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Measuring substrate-independent modulus of dielectric films by instrumented indentation

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Abstract

Substrate influence is a common problem when using instrumented indentation (also known as nanoindentation) to evaluate the mechanical properties of thin films. In this work, finite element analysis was used to develop an ad hoc model that predicts the substrate influence when testing thin dielectric films on silicon. The model was evaluated experimentally using three sets of films that were nominally the same except for thickness. Using the model significantly reduced the measurement error for the thinnest films (>250 nm) by accurately accounting for the influence of the substrate. The model also significantly reduced the measurement uncertainty, because properties were evaluated using larger indents that would normally be unduly affected by the substrate. The process for developing this model may be useful in developing other ad hoc models for analyzing film-substrate systems.

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Abbreviations

k:

Permittivity or dielectric constant

err (E*OP):

Error in the measured quantity, E*OP

A:

Contact radius

t:

Film thickness

E r :

Reduced modulus

E in :

Value of E used as input to the finite element simulation

E:

Young’s modulus; subscripts “f” and “s” refer to film and substrate, respectively

E*OP:

E, evaluated using Oliver-Pharr data analysis, uncorrected

E OP :

E of film, evaluated using Oliver-Pharr data analysis, corrected for substrate influence

E OP-bulk :

E of a bulk sample of the film material, evaluated by simulation and application of Oliver-Pharr analysis

E OP-sub :

E of substrate, evaluated using Oliver-Pharr data analysis

E TAN :

Slope of bilinear stress-strain curve after yield

v:

Poisson’s ratio

sy:

Yield stress

A:

Projected cross-sectional area of indenter

d:

Distance from the apex along the axis of the indenter

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Authors and Affiliations

  1. Agilent Technologies, Oak Ridge, Tennessee, 37830, USA

    Jennifer Hay

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  1. Jennifer Hay
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Correspondence to Jennifer Hay.

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Hay, J. Measuring substrate-independent modulus of dielectric films by instrumented indentation. Journal of Materials Research 24, 667–677 (2009). https://doi.org/10.1557/jmr.2009.0132

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  • DOI: https://doi.org/10.1557/jmr.2009.0132

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