Method for obtaining the dielectric constant of a dielectric sheet
In a method for obtaining the dielectric constant of a dielectric sheet, a modulation voltage is applied to a semiconductor capacitor and a first parallel plate capacitor to measure a first scanning capacitance microscopy signal. Then, the first parallel plate capacitor is replaced with a second parallel plate capacitor to measure a second scanning capacitance microscopy signal corresponding to the semiconductor capacitor and the second parallel plate capacitor. Finally, the second parallel plate capacitor is replaced with a third parallel plate capacitor to measure a third scanning capacitance microscopy signal corresponding to the semiconductor capacitor and the third parallel plate capacitor. Based on the scanning capacitance microscopy signals and dielectric constants and the equivalent physical thicknesses of the dielectric sheets of the first parallel plate capacitor and second parallel plate capacitor, the dielectric constant of the dielectric sheet of the third parallel plate capacitor is obtained.
1 . A method for obtaining the dielectric constant of a dielectric sheet comprising:
connecting a semiconductor capacitor and a first parallel plate capacitor in series, wherein a first dielectric sheet of the first parallel plate capacitor has a known first equivalent physical thickness d1 and a known first dielectric constant ε1 and the semiconductor capacitor has a depletion region;
by a scanning capacitance microscopy, applying a modulation voltage to the semiconductor capacitor and the first parallel plate capacitor to periodically change a width of the depletion region and measuring a first scanning capacitance microscopy signal corresponding to the semiconductor capacitor and the first parallel plate capacitor;
replacing the first parallel plate capacitor with a second parallel plate capacitor and connecting the semiconductor capacitor and the second parallel plate capacitor in series, wherein a second dielectric sheet of the second parallel plate capacitor has a known second equivalent physical thickness d2 and a known second dielectric constant ε2;
by the scanning capacitance microscopy, applying the modulation voltage to the semiconductor capacitor and the second parallel plate capacitor to periodically change a width of the depletion region and measuring a second scanning capacitance microscopy signal corresponding to the semiconductor capacitor and the second parallel plate capacitor;
calculating an impedance ratio based on the first scanning capacitance microscopy signal, the second scanning capacitance microscopy signal, and (d2/d1)×(ε1/ε2);
replacing the second parallel plate capacitor with a third parallel plate capacitor and connecting the semiconductor capacitor and the third parallel plate capacitor in series, wherein a third dielectric sheet of the third parallel plate capacitor has a known third equivalent physical thickness d3 and the first dielectric sheet, the second dielectric sheet, and the third dielectric sheet have the same areas;
by the scanning capacitance microscopy, applying the modulation voltage to the semiconductor capacitor and the third parallel plate capacitor to periodically change a width of the depletion region and measuring a third scanning capacitance microscopy signal corresponding to the semiconductor capacitor and the third parallel plate capacitor; and
obtaining a third dielectric constant of the third dielectric sheet of the third parallel plate capacitor based on the first scanning capacitance microscopy signal, the third scanning capacitance microscopy signal, the third equivalent physical thickness, and the impedance ratio.
2 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 1 , wherein the semiconductor capacitor is a metal-oxide-semiconductor capacitor.
3 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 1 , wherein the semiconductor capacitor further comprises a conductive probe that is electrically grounded.
4 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 1 , wherein the first dielectric sheet, the second dielectric sheet, and the third dielectric sheet comprise an insulating material.
5 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 1 , wherein the first scanning capacitance microscopy signal, the second scanning capacitance microscopy signal, the first equivalent physical thickness, the second equivalent physical thickness, and the impedance ratio meet a following equation:
S1/S2=ZR×(d2/d1)×(ε1/ε2)+(1−ZR), where S1 represents the first scanning capacitance microscopy signal, S2 represents the second scanning capacitance microscopy signal, and ZR represent the impedance ratio.
6 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 5 , wherein the first scanning capacitance microscopy signal, the third scanning capacitance microscopy signal, the first equivalent physical thickness, the third equivalent physical thickness, and the impedance ratio meet a following equation:
S1/S3=ZR×(d3/d1)×(ε1/ε3)+(1−ZR), where S1 represents the first scanning capacitance microscopy signal, S3 represents the third scanning capacitance microscopy signal, ZR represent the impedance ratio, and ε3 represents the third dielectric constant.
7 . The method for obtaining the dielectric constant of a dielectric sheet according to claim 5 , wherein the impedance ratio=an impedance corresponding to the first dielectric sheet divided by (an impedance corresponding to the semiconductor capacitor+the impedance corresponding to the first dielectric sheet).