Evaluation of the Cu atomic
density during sputter deposition
process with optical emission
spectroscopy
Takeo Nakano, Kouji Tanaka
and Shigeru Baba
Dept. of Applied Physics,
Seikei University, Japan1

Outline
Optical Emissions and absorptions
between low-energy levels of Cu neutral Evaluation of copper atomic density
using intensity profiles of 2 emission
lines from CuI Comparison with the atomic density
deduced from a one-particle MonteCarlo simulation
2

Energy levels of Cu neutral
10-1

3.817eV (4p P: g = 4)
8-1

A=9.46x106 (s-1)

A=1.68x10 (s )510.6nm
324.8nm1.389eV (m 2D: g = 6)

Decay Length (m)210-20eV (4s 2S: g = 2)
10-3 1610(Vacuum 59 (2000) 581.)

1017

1018
-3

Cu atomic density (m )In this viewgraph, energy levels used in this study are shown. The line at 0eV isthe ground state of Cu, and there is an excited state at 3.8 eV above the groundstate. The transition from this state to the ground state is permitted, and 324.8nm emission occurs. There is another transition from this state to theintermediate state, which causes 510.6 nm emission.
The transition probabilities of these emissions are also shown. The probability of
324 is about 20 times larger, so this emission occurs more preferably.
We have been observed these two emissions from the copper sputter plasma,and found that the 510 emission becomes relatively stronger when Cu atomic
density is high. For example, high discharge power or high gas pressure cases.
We think that this is due to the absorption of 324 emission by other copper atoms
at ground state in the plasma environment. This self-absorption effect is wellknown to chemists using plasma emission for their quantitative analysis.
The right part of this viewgraph is the relation between the decay length of 324
emission and Cu atomic density. Both axes are in log scale. Decay length isabout 1 centimeters when atomic density is 10^17 per cubic meters, and isinversely proportional to the atomic density.

3

Sputter Plasma
16 Pa

3000
2000
1000
0200300

400

Wavelength (nm)500

Intensity (arb.)

Intensity (arb.)

1.6 Pa

3000
2000
1000
0200

300

400500

Wavelength (nm)

These are the photographs of the sputter plasma we observed. The left is at 1.6Pa, and the right is 16 Pa. You can see remarkable green emission at higher gas
pressure case. The emission spectra of these plasma are given at the bottom.
They are taken at about 1cm above the target.
At 1.6 Pa, 324 emission can be seen clearly, and 510 emission is weak. It
reflects the difference of transition probabilities of these spontaneous emissions.
The purple color of the discharge is derived from Argon lines around 400~450 nm.
At 16 Pa, we can still see the strong 324 emission, but 510 emission is also verystrong. This relative increase of the 510 emission is caused by the absorption of324 emission.

4

OES measurement

We observed the optical emission from the plasma with an equipment shown inthis photograph. There is a quarts viewport of 7 times 5 centimeters, and the
sputter chamber is located at the right side of this photo.
The camera body at the left is a commercially available reflex camera, but thelens is replaced with a quartz plano-convex lens, and the intake of this opticalfiber is placed at the focal point of the lens. The optical system is mounted on
this PC-controlled stage and moves horizontally.

5OES measurement

Optical System with aniris (2.0mm φ) and aplano-convex lensWavelength 185〜525nm(with 1024 channels)
Balanced-magnetron(targetφ5cm）

DC power 50 W



Ar flow-rate 10 sccm



Ar pressure 1.6〜16 Pa

This is a schematic drawing of the measurement. The modified camera moves
automatically as shown in the top view.
With an iris and the plano-convex lens, we can collect the emission from the tube
region. And by sweeping the camera, we obtain the emission profile of theplasma.
The collected emission is lead to the spectrometer by the optical fiber, and thespectrum between 185 and 525 nanometers is recorded with an CCD array of1024 channels.
The sputter plasma was generated by the balanced type magnetron HERE. Cu
target is a disc form and its diameter is 5 centimeters. It is located at thesymmetric axis of the chamber, so we can expect that the plasma is also
axisymmetric.
DC power was 50 watts in this study. Argon flow rate was 10 sccm, and thepressure is changed from 1.6 to 16 pascals.
It was not appeared in the previous photos of plasma, but in actual
measurements, substrate holder was located at 4cm above the target. At thecenter of the holder, thickness monitor is equipped and the deposition rate ofcopper film was recorded during the OES measurement.

6Emission Profile (16Pa)
50

Intensity (arb.)

Intensity(arb.)

150
324nm
510nm

4030

10020
1000500-3123

Radial Position (cm)-2-10123

Lateral Position (cm)Computed Tomography.
(Vacuum 74 (2004) 387.)

This is an example of the emission profile of 324 and 510 emissions at 16 Pa. Itis taken at 1 cm above the target, and the camera was moved parallel to thetarget surface. At this pressure, 510 emission is stronger than the 324.
In case of no absorption, we can apply a computed tomography technique toobtain the radial emission profile. Please note that the system is axisymmetric.
So the line profile from 1 direction is OK to reconstruct the profile. By applying theCT to 510 emission, we can obtain the radial profile like this.
We can expect 324 emission also has the form like this, with the ratio of transition
probabilities. However, it is absorbed as it passes through the sputter plasma
region, the observed intensity profile becomes weak.

7

Evaluation of Cu density:
ConceptLine Profile

Radial ProfileCT×absorption?

A324
A510

k (r )In this cartoon, I would like to explain the concept of the density evaluation.
By the OES measurement, we can obtain the side view line profile of 324 and510 emissions like the ones at the left. Because our chamber is axisymmetric, wecan construct a radial profile by Computed Tomography, if the absorption can beneglected. And we neglect the 510 absorption, and calculate the radial profile.
When the spontaneous emission is dominant, the ratio of the emission profile of324 can be determined from the 510 profile and the ratio of transition probabilities
of both emission. Actually, the transmission function of the measurement system
is also taken into account.
If there is no absorption for 324 also, the side-view line profile is obtained by theline integral of this radial profile and have the profile 20 times larger than the 510
profile. But it is not the case in actual measurements, so we have to consider thedistribution of absorption coefficient. It should be axisymmetric, too.
And from the absorption coefficient, we can evaluate the atomic density of Cu atground state.
In summary, I can say that we are making the absorption measurement using theplasma itself as a light source.

8

Evaluation of Cu density:
Assumptions
Radial emission profile of the 510.6 nm line canbe obtained by the Computed Tomography (noabsorption for 510.6 nm).
 Emission profile I 324(r ) of 324.8 nm line isgiven by the 510.6 profile and the ratio oftransition probabilities of these emissions.
 Absorption coefficient k (r ) for the 324.8 nm
line is determined by the density of Cu atoms atground states.
This slide summarize the assumptions of this method. Actually, we have to say
they may be quite naïve in some cases.

9Evaluation of Cu density:
Effect of the Absorption{lV (t ) = ∫ dl I 324 (r ) exp − ∫ dl 'k (r ' )−∞}

r 2 = t 2 + l 2 , r '2 = t 2 + l '2V (t)
tr

lI(r)

The relation between the radial emission profile, absorption profile, and the sideview line profile is shown in this viewgraph.
This is a plane by which the plasma is cut parallel to the target face, and here weplace an origin on the symmetric axis.
t axis denotes the direction along which the camera moves and takes the lineprofile. And l axis is perpendicular to the t axis. Radial distance r from the centeris given by these two coordinates.
The line profile V has a form of integration. The contribution at l dl is, theemission there, times the exponential of the integration of the absorption
coefficient.
In this case, V and I are known, we should be able to determine k(r) by solving
this inverse problem.

10

Radial profile of the Cu atomic
density
Atomic Density (m-3)

1019

1.6 Pa

4 Pa

8 Pa

16 Pa

1018

1017
0

123 0

123 0

1

23 0

12

3

Radial Position (cm)Unfortunately, at the moment, we have not found an analytical solution of thisinverse problem. So we tried to represent the absorption profile by a splinefunction. And by moving the nodes to reproduce the side-view line profile as wellas possible, we obtained these atomic density profiles.
Actually, if we move every nodes freely, the noise of higher frequency component
appears and some of the results show unreasonable oscillations. So we have to
add one more limitation that the density profile is a decreasing function with r,that is, a node cannot be larger than the inside neighbor.
The resultant density was the order of 10^17 to some 10^18 m^-3, and generally
increased as the argon gas pressure increased.
The order of the density corresponds to the decay length of some centimeters tomillimeters. It is the similar order with the size of our sputter system, and that’s
why the ratio of the intensity changed significantly in our case.

11

One-particle MC Simulation
Monte Carlo simulation of
the sputtered particles
treats the “life” of themthrough:
1. Sputtering ejection
from the target.
2. Collision and scatteringwith gas atoms
3.Deposition on thechamber wall.

Depositionon the wall
collision &scatteirngwith gases
Sputtering

Residualtime Tp
in a cellFrom now on, I’d like talk about the another approach to evaluate theatomic density using one-particle Monte Carlo simulation.
This is a method to chase sputtered particles one by one from they
sputtered from the target, collides and scattered by the ambient gas atoms
until they reach some part of the chamber wall. With trials of some millionsof particles, we can obtain the distribution of arrival flux on the substrate
as well as chamber boundary.

12

One-particle MC simulation (2)(Appl. Surf. Sci. 113/114 (1997) 642.)

Boundary Condition
 Axisymmetric Uniform gas temperature (400K) and pressure Sticking Coefficient at the boundary is unity.
 Ejection of the particles
 Position
proportional to the erosion track depth Energy
Thompson’s formula Anglecosine law
 Scattering with gas atoms
 Thermal motion of gas atom (Maxwellian) Elastic scattering with the Born-Mayer potential( U (r )=A exp(-br ) )The detail of the MC simulation we used is summarized here.
We use an axisymmetric boundary, uniform gas temperature at 400K and uniformgas pressure. Sticking coefficient at the boundary is assumed to be unity.
Ejection of particles is proportional to the erosion track depth measured after theactual sputtering experiment, ejection energy distribution is Thompson’s formula,and angular distribution is the cosine law.
This simulation includes the thermal motion of colliding gas atoms as Maxwellian.
Scattering process is assumed to be elastic, and we used the Born-Mayer type
repulsive potential.

13

Density evaluationby the MC simulation
Split the space into cells
 Count the staying time Tp of Cu atoms ineach cell during the simulation
 Compare the arrival flux of atoms(simulation) with the experimental
deposition rate, and obtain Ts Average atomic number in each cell isgiven by Tp /Ts
Using this one-particle MC simulation, we deduced the atomic density as follows.
Before the simulation, we split the chamber space into cells, and we count andsum up the staying time of trial atoms Tp during the simulation.
At the same time, we compare the arrival flux of atoms by the simulation, with theactual deposition rate at the same place of the chamber. By this, we canelucidate the time Ts of the simulation corresponding to the actual deposition
experiment.
And by dividing Tp by Ts, we can obtain the average number of atoms in eachcell, and we can obtain the density from the cell volume.

14

Atomic density profile of Cu(MC calculation)

And this is the result of the simulation. Target face is here, and this is thesubstrate holder. At the center of it, there is a thickness monitor. The deposition
rate in this case was about 0.8 nm/s at 16 Pa, and 1.5 nm/s at 1.6 Pa.
The color bar is given at the top in log scale, from 10^17~10^20 m^-3.
The position we made the density evaluation by OES is 1 cm above the target soaround here. The value is about 10^17~10^19, similar to the OES values.
You can also see that the higher argon gas pressure is, the higher the Cu atomic
density is. It is also the same tendency with the OES result.

15

Summary
A method is proposed to evaluate the atomic
density profile of copper sputter plasma using
the Optical Emission Spectroscopy.
 The result was agreed with the one obtainedby the one-particle MC simulation in:1017~1018 m-3 of density was obtained.
 The higher the pressure was, the higher the atomic
density became.
The solver of the inverse problem should beimproved.

http://surf.ap.seikei.ac.jp/~nakano/16