Koster G., Rijnders G. (Eds.) In situ Characterization of Thin Film Growth

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102 In situ characterization of thin ﬁlm growth

To understand how optical measurements characterize thin lm properties,

consider the interaction of light with a single-layer coating as shown in Fig.

5.2. When light arrives at the surface, a portion is reected and the remaining

light enters the thin lm. Light traveling through the lm will recombine with

the light reected from the lm surface, but with delayed phase and different

amplitude for both p- and s-components. Thus, the light measured by SE

(the recombined light) will depend on the thickness and optical constants

of the lm, represented by either complex refractive index (Fujiwara, 2007,

p. 347):

= n + ik [5.2]

where n is the index of refraction and k is the extinction coefcient, or by

complex dielectric function (Fujiwara, 2007, p. 347):

= e

+ ie

[5.3]

The two are related by:

= n

[5.4]

Thus, SE data contain information about the surface, thin lm, and substrate

because the detected light includes multiple components which have traveled

various paths in the sample.

SE data may also exhibit coherent interference effects from multiple

light beams. For thick, transparent lms the data will oscillate when plotted

against wavelength because the wavelength inuences whether the phase

of recombined light is aligned for constructive or destructive interference.

Figure 5.3 shows measured SE spectra for two transparent thin lms. The

thicker layer (350 nm) exhibits additional oscillations in the measured spectra

ambient

ﬁlm

substrate

5.2 A light beam interacts with a thin ﬁlm structure. At each

interface, a portion of light is reﬂected and transmitted. The

ellipsometer measures the polarization state of light from regions

and interfaces in the sample. With planar interfaces and coherent

light, interference can occur.

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103In situ spectroscopic ellipsometry (SE)

compared with the thinner layer (100 nm) because of the longer optical path

length.

SE spectra also reveal the optical constants of the lm. Index of refraction

(n) describes the phase velocity for light traveling within the material and

determines angle of refraction at each interface described by Snell’s Law

(Hecht, 1987, p. 84). Extinction coefcient (k) determines how quickly light

is absorbed as it travels through a material. In addition, the optical constants

determine how much light is reected at each interface.

5.2.2 Data analysis

While SE measurements are sensitive to both optical constants and lm

thickness, they are not a direct measurement. In a few simplied cases, the

equations can be inverted to calculate optical constants or lm thickness from

measured Y, D data (Azzam and Bashara, 1977, pp. 315–317). Fortunately,

there are many cases where the sample properties are over-determined with

hundreds or thousands of measured data points to determine a few unknown

thin lm properties. SE characterization is generally subject to the ‘inverse

problem’ where the measurement can be predicted from a sample description,

but sample properties cannot be directly calculated from the measured data.

350 nm ﬁlm

100 nm ﬁlm

0 300 600 900 1200 1500 1800

Wavelength (nm)

Psi (degrees)

5.3 SE measurements from two transparent thin ﬁlms on silicon

substrate – one 350 nm and the other 100 nm thick. The number of

data oscillations is a result of ﬁlm thickness-dependent coherent light

interference.

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104 In situ characterization of thin ﬁlm growth

Regression analysis is commonly used to determine the best-t results

considering all acquired data simultaneously. figure 5.4 summarizes the

process of ellipsometry analysis.

The rst step is to collect SE data on the sample. The ellipsometer shines

light with known polarization onto the sample and detects the reected or

transmitted polarization state. This measurement requires the following

basic ellipsometer components: light source, polarization generator, sample,

polarization analyzer, and detector (Fig. 5.5). The light source and polarization

generator are often combined into the ‘source head’, which directs a light beam

of known polarization onto the sample surface at oblique angle of incidence.

5.4 Data analysis ﬂowchart for spectroscopic ellipsometry

measurements. Regression analysis helps determine unknown

parameters of the optical model such as ﬁlm thickness and optical

constants.

1 Measurement

Wavelength

3 Analysis

2 Model

5 Results

Wavelength

Exp Y

Exp D

Psi (Y)

Delta (D)

Exp

Model

Index, n

d = 749 nm

ﬁlm

= ?

substrate

= known

d = ?

4 Adjust

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105In situ spectroscopic ellipsometry (SE)

The light reects or transmits into the ‘receiver head’ (often consisting of both

polarization analyzer and detector), which determines the new polarization

state. In addition to these basic components, a spectroscopic ellipsometer

must be equipped to scan and detect at various wavelengths. Many different

SE designs are available, with details available in the literature (Johs et al.,

1999; Collins, et al., 2005a, 2005b; Jellison and Modine, 2005; Fujiwara,

2007).

In step 2, the sample is described using a planar optical model, which

represents layer thicknesses and optical constants for each material. The

model-generated response is calculated based on Fresnel equations (Hecht,

1987, pp. 94–96). For unknown sample properties, initial estimates are also

given at this step. reference optical constant values for many materials

are available in the literature (Palik, 1998a, 1998b, 1998c; Adachi, 1999).

However, SE measurements are often sensitive to optical constant values in

the third or fourth decimal place, so any deviation between published values

and the measured material will produce errors in the model calculations. For

this reason, reference optical constants often serve only as initial estimates;

the model optical constants are then allowed to vary to ‘best match’ the

measured Y,D data.

In Step 3, regression analysis is used. The unknown model parameters are

varied to improve the match between model-generated curves and collected

data by minimizing differences between the curves, as described by a

comparator function, such as mean squared error (MSE). The model can be

modied, as shown in Step 4 of Fig. 5.4, in a further attempt to improve the

match between model predicted data and measurement. As a general rule,

the best sample description is often the one produced by the simplest model

that matches data adequately; still, it is important to ensure a unique result

for each unknown sample property.

Source

head

Light

source

Polarization

generator

Polarization

analyzer

Detector

Receiver

head

Sample

5.5 Basic ellipsometer components: light source, polarization

generator, sample, polarization analyzer, and detector. In some

ellipsometer designs, the source and receiver heads may combine

multiple components.

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106 In situ characterization of thin ﬁlm growth

The best model provides information about the unknown sample properties,

as shown in Step 5. SE measurements are commonly used to determine thin

lm thickness and optical constants. However, many additional material

properties can be determined through their effect on material optical constants:

crystallinity, conductivity, composition, porosity, strain, and surface roughness.

Figure 5.6 shows the optical constants for a series of Si

1–x

thin lms

with varying composition (x). As the composition changes, so do the critical

points associated with electronic transition energies, which in turn causes

a shift in Si

1–x

optical constants. The composition can be deduced from

SE by measuring this variability in the optical constants of a Si

1–x

layer.

for additional information regarding ellipsometry analysis procedures, see

Fujiwara (2007), Jellison (2005), and Tompkins and McGahan (1999).

5.2.3 In situ SE

In addition to the fundamental advantages of SE (non-destructive, non-

invasive, precise, accurate, and versatile), in situ SE has the ability to monitor

a process of thin lm deposition or etch as it occurs. Modern SE systems can

perform precise measurements within a second or less, so most processes

can be monitored in real time. In addition, in situ SE measurements can be

made directly on the sample of interest, rather than a witness sample or at

a separate location within a process chamber.

x = 0.0

x = 0.2

x = 0.4

x = 0.6

x = 1.0

0 300 600 900 1200 1500 1800

Wavelength (nm)

Index of refraction (n)Extinction coefﬁcient (k)

7.0

6.0

5.0

4.0

3.0

2.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

5.6 Optical constants for Si

1–x

with different compositions, x.

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107In situ spectroscopic ellipsometry (SE)

Because modern SE optical heads have a small footprint, they can be

conveniently integrated with optical ports in large chambers commonly

used for deposition and etch of thin lms. Figure 5.7 shows an atomic layer

deposition (ALD) chamber incorporating in situ SE as a real-time monitor for

thin lm growth. For processes that require only small space, such as liquid

ow-cells or variable-temperature stages, the process itself may be integrated

directly into standard ex situ SE hardware. Figure 5.8 shows a 100 ml liquid

ow-cell mounted on a conventional SE system. This cell combines in situ

SE with a quartz crystal microbalance with dissipation monitoring (QCM-D)

which allows real-time study of surface adsorption from a liquid solution.

Figure 5.9 shows an in situ SE measurement during growth of a dielectric

lm on silicon. For the purpose of illustration, data for only four wavelengths

are plotted against time; actually, data at hundreds of wavelengths are collected

for each measurement time. In situ Se can collect data during various stages

Spectroscopic

ellipsometer

‘source head’

Spectroscopic

ellipsometer

‘receiver head’

5.7 Spectroscopic ellipsometer mounted to an atomic layer

deposition (ALD) process chamber (photo courtesy of Oxford

Instruments).

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108 In situ characterization of thin ﬁlm growth

5.8 Quartz crystal microbalance with dissipation monitoring (QCM-D)

with liquid ﬂow-cell and optical windows mounted to a spectroscopic

ellipsometer for combined in situ SE and QCM-D characterization

(photo courtesy of Biolin Scientiﬁc/Q-Sense).

0 2 4 6 8 10

Time (min)

Psi (degrees)

I II III

Psi – 250 nm

Psi – 440 nm

Psi – 630 nm

Psi –1000 nm

Model

5.9 In situ SE measurements during growth of a transparent layer.

Three designated regions provide information (I) before, (II) during,

and (III) after processing.

Spectroscopic

ellipsometer

‘source head’

Quartz crystal microbalance

with dissipation monitoring

(QCM-D) with liquid ﬂow-

cell and optical windows

Spectroscopic

ellipsometer

‘receiver head’

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109In situ spectroscopic ellipsometry (SE)

of processing, charting unknown sample properties as they emerge. The

substrate surface is rst monitored before the lm is deposited (Region I).

Measurements before processing provide a ‘baseline’ of substrate optical

constants, surface quality and measurement angle of incidence. This can be

critical information for sensitive measurements, such as protein adsorption on

the surface of only a few nanometers thick. For the silicon substrate in Fig.

5.9, the pre-process region is used to determine native oxide thickness and

angle of incidence, two values that are not always well known a priori.

As a lm grows, each dynamic measurement point captures the interaction

with a different thickness and data continue to change with time (Region II).

if ex situ measurements were used to collect the same information, hundreds

of samples with different lm thickness would be required. By contrast, in situ

SE measurements do not interrupt growth, and provide continuously evolving

information about growth rate, lm thickness, and optical constants.

in region iii, the process is complete and the sample structure is measured

to determine nal lm thickness and optical constants. This region also

shows the sample before aging, or in the case of ultra-high vacuum (UHV)

processes, before surface oxidation. In-line SE typically measures region I

or III, but the real power of in situ SE is the wealth of information made

available during the process.

5.3 In situ spectroscopic ellipsometry (SE)

characterization

In situ SE measurements are sensitive to a wide variety of material properties

and process conditions. They can also yield the dynamics of these properties

during the process. This section reviews common in situ Se measurements, as

well as basic analysis procedures that enable in situ Se characterization.

5.3.1 Growth and etch rate

When in situ SE measurements are collected during thin lm growth or

etch, the lm thickness changes from measurement to measurement. The

unknown sample properties are determined at each measurement time-

point, when adequate information is available. In many cases, to simplify

data analysis, a constant growth/etch rate is assumed over a specic time

period. Data analysis is further simplied if the layer optical constants are

stable and do not vary with thickness. Figure 5.10 shows lm thickness

measured during sputter deposition of a dielectric layer on metal. Dashed

lines indicate the beginning and end of deposition. At 13 minutes, sputtering

power was doubled to increase lm growth rate. In this experiment, thickness

was determined separately for each measured time-point and growth rate

calculated for each interval.

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110 In situ characterization of thin ﬁlm growth

As another example, Kokkoris et al. (2008) applied in situ Se during plasma

etch. Figure 5.11 shows lm thickness and etch rate for a poly(methacrylate)

(PMMA) thin lm. They found the etch rate decrease as the PMMA layer

reaches a thickness equal to the surface roughness. The ‘corner point’, where

etch rate starts to decrease, allowed the authors to estimate surface roughness,

0 10 20 30 40 50

Time (min)

Film thickness (nm)

350

300

250

200

150

100

Growth rate

= 0.68 Å/s

Sputter power

doubled

Growth rate

= 1.78 Å/s

5.10 Film thickness of a dielectric layer measured by in situ SE

during sputter deposition. The growth rate increases at 13 minutes,

as the sputter power is doubled.

0.0 0.5 1.0 1.5 2.0

Etching time (min)

Remaining thickness (nm)

Etching rate (nm/min)

350

300

250

200

150

100

300

250

200

150

100

= 32.5 nm

Corner point

5.11 Film thickness and etch rate for a PMMA thin ﬁlm during plasma

etch process. At the corner point, which occurred with 32.5 nm

remaining ﬁlm, the etch rate decreases signiﬁcantly (reprinted from

Kokkoris et al., Plasma Processes and Polymers, vol. 5, pp. 825–833,

2008 with permission from Wiley-VCH).

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111In situ spectroscopic ellipsometry (SE)

which was conrmed by atomic force microscopy (AFM) measurements of

the same surfaces.

Maynard et al. (1998) demonstrated end-point detection with in situ Se

during plasma etch of patterned thin lms. They etched optically absorbing

layers such as TiN and poly-Si, which limited thickness determination to thin

layers where light can penetrate the lm. Metals absorb light at wavelengths

across most of the typical spectrum, which prevents thickness measurements

for thick layers (typically > 50 nm). Thin layers can be measured, but require

special techniques to determine both optical constants and thickness (Hilker

et al., 2008a).

An experiment by Pribil et al. (2004) combined in situ transmission Se

and transmitted intensity measurements to determine the optical constants

for thin metal layers deposited on glass with magnetron sputtering up to a

thickness of 35 nm. The additional information available from simultaneous

SE and T proved essential as metal optical constants did vary with thickness.

Figure 5.12 shows the evolution of thickness-dependent optical constants

for cobalt and titanium lms (Pribil et al. 2004).

Wide spectral ranges available with modern SE systems help expand

characterization for materials which remain semi-transparent in a portion of

the measured spectrum. Consider the in situ Se measurements in fig. 5.13

for deposition of an AlGaAs thin lm on GaAs. Data at three wavelengths

are graphed versus time to demonstrate the effect of lm absorption on in

situ SE data. Data oscillations correspond to increasing lm thickness, where

coherent interference still occurs between the surface reection and light

traveling through the thin lm. The oscillations are quickly dampened at

350 nm, where the AlGaAs lm is strongly absorbing. Data at both 475 nm

and 600 nm continue to oscillate throughout the growth because at these

wavelengths the AlGaAs remains semi-transparent.

5.3.2 Virtual interface approaches

Standard Se analysis requires the model response is calculated from every

layer in the stack. Errors from underlying lms propagate through the entire

structure. A virtual interface (VI) can approximate the underlying structure

as a single interface, rather than tracking the entire sample history. The VI is

placed towards the surface, as shown in Fig. 5.14. Here the VI intersects the

third layer and growth is modeled on this interface with no knowledge retained

for the underlying structure. There are various methods for calculating a VI

(Aspnes, 1993, 1996; Urban and Tabet, 1993; Kouznetsov et al., 2002; Johs,

2004), but the mathematical details are beyond the scope of this chapter.

The common pseudo-substrate approximation (CPA) described by Aspnes

(1993, 1996) converts the measurement at this point into a ‘pseudo-substrate’.

The main shortcoming of the CPA is that it requires underlying materials

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