Review Report
Manuscript title: Field emission: calculations supporting a new methodology of comparing theory with experiment
Manuscript ID: RSOS-220748
The work presented in this manuscript is a theoretical investigation of the voltage dependence of the notional emission area for individual emitters with well-defined geometries. This dependence, of the notional area, is investigated by calculating the notional cap-area efficiency and the corresponding exponent (k) to which the voltage (in the pre-exponential term of the FN and/or FN-like equation(s)) is raised. Some experimental and theoretical values of this exponent are also presented for electronically ideal field emission systems and compared with the predicted values for the geometries presented.
The work and results presented in this manuscript are very interesting and worth publishing provided minor revisions are made as suggested below:
Page #2, Equation (1): It is suggested that the voltage conversion length “ζ” be linked to the previously used term “field-to-voltage conversion factor β”. The statement “The VCL (ζC) is a system characterization parameter, not a physical length.” may be elaborated because generally, the conversion factor (relating the electrostatic field and the measurable quantity of voltage difference) is a physical parameter. So authors have to make it clear that in a field emission system the conversion factor may be considered as a system characterization parameter.
Page #2; the statement “If the characteristic VCL is constant for a given FE system”. Authors are requested to give an example of such a system.
Page #2; the sentence “If the characteristic VCL is not constant, due to some "system complication" (e.g., significant series resistance, but many other possible complications exist),”. Complications related to emitter geometry must be referred to in this location because series resistance effects may not be well realized in connection with equation (1).
Page #3: The statement “This curvature makes it difficult to reach accurate quantitative conclusions from the plot intercept on the vertical axis.”. Authors are requested to comment on the fact that the plot intercept on the vertical axis (of the FN plot; a graph of the I(V) data as ln(I//V2) versus 1/V)) occurs at V= ∞ which is (mainly) not physically achievable.
Page #4; The introduction of Equation (2): Authors are invited to refer to recent work by M. Zubair et al.*, where an FN-type equation with a similar exponent is derived to account for the emitter surface condition.
* Muhammad Zubair , Yee Sin Ang, Lay Kee Ang, Fractional Fowler–Nordheim Law for Field Emission From Rough Surface With Nonparabolic Energy Dispersion, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 65, NO. 6, JUNE 2018. http://dx.doi.org/10.1109/TED.2017.2786020.
Page #4: The term AHFP. I am of the opinion that the term AHFP is avoided or replaced with a more convenient term. Forbes in 2009 used the term “correction factor” to refer to the exponent k appearing in equation (1) of the present work. Zubair et al. used the term “fractional dimension space parameter” in their work to refer to the exponent. The latter seems more convenient as it reflects the sensitive dependence of the exponent value on the emitter shape.
Equations 17 and 18 on Page #9 and Figure 1 on Page #11. Results show that the notional area efficiency factor (g_n) varies with the apex electric field. This conclusion is supported by work accomplished by Jensen using analytical approximation (cited as reference [14] in the present work). The reviewer agrees with the conclusion made. In addition, further support of this conclusion from the experiment may also be referred to (see for example the application of data extraction model on field emission data from LaB6 nano-emitter by Ahmed Al-Tabbakh, Turkish Journal of Physics 42, 27-32 (2018)). In this work, the idea of the notional emission area is determined from the experimental data analysis.
Authors presented notional area efficiency equations for HSP and HEP geometries. What about HCP and SRC geometries?
Pages #9 and #10, Equations (18), (19) and (23) must be written clearly.
The term “apex sharpness ratio” may better be replaced with “emitter aspect ratio”.
Which theory proves better the idea of the notional emission area and its variation with the apex field?
Did the authors attempt primary comparisons of the total emission current (resulting from the application of the calculated exponent) with some experimental data?
End of report