*Wenqing Shi, Gerald Pascual, Byong Kim, and Keibock Lee Park Systems Inc., Santa Clara, CA USA*

### ABSTRACT

Nanomechanical property measurement is one of the most popular functions of atomic force microscopy (AFM). Conventional nanomechanical measurement techniques are mainly based on AFM force-volume spectroscopy, which collects force-distance (F/D) curves at each pixel to calculate material elastic properties. However, these techniques have been recognized as being extremely slow, and it usually takes hours to acquire an elasticity map. Driven by the demand for a faster and more efficient technique, Park Systems developed PinPointTM Nanomechanical Mode to provide a solution that is at least 100 times faster than traditional techniques. This mode enables acquisition of an elasticity map with a correlated topography image within minutes, and it represents a new application tool for collecting real-time topography and quantitative mechanical property maps of various materials, ranging from hard disks to soft tissues. To better access the capability of the PinPointTM Nanomechanical Mode, we select three cantilevers with stiffness ranging from 0.2 N/m to 25 N/m and investigated their influence on the measured modulus values. In addition, for all three cantilevers, we also examine the influence of applied force on the resulted modulus. Findings show that cantilevers with smaller force constants will lead to smaller measured modulus values, and vice versa. With the same cantilever, a larger applied force results in a larger measured modulus compared to that obtained with smaller force values. The most important finding is that, with PinPointTM, the relative modulus difference/ratio within a sample can be accurately acquired regardless of the force constant of the cantilever or the applied setpoint force values.

#### INTRODUCTION

PinPointTM Nanomechanical Mode from Park Systems enables high-resolution concurrent acquisition of topographical data and force-distance (F/D) data at each pixel in an entire scan area.1 Using PinPointTM mode, surface morphology as well as the quantitative nanomechanical properties (i.e., modulus, adhesion, deformation and dissipation) of the sample can all be obtained at once. The process is achieved using Park Systems's unique methodology: while measuring the morphology of the sample, the XY scanner halts at each data acquisition point and takes a rapid F/D curve with finely-controlled contact force, distance and contact time between the tip and the sample. This makes evaluation of mechanical properties in materials a seamless operation for material science professionals, creating a reliable analysis at vastly improved levels of speed and accuracy.

In this report, to investigate the influence of cantilever stiffness on measured modulus results, we use three cantilevers with varying stiffness to image a standard PinPoint polymer sample (consisted of polystyrene/PS matrix with a nominal modulus of 2 GPa, and low density polyolefin/LDPE with a nominal modulus of 0.1 GPa). Results demonstrate the capability of PinPointTM mode to differentiate the two surface domains with high fidelity. In addition, we calculate and plot the modulus ratio between the measured modulus value of PS and that of PE. The calculated ratio remains ~20 for all three cantilevers, proving that PinPointTM mode by Park Systems is superior in its performance of quantitative modulus mapping.

#### EXPERIMENTAL

*Sample*

Polystyrene, a low-density polyolefin elastomer (PS-LDPE) sample was used. PS-LDPE is a copolymer sample and was mounted on a 12 mm steel sample chunk. A blend of PS and PE were spin-cast onto a silicon substrate to create a film with different modulus properties. PS, with an elastic modulus of ~2 GPa, served as the matrix, while PE was the low-density doping component with an elastic modulus of ~0.1 GPa. The ratio between PE and PS was ~20.

*Tip*

Three cantilevers with different spring constants were used in the PinPoint imaging experiments. Force constant calibration of was performed for all three probes according to the procedure described in the PinPoint User Manual, and the calibrated force constants are listed in Table 1

*PinPoint Imaging Conditions*

Three cantilevers with different spring constants were used in the PinPoint imaging experiments. Force constant calibration of was performed for all three probes according to the procedure described in the PinPoint User Manual, and the calibrated force constants are listed in Table 1

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#### RESULTS AND DISCUSSION

*CONTSCR*

Topography and modulus images taken with a CONTSCR cantilever (Force constant = 0.236 N/m) at setpoint values of 1 nN, 2 nN and 4 nN are shown in Figure 1. Line profiles along the red (1 nN), green (2 nN), and blue (4 nN) lines, drawn in both the topography and the modulus images using Park XEI software, are also included. Quantitative results of the modulus values and the calculated modulus ratio are shown in Table 2. As a result of larger loading force applied to the sample, as the setpoint values in the topography image increase, the measured heights of the circular PE features decrease.

The measured modulus values for PS and PE were ~10.8 MPa and 0.5 MPa at the 1 nN setpoint, respectively; 26.2 MPa and 1.2 MPa at 2 nN, respectively, and 35.2 MPa and 1.8 MPa at 4 nN, respectively. The modulus values measured with the CONTSCR cantilever are two orders of magnitude smaller than the actual values (i.e., 2 GPa for PS and 0.1 GPa for PE). Despite the discrepancy in the measured modulus values, the calculated modulus ratio between PS and PE is 21.9 at the 1 nN setpoint, 21.2 at 2 the nN setpoint, and 19.4 at the 4 nN setpoint, all of which are close to the actual ratio of 20.

*FMR*

Topography and modulus images taken with the FMR cantilever (Force constant = 3.49 N/m) at setpoint values of 10 nN, 20 nN and 40 nN are shown in Figure 2. Line profiles along the red (10 nN), green (20 nN), and blue (40 nN) lines drawn in both the topography and the modulus images are also included. Quantitative results of the modulus values and the calculated modulus ratio are shown in Table 3.

Modulus values of 126 MPa for PS and 6.2 MPa for PE were obtained at the 10 nN setpoint; 231 MPa for PS and 11 MPa for PE at the 20 nN setpoint, and 675 MPa for PS and 33 MPa for PE are obtained at the 40 nN setpoint. The values measured with the FMR cantilever are one order of magnitude smaller than the actual values. However, calculated modulus ratio values of 20.2 at the 10 nN setpoint, 20.9 at the 20 nN setpoint, and 20.5 at the 40 nN setpoint are in proximity of the actual modulus ratio of 20.

*AC160TS*

Topography and modulus images taken with the AC160TS cantilever (Force constant = 25.5 N/m) at setpoint values of 40 nN, 80 nN, and 100 nN are shown in Figure 3. Line profiles along the red (40 nN), green (80 nN), and blue (100 nN) lines drawn in both the topography and the modulus images are also included. Quantitative results of the modulus values and the calculated modulus ratio are shown in Table 4.

The circular PE features appears to be more indented when compared to topography images taken with CONTSCR and FMR cantilevers. Modulus values of 380 MPa for PS, and 20 MPa for PE were measured at the 40 nN setpoint. As the setpoint was increased to 80 nN, the measured modulus values for PS and PE increased to 1028 MPa and 54 MPa, respectively. Finally, at the 100 nN setpoint, 1264 MPa was obtained for PS and 64 MPa was obtained for PE. The measured modulus values obtained with AC160TS cantilever were on the same order of magnitude as the actual modulus values. The calculated modulus ratio values were 19.0 at the 40 nN setpoint, 19.0 at the 80 nN setpoint, and 19.8 at the 100 nN setpoint, and they were again in close proximity to the actual modulus ratio.

The measured PE and PS modulus values and their calculated ratios are plotted against different setpoints in Figure 4. Results obtained with the CONTSCR, FMR, and AC160TS cantilevers are illustrated in green, red, and blue, respectively.

The measured PE and PS modulus values are plotted against different setpoints in Figure 4a and 4b, and two trends were observed. First, increasing setpoint values led to increased measured modulus values for all three types of cantilevers. Second, as the spring constant of the cantilever increases, the measured modulus also increased.

The calculated modulus ratio between PS and PE are plotted against the respective setpoints in Figure 4c. The ratio values are approximately 20 for all three cantilevers.

#### CONCLUSIONS

In conclusion, cantilevers with smaller force constants lead to smaller measured modulus values, while cantilevers with larger force constants result in larger measured modulus values. Using the same cantilever, higher setpoint values result in larger modulus measurements than when lower setpoint values are used. Therefore, in order to obtain accurate modulus measurements, a cantilever with the proper force constant needs to be selected. For example, if the modulus value of a sample of interest ranges between hundreds of MPa to several GPa, an AC160TS cantilever and a setpoint of ~100 nN are recommended. Nonetheless, the relative modulus difference/ratio within a sample can be accurately acquired via Park PinPointTM mode, regardless of the force constant of the cantilever or the applied setpoint force values.

#### REFERENCES

1. PinPoint Nanomechanical Mode | http://www.parkafm.com/index.php/park-afm-modes/nanomechanical-modes?i=0