Logo of the Physikalisch-Technische Bundesanstalt
Production sequence of Si-spheres and interferometrical determination of the sphere volume

Reduction of measurement uncertainty of step height and etching depth calibration down to 0.3 nm

[Translate to English:]


Accurate and traceable calibration of step height and/or etching depth of micro- and nanostructures is a fundamental task in nanometrology. Today, metrological atomic force microscopy (Met. AFM) is one of the most accurate methods for step height calibration, which offers a typical expanded measurement uncertainty of U of 1.0 ~ 2.0 nm (k = 2), as confirmed by the international comparison NANO2. However, there are increasing demands on the reduction of U to below 0.5 nm (0.3 nm desired) by some industrial sectors, for instance, the metrology of absolute feature heights of photomask structures and diffractive optical elements (DOEs) for the simulation and thus control of their (optical) functions.

To further improve the measurement accuracy of Met. AFM, recently a thorough study has been performed at the PTB, the national metrology institute of Germany. The study has focused on three key factors: (i) high-order nonlinearity errors of interferometers; (ii) ghost interference fringe present in the AFM optical detection system; and (iii) form deviation of measurement mirrors. Significant progress has been made, which lead to a reduction of measurement uncertainty for step height and etching depth calibrations from U > 1.0 nm to 0.3 nm. 

Experimental studies show that the interferometers embedded in the Met. AFM suffer from high order nonlinearity error, which cannot be corrected by the conventional Heydemann method. To overcome this challenging issue, PTB has developed a new approach for correcting the high order nonlinearity errors by using external sensors/standards, which is feasible to correct the nonlinearity error down to 40 pm. Furthermore, the propagation of the (residual) nonlinearity error for the step height calibration is studied systematically. 

To demonstrate the performance of the state-of-the-art Met. LR-AFM after improvement, the calibration results of a highly demanding industrial sample are plotted in figure 1. In this calibration, the sample is measured at 25 different locations. Six sets of measurements are repeated, performed with three different AFM heads (AFM1, AFM3 and AFM4) and six different AFM probes (3 with type PPP_NCLR and 3 with type PPP-NCHR, all from Nanosensors®). It can be seen that the results have excellent reproducibility. The standard deviation of the mean feature height of 6 sets of measurements reaches 0.02 nm, indicating the measurement stability and reproducibility of the metrology tool. The standard deviation of all 150 results (i.e., 6 sets  25 results per set) is 0.08 nm, indicating both the reproducibility of the metrology tool and the sample uniformity.  The preliminary measurement uncertainty of this calibration is estimated as 0.3 nm, which is a significant improvement compared to the previous result (about 1.0 ~ 2.0 nm).

[Translate to English:] Figure 1. Metrology performance of the state-of-the-art Met. LR-AFM after improvement shown as the calibration result of a highly demanding industrial sample