Peak-tracking scanning capacitance force microscopy with multibias modulation technique

Medientyp: E-Artikel
Titel: Peak-tracking scanning capacitance force microscopy with multibias modulation technique
Beteiligte: Fukuzawa, Ryota; Takahashi, Takuji
Erschienen: IOP Publishing, 2022
Erschienen in: Measurement Science and Technology, 33 (2022) 6, Seite 065405
Sprache: Nicht zu entscheiden
DOI: 10.1088/1361-6501/ac5e62
ISSN: 0957-0233; 1361-6501
Schlagwörter: Applied Mathematics ; Instrumentation ; Engineering (miscellaneous)
Entstehung:
Anmerkungen:
Beschreibung: <jats:title>Abstract</jats:title> <jats:p>Scanning capacitance force microscopy (SCFM) is a good method for capacitance measurements using electrostatic force detection. However, to obtain an entire capacitance–voltage (<jats:italic>C</jats:italic>–<jats:italic>V</jats:italic>) curve by SCFM, a sweep of a direct current (DC) bias voltage is required at a certain fixed point on a sample surface during scan suspension, and thus the measurements become very time-consuming when we want to observe some types of image related with <jats:italic>C</jats:italic>–<jats:italic>V</jats:italic> characteristics. In this paper, we propose peak-tracking scanning capacitance force microscopy (PTSCFM) for the purpose of extracting the main feature of the <jats:italic>C</jats:italic>–<jats:italic>V</jats:italic> curve without DC voltage sweep. In PT-SCFM, alternating current voltages at three different angular frequencies, <jats:italic>ω</jats:italic> <jats:sub>1</jats:sub>, <jats:italic>ω</jats:italic> <jats:sub>2</jats:sub>, and <jats:inline-formula> <jats:tex-math><?CDATA $\omega_\mathrm{m}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, are applied together with DC voltage, <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{DC}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">D</mml:mi> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, to generate an electrostatic force, and high-order components at the angular frequencies of <jats:inline-formula> <jats:tex-math><?CDATA $\omega_2-2\omega_1$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\omega_2-2\omega_1-\omega_\mathrm{m}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>, which represent a voltage derivative of a capacitance (<jats:inline-formula> <jats:tex-math><?CDATA $\partial C/\partial V$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>V</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>) and a second-order derivative of the capacitance (<jats:inline-formula> <jats:tex-math><?CDATA $\partial^2 C/ \partial V^2$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:msup> <mml:mi>V</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>), respectively, are extracted from the electrostatic force. Then, a DC voltage, <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{p}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn7.gif" xlink:type="simple" /> </jats:inline-formula>, giving the peak of <jats:inline-formula> <jats:tex-math><?CDATA $\partial C/\partial V$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>V</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn8.gif" xlink:type="simple" /> </jats:inline-formula> is determined from <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{DC}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">D</mml:mi> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn9.gif" xlink:type="simple" /> </jats:inline-formula> to be adjusted to nullify the <jats:inline-formula> <jats:tex-math><?CDATA $\omega_2-2\omega_1-\omega_\mathrm{m}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn10.gif" xlink:type="simple" /> </jats:inline-formula> component using a feedback controller. From the obtained values of <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{p}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn11.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\partial C/\partial V$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>C</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mi>V</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn12.gif" xlink:type="simple" /> </jats:inline-formula> at <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{p}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn13.gif" xlink:type="simple" /> </jats:inline-formula>, the <jats:italic>C</jats:italic>–<jats:italic>V</jats:italic> curve can be outlined. In PT-SCFM, the distributions of those values are simultaneously imaged together with a topography without <jats:inline-formula> <jats:tex-math><?CDATA $V_\mathrm{DC}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">D</mml:mi> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn14.gif" xlink:type="simple" /> </jats:inline-formula> sweep, and when we operate PT-SCFM under various modulation frequency conditions, analyses similar to those based on the frequency dependence of the <jats:italic>C</jats:italic>–<jats:italic>V</jats:italic> property are realized. We have applied the PT-SCFM to a microcrystalline <jats:inline-formula> <jats:tex-math><?CDATA $\mathrm{Cu(In,Ga)Se_2}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi mathvariant="normal">S</mml:mi> <mml:msub> <mml:mi mathvariant="normal">e</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mstac5e62ieqn15.gif" xlink:type="simple" /> </jats:inline-formula> material to discuss the effects of surface depletion and deep-level states, from which the validity of PT-SCFM has been examined.</jats:p>

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