Correction: Stabilization of negative capacitance in ferroelectric capacitors with and without a metal interlayer

Abstract

Correction for ‘Stabilization of negative capacitance in ferroelectric capacitors with and without a metal interlayer’ by T. Rollo, et al., Nanoscale, 2020, 12, 6121–6129, DOI: 10.1039/C9NR09470A.

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The authors regret that the value of β in the caption of Fig. 4 was incorrectly given as 4.5 × 10⁹ m⁵ C⁻² F⁻¹. The correct value of β is 2.25 × 10¹⁰ m⁵ C⁻² F⁻¹. Fig. 4, along with the full corrected caption, is displayed below.

Fig. 4 Comparison between simulations and experiments. Measurements (symbols) and simulations (lines) for the MFIM structures in ref. 12 and 13. For the Hf_0.5Zr_0.5O₂–Ta₂O₅ capacitor the simulation parameters are ε_F = 33, ε_D = 23.48, t_F = 11.6 nm, t_D = 13.5 nm, α = −4.6 × 10⁸ m F⁻¹, and β = 9.8 × 10⁹ m⁵ C⁻² F⁻¹, while for the Hf_0.5Zr_0.5O₂–Al₂O₃ system the parameters are ε_D = 8, t_F = 7.7 nm, t_D = 4 nm, α = −9.45 × 10⁸ m F⁻¹ and β = 2.25 × 10¹⁰ m⁵ C⁻² F⁻¹;^12,13 for both capacitors we used ρ = 0.5 mΩ m and k = 2 × 10⁻⁹ m³ F⁻¹ m⁻¹. (a) Reversibly stored and released charge, Q, versus the top value V_MAX of the trapezoidal voltage waveform across the capacitor. (b) Simulated ferroelectric field and charge versus time produced by a trapezoidal input V_T with a pulse width of 1 μs and for different V_T amplitudes. (c) Polarisation versus ferroelectric electric field for the Hf_0.5Zr_0.5O₂–Ta₂O₅ MFIM capacitor. (d) Polarisation versus ferroelectric electric field for the Hf_0.5Zr_0.5O₂–Al₂O₃ capacitor. (e) Sketch of the band structure of the MFIM device with representation of the emission and capture mechanisms. (f) Simulated charge versus ferroelectric E_F curves for different pulse widths of the input signal and fixed density N_T = 7.5¹² eV⁻¹ cm⁻² of acceptor type interface traps with a uniform energy distribution. In these simulations the emission rate is e_n0 = 5 × 10⁴ s⁻¹, the metal gate work-function is Φ_M = 4.05 eV, and the electron affinity is χ_F = 2.2 eV for Hf_0.5Zr_0.5O₂ and χ_D = 3.2 eV for Ta₂O₅.²⁹

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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