Demonstration of resonant tunneling effects in metal-double-insulator-metal (MI2M) diodes

Although the effect of resonant tunneling in metal-double-insulator-metal (MI2M) diodes has been predicted for over two decades, no experimental demonstrations have been reported at the low voltages needed for energy harvesting rectenna applications. Using quantum-well engineering, we demonstrate the effects of resonant tunneling in a Ni/NiO/Al2O3/Cr/Au MI2M structures and achieve the usually mutually exclusive desired characteristics of low resistance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{0}^{DC} \sim$$\end{document}R0DC~ 13 kΩ for 0.035 μm2) and high responsivity (β0 = 0.5 A W−1) simultaneously. By varying the thickness of insulators to modify the depth and width of the MI2M quantum well, we show that resonant quasi-bound states can be reached at near zero-bias, where diodes self-bias when driven by antennas illuminated at 30 THz. We present an improvement in energy conversion efficiency by more than a factor of 100 over the current state-of-the-art, offering the possibility of engineering efficient energy harvesting rectennas.


Simulation-based resonant tunneling analysis:
In p. 2, Col. 2, L. 16, you mention "These measured values were used as a starting point for the simulations, and were varied…"referring to the diode cross section area and the nominal oxide layer thickness where these values have been measured using (SEM), and (VASE) methods respectively. My questions here are: 1. For this area, is there a variation among the fabricated devices? How much is that? 2. For the thickness, a similar statistical analysis of the variation is quite beneficial (just for the measured and not for the simulated which you have already done). 3. For the interface between the oxides, the surface metal roughness is considered very important as it could give rise to other forms of tunnelling (i.e. a smoother surface gives closer results to theoretical study output). Also here, an indication of the surface roughness is useful. 4. The variation of effective mass, electron affinity, and work function values (even for the same oxides and metals but for different junctions and crystallization forms, plays a vital role in defining the current values) if you could provide a table to compare your values with other results from the literature?
Rectification enhancement at 10.6 µm: In p.4, Col.2, L.22 regarding the discussion of the voltage division difference between AC and DC: This point is unclear and needs more explanation.
For the use of the dielectric constant, I think they have been used just for the calculation of the image forces lowering. If you are talking about typical voltage division techniques calculation for MIIM diodes as the one mentioned in [3], then I think the electric field density continuity at the boundary condition is true down to the DC! On the other hand, if you are talking about this point based on the "bypassing" of the tunnelling structure that happens at higher frequencies due to the reduced capacitor reactance, which results in poor rectification for the whole system -simply because much more current passes in the linear capacitive part than the nonlinear part-, then it needs to be explained in a different way to not get it wrong.
A mathematical model how you find RDC is highly beneficial to support what you say both in your paper [22] and in this paper.
Format and Language: • In p.5: Figure 3: Seems to not be cross referenced in the text.   Yes, but metal-insulator interfaces should has been discussed in depth since the thinner the oxide layers the more electrons would be trapped at these interfaces due to inter-atomic diffusion and electron drift and grain boundary and oxygen vacancy effects that are resulting in less mobility and lower responsivity (i.e.,high resistivity due to that the area is in nanometer scale) and nonlinearity (anisotropy)!? Moreover,it is recommended to try different metal/oxide/oxide/metal combinations in addition to Ni/NiO/Al2O3/Cr/Au to show if this observation is independent of metal and oxides type and amount of layers.
Reviewer #3: Remarks to the Author: The authors reports improvement of responsivity and conversion efficiency for electromagnetic wave at 30THz using metal-insulator-metal (MI2M) rectifier with antenna structure, which can be reasonably explained by current-voltage characteristics derived from resonant tunneling transport model. The results are important and suggestive. For further understandings, the manuscript should be revised accordance with the following questions and comments.

1)
The basic principle of rectification is the nonlinearity or asymmetry around V=0 of the currentvoltage characteristics. Among the possible conduction mechanisms of MI2M, it should be described in the text why resonant tunneling is more advantageous for developing asymmetry in the current-voltage characteristic than other conduction mechanisms. In particular, discuss the advantages comparing to for example Schottky junctions or single barrier tunneling diodes.

2)
Frequency of 30THz used in this study is much higher than cut off frequency (1/2*PI*CR) of the MI2M diodes. Is it consistent to rectification output of the diode? Equivalent circuit may be helpful to discuss the detail.

3)
Relation between Fig.1(a) and (b) is difficult to understand. Red solid line in Fig.1(a) exhibits steep increase of responsivity with keeping resistance almost constant under resonant tunneling region. However, in the Fig.1(b), experimental plots distributes in wide range of resistance (10^3-10^5 ohm) and significant increase of responsivity can not be seen and the responsivity values seems to be smaller than the value shown in Fig.1(a). Therefore it is difficult to determine the validity of the description that the results plotted in Fig.1(b) is based on resonant tunneling.

4)
There are some miss-type errors in figure caption of Fig.4.

5)
In Fig.4, mechanism of resonant tunneling is comprehensive and the reason of resistance reduction at resonant tunneling shown in (b) is understandable. However, it is difficult to understand increase of responsivity because origin of responsivity is asymmetry of I-V curve instead of resistance itself. Explanation of the origin of responsivity may be helpful in the text.

Introduction
The presented paper provides an insight into the operation of double-insulator tunnelling diodes (MIIM) from a more industrial point of view. The novel contribution of the paper to the field is based on: • The work is aimed at better understanding of the adopted theory and the artifacts that accompany the tunnelling diode industrial process. • Discovery, for a certain insulator thickness range, of an inverse relationship between the insulator thickness and the zero-bias resistance 0 • A parametric sweep research is conducted to analyse the impact of the design parameters on the overall performance in a yield-analysis-like study.
According to the journal regulations, the article features the same structure as other published materials, so a brief introduction is presented first followed by a demonstration of the obtained results for different scenarios. In the end, a discussion is demonstrated and the utilized methods in the study are showcased.
Although the contribution of the paper is worth publishing, there are, however, some conceptual issues that need to be addressed by the authors to consummate the work in the final version.
The formatting and language is okay with just minor misprints which are mentioned in this letter.

Response:
We thank the reviewer for their thorough and insightful review of our paper. We have addressed Each of the reviewer's points below and have revised the manuscript to clarify all the points and add the details needed to support them.

Conceptual Issues:
Abstract: You mentioned that you "achieve the usually mutually exclusive desired characteristics of low resistance ( 0 ~ 13 0.035 2 ) and high responsivity ( 0 = 0.5 / )" with conversion efficiency more than 100 times more than the state-of -the-art energy harvesting rectennas. In [1], for example, the writers set the figures of merit that can be considered for an efficient rectenna -or rectifier-. That is, asymmetry, nonlinearity, responsivity, and dynamic resistance. Also, the results mentioned in Hemour et al [2], correspond to the set values. Comparing these values with what you have obtained, which I agree is outstanding, gives an indication that there is still way to improve. For the reader I think it is good to mention some comparison with more efficient commercial devices, even in the lower GHz range just to give a good idea where the tunnelling devices are placed.

Response:
We thank the reviewer for this suggestion and very good references. The mentioned four figures of merit are the ones we used to evaluate our diodes. We focus on responsivity since it is related to asymmetry and nonlinearity. The challenge lies in the dance between responsivity and resistance to achieve the needed cutoff frequency for the desired application. Schottky diode have high responsivities and high resistances that cannot be used for energy harvesting applications with terahertz cutoff frequencies. We agree such a comparison would be good for the audience.

Simulation-based resonant tunneling analysis:
In p. 2, Col. 2, L. 16, you mention "These measured values were used as a starting point for the simulations, and were varied…"referring to the diode cross section area and the nominal oxide layer thickness where these values have been measured using (SEM), and (VASE) methods respectively. My questions here are:  [5], which is different from our 4.7 eV used in the simulation. We are working on better understanding and characterizing that oxide. Our Al2O3 on the other hand has been extensively studied in our most recent paper [6]. Our value of 3.45 eV is due to the nonstoichiometric Al2O3 [6] compared to a value of 1.4-1.6 eV for thin stoichiometric Al2O3 [7,8,9].  Belkadi et al. [24].
For the use of the dielectric constant, I think they have been used just for the calculation of the image forces lowering. If you are talking about typical voltage division techniques calculation for MIIM diodes as the one mentioned in [3], then I think the electric field density continuity at the boundary condition is true down to the DC! Response: In [3] referenced here, the dielectric constant is not just used to calculate the image forces lowering but is in fact used to determine the voltage division of the structure using a capacitive method as would be done at high frequency. The simulator works by determining an energy-band profile at a certain bias using the condition for continuity of the electric displacement vector at each insulator interface, which depends on dielectric constants. This is an erroneous method since internal oxide resistances dominate at DC and not capacitive voltage division [6].
On the other hand, if you are talking about this point based on the "bypassing" of the tunnelling structure that happens at higher frequencies due to the reduced capacitor reactance, which results in poor rectification for the whole system -simply because much more current passes in the linear capacitive part than the nonlinear part-, then it needs to be explained in a different way to not get it wrong.

Response:
Though correct, that is not the point we are trying to make here. We simply want to point out one thing: that under the absence of resonant tunneling, resistance typically increases in MI 2 M structures from DC to under illumination. In this structure, the expected increase is due to the dielectric constants of Al2O3 and NiO. We hope rewording that section has helped in making and clarifying our point.
A mathematical model how you find RDC is highly beneficial to support what you say both in your paper [22] and in this paper.

Response:
We thank you for the suggestions. We have added this to our supporting material.
Format and Language: • In p.5: Figure 3: Seems to not be cross referenced in the text. Response: Figure 3 is cross referenced in the section titled "Rectification enhancement at 10.6 m".

Response:
We thank the reviewer for pointing these errors out. We have made the suggested corrections for points 1 and 2 in the manuscript (highlighted). Points 3, 4 and 5 cannot be found in our manuscript.

Reviewer #2 (Remarks to the Author):
-What are the major claims of the paper?
An improvement in energy conversion efficiency by more than a factor of 100 over the current state-of-the-art using oxide thicknesses to sub-nanometer accuracy.
Are they novel and will they be of interest to others in the community and the wider field?
[Comment] Yes, but metal-insulator interfaces should has been discussed in depth since the thinner the oxide layers the more electrons would be trapped at these interfaces due to inter-atomic diffusion and electron drift and grain boundary and oxygen vacancy effects that are resulting in less mobility and lower responsivity (i.e.,high resistivity due to that the area is in nanometer scale) and non-linearity (anisotropy)!?

Response:
We thank the reviewer for the comments. We agree with the reviewer that the thin nature of our metals and insulators creates non-ideal interfacial layers. If these anomalies were present in our structures, electron mobility of the electrons that traverse through NiO/Al2O3 layers would be reduced because the carrier transport would be dominated by bulk conduction (Poole-Frenkel). In other words, carrier transit time would not be in the order of femtoseconds as we would expect for quantum mechanical tunneling. One key requirement for a MIM based rectenna structure that operates at optical frequencies is to have a sufficiently fast (transit times must be in femtoseconds) carrier transport mechanism. In this work, we verified the high frequency operation of Ni/NiO/Al2O3/Cr/Au rectenna devices at 28.3 THz. Therefore, we can determine these interfacial and material defects are not present in our structures.
Unfortunately, because out metals are reactive and therefore pose issues when attempting to perform surfacesensitive measurements such as XPS, UPS and IPES which require pure metallic films to acquire clean core level information. Our reactive metals form native oxides that would lead to wrong conclusions about the whole MIM stack in the analysis process. Although we acknowledge that issue, we had to take an experimental approach that relies on predictions by a quantum tunneling simulator. To verify whether these interfacial issues were the reason for the improvement in responsivity and nonlinearity, we extended our analysis to 28.3 THz..
We have added the following sentence in the manuscript on page 4, column 2: This high frequency response confirms that the observed responsivity and resistance relationship is not related to electron mobility or interfacial issues.
[Comment] Moreover,it is recommended to try different metal/oxide/oxide/metal combinations in addition to Ni/NiO/Al2O3/Cr/Au to show if this observation is independent of metal and oxides type and amount of layers.

Response:
Based on our experience, Ni/NiO and Nb/Nb2O5 yield small barrier heights. Since our GSM fabrication process requires angled and directional evaporations, Nb was not an option (its melting point is too high for thermal evaporations). Therefore, we chose NiO because of the small barrier (~0.1 eV) it creates with Ni. This is important to achieve a small differential resistance and also to push resonant tunneling towards zero-bias [1][2][3]. If we chose a different interface, a large bias would need to be applied to get the metal Fermi level aligned with a bound state in the quantum well [1][2][3][4][5]. Many groups have worked on metal-insulator-metal diode technology with various material combinations, aiming at thermal energy harvesting. One common factor among most of MIM diode researchers is using Al2O3 as a dielectric in their material stack [Al2O3 paper, table 1]. This is solely due to its small dielectric constant of 0.8 at 28. 3 THz, leading to a low capacitance and the possibility of high-frequency operation. Most of the high frequency friendly uncompensated rectennas were fabricated with Al2O3 [6,[8][9][10].
Without going into the details of other materials tested, we have added the following sentence in the manuscript on page 6, column 2: We believe this is why this behavior of decreasing resistance with increasing responsivity has not been observed in any of our other MI 2 M diode material combinations such as Co3O4/TiO2, NiO/Nb2O5 or NiO/TiO2.