Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Set-Up
2.2. Samples
2.2.1. Reference Samples
2.2.2. Piezoelectric Samples
2.3. Calibration Method
2.4. Measurement Protocol
3. Results
3.1. Capacitance Model
3.1.1. Theory
3.1.2. Dimensional Measurements
- Layer thickness
- Gold pad areas
3.2. Capacitance Measurements
3.2.1. Dielectric Constant Determination
3.2.2. Frequency Measurements
3.3. Uncertainty Budget
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Pad Number | Atopo (PZT) (µm2) | uAtopo (PZT) (%) | N |
---|---|---|---|
1 | 0.02 | 7.8 | 4.47 |
2 | 0.05 | 9.5 | 2.48 |
3 | 0.10 | 3.1 | 2.22 |
4 | 0.16 | 3.3 | 1.99 |
5 | 0.24 | 2.6 | 1.70 |
6 | 0.35 | 1.5 | 1.56 |
7 | 0.45 | 1.3 | 1.47 |
8 | 0.56 | 1.3 | 1.47 |
9 | 0.70 | 1.7 | 1.47 |
10 | 1.02 | 1.3 | 1.34 |
11 | 1.40 | 1.1 | 1.29 |
12 | 1.83 | 1.2 | 1.32 |
13 | 2.34 | 1.0 | 1.28 |
14 | 2.92 | 1.4 | 1.24 |
15 | 3.56 | 0.5 | 1.21 |
Uncertainty Sources | PZT u (%) | PMN-PT (1st Series) u (%) | PMN-PT (2nd Series) u (%) |
---|---|---|---|
Capacitance calculation | (2.5; 9.7) | (6.5; 20.5) | (6.5; 23.6) |
Area, uA | (1.3; 9.5) | (3.5; 19.7) | (3.4; 22.9) |
Thickness, ud | 2.1 | 5.5 | 5.5 |
Capacitance measurements | 3.2 | 3.3 | 3.2 |
Type-A (Histogram, repeatability) | (0.1; 0.2) | (0.2; 0.6) | (0.2; 0.6) |
SMM calibration | 3.1 | 3.1 | 3.1 |
Others | <1.8 | <1.8 | <1.8 |
Combined uncertainty, uc (%) | 3.5 | 9.1 | 10.6 |
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Richert, D.; Morán-Meza, J.; Kaja, K.; Delvallée, A.; Allal, D.; Gautier, B.; Piquemal, F. Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy. Nanomaterials 2021, 11, 3104. https://doi.org/10.3390/nano11113104
Richert D, Morán-Meza J, Kaja K, Delvallée A, Allal D, Gautier B, Piquemal F. Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy. Nanomaterials. 2021; 11(11):3104. https://doi.org/10.3390/nano11113104
Chicago/Turabian StyleRichert, Damien, José Morán-Meza, Khaled Kaja, Alexandra Delvallée, Djamel Allal, Brice Gautier, and François Piquemal. 2021. "Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy" Nanomaterials 11, no. 11: 3104. https://doi.org/10.3390/nano11113104
APA StyleRichert, D., Morán-Meza, J., Kaja, K., Delvallée, A., Allal, D., Gautier, B., & Piquemal, F. (2021). Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy. Nanomaterials, 11(11), 3104. https://doi.org/10.3390/nano11113104