## 2 Instrumentation Developments
### Boss-Membrane Piezoresistive Microprobe  
Several micro-CMM probes are being further developed at PTB, including a boss-membrane piezoresistive microprobe, a fibre probe and probes based on atomic force microscope (AFM).  
Figure 2 shows the measurement principle of the boss-membrane piezoresistive microprobe. The fabricated sensor chip includes a centre boss, a membrane having a thickness of tens of micrometres, and a frame. On this chip, a shaft with a length of about 10 mm is glued to the centre boss, and a probing sphere with a diameter of some hundred micrometres is glued to the free end of the shaft. Four groups of piezoresistive sensors, arranged as Wheatstone bridges as shown in Figure 2b, are fabricated on the back of the membrane by the ion implantation technique and act as sensor elements. When the probing sphere touches the measurement object, strains are produced on the membrane by the probing force which leads to changes in the resistances of the piezoresistive sensors. The finite element method (FEM) has been used during the probe design to calculate the position where the maximum strains occur. At these positions, the piezoresistive sensors are located in order to achieve optimum measurement sensitivity. The resistance changes of the sensors are converted into electric signals which are used to determine the probe's displacement, i.e., for measurement. A photo of such a sensor chip is shown in Figure 2c. The probe was originally designed and fabricated at the Institute for Microtechnology of the Technical University Braunschweig (Braunschweig, Germany) [16], and PTB has applied this technique to micro-CMM applications and has fully investigated its performance in order to achieve improvements [10; 36].  
A major shortcoming of the probe is its anisotropic stiffness. For instance, for one probe which was investigated in detail, the stiffness values along the \(x\)-, \(y\)- and \(z\)-axes were 208.8 N/m, 313.8 N/m and 5642.9 N/m, respectively. As the styli deformation differs in the different probing directions, such  
Figure 1: (**a**) Schematic diagram showing the measurement principle of the nanopositioning and namemeasuring machine (NMM); (**b**) positioning noise along the \(z\)-axis before and after machine upgrade; (**c**) example showing the positioning of the NMM along the \(x\)-, \(y\)- and \(z\)-axes simultaneously by steps of 10 \(\upmu\)m; and (**d**) the positioning stability of three axes after reaching the target position.  
behaviour will lead to form measurement errors, particularly in the scanning measurement mode. In addition, it may also result in a slipping of the probing sphere with respect to the workpiece during the measurements.  
To solve this problem, a double triangle design has recently been realized which consists of two structured boss membranes mounted face-to-face as shown in Figure 2d [37]. The states of stress occurring in this structure when it is loaded with vertical and lateral probing forces are also illustrated in the figure. In early stages of the development, the sandwich structure was fabricated by gluing two single chips together whereby one of the chips did not have any electronic components on it. The capillary forces which occurred during the gluing processes yielded a very good alignment of the two chips. Experimental investigations show that the stiffness ratio between the \(x\)-, \(y\)- and the \(z\)-direction has been improved to approximately 2 by the improved design [37]. Currently, a joint research project is also being carried out by the Technical University of Braunschweig in collaboration with PTB to further develop the probe. With the improved design, the probe is capable of measuring with a probing speed of up to 1 mm/s and of achieving a 3D probing repeatability of 50 nm. Testing its probing error according to ISO 10360 has not been done yet.