NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Density Profiles in Sputtered 

Molybdenum Thin Films and 

Their Effects on Sodium 

Diffusion in Cu(InxGa1-x)Se2

Photovoltaics

Preprint

Jian Li 

National Renewable Energy Laboratory and University 

of Michigan

Stephen Glynn, Lorelle Mansfield, Matthew 

Young, Yanfa Yan, Miguel Contreras, Rommel 

Noufi, and Dean Levi 

National Renewable Energy Laboratory

Fred Lewis Terry Jr.

University of Michigan

Presented at the 37th IEEE Photovoltaic Specialists Conference 

(PVSC 37)

Seattle, Washington

June 19-24, 2011

Conference Paper

NREL/CP-5200-50701

July 2011
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1 

DENSITY PROFILES IN SPUTTERED MOLYBDENUM THIN FILMS AND THEIR 

EFFECTS ON SODIUM DIFFUSION IN Cu(InxGa1-x)Se2 PHOTOVOLTAICS

Jian Li,1,2 Stephen Glynn,1 Lorelle Mansfield,1 Matthew Young,1 Yanfa Yan,1 Miguel Contreras,1 

Rommel Noufi,1 Fred Lewis Terry Jr.,2 and Dean Levi1

1

National Renewable Energy Laboratory, Golden, CO 80401, USA 2

Department of Electrical Engineering & Computer Science, University of Michigan, Ann Arbor, MI 48109, USA

ABSTRACT

Molybdenum (Mo) thin films were sputtered onto soda lime 

glass (SLG) substrates. The main variable in the 

deposition parameters, the argon (Ar) pressure pAr, was 

varied in the range of 6 – 20 mTorr. Ex situ spectroscopic 

ellipsometry (SE) was performed to find out that the 

dielectric functions ε of the Mo films were strongly 

dependent on pAr, indicating a consistent and significant 

decrease in the Mo film density ρMo with increasing pAr. 

This trend was confirmed by high-angle-annular-dark-field 

scanning transmission electron microscopy. ε of Mo was 

then found to be correlated with secondary ion mass 

spectroscopy profiles of Sodium (Na) in the Cu(InxGa1-

x)Se2 (CIGS) layer grown on top of Mo/SLG. Therefore, in 

situ optical diagnostics can be applied for process 

monitoring and optimization in the deposition of Mo for

CIGS solar cells. Such capability is demonstrated with 

simulated optical transmission and reflectance of variously 

polarized incident light, using ε deduced from SE.

INTRODUCTION

Thin film photovoltaics (PV) based on the CIGS 

technology is a promising candidate for low-cost, highefficiency solar cell applications as it has demonstrated 

the highest energy conversion efficiency among all thin 

film PV technologies [1 - 3]. For CIGS cells, the most 

commonly used substrate is SLG coated with sputterdeposited Mo thin films as the metal contact [1 - 3]. An 

important process associated with this substrate is the Na 

diffusion from SLG through the Mo layer into the absorber 

layer. A proper amount of Na diffusion is known to be 

important for optimized cell performance [1]. For such 

diffusion, the Mo layer acts as the barrier, and hence may 

provide a mechanism to control the diffusion process by 

varying the Mo properties.

Some physical properties, such as conductivity, intrinsic 

stress, and morphology, of sputtered Mo films were 

studied extensively and were found to vary significantly 

with deposition parameters [4, 5]. However, the variation

of Mo film density ρMo was only studied briefly, even 

though it is expected to be closely related to the Na 

diffusion. Moreover, most of the previous studies were 

based on ex situ characterization methods, such as X-ray 

diffraction and scanning electron microscopy, that either 

provide only qualitative information or are incompatible

with in situ high-throughput measurements. On the other 

hand, optical probing methods, such as ellipsometry, 

reflectance, and transmission, have the advantages of 

being able to be implemented in situ, in-line with real-time 

quantitative responses, and being sensitive to depth 

profiles, and thus are uniquely useful for studying thin film 

materials. [6]. If an optical diagnostic can be established 

that measures Mo film properties and correlates them with 

Na diffusion, it will greatly facilitate the research as well as 

manufacturing of CIGS solar cells.

EXPERIMENTAL DETAILS

A series of Mo thin films were sputtered onto SLG 

substrates with a DC power of 650 Watt and an Ar flow 

rate of 50 sccm. The total film thicknesses are in the range 

of 0.40 – 0.55 μm. The 6”x6” substrates were scanned in 

front of the 2”x10” target in order to cover the whole 

substrate area. Each Mo film was deposited with two 

substrate scans with the same scan speed. There was no

external heating to the substrate. The key process 

variable, pAr, was varied in the range of 6 – 20 mTorr.

After deposition, the Mo/SLG samples were characterized 

by SE in the photon energy range of 0.75 – 3.6 eV where 

SLG is transparent. Since SE is very sensitive to surface 

non-idealities, such as oxide layer or surface roughness, it 

has been discussed before that improper treatments of the 

surface layer usually result in large errors in the deduced 

optical properties of the underlying film [7]. On the other 

Figure 1 Through-the-glass configuration was used for 

SE measurements in this study with a rotatable sample 

holder. The Mo film side is indicated with texture.

to SE

detector
2 

hand, the film/glass interface was found to be almost free 

of these non-idealities. Therefore, through-the-glass 

geometry was selected for the SE measurements as

shown in Fig. 1. The Mo films in this study were found to 

be optically anisotropic, so SE measurements at multiple 

orientations were needed in order to obtain both the 

ordinary and extraordinary dielectric functions. This was 

accomplished by fixing the sample on a rotatable holder. 

At each orientation, anisotropic SE data were taken at 

angles of incidence (AOI) from 45 to 70o. Focusing optics 

were used to eliminate the beam reflected at the SLG/air 

interface from the probing beam reflected at the SLG/Mo 

interface, as these two beams are optically incoherent.

RESULTS AND DISCUSSIONS

In SE analyses, it was found that uni-axial anisotropy was 

sufficient to model the Mo films in this study, that exhibit 

clear in-plane optical anisotropy. Therefore, two sets of 

complex dielectric functions, the ordinary one εo and the 

extraordinary one εe, were needed to describe each Mo 

film. The anisotropic SE data taken at multiple orientations 

and AOIs for each sample were analyzed together in order 

to extract its εo and εe simultaneously with good 

confidence limits or error bars. The resulting optical 

properties are plotted in Fig. 2.

It can be seen that both εo and εe vary significantly with 

pAr. In general, high pAr Mo films are optically less 

anisotropic, indicated by smaller difference between their 

εo and εe compared to low pAr films. The most important 

difference between various pAr Mo films, however, exists in 

the amplitudes of their dielectric functions. This is more 

clearly observed in ε2 in the right panel of Fig. 2.

In the classical theory of materials optical properties, ε can 

be expressed as a sum of a series of Lorentzian 

oscillators:

∑ −− += ∞

n n

2 2

n

n

1

)E(E Γ Ei

A εε(E) (1) 

where E is photon energy; ε1∞ is the contribution to ε1

from the oscillators located at photon energies much 

higher than the studied spectral range; An, En, and Γn are 

the amplitude, resonance energy, and the broadening of 

the nth oscillator [6]. A similar expression exists as 

deduced from modern quantum theory of materials optical 

properties. It should be noted that En and Γn have different 

physical meanings in these two theories, but in either 

case, An is always proportional to the number of atoms per 

unit volume, or the density of the material [6].

As is for typical metals, the dominant feature in Fig. 2 is 

the free electron absorption (< 1.2 eV), corresponding to a

Lorentzian oscillator in Eq. (1) with En=0, or the Drude 

oscillator [6]. In this case, neglecting ε1∞ as it is usually 

much smaller than the Drude oscillator, the negative 

amplitude in ε1 or the positive amplitude in ε2 is 

proportional to An as well as the Mo film density ρMo [6]. 

Above 1.2 eV, two critical point (CP) structures [6], with 

resonance energies located at ~1.7 and 2.4 eV 

respectively, are observed. In these two cases, An cannot 

be estimated from ε1 because of the non-negligible 

contribution of ε1∞, but can be estimated from the 

amplitude of ε2. It is observed that in all the main 

structures in ε described above, the amplitudes in both εo

Figure 2 Real (left) and imaginary (right) part of the complex dielectric functions of the near substrate part of the 

Mo films as functions of pAr. εe and εo of a specific film are marked with the same color coding.
3 

and εe decrease significantly, indicating a consistent and 

significant decrease in ρMo, with increasing pAr. It should 

also be noted that all the Mo films in Fig. 2 are highly 

absorbing, with the calculated penetration depth in this 

photon energy range no more than 27 nm. Therefore, the 

optical properties and the associated indication in ρMo only 

apply to the near substrate part (~ 50 nm) of the Mo films.

To confirm the SE indication in ρMo above, the 

microstructure and morphology of selected Mo films were

examined by high-angle-annular-dark-field scanning 

transmission electron microscopy (HAADF STEM). An FEI 

Tecnai F20-UT microscope operating at 200kV was used 

for imaging. Cross sectional TEM samples were prepared 

by focused ion beam technique (FIB) using a FEI Nova200 

dual beam FIB system. The intensity of a HAADF STEM 

image is proportional to the atomic number and the 

thickness of the film [8]. Because the only element probed 

here is Mo, there is only one atomic number for all the 

samples; and the TEM sample prepared by FIB have 

rather uniform thickness, the intensity of HAADF STEM 

images can then be related to the local density of Mo in 

the films – lower intensity indicates lower density. It can be 

seen from the HAADF STEM images shown in Fig. 3 that 

the near substrate ρMo of the pAr=6 mTorr Mo film is 

significantly higher than that of the pAr=20 mTorr Mo film, 

consistent with the SE results described above. It is also 

noticeable that within a specific Mo film, local ρMo

decreases with distance from the SLG substrate. 

In the fabrication of CIGS solar cells, the Mo layer acts as 

a barrier to Na diffusion from SLG into the absorber layer 

grown on top of Mo/SLG. The diffusion coefficient should 

be inversely dependent on ρMo. Even though, as stated 

earlier, the SE indication in ρMo only applies to the near 

substrate part of the Mo films, it may be used to estimate 

the average density of the entire Mo film. Additionally, as 

seen in Fig. 3, the near substrate part is the densest in a 

specific Mo film, and thus should be essentially the bottle 

neck for the Na diffusion. Therefore, the near substrate 

ρMo, which the optical property is sensitive to, as shown in 

Fig. 2, is expected to have a strong effect in determining 

the Na diffusion. 

To verify this hypothesis, standard CIGS layers were 

grown by the three-stage method with identical deposition 

parameters [9] on selected Mo/SLG samples from the set 

in Fig. 2. The resulting CIGS films were depth profiled 

using secondary ion mass spectroscopy (SIMS) to 

determine the Na distribution. The SIMS results plotted in 

Fig. 4 not only show an expected trend of increasing Na 

concentration with increasing pAr, and hence decreasing 

ρMo, but also vary on a relative quantitative scale similar to 

that in Fig. 2. This demonstrates a close correlation 

between the optical properties in Fig. 2 and the Na 

distribution in Fig. 4.

A proper amount of Na diffusion is known to be important

for the fabrication of high efficiency CIGS solar cells [1]. 

The observations above present an opportunity of setting 

up an optical diagnostic for the optimization and control of 

Na diffusion. To demonstrate such capabilities, the normal 

incidence (AOI=0°) transmission from the Mo side, the 

AOI=45° reflectance from the Mo side for p-polarized light, 

and the AOI=45° reflectance from the back side of the 

SLG substrate for s-polarized light are simulated in Fig. 5, 

assuming a sample structure of 20 nm Mo layer deposited 

on SLG and using the optical properties in Fig. 2. It can be 

seen that in all the cases of Fig. 5, the difference between 

Figure 3 Cross-sectional HAADF STEM images of the 

Mo film deposited at an Ar pressure of 6 mTorr (left 

two panels) and 20 mTorr (right two panels).

glass substrate

gold protection

6 mTorr 20 mTorr

6 mTorr 20 mTorr

Figure 4 SIMS depth profile for Na in the CIGS layer 

grown on Mo/SLG with indicated pAr for Mo deposition.
4 

the two samples is significant and hence detectable by the 

optical diagnostics based on intensity measurements. For 

the optical diagnostics based on polarization 

measurements, such as SE with two measured quantities, 

or for thicker Mo films on SLG, the sensitivity is expected 

to be higher.

SUMMARY

A series of Mo thin films were deposited on soda lime 

glass by sputtering at different Ar pressures. The Mo films 

were characterized by through-the-glass spectroscopic 

ellipsometry. The optical properties of the near substrate 

part of the Mo film were found to vary significantly, 

indicating a consistent and significant decrease in the 

near-substrate Mo density with increasing Ar pressure. 

This trend was confirmed by cross-sectional HAADF 

STEM images. It was also found that the near substrate 

part is the densest in a specific Mo film. Therefore, this 

part is expected to play an important role in determining 

Na diffusion. The effect of Mo density profiles on Na 

diffusion was confirmed by SIMS profiles of Na in the 

CIGS layers grown on top of different Mo/SLG samples. 

Finally, the capability of an in situ optical diagnostic for the 

control of Na diffusion for CIGS solar cells was 

demonstrated through simulations.

ACKNOWLEDGEMENT

This work was supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

NREL and by the University of Michigan under 

Subcontract No. XEJ-9-99035-01. 

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Figure 5 Simulated normal incidence transmission and 

AOI=45° reflectance from both the Mo film side and the 

back side of SLG for a 20 nm Mo layer deposited on 

SLG substrate, using the optical properties in Fig. 2.