THIN FILM ANALYSIS USING

SPECTROMETRY AND ELLIPSOMETRY

 

OBJECTIVE 2:

II.1  Ellipsometry:

     Ellipsometry involves illuminating a sample with an elliptically polarized light source and analyzing the reflected beam with a polarizer and a detector.  Ellipsometry can determine the complex indices of refraction or indices and thicknesses of single or multiple film layers.  Ellipsometry is typically used in the semiconductor industry to analyze thin films, in the optics industry to measure the reflectivity of mirrors, and elsewhere to analyze the properties of thin surface films.

     Schematics of key ellipsometer elements is shown in Figure 15.  A monochromatic light source is linearly polarized by a plane polarizer and traverses a compensator which causes elliptical polarization.  The elliptically polarized light then strikes a sample at an angle of incidence between 60o and 80o.  The resulting reflected wave is sent through another plane polarizer, which is aptly called an analyzer, before entering a detector.  The first polarizer, the compensator and the analyzer can all rotate in order to make measurements.  Usually however, the compensator is held fixed and the polarizer and analyzer are rotated into positions which cause a null at the detector.  A null is caused when the reflected wave is linearly (or plane) polarized and the analyzer aligned with the angle of polarization of the reflected wave.  Therefore, both the polarizer and the analyzer have to rotate to particular angles to produce a null.  Equipment which use this technique are called nulling ellipsometers.   

FIGURE 15:  The component parts of an ellipsometer.

     The two azimuth angles of the polarizer and the analyzer (P and A) required to produce a null, can be measured with high resolution and accuracy with this technique.  It eliminates effects caused by variation in incident beam intensity or detector sensitivity.  The polarizer and analyzer angles needed to produce a null (P and A) are immediately converted into theoretically defined angles:  ψ and Δ, which will be described in the next section.

     The AutoEL-II, used in the cleanroom, is a nulling ellipsometer.  It uses a laser (λ = 632.8 nm) at an incident angle of 70o. Illustrations of the AutoEL-II are shown in Figure 16 and 17, and its specifications are described in Table IV.  Using this equipment is simple.  A wafer is placed on the sample stage.  An autocollimator microscope allows the operator to adjust the stage so that the wafer surface is level and at the proper height.  Adjustments for level were performed prior to each measurement.  After a measurement, the AutoEL-II returns values of ψ and Δ.  These values are then entered into a PC-run program, which will calculate the desired property values.  A list of programs available from Rudolph Research is shown in Table V. 

FIGURE 16:  Auto El Optical Diagram.

FIGURE 17:  Auto El Simplified Block Diagram.

 

II.2  Ellipsometry Theory:

     The reflectivity, ρ, is the ratio of the parallel and perpendicular radiation reflected from a surface:

                                          9

so:

                                       10

where rp and rs are the amplitudes of the reflected wave parallel and perpendicular to the plane of incidence, δp and δs are the phase changes between the incident and reflected waves in the parallel and perpendicular polarization directions, respectively.  Since rp, rs, δp, and δs are related to properties of a surface, such as complex indices and film thickness, the values of ψ and Δ can be used to determine such properties.  The formulas derived to evaluate properties from ψ and Δ are complicated and usually require computer iteration to evaluate. 

     ψ and Δ are functions of the following variables:  the angle of incidence (φ), the wavelength of incident light (λ), the ambient index of refraction (n0), the complex index of refraction of the substrate (or metal) (ns + i*ks), the complex indices of refraction for each thin film (ni + i*ki), and the thicknesses of each thin film layer (di).  (Note:  for transparent thin films, ksi is assumed to be zero and the indices real.)  For a particular ellipsometer set-up the pair of ψ and Δ values returned can be used to determine only two of the variables above, all others must be known.  The pairs of variables typically chosen are the real and imaginary index parts of a bare substrate or the thickness and index of the upper-most thin film layer.  Other pairs are much harder, mathematically, to determine. 

     If the determination of more than two variables is required or if the two variables chosen cannot be determined accurately (for reasons described later), then (an) additional set-up(s) will have to be used to generate (an) additional pair(s).  This can be done by changing the angle of incidence, the wavelength, or the index of refraction of the ambient environment.  If the angle of incidence is changed, the new angle must be located or determined with high accuracy.  An error of even 0.1o will cause unacceptable calculations.  Errors in angle of incidence is generally assured no greater than 0.02o.  Changing the wavelength can be easier with proper equipment. 

     The ambient index of refraction can be changed using a special chamber to submerge the sample in a liquid.  The chamber is designed to allow the light beam to enter and exit the chamber at normal incidence (it is probably also designed to allow for proper alignment of the sample).  Sometimes the liquid used as the ambient can have an index matching the upper-most film, thereby eliminating the influence of the that film from the calculations.

     As mentioned before and shown in Equation 9 for ρ, ψ and Δ can be related to surface properties.  Often this is done by separating a complex equation into real and imaginary part, resulting in two equations.  These equations can be solved by iteration or graphically.  Figure 18 shows a plot of a series of ψ vs. Δ curves for graphical analysis.  Each curve has a different constant value of n.  Positions along a single curve, determines values of δ, represented by the tick marks and numbers (0 to 180o).  δ is represented by the following equation:

                                   11

Once δ is determined from the plot, d can calculated, using the value of nf from the curve.  

     It can be seen from Figure 18 that there are certain values of δ (from about 0 to 40 and 140 to 180) where n cannot be determined with confidence.  This has to do with the fact that when the path length through a film is equal to a whole number of wavelengths the ellipsometer data is the same as if there where no film at all.  Therefore, any particular sample could potentially have properties which yield ellipsometry analysis with large errors.   

 

II.3  NanoSpec:  

FIGURE 19:  The Schwarzchild reflection objective lens used in the 210UV System is completely free of chromatic aberration.  Because the system uses an achromatic lens, the operator can focus both the visible and UV light sources simultaneously.

     The NanoSpec, in the cleanroom, looks like a microscope.  One places a wafer onto its stage and focuses on the wafer surface.  The NanoSpec then performs as the spectrophotometer does by reflecting a varying monochromatic light source off of the wafer surface.  A schematic of the optical elements in the NanoSpec is shown in Figure 19.  The NanoSpec is so similar to the spectrophotometer described in the last chapter, that only the key differences will be described here:

     1.  The NanoSpec analyses a small spot (from 50 to 6.5 μm) rather the 79 mm2 (0.12 inch2) area of the Cary 5.  This allows the NanoSpec, like the ellipsometer, to focus on a particular film on an integrated circuit.  This is very useful, and probably more accurate than the Cary 5 if the film thickness is varying.

     2.  The NanoSpec is designed to be linked to a computer and many programs are available to evaluate various properties.  This makes the NanoSpec extremely powerful.  It can evaluate numerous film and film combinations.  It can analyze impurities, by determining the absorption characteristics of transparent films.  This ability is not due to the NanoSpec having better hardware than the Cary 5, but the Cary 5 apparently does not have software to generate such information, and certainly have not developed the software for specially adapted reflectometry fixture presented in the last chapter. 

     The software for the NanoSpec is also advanced.  For example, Figure 20 shows how the NanoSpec determines thin film thicknesses--by separating out shapes of the spectrum-generated curves, rather than looking maxima or minima as was done in the last chapter.  The NanoSpec stresses the use of ultraviolet light for very thin film (less than 10 nm) and for causing certain  multi-film conditions to be reduced to a single film analysis because the polysilicon is opaque in the ultraviolet.   

FIGURE 20:  Reflectance versus Wavelength for Nitride on Silicon with UV light.

     3.  While the fixture designed for the Cary 5 has a precise incidence angle of 30o, the NanoSpec does not list a value for incidence angle.  Furthermore, observing the schematic in Figure 19, shows that the incident light has been focused onto a sample by a reflecting lens.  This indicates that the angle of incidence may have a range associated with it and also that this range will change when the magnification (or spot size) is changed (a NanoSpec capability).  It is unknown how the NanoSpec programming deals with this. 

     4.  The NanoSpec has a wavelength range of 200 to 900 nm, this is a wide enough range for the type of measurements required in the semiconductor industry and a wider range than many similar pieces of equipment.  However, the Cary 5 has a wider wavelength range of 175 to 3300 nanometers. 

     5. The NanoSpec scans quicker than the Cary 5, which is even slower because it has to change filters at 800 nanometers.  The NanoSpec sends all radiation from two light sources on to the sample and scans monochromatic frequencies before reaching the detector.  Where the Cary 5 separates the light to be monochromatic before contacting the sample.

 

II.4  Comparison of Data:

     Data was taken by the ellipsometer and the NanoSpec at several points on each wafer, while the Cary 5 spectrophotometer took data at only one large area per wafer, due to the time the spectrophotometer took.  Twelve data points were taken by the ellipsometer and the NanoSpec on each wafer.  Figure 21 shows how these points are identified.  Each wafer is denoted by a number (1,2,3...), each quadrant on a wafer is denoted by a roman numeral, and the three points taken in each quadrant are denoted by A,B or C (an example being a data point taken at 2-IV-A).  This many data points were taken to indicate how the film thickness varied over the wafer, knowledge which can be helpful in analyzing the area that the Cary 5 set-up covers.  

FIGURE 21:  Location of Measurement Points on Wafers.  (Wafers were measured at three points in each quadrant, divided by the X.)  Each wafer is identified by a single digit (i.e. 1, 2, 3...) each quadrant is denoted by a roman numeral, and each point is given a letter (A, B, or C).

     At each data point the ellipsometer returned a pair of ψ and Δ values, which were typed into a near-by computer.  The computer program returned a value for the index of refraction of the film and a series of possible values for thickness of the film.  Multiple thickness values were returned because of the cyclical nature of the phase change due to optical path difference.  Therefore, a value for the thickness was chosen by referring the value obtain from the Dektak, a rough profilometer-like device discussed in Chapter II. 

     The NanoSpec feed the information it generated directly into a computer.  The computer then returned a value for thickness.  Note that the NanoSpec does not return several thicknesses.  This is because the NanoSpec, as well as the spectrophotometer data obtained from the Cary 5, contain enough information to determine the order.  For example, two consecutive inflection points will determine the order for n*d when looking at a spectrometer trace.  The NanoSpec may use a more advanced method. 

     One glaring flaw in the NanoSpec data was that the thickness value was determined assuming a certain index for each type of film.  For instance, the thickness for silica is determined assuming a value of n=1.45.  The operation manual instructs an experimenter to use the following formula if the experimenter has reason to believe that the index varies from 1.45:

                                             12

where nold and Thold are the index and the resulting thickness used and obtained by the NanoSpec software; nnew and Thnew are the new index the experimenter has determined and the final thickness evaluated.

     The last equation suggested by NanoSpec calls the quality of its programming math into question.  The equation and the fact that the program does not allow a new index to be input suggests that the software does not take proper account of the dispersive nature of n nor the influence of n on the phase change due to reflection off the substrate. 

     Table VI shows the data obtained for two wafers with a silicon dioxide film and Table VII for one wafer with a silicon nitride film.  The data used in the program which processed the ellipsometer values are:  λ = 632.8 nm, φ = 70o, and the real and imaginary values for silicon are:  ns = 3.858 and ks = 0.018.  Such values were not given for by the NanoSpec.  The nnew used in Equation 12 to determine Thnew was set at the value of n returned by the ellipsometer.  Therefore, the accuracy of the NanoSpec is linked to the accuracy of the ellipsometer.

     Table VI shows that thickness values from the NanoSpec is always 2 to 5% lower than values from the ellipsometer.    

TABLE VI 

    Data Points Taken on Two Silicon Dioxide Coated Wafers

 

Ellipso

meter

 

   Nano

Spec

Data

Point

Number

Delta

(Δ)

deg.

Psi

(ψ)

deg.

Index

of film

(n)

thick-

ness (d) A

(d) A

for

n=1.45

(d) A

for

nellip

1-IV-A

 276.20

  31.84

  1.426

 10,990

 10,520

10,697

1-IV-B

 276.16

  31.84

  1.425

 11,000

 10,520

10,705

1-IV-C

 277.24

  33.24

  1.429

 10,898

 10,520

10,675

1-III-A

 277.72

  34.12

  1.431

 10,853

 10,682

10,824

1-III-B

 278.08

  45.12

  1.443

 10,483

 10,275

10,325

1-III-C

 278.80

  41.08

  1.440

 10,590

 10,638

10,712

1-II-A

 262.96

  22.84

  1.409

 11,512

 10,868

11,184

1-II-B

 258.56

  21.00

  1.407

 11,608

 10,957

11,291

1-II-C

 249.36

  18.12

  1.376

 12,200

 11,045

11,639

1-I-A

 265.44

  24.04

  1.410

 11,462

 10,762

11,067

1-I-B

 252.44

  19.00

  1.387

 11,984

 11,061

11,563

1-I-C

 265.40

  24.00

  1.411

 11,449

 10,822

11,121

4-IV-A

 271.88

  27.68

  1.422

 11,163

 10,687

10,897

4-IV-B

 276.12

  31.56

  1.428

 10,969

 10,552

10,715

4-IV-C

 278.28

  36.60

  1.430

 10,797

 10,459

10,605

4-III-A

 267.92

  25.24

  1.417

 11,316

 10,769

11,013

4-III-B

 277.32

  33.24

  1.431

 10,879

 10,539

10,679

4-III-C

 256.04

  20.12

  1.401

 11,737

 10,946

11,329

4-II-A

 258.52

  20.92

  1.413

 11,527

 10,942

11,229

4-11-B

 251.56

  18.68

  1.392

 11,926

 11,004

11,463

4-II-C

 247.32

  17.52

  1.376

 12,210

 10,959

11,549

4-I-A

 264.96

  23.80

  1.410

 11,474

 10,876

11,184

4-I-B

 252.16

  18.76

  1.406

 11,707

 11,000

11,344

4-I-C

 260.76

  21.96

  1.403

 11,644

 10,796

11,158

  

                           TABLE VII

    Data Points Taken on a Wafer Coated with Silicon Nitride

 

Ellipso

meter

 

   Nano

Spec

Data

Point

Number

Delta

(Δ)

deg.

Psi

(ψ)

deg.

Index

of film

(n)

thick-

ness (d) A

(d) A

for

n=2.00

(d) A

for

nellip

5-IV-A

  32.76

  38.20

  1.996

   770

   779

  781

5-IV-B

  32.36

  38.36

  1.995

   772

   775

  777

5-IV-C

  28.84

  39.20

  1.998

   788

   788

  789

5-III-A

  30.44

  38.84

  1.997

   782

   789

  790

5-III-B

  26.76

  39.76

  1.997

   797

   810

  811

5-III-C

  25.64

  39.92

  1.999

   800

   808

  808

5-II-A

  30.64

  38.88

  1.995

   781

   789

  791

5-II-B

  32.64

  32.64

  1.994

   772

   774

  776

5-II-C

  24.24

  40.36

  1.997

   808

  

 

This could be due to the correction for n as described above, but then data would be more consistently different.  Another reason why there may be difference is the fact that it was impossible to take the ellipsometer and NanoSpec data on the exact same point, just in a close vicinity to one another.  This is also why repeatability test were not performed.  To conduct a reasonable repeatability test one would have to move the wafer.  But there was no way to realign test beam with the previous test point. 

     The wide difference between the ellipsometry and NanoSpec data calls into question the claims that the equipment makers state.  The AutoEL-II claims the ellipsometer is accurate to "a few angstroms" up to a film thickness of 125,000 A.  The NanoSpec makers claim accuracy of �5 A for thicknesses between 500 and 50,000 A (500 and 40,000 A for a nitride).  The error claims for the NanoSpec are evaluated as �3σ "based upon measurement of the same spot 50 times in succession."  This may be true, but the reason why this statement is mis-leading, and why there was no repeatability study done, is due to operator error.  Each time another data point is taken the operator has to focus or align the sample.  These are subjective decisions of the operator and the effectiveness of the equipment that allows the operator to do the adjustments. 

     Another strange fact is that, what is called "accuracy" here has been stated as "precision" by the equipment makers.  However, they speak of "the precision" as if it were accuracy.  For instance, one does not have to take the standard deviation of 50 points to determine precision, one simply looks at the last digit in the read-out.

     It can be seen that the silicon dioxide grown by wet oxidation varies much more in both index and thickness, that does the deposited nitride.  This verifies that the wet oxidation process produces a low quality (low index) and less than uniform oxide.

     Table VIII compares the ellipsometer, the NanoSpec, and the Cary 5 data determined in Chapter II.  The data points compared were taken at point 1-IV-A for the silica and at point 5-III-A for the nitride.  But the data taken on the Cary 5 was larger in area (79 mm2) which extended into the area between points B and C, as shown in Figure 21.  Again the ellipsometer determined the value of n and that value was used in with both the Cary 5 and the NanoSpec.

     The three techniques have generated different values.  This may be somewhat due to the fact that exactly the same areas were not used with each.  However, accuracy claims made by the AutoEL-II  and the NanoSpec have to   be challenged.  Especially since the last Chapter showed that the thickness for silica determined by the reflectometer set-up had an accuracy of �0.5% (or �54A).  The values from the other equipment is far outside this error.

                           TABLE VIII

 Data for Silica and Nitride Films Determined by Three Methods

Film

 

Silica

 

 

Nitride

 

Point

 

1-IV-A

 

 

5-III-A

 

Value

   λ

   n

 (d)  A

   λ

   n

 (d) A

AutoEL-II

 632.8

 1.426

 10,990

 632.8

 1.997

  782

Cary 5

 643

 1.426

 10,820

 612

 1.998

  766

NanoSpec

   ?

 1.426

 10,697

   ?

 1.997

  790

 

II.5  Comparison of Techniques:

     Comparison of the three equipment set-up and techniques has already been discussed in the course of descriptions.  However, final points will be made in the form of comparison Table IX:

  

                           TABLE IX

           Comparison of the Use of the Cary 5 set-up,

                the AutoEL-II, and the NanoSpec

#

Equipment and Technique

Cary 5

AutoEL

NanoSp

1

Returns both n and d

  No

  Yes

  No

2

Order determined

  Yes

  No

  Yes

3

Dispersive equation determined

  Yes

  No

  ?

4

Thinnest film measurable

  ?

~700 A

  20 A

5

Complex index--substrate w/o film

  No

  Yes

  No

6

Speed at which data is taken

  Slow

  Fast

  Fast

7

Area of light beam for data point

 Large

  Spot

  Spot

8

Polysilicon made opaque by UV

  Yes

  No

  Yes

   

     The eight comparison points listed in Table IX will be expounded upon:

     1.  Returns both n and d:  This is a crucial feature which only the ellipsometer possesses.  If both are not returned the index has to be assumed to determine d and this can cause error so large that the technology of the equipment is lost on the effort.

     2.  Order Determined:  If the order is not determined then separate equipment is required to obtain a "ball park" value.  Furthermore, if a profilometer-type device serves in this capacity, then a test wafer is required to be included with the batch for this test.  Therefore, this test can be very expensive and time consuming in a production scenario.

     3.  Dispersive Equation Determined:  The ellipsometer determines n at only one wavelength.  However, as shown in Chapter II, the spectrophotometer can determine the dispersive nature of n.  The equation can be useful for predicting n at other wavelengths.

     4.  Thinnest film measurable:  As devices become smaller and faster, thinner films are required.  Currently, 16 megabit memory chips require oxide film thicknesses of 100 A or less.  Such thin films cannot be measured by the ellipsometer, unless its Helium-Neon laser is replaced with a laser with an ultra-violet wavelength.  The AutoEl-II manual claims that it is able to measure very thin films, but this is doubtful.  If Equation 11 for δ is considered along with Figure 18, it can be seen that for δ to be above about 40o, d should be above about 700 A (for n=1.426).  Below d = 700 A, the value of n rapidly decreases in accuracy.  Again it should be noted that the ellisometer may return inaccurate values at any thickness range.

     5.  Complex index of a substrate without a film:  The ellipsometer can determine the complex index of a bare substrate.  Not only can this have importance in production, but the complex index values are required for the determination of transparent film properties by all three methods.  Chapter II showed that more attention should be given to the determination of the complex index of silicon, especially in the ultraviolet range.  (Chapter II showed by baseline analysis a large difference between the complex index for the experimental wafers and that from literature for ultraviolet radiation.)  This calls into question the claims that the NanoSpec can measure films as thin as 20 A, by using the ultraviolet region.  The NanoSpec would have to be certain of the complex index to do this.  No matter what, the complex index will be a source of error if not determined for a substrate with the particular conductivity of the test substrate.

     6.  Speed at which data can be taken:  The AutoEl-II and the NanoSpec are rapid and therefore useful in a production environment.  With the Cary 5 set-up, a baseline and a sample trace must be taken, and each takes some time.

     7.  Area of light beam for data point:  The AutoEL-II and the NanoSpec, both measure over small spot sizes.  This is superior to the Cary 5's large rectangular area for three reasons.  The spot can test a small area, as on a wafer with integrated circuits built on it, the spot can scan over an area and determine how the film varies, and the area is not advantageous as a averaging device because measuring an area in which the film varies will only serve to distort the values not average them.

     8.  Polysilicon made opaque by UV:  It was mentioned before, that it can be very advantageous to reduce a multi-layer film scenario to a single film on polysilicon scenario by using ultraviolet light for the measurement.  The ellipsometer, with its current laser does not have this capability.  Therefore, the expensive practice of using a test wafer in certain procedures would have to be used.

 

II.6  Polarized Spectrophotometer:

     It was mentioned at the end of Chapter II that both n and d values could be obtained from the spectrophotometer set-up if traces were taken in the two polarization directions.  One way to obtain this result with the existing set-up would be to design another fixture, similar to the one designed, but this one would set on its side (turned 90o from the first).  A mock example of such a plot is shown in Figure 22.  If a vertical (constant λ) line is drawn anywhere on the plot, the line will cross the values of Rp and Rs for a particular wavelength.  This is enough to determine ψ by:

                                                13

FIGURE 22:  Parallel and Perpendicular Reflection versus Wavelength.

 Also each maximum or minimum for one curve is adjacent to a maximum or minimum for the other polarized component curve, with the same value of m (the order integer).  Therefore, Δ can be evaluated by:

                                   14

 where λp and λs are the wavelength at the inflection points for parallel and perpendicular components respectively.  Since Δ is small for silicon, it can be assumed that n remains constant from λp and λs in Equation 14. 

     Therefore, this system behaves as a ellipsometer by returning ψ and Δ.  But it returns a pair of these values at several points allowing much more capabilities, such as determining all the values in multiple films.  Furthermore, n*d values are determined at each inflection point.

 

Go to Abstract & Intro.         Go to Objective #1                Go to Objective # 3                Go to Objective # 4

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