : '.. .. --Final iteration, 1=234.68A i ~perimental Data.........

. ---..r-...: ..........--....

, ......IDelta ....' ..... in degrees - .....- ' ... ....., ......

... --it

70'--......._ ......._oL-.......J'--......._...L.-_.L...-......._ .......----l

300 400 500 600 700 800 Wawlenglh in nm !

Figure 8. The Levenberg-Marquardt non-linear regression algorithm converges ivery quickly for most analyses,

Ii

Such regression analysis requires the correct model to achieve good fits to the ;

experimental SE data. If the model does not adequately represent the true sample ;

structure, then good agreement between experiment and theory (such as seen in Figure i

It

8) is not found, and the model needs to be refonnulated. For most materials and structures good optical models can be found, and the process works marvelously. Typically, the simplest model is first assumed, and then successively more complex models are tried until an excellent data fit is achieved. The model must be complex

~ -~

I enough to adequately model all of the structure in the data. As well, there should also be enough information content in the data to uniquely determine aU model parameters. tThat is, the danger in making the model more complex is that parameters become I . correlated, in which case multiple sets of parameters will give the same good MSE fit. Parameter correlation (and how to reduce it) will be discussed in detail in a subsequent \ section of the paper. Also in a later section we illustrate a few of the many cases in which ellipsometric analysis works extremely well. All examples in this article are from real experimental VASE data. I,

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II

\

__


1.5. Classic Example of VASE Analysis: SiOl on Si

A classic sample which is often characterized by ellipsometry consists of an Si02 film on a Si substrate. In the example below, the Si02 film thickness and index of refraction is extracted from the analysis of VASE data. To model the mild dispersion in index of refraction. a Cauchy formula (Equation 4) is used to calculate the Si02 refractive index as a function of wavelength. The model fit parameters for this analysis were the thickness of the Si~ film, and the 3 Cauchy parameters A, B, and C. After 5 iterations, the regression algorithm converged to the near perfect data fits shown in Figure 9, and final parameter values of: Thickness=3537A, A=1.44, B=4.22 x lO-3, C=1.89xlO-5 (the

fit MSE = 2.25). The resulting Si~ optical constants are also shown in Figure 10.

B C n(A.) =A + A.2 + A.4 ' k(A.) =a (4)

Gen. and Exp. Data, after 5th (final) L-M Iteration 100,-~----,-~---r-~---r-~---r--r----,--~---,

-ModeIF~

.... ExpE35° --Exp E 75°

80

~ 60 Cl Ql

"'0 .5 40·iii ll.

20

0 0.0 5.0 6.0

(a)

Gen. and Exp. Data, after 5th (final) L-M Iteration 400,-~-,-~-,-~-.-~-,-~-.-~----,

1.0 2~ 3~ 4~

Energy in eV

300

~ 2'"'0200 .5 ~ Ql 0 100

(b)

Figure 9. Experimental and Model Fit VASE data from a Si02 on Silicon sample. Note the near perfect data fits; on this scale the solid Model Fit curves lie directly on top of the dashed Experimental curves.

O,-::-~----,-L-~_L-~----,-L-~_-"-:---~_-"-:------'-

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Energy in eV


Cauchy Optical Constants for Si02 Film 1.56.----r-.----r---..,r---r----.r---r---.--r---.--r----.

:c: 1.54

~1.52 .= l!!1.50 '0 ~1.48 E

1.46

1.44L;:-.........----;l:::--.........-::'":::--"---=-=---'''---:L::-----'-----;:l:-..........--= 0.0 1.0 2.0 3.0 4.0 5.0 6.0

Energy in eV

Figure 10. Si02 optical constants detennined from the VASE data analysis, parameterized by the Cauchy dispersion fonnula.

2. IMPORTANT CONSIDERATIONS FOR VASE ANALYSIS

2.1 Initial Guesses for Parameter Values

Figure 11 illustrates an important consideration in analyzing VASE data: if the initial guess for a parameter value (thickness in the present case) is too far from the actual value, the regression algorithm can land on a secondary minimum in the MSE, thus yielding an erroneous value for the parameter. In Figure 11, there are at least three MSE minima shown, but only the 'global minimwn' gives the correct thickness. To ensure that the true 'global' minimum MSE is found, the regression algorithm can be started with a wide range of initial parameter values (some commercial software does this 'global searching' automatically). Fit convergence to the same final parameter values with different initial values is also a good test of the 'uniqueness' of the fit (the related problem of parameter correlation is discussed later).

MSE

Thickness

Figure 11. Illustration of Secondary MSE Minima.

.

Optical Metrology / 13 I 2.2. Building an Appropriate Optical Model

To extract accurate material properties from VASE analysis, it is very important to build an appropriate optical model which has enough flexibility to accurately fit the experimental data. As an example, consider the VASE data shown in Fig. 12 which was acquired on a bulk Hgl-xCdxTe sample. The goal of the VASE analysis was to accurately detennine the alloy fraction 'x', which was nominally 0.21 for this sample (a composition-parameterized optical constant database was used for detennine the alloy fraction, the details of which are not important here). The resulting fit parameters from the first analysis (shown in Figure 12) in which an ideal bulk optical model (i.e. no surface overiayer) was used are: MSE=48.9 and x=0.147. As the MSE value was unacceptably high, and the fit was noticeably poor, another more complex optical model was tried. In this second model, a surface roughness layer was added to the bulk Hg1_xCdxTe substrate. Surface roughness is optically modeled by a layer with optical constants derived from a 50-50% mixture of air (void) and the substrate optical constants (using the Bruggeman effective medium approximation). The fit results for this model are shown in Figure 13, and the resulting fit parameters were: MSE=3.92, x=.222, and surface roughness thickness=18.9A. By adding a single fit parameter to the analysis (surface rouglmess), the MSE was reduced by an order of magnitude, and the resulting alloy fraction was in much better agreement with the nominal value. In this example, the more complicated 'surface roughness' optical model is easily justified, and in fact, the surface roughness model must be used to obtain reliable results in the parameter of interest (alloy composition in this case). As a sidenote, VASEdetermined roughness values have also been corroborated by other techniques such as AFM20

.

HgCdTe Data Fit, Simple Bulk Model 35.----~-...._---.----~-...._------,

HgCdTe Data Fit, Simple Bulk Model160,..-_----=....._----,------,------,

o'=-~-~-~~o--~-"'::_-~_=' 1.0 2.0 3.0 •.0 5.0

Energy in.V

30

; 25

t20 .5

:. 15

10

-ModetFlt ···--EJpE70"' --·ElIPE 7S- - EIi'PE 80"'

150

~~ "",. [120 --.' 3 90

/-:J:;=~==~ .5.. 'I 60 Q

30

Energy in eV

-IrlllodiIlFit .-.- El¢lE 10" ---ElIPE 15- • ElI;IE8O"'

Figure 12. VASE data fits for a Hg1_xCdxTe sample, analyzed by a simple bulk model; note the poor agreement between the solid Model Fit curves and the dashed Experimental curves.

5.0•.0

_MocMIFit .--- EllpE 10__ EllpE7S

- • EllpESO

3.02.0

HgCdTe Data Fit, SurfaCil Roughness Model 150

120

;

" 903 .5

i 60 Q

30

0 5.0 1.0

-~FII

····-EIi'P E to---EIi'PE1S· - - El¢l eso-

5'=-~--=--_='=_-~____='=-~-~-~-,J 1.0 2.0 3.0 •.0

HgCdTe Data Fit, Surface Roughness Model35.--------."_---.-__--,.----_.e..----.--_---,

10

30

·25

1320 .5

~ 15

Energy in eV Energy in eV

Figure 13. Excellent VASE data fits on a bulk Hg1.xCdxTe sample with surface roughness included in the optical model.


2.3. Parameter Sensitivity and Correlation

Parameter sensitivity is simply a measure of how much the experimental data would be expected to change for a given change in the parameter. It is obvious to note that having parameter sensitivity greater than the accuracy level of the measurement is a necessary prerequisite to determining that parameter from a data fit, and that the potential accuracy with which the parameter can be determined increases with increasing sensitivity. However, that potential accuracy will be reduced or eliminated if correlation with other parameter(s) exists.

Parameter correlation is a condition of the data fitting process which arises if the sensitivity of two or more parameters singly, or in combination, exhibit the same spectral signature. It is not limited to ellipsometric analysis, but is a general feature of any model-dependent fitting process. What this means is that even if a good fit is obtained with sensitivity to all fit parameters, not all the parameters will necessarily have been uniquely determined. Correlation is important to understand, and is often not sufficiently considered because it does not affect the ability to fit the experimental data, but it does place a limit on the infonnation available from an ellipsometric data analysis. Two-parameter correlation information is a natural output of most fitting algoritluns.14

One technique to deal with correlation is to simplify the model to reduce unnecessary fit parameters. The previous section demonstrated that the optical model needs to be sufficiently complex to fit the data. There are however a limitless set of sample models with increasing complexity which would also fit the data, so some limits on complexity are needed. Generally, the simplest model which fits the data is probably best. Simplest meaning, for example, that existing optical constants are preferred over fitting new ones, that interface roughness should be ignored unless necessary, and so forth. Each additional level of complexity needs to produce an improved fit, or the complexity can not be proved necessary. (Ofcourse, a more complex model can never truly be excluded as the correct physical model.) Sometimes including an additional physical constraint such as rigorously enforcing the Kramers-Kronig relation for a set of optical constants can break the correlation. Additional data, including non-ellipsometric data (multi-data-type analysis, as in the following example) and data from different samples (multi-sample analysis), might be added to the fitting process to change the spectral sensitivity signatures for the pai:ameters, thus breaking the correlation. (The follow-on companion paper discusses some of these advanced techniques in more detail.) In other cases, it may be possible to redefine the fit parameters in the model to make the parameters more orthogonal. For example, it may be more informative to make an index difference between films (l1n =n2 • nJ> and the average index (o.ve =Y:z(n2 + nl» the fit parameters instead of n2 and nl directly. Also, consider whether the parameters which are correlated are really of primary interest, and if not, then it is reasonable to ignore the correlation. The mere existence ofcorrelation among the fitting parameters does not invalidate the procedure, it just limits the amount of unique infonnation that can be properly extracted.

The following example demonstrates a case of parameter correlation when VASE data alone is available and then shows how the addition of intensity transmittance data breaks the correlation. Consider the analysis of VASE data acquired from a silver film

Optical Metrology I 15

on glass sample, in which it is desired to simultaneously determine the silver layer thickness and optical constants. The problem is that identical data fits over a range of silver film thicknesses from 330 - 430A can be obtained. Depending on the assumed thickness, the silver optical constants 'n' and 'k' shift to compensate while yielding the same good fit. That is, the silver film thickness and optical constants are correlated parameters, and neither correct thicknesses nor correct optical constants can be detennined from VASE data alone. (See Fig. 14)

45 Thin Silver Film on Glass, Ellipsometric Data Fit 180 Thin Silver Film on Glass, Ellipsometric Data F~ , j!35

-tr.lod8IFil1Io ·····ExpE&S4~30 ---EJpE TO

.E - - EJpE7S·

:25 20

15 0.0 1.0 2.0 3.0

Energy i1 eV(a)

\

l~ V

4.0 5.0 Energy in eV

150 _WodeIFII ·····ExpE 65--·EJpE 10" . ~ ExpE1S·

g,::-o~----:-,';o-.o ~---;:2';o-.0 ~-----;3f;:.0~-4:':.O'-------='U

Thin Film Silver Optical Constants vs. Thickness 1.8 14

121.5 m-T=330A,n:c ---.·T=380A, n 10 g.c 1.2 ~ - - T=430A, n !1.'i;1 -T=330A,k ci"

i 'i

g 8 ::J.- -. T=380A, k

0.9 " - - .T=430A, k 0 ~" 6'0 ~ :!I

nill 0.6 (D''t:I " 4 3-= 0.3 ~~~" oC2".~:--

..... -. --. ---~ ..

0.0 0 0.0 1.0 2.0 3.0 4.0 5.0

Energy in eV (b)

Figure 14. (a) Equivalent VASE data fits obtained over a range of assumed thickness for a silver film on glass sample. (b) Optical constants for the silver film, extracted over a range of layer thicknesses.

To de-correlate the silver film thickness and optical constants, spectroscopic transmission data from the sample was combined with the VASE data, and regressed simultaneously!7. Only a single, unique silver thickness can fit both the eUipsometric and transmission data. as shown by Figure 15. As a result of the combined VASE and transmission analysis, the silver film thickness was determined to be 341.7Awith a 7.4A surface roughness layer, and unique silver optical constants were simultaneously extracted. Addition of transmission data not only de-correlated the model parameters, it also provided enough extra information to determine surface roughness, that is, it enabled the use of a more complex optical model.

16 I Critical Reviews Vol. CRn

5.04.01.0

-Best Fit Thickness = 342A ----.Thickness Fixed @ 330A --'Thickness Fixed @ 380A - - Thickness Fixed @ 430A ----. Experimental Data

0.8

0.6

c 0·iii 0.4II)·e II) c e! 0.2I

0.0 0.0 2.0 3.0

Energy in eV

Figure 15. Experimental and model generated transmission data for thin silver fIlm on glass sample, illustrating the unique determination of film thickness.

Transmission Data on Thin Silver Film

Thus an important part of making VASE measurements is to identify the angles and wavelengths at which the data is most sensitive to the parameters of interest. This can be done by simulations, such a!i that shown in Figure 16. In general, the regions of sensitivity can be highly parameter-dependent, for example, some parameters may have high sensitivity at 65°, while others may be more sensitive to data at 75° (and likewise for various wavelength ranges). To achieve acceptable sensitivity to multiple parameters, Variable Angle Spectroscopic Ellipsometric (VASE) measurements, performed at an appropriately chosen range of angles, are often required.

Figure 16 shows the sensitivity in the ellipsometric Ii. parameter to a 0.1 om change in a thin oxide thickness. Note that the maximum sensitivity to the measurement of thickness is just above and just below 75° angle of incidence for wavelengths greater than about 600 DID. (At shorter wavelengths, the high sensitivity moves to slightly higher angles of incidence.) High sensitivity occurs near the Brewster angle], which is defined in Figure 17; this generally corresponds to Ii. ~ 90° for samples with very thin, or no, overlayers.

2.4. Maximizing Sensitivity: Optimum Angle of Incidence

""..

I

__


0.30 l3 0.20 ~ 0.10 ~ 0.00.

"lJ -0.10 !ii;i;l"".'.',< .. ' .S -0.20 <l -0.30 to -0.40

200

\'')70 ~e'(\ce

~\'(\C; j)S'9\e 0

Figure 16. Sensitivity in the ellipsometric ~ parameter to a O.lnm change in Si02 1ayer thickness vs. Wavelength and Angle of Incidence.

Generated Data for Si Substrate at 633nm

0.8 -p-palarized_tv ..... &1'CIOrtzed_tv

:f O .6

~ ~ 0.4

r-~~

0.2

10 20 30 40 50 60 70 80 90 Angle of Incidence (0)(a)

Generated Data for Si Substrate at 633nm 50,---,..--,--r----r--.--..-.,...-.,...-.-.......-.--r-....--....--...-..-..--. 210

=:c::-:-~_ _ _ . 180 40

150

~30 [>

120 or ~ -c

-'i' ••••. <1

90 ceil cc

.5 20 3

60 m

10 30

0

0 -30 0 10 20 30 40 50 60 90

(b) Angle of Incidence (0)

Figure 17. Model generated (a) reflectivity and (b) ellipsometric data vs. angle of incidence for a Silicon substrate at 633nm. The Brewster angle is dermed as the angle where the ppolarized reflectivity and'P are minimized and &0=90°, which is near 76° in this case.


3. TYPICAL VASE EXAMPLES FOR INDUSTRIAL APPLICATIONS

3.1 Semiconductor Industry

3.1.1. ONOPO I Si Stacks

A common material system in the Si-based semiconductor industry with important metrology needs consists of a thin-film stack of oxide on nitride on oxide on polysilicon on oxide on crystalline silicon: ONOPO I Si. A VASE measurement can determine all 5 layer thicknesses, as well as the poly-Si optical constants. Example VASE data and analysis are given in Figure 18. Notice that VASE data are acquired and fit at four angles of incidence. The optical constants of poly-Silicon depend strongly on crystallinity, which in turn depends on process conditions (Figure 19).

5 Si02 12.73 nm 4 Si3N4 10.49 nm 3 Si02 17.65 nm 2 Poly-Si 262.2 nm 1 Si02 8.838 nm o Si Substrate 2mm(a)

Generated and Experimental Generated and Experimental 80

-M0<»4FII: -.- •. EJp E 6S·

80 --·EJr;lE7Q

: 1

-·EJpE75" --EJpESO

40

~

il20

0 200 400 800 eoo '000

W.-.gm(IWn)(b)

Figure 18. Optical model (a) and VASE data fits (b) from a ONOPO/Si stack.

&o:O------;400::-------:600=-~--=8OO=--~----::',000 W.-.gm(IWn)

1.0L...---'------'-_"----'---'-_-'----..L.-----'_--'------'-_'---'---'-----' 200 300 400 500 600 700 800 900

Wavelength in nm

Figure 19. Index of Refraction ofPoly-Si as a Function of Crystallinity.


3.1.2. Optical Constants of Photoresist

Ellipsometers are used regularly in the optical characterization new photoresists, and for process control of photoresists on the production line. In Figure 20, the optical constants for a typical photoresist are shown23

, both before and after 'bleaching' (i.e., 'exposing' the resist by UV light), which induces large changes in the optical properties of the resist. To prevent exposure of the photoresist by the measurement beam, it was extremely important to have the monochromator placed before the sample in the VASE system. Another photoresist example (Figure 21) involves a multilayer of photoresist with an antireflective coating (ARC) beneath it. Both layer thicknesses can be extracted from the VASE data, but only by including UV data in the analysis, as this spectral region exhibits optical contrast between two materials.

AZ~200 Refractive Index

1.80 -l.lr'CIIa:I'I8d,n .• _- 8lNcnecl,n

~ 15 1.75 'iii 1.70

~ 1.65

i1.80

AZ"6200 Refractive Index 0.050r-_-,-__,-_--,.-_--r-_---,

?< 0.040

1i0 0301.

u § 0.020

~ ;1j 0.010

1.5~ 400 600 800 1000 1200 0.OOO200'-=--~~"-----c800,!>,-~~800-:---""1000l,-,----...,-,!1200·

WwveIenglh (Ml) Wa~h (Ml)

Figure 20. Optical constants of photoresist detemtined by VASE measurements, before and after bleaching (by exposure to UV light).

j:: 2.

.Q"1; 1.

6117.9A 1 i-linefIR0:HilJ 31fJl.7A o SlicmsJSJae 1nm

eo ~ i5 1.

11(a) '" -= 1.

~ ···..··Organic ARC ;, A ·--···i-line resist :{~ jl:It \. \

f \i·.~, ! \ i ~.~",,"";"'~-i"V" ., ·-v·...c..

i V

1.20~-='20±-:O~40±-:O,......"60±-:O,......,,60~O,......,,1000='=...,.12::':OO,,,....,.1'""400='c1c='600'="1:c='800· (b) WaYelength (nm)

Generated and Experimental Generated and Experimental 100

. SO

l60 ~ E. 40

'" 20

0 0

(C)

180

lSO

.,20 tso c ~ 80

30

01800 0 1800

Figure 21. Multilayer photoresist on anti-reflective coating (ARC) example: (a) optical model, (b) optical properties of the resist and ARC fUms (note the optical contrast in the UV spectral range), and (c) VASE data fits.

r


3.1.3 Compound Semiconductors: AlsGat.sAs Multilayer Structure

The thicknesses and compositions ofcomplex compound semiconductor structures can I,also be determined by VASE measurements. Figure 22 shows an example in which

II

VASE unambiguously determined the surface oxide thickness, three layer compositions, and eight layer thicknesses. Note that some of the layer thicknesses and compositions were coupled together (via the definition of 2 and 3 period superlattices in the optical model) in the analysis to reduce parameter correlation. Due to the in-run reproducibility of the deposition technique used to fabricate the sample (MBE in this case), this assumption is readily justified. Ellipsometric data at multiple angles (three in this case) helped to extract the many thicknesses and alloy ratios with high precision and accuracy. The uniqueness of the fit was demonstrated by the convergence of the regression analysis to the same final values over a wide range of initial parameter guesses.

9 gaas-ox 19.892 A

8 gaas 3348.1 7 algaas x=O.365 (coupled to 5) 995.59 6 gaas 849.29 5 algaas x=O.365 995.59 A 4 gaas 852.89 3 algaas x=0.274 866.51

2 gaas 843.32 A 1 algaas x=O.168 742.48 A

(a) 0 gaas 1 mm

J2

J3

~.

J3

Generated and Experimental Data Generated and Experimental Data400'.-_--,-__,-----_--..-_-.-_--.JO,.........---r--...--------,-----,---------,

-ModeIFII -Mode/Fll .••• E.>;IE65··-··~E65·

--'~E70'" - - EJOE 70· _. ~E75· -. ~E15·

l. 10

(b)

Figure 22. VASE analysis of a AlxGa•.xAs multilayer structure: (a) optical model, and (b) data fits. Note the near perfect fits to all of the structure in the data, which were essential to simultaneously and accurately extract all the layer thicknesses and compositions.

-Io4odflIFlt ---- EJooTO'"

0.8


3.2. Optical Coatings Industry

3.2.1. Five Layer Hi-Lo Index Stack

In this example (Figure 23), 5 layer thicknesses and 3 sets of optical constants in a 'HiLo' index multilayer stack were simultaneously detennined. To achieve this result, multiple data types were included in the analysis: VASE data acquired from front side and back side of the sample (both of which included the reflections from the opposite side of the transparent substrate), and spectroscopic transmission acquired at nonna! incidence. The Cauchy dispersion formula was used to model the dispersion in index of refraction for the three materials in the stack. From a simultaneous analysis of all the data, unambiguous results for this multilayer structure were obtained: five layer thicknesses (plus a surface roughness thickness), and the indices of refraction for three materials.

Hi-Lo Stack Optical Constants

-SUl5ll'''2.7 •••• 'Hi' indn: rnlJIeruf

l: -- \.O·I~rnlJIeri.1.7rm - . 1J9.4rm -6 2.4

188.2rm tlj3l.6rm i 21

3l1.7mi ~ 1.8 121.2rm f- 1.5r-===~-==-=_=_=_=_=_=_====~~(a)

l1oo=-~500=-~-::600=---:::700=-"'--:800=-~--=900=-~-:-::1000 Wo-.glh(rwn)

VASE Data, Hi-Lo Stack, Front and Back data. 180 VASE Data, Hi-Lo Stack, Front and Back data.

(b)

1~'::-"'--:500=-~-::600~--:::700'::-"'--:BOO=-~-::9OO'::-"----:-:!looo'

wavetengthinrm(c) 1000

.50

Transmission, Hi-Lo Stack 1.0,-~-r---,---_--..,..._----,,-_-r-_-,

500 BOO 700 BOO 900 1000

(d)

Figure 23. Analysis of a Slayer Hi-Lo index optical stack using multiple data types: (a) best fit optical model. (b) extracted indices of refraction for the three constituent materials in the stack, (c) ellipsometric data fits. in which the 'Eb' curves correspond to ellipsometric data acquired on the front side of the sample (including the 'backside' reflection), and the 'Er' curves correspond to ellipsometric data acquired in the 'reverse' direction. i.e. from the backside of the sample (including the 'frontside' reflection), and (d) fit to normal incidence transmission data.

WJivetenglh in rm

r (


3.2.2. Variations in Optical Coating Index vs. Depth

In this example, the initial requirement was to simply detennine the film thickness and index of refraction for a ShN4 coating on glass. However, the first modeling attempt of the VASE data (shown in Figure 24a) was not successful, as evidenced by the poor data fits and high MSE value. A second model, which included a surface roughness layer, was also tried (Figure 24b), but this optical model did not adequately fit the experimental VASE data either. After extensive trial and error, an optical model was found which provided excellent fits to the data (Figure 24c). This best fit model had an optically less dense 'interfacial' layer embedded in the film, the optical properties of which where modeled by a 50% Bruggeman EMA mixture of the ShN4 film index and void (similar to the optical modeling of surface roughness). After the VASE analysis of this sample, it was learned that the film was deposited in two passes, thus explaining the double layer with embedded interface solution. TIlis example conclusively demonstrates the sensitivity of VASE measurements to non-uniformity (gradients) in film optical properties as a function of depth in the film.

3Or-_Si_·3~N4_F_im.:....,Si_·...,...:..---cCc.:...uchy---'-M~odet__-,Optical Model #1 ........

-lIIDdIt'~ ••• E.,£!II° - fop!!;8:1'"

MSE = 176.6

Cauchy Layer 2896.2 A Glass substrate

Optical Model #2: Add Rouahness '" Si3N4Film,C.uehyl.oyor"lhs.mc.R~.

Surface Roughness 108.34 A Cauchy Layer 2878.1 A 15

10 - .... ,.Glass substrate ····I!IP£'5D" -- E.,ellr

~l:;--~---,.*,,";"----,...=--------;0;800;;----::::100,MSE = 165.7 W.....-.ngctlrrorfl'l(b)

30 Si3N4 Film, Best Fit Model (Roughness & Interface) 180Best Fit oDtical Moifel

4 Surface Roughness 90.742 A

3 Cauchy coupled to #1 1304.8 A

2 'Interface' (50% void) 274.84 A

1 Cauchy Layer 1324.6 A

Glass Substrate

Final MSE = 10.31 (c)

Figure 24. Progression of optical models used to analyze a Si~4 coating on glass sample: (a) simple single film model, (b) single f1lm with surface roughness, and (c) best fit optical model, which included a less dense' interfacial' layer within the film (this was introduced by the twopass deposition of the film).

30

,.. 120& 90 S"

-, 60 i~_FI

----E>p ... E ..• ---E>p"'E'" - ..... n ·····EJpDel.EW --·E>pDobE ....

5

25

Ii


3.3. Data Storage Industry

3.3.1. Diamond-Like Carbon (DLC)

Due to their excellent protective and lubricative properties, diamond-like carbon (DLC) films are commonly applied to hard disk media and read-write heads. DLC fihns are usually made by plasma CVD using a mixture of hydrocarbon gasses, such that a wide range of film mechanical properties can be obtained by adjusting the process conditions. As there is a correlation between variations in the DLC mechanical and optical properties (see Figure 25), VASE is very useful in the monitoring ofDLC processes. The sensitivity of VASE to ultra-thin films is also advantageous when characterizing DLC coatings, which are typically <lOoA (Figure 26).

0.60

240 -OLC1 ~O.50 .... ·OLC2

l!~ 2.30 ---OLC3 -a 0.40 .. 'OLC'

~ 220 ~ 8°·30! 2.10 /o ,.. .......

4 .... ~~, ..•..... .._---------J i 0.202.00 _

~ 0.10-1.90V--0.001·~':::-~--:400~~----;:!500:::---'""eoo':::-~--;;7=00;---7.

-OLC1 .... ·OLC2 ---OLC3

- •. -OLC' , , , ,

-'

I

800 300 '00 500 eoo 700 eoo Wavelength (nm) WINeIer9h (nm)

Figure 25. Variation in diamond-like carbon (DLC) optical constants; these optical constants were extracted from a VASE analysis of four different samples, in which the DLC deposition conditions were systematically varied.

o o

Depostlon Run

Figure 26. Systematic study ofDLC films coated on two different substrates; the high sensitivity of VASE to ultra-thin ftlms enable precise thickness detennination in this application.

Comparison OLC Thicknesses

• SUbstrate /'.1

../_SUbslr8te 12

r ./ / ./"

~ ~ y

/'--

180

160 01)

E 140 g 01) 120 Clc:: c( 100

iii 01) 80GIc:: .¥ 60.s.! .c l '0 0 ...J 20C


3.3.2. Thickness of Thin Magnetic Films

The perfonnance of advanced read heads is critically dependent on the thickness of thin magnetic films. Accurate characterization of such films requires accurate thin film optical constants for the metallic layers of interest, which may differ significantly from the bulk optical constants found in the literature. By performing VASE analysis on a thin magnetic layer deposited on a thick dielectric film, it is possible to simultaneously and accurately extract optical constants of the metallic layer, along with the metal and dielectric film thicknesses. In this analysis, the multiple angles of ellipsometric data provide a change in the optical path length through the layers (this effect is enhanced by the thick underlying dielectric film21

), which breaks the correlation between the thickness and optical constants of the metal film. See Figure 27.

NiFe Optical Constants, Sample 61 3.or-_r-.,.....c...--_....-_--,--'---,-~__,5.0

2 NiFe 32.73 nm

491.05nm

~ 2.7 •.5

.~r· 0 2.1

La

-0

.0_- k

3.5

3.0

'.0

(a) 0 Si substrate t .iJo!;;-----:400=--'---;500::::-~=::800::--'---;:700!;;----:800=-----:!~.5

(b) ~"rwn

Generated and Experimental Data 38

34

i 32 ... .530 'm a.

28

26

(c)

160r-T::_=,,--,.--r--~----,----, ••• - EJrpE6S-

140 -- .... ~[ ---------= = !t20 :....-_~E~~~ == • 100

~ 80

!.:--~_~----=~~~'--:::~~~800~~OOO ~'-o----'--"400~=--~500::--'--=800=-~7~OO:--'----:::800=--'---::"OOO ~inrwn

300

Generated and Experimental Data

Figure 27. Simultaneous thickness and optical constant determination for a thin NiFe layer deposited on a thick Si02 film on Si: (a) optical model, (b) resulting NiFe optical constants, and (c) VASE data fits.

-ModelFII •.• E:.pE so--·ExpEW - . E~e70"'

eoo e50

-ModeIFII ·····e,.,E 50" --·ElcpE 60· • - ElcpE 10



-McdeIFiI ----EJcpE~

---ExpEl50'" - - E41E 70"

40

900 1200 1500 1800 1500 1800

ITO Optical Constants

-BolIomo'"WT1,K -··-·T~oIFikn.k

" .. .....

180

150

i 120

90

80

30


3.4. Flat Panel Display Industry

3.4.1. Indium Tin Oxide (ITO) Films

Indiwn Tin Oxide (ITO) is a transparent electrically conducting film used extensively in the flat panel display industry as a large-area electrode. Optical characterization of ITO films is challenging, as the ITO optical properties are highly dependent on the film deposition and annealing process. Furthermore, significant gradients in the optical constants (vs. depth in the film) are commonly observed in ITO films. A VASE analysis ofa typical ITO sample22 is presented and described in Figure 28. To adequately fit the experimental VASE data and properly characterize the ITO film, a

1.5

.. 1.2 !! It'Ii 09 0

"Ii o.e ~ ~ 03

0.0 300 800 900 1200 1500 1800 300 eoo 900 1200 lS00 1800

(C) WIYltenglh in nm Wave6et9h in 1m

Figure 28. VASE characterization of an ITO film: (a) Data analysis using a single Cauchy film optical model results in poor data fits, even over the limited spectral range sho\\'tl here. (b) A graded-film optical model (using Lorentz oscillators to model the dispersion in the ITO film) results in excellent fits to the VASE data over a wide spectral range. (c) The ITO optical constants at the top and bottom of the fUm are compared in this plot; the amplitude and shape of the free-carrier absorption tail (seen in the ok' plot at the longer wavelengths) is directly related to the electrical conductivity of the film.

complex graded optical model is required.

25

20

115

.S 10 "iI...

5

0 350 400 4SO 500 550 eoo 850

Wa~inrwn(a)

5O,.--~_G.,..e_n_era~ted---,ar--nd_Ex...,..:..pe_ri.,..m_en_ta~1 Data---r_~....,

(b)

"c 2.0 "Ii 'll 1.S

i '!i 1.0

!os 0.0


-MocIelF,t .- •• &PESO"' -- EllpE6IT •• EllpE nr -B"

.5.

.5

WI'IOIeftlIlhinrrn

ITO Optical Constants

-BoII:ornorFlftI,n •• -.- Top 01 FiW11, n


3.4.2. Thin-Film Transistors (TF1) Structures

Thin film transistors (TFI) are important in active matrix liquid crystal display technology. VASE can be used to characterize important TFf layer thicknesses, as shown in Figure 29. By acquiring VASE data into the NIR spectral range, the ability to characterize thicker amorphous Silicon (a-Si) films is greatly enhanced, as a-Si becomes essentially transparent in this spectral range.

4 sio2 22.994 A 3 a-si 1837.3 A 2 si3n4 3315.5 A 1 cr 3700 A 0 1737 glass 1 mm (a)

-Model Fit

eo ~~~~~:: .. ---E>cpE70"! eo --E>cp E 75· t --·E>cpE8O"

.S 40 ~

900 1200 1500 1800 800 900 1200 1500 1800 Wa-.glh (rwn) Wlvelonglh (rwn)(b)

Figure 29. VASE analysis ofa TFT structure: (a) optical model (only the top 3 layers were detennined in this analysis, as the Cr metal layer was optically thick and therefore fixed at its nominal value), and (b) data fits.

"


4. AUTOMATION OF VASE MEASUREMENTS

Most of the preceding VASE examples required a time~onsuming and sometimes subjective process of 'fine-tuning' the optical model to achieve acceptable data fits which accurately characterize the sample properties. However, once an appropriate optical model has been developed, it is very straightforward to apply it to the VASE data analysis of similar samples. In fact, with commercially available software, the complete VASE data acquisition and analysis procedure can be encapsulated into a recipe, such that powerful VASE metrology can be performed with the push of a button. An example of an automated VASE analysis (and reporting of extracted material parameters) is shown in Figure 30.

a-51 Thickness Si02Ja-5i1Si02JGlass

Mean = 5403.469 Min =5181.100 Max = 5468.000 SId Dev =50.054 Uniformity = 0.93

(a)

Top oxide Si02Ja-5i/Si02JGlass

Mean =4581.874 Min = 4339.200 Max = 4802.700 SId Dev = 124.67 Uniformity = 2.72

3 sio2 456.36 nm

2 a-si _ptype 546.81 om

1 sio2 200nm

(b) o 7059 Imm

Figure 30. (a) Unifonnity in layer thicknesses extracted from automated VASE measurements across the surface of a flat panel display, using the optical model shown in (b).

SUMMARY

The ability to accurately acquire and quantitatively analyze VASE data on a wide range of samples was demonstrated. Variable angle spectroscopic ellipsometry is now wellestablished as an important metrology tool in several different industries, and as an important technique for industrial research on new materials and processes.

ACKNOWLEDGMENTS

The authors wish to thank the many sponsors who contributed to the development of the work presented here, including NASA, BMDO, the U.S. Army and Air Force, DARPA, and numerous corporations which supplied samples.


REFERENCES

I. RMA Azzaro, and N.M.Bashara, Ellipsometry and Polarized Light, North Holland Press, Amsterdam 1977, Second edition 1987.

2. RM.A.Azzam, Selected Papers on Ellipsometry, SPIE Milestone Series MS 27, 1991. 3. lDJackson, Classical Electrodynamics, John Wiley & Sons, New York, 1962 4. H. G. Tompkins, and W.A.McGahan, Spectroscopic Ellipsometry and Reflectometry, John

Wiley & Sons, New York, 1999. 5. A Roseler, Infrared Spectroscopic Ellipsometry, Akademie-Verlag, Berlin, 1990. 6. Ellipsometry in the Measurement of Surfaces and Thin Films, ARothen, E.Passaglia,

R.RStromberg, and J.Kruger, NatI.Bur.Std. Misc. Publ. 256, U.S. Government Printing Office, 1964.

7. Proceedings of the Symposium on Recent Developments in Ellipsometry, N.MBashara and AB.Buckman, and AC.Hall,,-North Holland Publishing, Amsterdam, 1969.

8. Ellipsometry, Proceedings of Third International Conference on Ellipsometry, N.MBashara and RM.A. Azzam, eds, North Holland Publishing, Amsterdam, 1976.

9. Ellipsometry and other Optical Methods for Surface and Thin Film Analysis, 1. de Physique, Les Ulis Cedex, FR, 1983.

10. Spectroscopic Ellipsometry, AC.Boccara, C.Pickering, J.Rivory, eds, Elsevier Publishing, Amsterdam, 1993.

11. Spectroscopic Ellipsometry, R W.Collins, D.E.Aspnes, and E.A Irene, Editors, Elsevier Science S.A.,1998 , Lausanne, Switzerland; also appears as Vol. 313-314 Thin Solid Films, Numbers 1-2, 1998, pp 1- 837.

12. G.H. Bu-Abbud, S.A.Alterovitz, N.MBashara, and J.AWoollanl, "Multiple-WavelengthAngle-of-Incidence Ellipsometry: Application to Silicon Nitride-Gallium Arsenide Structures", J.Vac.Sci.Technol. AI, 619 (1983).

13. RW.Collins, "Automatic rotating element ellipsometers: Calibration, Opemtion, and Realtime Applications", Rev.Sci.Instrum. 61, 2029 (1990).

14. W.H.Press, B.P.Flannery, S.A.Teukolsky, and W.T.Vetterling, Numerical Recipes in C, Cambridge University Press, Cambridge, 1988.

IS. G.E.Jellison, Jr. "Spectroscopic ellipsometry data Analysis: Measured Versus Calculated Quantities", Thin Solid Films 313-314, 33 (1998).

16. F.Wooten, Optical Properties ofSolids, Academic press, New York, 1972. 17. C.M.Herzinger, BJohs, W.A.McGahan, and J.AWoollam, "Ellipsometric Determination of

Optical Constants for Silicon and Thermally Grown Silicon Dioxide Via a Multi-sample, Multi-wavelength, Multi-angle Investigation", lAppl.Phys. 83, 3323 (1994).

18. BJohs, W.A.McGahan, and 1.ArWoollam, "Optical Analysis ofComplex Multilayer Structures Using Multiple Data Types", Optical Interference Coatings, SPIE 2253, 107 (1994)

19. C.MHerzinger and BJohs, "Dielectric Function Parametric Model, and Method of Use", U.S. Patent 5,796,983, issued Aug 18, 1998.

20. RW. Collins, I. An, H. Fujiwara, 1. Lee, Y. Lu, J. Koh, and P.I. Rovim, "Advances in multichannel spectroscopic ellipsometry", Thin Solid Films 313-314, 18 (1998).

21. W.A McGahan, B. Johs, and J.A. Woollam, "Techniques for ellipsometric measurement of the thickness and optical constants of thin absorbing films", Thin Solid Films 234, 443 (1993).

22. R.A. Synowicki, "Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants", Thin Solid films 313-314, 394 (1998).

23. RA Synowicki, IN. Hilfiker, RR Dan1mel, C.L. Henderson, "Refractive index measurements of photoresist and antireflective coatings with variable spectroscopic ellipsometry", Proceedings of the SPIE Vol. 3332,384 (1998).

overview of variable angle spectroscopic ellipsometry vase, part 1

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