Propagation of error in a birefringence modulation ellipsometer

Abstract

The error in measurements by variable angle birefringence modulation ellipsometer, Beaglehole Instrument Ltd (BIL) Picometer Ellipsometer, was examined. Although the Picometer is easily configurable for spectroscopic work, all measurements were made here using a He/Ne laser at 632.8nm. The operation of the Picometer was investigated using a photomultiplier and Si photodiode detector, 12 bit and 16 bit ADC Measurement Controllers and Stanford Research SR510 Lock-in Amplifiers. This lock-in is non-standard on BIL's commercial model. Errors introduced into a measurement by the electronic components, by alignment and calibration errors, and by the non-ideal behavior of optical elements were determined. When used with a photomultiplier, the instrument's precision is largely limited by shot noise or by noise in the Measurement Controller. The limit achieved depends on the sensitivities of lock-in, photomultiplier and Measurement Controller, and lock-in time constant. The shot noise limit was not achieved with Si photo diode detector examined here because noise in the electronics of the detector. Assuming that a correction for stray birefringence in the modulator head is made, the instrument's accuracy is limited by alignment errors. A significant improvement in the accuracy can be achieved by zone averaging over the analyzer. The accuracy after zone averaging is largely dependent on the alignment of the modulator head. Zone averaging over the analyzer also appears to remove a residual offset associated with anisotropy in the glass of the modulator head. A comparison of the precision of the Picometer with the specified precision of three other ellipsometers was made. It was estimated that the average standard deviation of the common ellipsometry parameters Δ and Ψ was between 1.4 and 28 times lower for the Picometer. The instrument's calculated accuracy was used to estimate the error in the thickness of a thin transparent SiO2 layer on a transparent Si substrate, using Lekner's analytic inversion [15] for a range of layer thicknesses. The average standard deviation for the estimate of the layer thickness was found to be a σ = 0.12nm.