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Contactless Measurement of Sheet Resistance of Nanomaterial Using Waveguide Reflection Method
oleh: Ming Ye, Raja Usman Tariq, Xiao-Long Zhao, Wei-Da Li, Yong-Ning He
Format: | Article |
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Diterbitkan: | MDPI AG 2020-11-01 |
Deskripsi
Conductive nanomaterials are widely studied and used. The four-point probe method has been widely used to measure nanomaterials’ sheet resistance, denoted as <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>. However, for materials sensitive to contamination or physical damage, contactless measurement is highly recommended if not required. Feasibility of <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> evaluation using a one-port rectangular waveguide working on the microwave band in a contact-free mode is studied. Compared with existed waveguide methods, the proposed method has three advantages: first, by introducing an air gap between the waveguide flange and the sample surface, it is truly contactless; second, within the specified range of <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>, the substrate’s effect may be neglected; third, it does not require a matched load and/or metallization at the sample backside. Both theoretical derivation and simulation showed that the magnitude of the reflection coefficient <inline-formula><math display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> decreased monotonously with increasing <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>. Through calibration, a quantitative correlation of <inline-formula><math display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> was established. Experimental results with various conductive glasses showed that, for <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> in the range of ~10 to 400 Ohm/sq, the estimation error of sheet resistance was below ~20%. The potential effects of air gap size, sample size/location and measurement uncertainty of <inline-formula><math display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> are discussed. The proposed method is particularly suitable for characterization of conductive glass or related nanomaterials with <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> in the range of tens or hundreds of Ohm/sq.