Cost Effective SPC/APC monitoring of a Film’s Dielectric Constant on Product
Measurement of dielectric constant presents the semiconductor industry with many challenges. Problems can often be related to the unique properties of the low k material in question. Liam Cunnane, Adrian Kiermasz PhD, Rob Wilby of Metryx Ltd, & Youssef Travaly of IMEC discuss the issues ranging from interface charge to modification of the film by the measurement technique. Demonstrated in the relationship between the density of a Low k material and its Dielectric Constant, is a robust and cost effective method of monitoring product non-destructively.
As ULSI design rules shrink below 0.18Ìm, the wide choice of Low k Materials is narrowed and ultimately decided by the ability to integrate the material into the fabrication process. Broadly speaking the choices can be broken into two groups, spin on materials and Carbon doped Oxides deposited by CVD. Many of these materials derive their low k characteristics through the introduction of porosity, which can be as high as 50%. Although the introduction of porosity has proven to be an effective means of lowering the dielectric constant of a film, it creates significant integration challenges. The porosity or density of the material must be controlled to maintain sufficient physical characteristics to allow it to be integrated successfully into the manufacturing process. Of particular interest is the relationship between porosity and the mechanical properties of the film. Increased porosity may lead to issues for CMP and/or bonding due to a reduction in the hardness of the material.
Discussion:
Relationship between Film Hardness and Film Density
A decrease in film density leads to a decrease in elastic modulus. According to theory of cellular solids, the elastic modulus of the material is solely a function of reduced density (density of nonporous solid):
Pores can be open or closed and the following equation represents the effect of these pores
For a given density (p.), closed cell foams have higher properties.
Where p= Fraction of solid contained in the edges.
For open cell, n =2 if edge bending is the predominant mechanism of deformation. Closed cells give effective n ~ 1.6.
Figure 2. illustrates how density, mechanical property and porosity relate to each other for a MSQ spin-on low-k dielectric [ref 2]. As illustrated from this graph, an increase in porosity is accompanied by a decrease in density together with a decrease in mechanical properties. Most importantly, as the density decreases linearly with porosity, mechanical properties decrease concomitantly following a power law.
Relationship between Film Density and Dielectric Constant
The material property Dielectric Constant and Film Density relate to each other through well-known equations. The Clausius-Mossotti (CM) equation, stipulates that the volume polarizability for a porous material with a random pore distribution is a function of film density and polarizability:
Where N0 is Avogadro number, ε0 is the vacuum dielectric constant, M is molecular weight, p is the density of the material, and · is the polarizability. The polarizability of a dielectric material can be written as the sum of electronic polarizability ae, atomic polarizability aa, and dipole polarizability ad, which are associated with the displacement of charges locally bound in atoms, in molecules, and in the structures, respectively.
Because the volume polarizability follows the same trend as the k-value [see Eq. (3)], techniques for lowering k-value consist in reducing the film density and/or in film polarizability. For reducing a, one can for instance replace highly polarized Si-O bonds by less polarized Si-C or Si-H bonds by incorporation of CH3 to the Si-O network. Note that this will also lead to a subsequent decrease in film density. To further reduce the film density and hence decrease the k-value, one can introduce porosity in the film, which according to the Eq. 5 causes a decrease in density:
Over a broad range of materials it can be shown that this relationship holds true. In the graph opposite standard Oxide to Aerogels obey this relationship. As the materials density decreases so too does the Dielectric contant. Materials with a density of 1.5 g/cc and below must be carefully monitored to ensure sufficient mechanical strength, particularly during packaging.
Typically for a particular process being monitored such as the Carbon doped CVD Oxide film in Fig. 4. The region of interest can be treated as having a linear relationship between Density and k Value. Statistical Process Control (SPC) limits maybe setup accordingly.1
Accurate methods for the determination of dielectric constant are becoming more and more important with devices scaling. The most commonly used techniques are Hg-probe, MIM and/or MIS structures. Hg-probe is a simple technique which does not require extra processing beside the dielectric deposition itself. However, having a highly doped substrate for accurate kvalue determination is highly desirable when using this technique. As a matter of fact, with such substrate, the measured capacitance is independent of the applied voltage. Alternatively one can use a substrate with a well-known doping level for insuring accumulation in the C-V plot. When these requirements are fulfilled, the next step is to accurately measure the dielectric thickness at the location where the Hg contact will be made. Another crucial aspect of this technique is a proper monitoring of the contact area made by the Hg on the surface. With the current aggressive down scaling, accurate thickness measurement becomes an issue. One of the most accurate techniques is XRR which enables a direct thickness measurement whatever the substrate. With ellipsometry technique, recipes need to be developed for each specific substrate. For MIM and MIS techniques, further processing is required. For both cases, this implies deposition of a top electrode which is then patterned by photolithography and metal etching.
While such processes yield top electrodes will well controlled area, dielectric exposure during metal etch (plasma damage of the low-k and subsequent moisture uptake) cannot be avoided unless an extra dielectric protection layer is used. In addition to that, multilayer stack makes accurate thickness measurement more complex. Finally, when using MIM structure, one needs to select a metallic substrate, which may also influence the final result (see fig 5.). Obviously measurement techniques of this kind are destructive and not used on production wafers. It has also been demonstrated that measuring a film’s Dielectric Constant can be influenced by the material on which it is deposited. In the following experiment the Low k Process was identical in both Chemistry and deposition conditions, but deposited over a number of different under lying films. Both Electrical and X-Ray techniques showed a significant sensitivity to the underlying surface. However calculating Dielectric Constant from Density gave consistent values as expected and due to the non-destructive measurement the technique can be used directly on production wafers. In production Low k materials will be deposited over a variety of under lying materials. To avoid additional complexity the measurement technique is required to show little or no sensitivity to the under lying film.
Application to SPC/APC:
Integration of this technology into existing Fab SPC/APC practices is simple. By correlating data gathered from thickness measurement tool in conjunction with the Metryx mass measurement system, the density of the film can be monitored to an accuracy of better than 1%. Film thickness changes should be accompanied by a corresponding mass change to maintain a constant film density.
Conclusion
The advantages of this technique are clearly (a) Simplicity (b) Non Destructive nature of measurement/ applicable to product wafers (c) Low Cost/sample. These advantages allow this technique to be employed as an inline SPC or APC technique, reducing significantly product at risk with a cost effective high sampling rate. The method is applicable to a wide range of Low k Materials which achieve low k characteristics through the introduction of porosity.
REFERENCES
(1) Micron Technologies: Determining Dielectric Constant Variation of SiOC Low k Film Using Density Measurement, AMC
(2) T. Abell, F. Iacopi, G. Prokopowicz, B. Sun, A. Mazurenko, Y. Travaly, M. Baklanov, A. Jonas, C. Sullivan, S. Brongersma, H.-C. Liu, J. Tower, M. Gostein, M. Gallagher, J. Calvert, M. Mainpour, K. Maex, AMC Conf. proceedings, eds. D. Erb, P. Ramm, K. Masu, A. Osaki, p. 457, 2004
