[Paper Review] Single-dopant band bending fluctuations in MoSe$_2$ measured with electrostatic force microscopy

Megan Cowie, Rikke Plougmann+2 more|arXiv (Cornell University)|Sep 30, 2021

Force Microscopy Techniques and Applications4 citations

TL;DR

This study uses frequency-modulated atomic force microscopy (fm-AFM) to directly measure single-dopant-induced band bending fluctuations in multilayer MoSe₂, revealing intrinsic, bias-dependent surface potential noise arising from localized charge state transitions. The key finding is that these fluctuations cause nonparabolic frequency shift responses in fm-AFM, with spatially heterogeneous timescales of charge reorganization, demonstrating that noise in such 2D semiconductor devices originates from individual dopant dynamics rather than external sources.

ABSTRACT

In this work, we experimentally demonstrate two-state fluctuations in a metal-insulator-semiconductor (MIS) device formed out of a metallic atomic force microscopy tip, vacuum gap, and multilayer MoSe$_2$ sample. We show that noise in this device is intrinsically bias-dependent due to the bias-dependent surface potential, and does not require that the frequency or magnitude of individual dopant fluctuations are themselves bias-dependent. Finally, we measure spatial nonhomogeneities in band bending (charge reorganization) timescales.

Motivation & Objective

• To investigate the origin of intrinsic noise in metal-insulator-semiconductor (MIS) devices formed by a metallic AFM tip and multilayer MoSe₂.
• To determine whether noise in such systems arises from bias-dependent fluctuations in individual dopant charge states or from external sources.
• To map spatial variations in the timescales of band bending (charge reorganization) due to single-dopant dynamics.
• To establish a quantitative model linking tip-sample force, surface potential, and fm-AFM frequency shift in semiconducting 2D materials.

Proposed method

• Employed frequency-modulated atomic force microscopy (fm-AFM) to measure tip-sample forces and extract frequency shift and excitation signals on multilayer MoSe₂.
• Modelled the MIS capacitor system using Poisson’s equation to calculate surface potential $V_S$ as a function of applied bias, acceptor concentration, and Fermi level difference.
• Derived the tip-sample force $F_{ts}$ from the surface potential and permittivity, using $F_{ts}/a_{ ext{tip}} = Q_S^2 / (2ar{})$.
• Simulated time-dependent force and frequency shift by tracking sinusoidal tip oscillation over varying tip-sample separation $z_{ ext{ins}}$ and surface potential.
• Fitted experimental frequency shift and excitation data to the model using 14 parameters, including material (band gap, $N_A$, $\epsilon$) and fm-AFM-specific (amplitude, $k$, $Q$) parameters.
• Performed sensitivity analysis on fit parameters to assess their influence on the shape and scaling of the frequency shift curve.

Experimental results

Research questions

• RQ1 What causes intrinsic noise in metal-insulator-semiconductor (MIS) devices based on multilayer MoSe₂ when probed with an AFM tip?
• RQ2 Is the observed noise in the frequency shift response due to bias-dependent fluctuations in individual dopant charge states?
• RQ3 How do spatial variations in band bending dynamics manifest across the MoSe₂ surface?
• RQ4 To what extent do material parameters such as acceptor concentration and permittivity determine the shape of the fm-AFM frequency shift curve?
• RQ5 Can a theoretical model based on electrostatics and Poisson’s equation quantitatively reproduce experimental fm-AFM measurements in 2D semiconductors?

Key findings

• The experimental frequency shift response in MoSe₂ is nonparabolic due to band bending, in contrast to the parabolic response observed on SiO₂, confirming the role of semiconducting behavior.
• Single-dopant fluctuations induce measurable, bias-dependent surface potential variations that directly cause nonparabolic frequency shift responses in fm-AFM.
• Spatially resolved measurements show that band bending relaxation timescales are non-uniform across the MoSe₂ surface, with fluctuations observed at some locations (e.g., C, E) but not others (e.g., A, B, D).
• The model accurately reproduces experimental data using only three material parameters—band gap $E_g$, acceptor concentration $N_A$, and permittivity $\epsilon$—while tip-specific parameters act as scaling factors.
• Sensitivity analysis confirms that the shape of the frequency shift curve is primarily determined by $E_g$, $N_A$, and $\epsilon$, while other parameters (e.g., tip radius, oscillation amplitude) only scale the response.
• The study demonstrates that noise in such 2D semiconductor devices arises intrinsically from localized dopant charge state transitions, not from external or frequency-dependent fluctuations.