Scholarly article on topic 'Terahertz harvesting with shape-optimized InAlAs/InGaAs self-switching nanodiodes'

Terahertz harvesting with shape-optimized InAlAs/InGaAs self-switching nanodiodes Academic research paper on "Physical sciences"

Share paper
Academic journal
AIP Advances
OECD Field of science

Academic research paper on topic "Terahertz harvesting with shape-optimized InAlAs/InGaAs self-switching nanodiodes"

Terahertz harvesting with shape-optimized InAlAs/InGaAs self-switching nanodiodes

Irving Cortes-Mestizo, Victor H. Méndez-García, Joel Briones, Manuel Perez-Caro, Ravi Droopad, Stefan McMurtry, Michel Hehn, François Montaigne, and Edgar Briones,

Citation: AIP Advances 5, 117238 (2015); doi: 10.1063/1.4936792 View online: View Table of Contents: Published by the American Institute of Physics

(■) CrossMark

VHi «-dick for updates

Terahertz harvesting with shape-optimized InAlAs/InGaAs self-switching nanodiodes

Irving Cortes-Mestizo,1 Victor H. Méndez-García,1 Joel Briones,2 Manuel Perez-Caro,3 Ravi Droopad,3 Stefan McMurtry,4 Michel Hehn,4 François Montaigne,4 and Edgar Briones1,2,a

1CIACyT, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78210 SLP, México 2Department of Mathematics and Physics, ITESO, Jesuit University of Guadalajara, Tlaquepaque, 45604 Jalisco, Mexico

3Ingram School of Engineering, Texas State University, San Marcos, TX 78666, USA 4Institut Jean Lamour, CNRS, Université de Lorraine, F-54506 Vandoeuvre Les Nancy, France

(Received 25 August 2015; accepted 16 November 2015; published online 24 November 2015)

In this letter, self-switching nanochannels have been proposed as an enabling technology for energy gathering in the terahertz (THz) regime. Such devices combine their diode-like behavior and high-speed of operation in order to generate DC electrical power from high-frequency signals. By using finite-element simulations, we have improved the sensitivity of L-shaped and V-shaped nanochannels based on InAlAs/InGaAs samples. Since those devices combine geometrical effects with their rectifying properties at zero-bias, we have improved their performance by optimizing their shape. Results show nominal sensitivities at zero-bias in the order of 40 V-1 and 20 V-1, attractive values for harvesting applications with square-law rectifiers. © 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. []


Self-switching diodes (SSDs) are planar semiconductor structures at the core of new advances in terahertz detection and generation.1-4 The novel functionalities that those devices exhibit such as the ability to detect extremely weak signals without applied bias,5,6 their high sensitivity7 and their capability to operate in the terahertz regime5,8 make the SSD concept a rewarding tool that have opened a broad range of applications.9 In this regard, an area of emerging interest where SSDs find potential applications is energy harvesting of long wave thermal infrared emission emitted by Earth.10-12 Earth's emitting thermal radiation represents a source of renewable energy, which covers the 7-20 ^m spectral range13 and also longer wavelengths, this range can be easily reached by increasing the SSD's mobility in low temperature process. The recently explored alternative to generate renewable energy from thermal radiation is the use of high-speed rectifiers coupled to terahertz and infrared antennas, known as rectennas.11 These devices convert the free-propagating infrared radiation into DC power by employing a rectification mechanism. The efficiency of the rectennas is directly related to the performance of the employed rectifier.11 In this context, novel functionalities like the high sensitivity without applied bias, make the SSDs good candidates for the development of high-speed rectifiers, able to recover the longer wavelengths of the thermal emission of Earth (>20^m) and also some other artificial thermal sources such as engines or furnaces.

Self-switching diodes are obtained by simply tailoring a narrow asymmetrical channel on a semiconductor. The channels asymmetry results in a remarkably diode-like behavior induced by the surface charges at flanges.14,15 The SSDs can be understood as a two-dimensional field-effect transistor with gate and drain short-circuited where flanges act as a double lateral-gate terminal.6 The basic

aAuthorto whom correspondence should be addressed. Electronic mail:, 2158-3226/2015/5(11 )/117238/10 5,117238-1 ©Author(s) 2015 ii^MSM

mechanism that leads to the transport asymmetry of a SSD is explained in terms of the opening of the channel due the modulation of carriers (electrons) along the channel by those lateral gates.14 This concept has been explored using two-dimensional electron gas (2DEG) systems such as In-AlAs/InGaAs14 and AlGaAs/GaAs7 heterostructures; but the work principle is not entirely based on the 2DEG properties. As far as known, these types of devices have been fabricated in bulk materials like Silicon,16 transparent semiconductors like ZnO17 and ITO;18 and recently a graphene-based SSD has been demonstrated.19-21

In this regard, the most explored channel's geometry presenting a self-switching behavior has been until now the L-shape channel.6 This planar geometry has permitted to reveal the diode-like behavior of such nanostructures and explain their transport properties in terms of the lateral surface charge density. Detection responsivities values around 75 V/W, has been exhibited by L-shape SSDs based on InAs/AlGaSb high-mobility samples.1 Furthermore, Pan et al.,22 recently developed a long-wave infrared device able to recover the energy of radiation emitted thermal blackbodies, opening a new route for the design of advanced harvesting devices.

In this contribution, we analyze and optimize the performance of two different types of self-switching diodes with regard to provide an enabling technology for energy gathering in the terahertz region. Since the self-switching diodes combine geometrical effects with their electronics transport properties their performance is improved by optimizing their shape. We particularly focus on the referred V-shape asymmetrical channels,3 and compare their performance with that of the L-shape channels. By using the V-shape geometry the lateral surface-charges are expected to be reduced leading to structures with lower resistance values; typically around some hundreds of kilo-ohms.1 At this respect, some drawbacks concerning the resistance of the channels such as the difficult impedance matching with an acquisition system are expected to be improved.


The goal of this contribution is to evaluate the harvesting performance of the V-shape channels and compare it with that of the L-shaped channels counterpart. We have performed a systematic analysis where the width W, the length L and the vertical and horizontal trenches width (WV and WH) of the channels are optimized. The parameters are depicted in Fig. 1. The aperture Wo or vortex width of the V-shape structure is also analyzed. The dimensions shown in Fig. 1, define the reference geometries from which the parametric study is performed; we have varied a chosen parameter while the others were fixed.

The transport properties of the self-switching geometries like the electron charge distribution and its dependence with the applied bias are evaluated by employing a commercial software package based on the finite-element method (ATLAS-SILVACO). As a first approach, we use a two-dimensional model as that reported for 2DEG-based InGaAs SSD8,23 and SOI16 structures. The analysis was performed on InAlAs/InGaAs heterostructures whose layered sequence is described by Song et al.15 Numerical simulations were run (at room-temperature) by introducing a background doping n = 1x1017 cm-3, an electron mobility ^ = 12000 cm2/Vs and the impurity scattering set to off. The grooves were filled by air (er = 1) leading to a surface charge density a = 0.4x1012 cm-2 at the semiconductor-dielectric interface. The contact resistivity was fixed to 1x10-8 Q cm2, resistivity value for InGaAs devices suitable to THz applications.24

The simulations were carried out in order to obtain the current-voltage curves of each single channel. By using these results, it was possible to evaluate the ability of channels to harvest the electrical energy of low-voltage signals. In the low-voltage regime, the channels behave as square-law rectifiers that generate DC electrical power. The magnitude of the DC out-put is given by:25-27

vdc = -1 ■ yV) ■ i Vn|2 = -1 ■ Y0 ■ Vn|2, (1)

'DC = - 4R0 ■ w) 1 vn 1 2 = - 4R0 ■ Y0 -|vn 1 2 (2)

FIG. 1. Schematic representation of the proposed self-switching nanochannels: (a) L-shape nanochannel and (b) V-shape nanochannel.

where Vin is the amplitude of the AC signal supplied to the cannel, R0 the resistance of the channel at zero-bias and I"(V)//' (V) the ratio the second to the first derivate of the current-voltage curve, currently referred as the sensitivity y0 of a square-law type rectifier at zero-bias.25 In particular, the higher the non-linearity of the current-voltage characteristic, defined as:


N = IV • (3)

the higher the sensitivity of the structures, which can be re-written as:26,27

Y0 = R0 ■ N0, (4)

and the higher the DC output.


A. Asymmetric charge distribution

As a first step, we have shown the self-switch behavior of the references geometries by evaluating and analyzing the electron-charge distribution n along their 2DEG-plane. Numerical results for different bias sates are presented in Fig. 2.

FIG. 2. Electron charge distribution along the 2DEG-plane inside the nanostructures under zero, reverse (V = -0.5V) and forward (V = +0.5V) voltage bias. The background carrier-density set at 1017 cm-2 (denote by the red color) is strongly lowered inside the channels due to lateral-charge effects.

When not-bias is applied, simulations show a drastic reduction of the background carrier-density (fixed at 1017 cm-3) inside the channels (Fig. 2(a) and 2(b)) as a consequence of the electron-filling of the surface-sates created at grooves walls. Carrier density decreases from the background value to values close to 1014 and 1012 cm-3 for the L-shape and V-shape geometries, respectively, defining high-resistive or not-conductive channels. By comparing both geometries, we remark resistivity changes are concentrated at vortex (-30 nm) for the V geometry while remaining homogenous all along the L-shape channel, as expected for that geometry.

On the other hand, the low-carrier density exhibited by the non-polarized structures (comparable to that of a typical insulator) indicates that a minimum bias or voltage threshold VTh, is required in order to propitiate electron conduction. In that direction, the lower the carrier concentration is the higher the VTh results. For the case of localized effects such as the high-resistivity vortex of the V-shape channel, the voltage threshold is considerably reduced. For short depletion-region length low bias is required to turn the SSD on.

When reverse bias is applied (e.g. Vbias = -500 mV) the charge-depletion effects are enhanced along the channel due to the transversal E-field that appears at the grooves-walls, lowering the carrier-density inside channels as observed in Fig. 2(c) and 2(d). This state is considered as a pinch-off condition blocking any current along the channel due to the lack of carriers. However, inverse current can be established when the bias is high-enough to overcome the lateral-depletion effects. Numerical results show these enhanced surface-effects are well established on the L-shape geometry (carrier density reduced by a 2 factor) while they are weak for the V-shape channel due to its small depletion region. Fig. 2(e) and 2(f) show the carrier distribution at Vbias = +500 mV for the L-shape and V-shape geometry, respectively. Under forward polarization the carrier-density increases several orders of magnitude, close to the background concentration (~1015-1016 cm-3 for both of the geometries) since the depletion-region is reduced by the transversal E-field. At this condition the electron transport along the channel takes place.

B. Diode-like behavior and DC power generation

The complete voltage-behavior of the reference structures is summarized by the current-voltage curves shown in Fig. 3(a). A well-established diode-like behavior is exhibited by the L-geometry,

FIG. 3. Simulations results of the reference self-switching nanochannels: (a) current-voltage characteristic curves, (b) differential resistance and (c) non-linearity of the current-voltage curves and (d) channels sensitivity. Circles refer to the results of the L-shape geometry and stars to the V-shape geometry.

presenting a voltage threshold around -50 mV. The V-shape channel exhibits a threshold of -100 mV, nevertheless it also presents a reverse breakdown voltage of -140 mV, which is related to the to the short depletion width (along the channel) that is easily filled up when a reverse bias above this value is applied.

The differential resistance, (dI(V)/dV)-1, key issue for determining the impedance matching between the channels and the signal acquisition system, is shown in Fig. 3(b). The results show that the resistance of the L-shape channel is bigger than the resistance exhibited by the V-shape channel; as expected for those geometries where the surface-charge effects are weak. However, this is not the case for the region close to zero bias (particularly from -100 mV to 200 mV). Even if the depletion region is reduced in the V-shape channel, effects at zero-bias are significant due to the near electric-field enhancement at vortex, as seen in Fig. 2(a). At zero-bias the resistances of the structures are around 0.8 M^ and 1.7 M^, for the L and V channel respectively.

The non-linearity of the current-voltage characteristic curve and sensitivity of both channels are shown in Fig. 3(c) and Fig. 3(d), respectively. Numerical values obtained for these parameters at zero-bias are 22 A/V2 and 5 A/V2 for the non-linearity, and 18 V-1 and 8 V-1 for the channel sensitivity. These parameters are key issues for the generation of DC power; the higher the sensitivity the higher the DC signals, according to the relationships (1) and (2). The most explored high-frequency rectifiers able to operate up to optical frequencies are based on metal-insulator-metal27,28 or metal-insulator-insulator-metal tunnel barriers.29 However, the efficiency of those devices is low because of their poor diode-like behavior. For example, recent advances on Cu/CuO/Au barriers had permitted those rectifiers to reach zero-bias sensitivity as high as 4 V-1.30 By using L and V-shape channels as THz high-speed rectifiers the sensitivity of the device can be increased by a 2 or 5 factor, respectively.

On the other hand, the DC signals generated by the channels will exhibit the so-called Johnson-Nyquist noise. This noise process has been identified as the dominating process for unbiased self-switching nanochannels.31-33 A first estimation of the noise-equivalent power (NEP) expected from these devices can be obtained by using the equation:6

NEP = ^, (5)

where Rv is the voltage responsivity, as:

^ = *>£ = ^, (6) P in 2

parameter that accounts the DC voltage generated from the power absorbed by the channels Pin in reference to the power absorbed by the SSDs. The NEP values are -154 pW/Hz1 /2 and -454 pW/Hz1 /2 and the values of Rv are -7.6 x 106 V/W and -7.2 x 106 V/W, for the L and V-shape channels respectively.

C. Geometric parameters results

The ability of structures to generate DC electrical power has been improved by optimizing their sensitivity. For this task, a systematic analysis was performed by exploring all their geometric parameters. All of them are expected to affect the in different ways the sensitivity, so their relevance must be unveiled from simulations.

As a first step, we have analyzed the effect of the width W on the sensitivity of the channels, geometrical parameter that should appear as the most important. The current-voltage characteristics, the differential resistance and the sensitivity of the channels at zero-bias voltages are shown in Fig. 4 as function of their width.

The current-voltage curves in Fig. 4(a) and 4(b) show in a clear manner that the diode-like behavior and threshold are optimized by reducing the channel width. These effects emerge because the depletion zone extends completely over to the width of the channel, affecting the lateral transport.

FIG. 4. Parameters of the self-switching channels as a function of their width: current-voltage characteristic of the L-shape (a) and V-shape channel (b); differential resistance (triangles) and sensitivity (squares) of the L-shape (c) and V-shape channels (d); effective sensitivity of channels when coupled to a 50 Q acquisition system, of the L-shape (e) and (f) V-shape channel.

These results have been experimentally demonstrated by Song et al.,14 and theoretically confirmed by Mateos et al.,8 on L-shape channels.

At the same time, by reducing the width of the channels the sensitivity has also been improved, increasing their value up to 100 times, as shown in Fig. 4(c) and 4(d): the narrower the channel, the higher its sensitivity. This sensitivity behavior is expected since the current-voltage characteristic increases the non-linearity as the channel width is reduced, as shown in Fig. 4(a) and 4(b). However, even if the sensitivity of the channels can be increased by reducing the width, the resistance will increase by several orders of magnitude (from few MQ to hundred times of MQ). These resistance changes introduce major impedance drawbacks limiting the power transfer between the channels and the source. In order to show how the device performance is modified under unmatched conditions we use a reference driven source of 50 Q. An effective sensitivity y50Q has been defined in order to account the effects of the unmatched 50 Q source through the relationship:6

Y50Q = Y0 ■ (1 - |r|2), (7)

where r refers to the coefficient of reflection defined as (R0-50 Q)/(R0 + 50 Q). The trade-off between the effective sensitivity y50Q and the resistance of the channels is shown in Fig. 4(e) and 4(f) for the L and V-shape channels, respectively. Results confirm that even if the narrower channels are more sensitive than other structures, they are not the best option to generate and transmit DC electrical power.

A similar study was performed in order to evaluate the relevance on the nominal sensitivity of the rest of the geometrical parameters. The sensitivity of the channels as a function of the size of each specified parameter is shown in Fig. 5(a) and Fig. 5(b), for the L and V-shape channel, respectively.

The plots in Fig. 5, allows identifying those parameters of the channels that would propitiate to reach higher sensitivities values y0. These parameters were the width W, for the L-shape channel and the aperture W0 of the V-shape geometry. As previously mentioned, by reducing the width of the L-shape channel the nominal sensitivity can be increased, reaching a value of 40 V-1 for the narrower channel. In the other hand, the sensitivity of the V-shape channel can be increased by reducing its aperture, having a value of ~23 V-1 for the 50 nm aperture channel. This aperture dependence indicates the lateral charges effects are weaker for V-shape geometries: the higher the aperture, the furthest the trenches and the weaker their effects. When the aperture of the V-shaped channel is substantially reduced the L-shape geometry is recovered.

On the other hand, the sensitivity of both types of channels exhibits the same trend when the length is adjusted (blue open-squares). By increasing the length of the channels, increases the resistance and the diode-like behavior improves; due to the fact that the channel is longer and the lateral charges effects become stronger. Both properties improve the sensitivity of the channels as indicated by the equation (4) and as shown by the simulation results. However, as remarked by Mateos et al.,8 the cut-off frequency is reduced by shortening the channels. A trade-off between the sensitivity and

FIG. 5. Sensitivity of the channels as a function of the size of the geometrical parameters for (a) the L-shape self-switching channel and (b) the V-shape self-switching diodes.

FIG. 6. Effective sensitivity y50Q of channels when coupled to a 50 Q impedance driven-source for: the (a) L-shape and (b) the V-shape geometries.

speed of operation must then be optimized for the required applications; analysis out of the scope of this contribution.

By tuning the amplitude of the electric field that modulates the surface charges of channels, the channel response can be adjusted. This task can be achieved by changing the width of the horizontal trenches. Results show that the sensitivity of both types of channels is increased by narrowing the trenches. On the other hand, the electric field controlling the surface-charges can be entirely suppressed by eliminating the "lateral-gates". By increasing the width of the vertical trenches the "lateral gates" can be continuously shortened and the sensitivity of the channels slowly reduced to values near zero, as shown by results in Fig. 5.

The effective sensitivity y50Q for all the explored geometrical parameters when coupled to a 50 Q source as it is shown in Fig. 6(a) and 6(b), for the L and V-shape channel, respectively. From results, it can be seen the L-shape reference geometry, highlighted with the red line in Fig. 6(a), shows the best performance. Any change in any of the dimension will drop the performance of these types of devices. Additionally, the response of the V-shape channel has been improved by adjusting its aperture.


As mentioned along the manuscript, a key issue that reduces the use of the self-switching diodes in harvesting applications concerns their high resistance. The impedance matching with an acquisition system is very difficult and the losses of the electrical power by reflection will be predominant. Some methods to better match the channels into the acquisition systems have been recently proposed with good results: for example, the use of parallel arrays of SSDs in order to reduce the overall device resistance.1,6 Here, we present have analyzed how the effective sensitivity y50Q of a parallel array of optimized L-shape channels (reference geometry) changes while the number of elements increases.

The current-voltage characteristic curves, the resistance and the nominal and effective sensitivity of such a parallel arrays are shown in Fig. 7. By increasing the number of elements the overall resistance Roveraii of the arrays is reduced by almost two orders of magnitude, as shown by the open triangles in Fig. 7(b). The changes in the overall resistance could be considered as Roverau = R0/N, where R0 refers to the resistance of the single L-shape element. This reduction of the overall resistance allows a higher current on the array, as shown in Fig. 7(a). On the other hand, the nominal sensitivity of the array, plotted with open squares in Fig. 7(b), remains constant. This is due to the fact that the increase of the non-linearity in the current-voltage characteristic curve and the reduction of the overall resistance, compensate themselves in the relationship (4). However, the effective sensitivity showed in Fig. 7(c), increases linearly with the number of elements incorporated into the array.

FIG. 7. (a) Current-voltage characteristic curves, (b) resistance (open triangles) and the nominal sensitivity (open squares), and (c) effective sensitivity of a parallel array of L-shaped channels, as a function of the number of elements.


In summary, the performance of L-shape and V-shape self-switching nanochannels to convert the electric energy of high-frequency signals into DC power was evaluated and optimized by using numerical simulations. Since those devices combine geometrical effects with their harvesting properties their performance was increased by optimizing their shape. From results we have identified as key parameters the width W and the aperture W0 of channels for the L-shape and V-shape geometries, respectively. By optimizing those parameters, the nominal sensitivity of the devices has been increased to values around 40 V-1 and 20 V-1, attractive values for harvesting applications with square-law rectifiers. By employing parallel arrays of self-switching diodes the impedance matching drawbacks when coupled to a driving source of 50 Q have been reduced (such as energy losses by reflection). Self-switching diodes seem to appear as good candidates for zero-bias harvesting applications.


The authors acknowledge the financial support from "Consejo Nacional de Ciencia y Tecnología" (CONACyT) México through the research fellowship CVU-40859 and grants 387856, Project CeMIESol 22 and INFRAESTRUCTURA-2015, 255489. La-Region Lorraine (France) is gratefully acknowledged.

1 C. Balocco, A.M. Song, M. Äberg, A. Forchel, T. González, J. Mateos, I. Maximov, M. Missous, A.A. Rezazadeh, J. Saijets, L. Samuelson, D. Wallin, K. Williams, L. Worschech, and H.Q. Xu, Nano Lett. 5(7), 1423 (2005).

2 A. Westlund, P. Sangaré, G. Ducournau, P. Nilsson, C. Gaquiere, L. Desplanque, X. Wallart, and J. Grahn, Appl. Phys. Lett. 103, 133504 (2013).

3 J.-F. Millithaler, I. Iñiguez-de-la-Torre, A. Iñiguez-de-la-Torre, T. González, P. Sangaré, G. Ducournau, C. Gaquiere, and J. Mateos, Appl. Phys. Lett. 104, 073509 (2014).

4 O. García-Pérez, Y. Alimi, A. Song, I. Íñiguez-de-la-Torre, S. Pérez, J. Mateos, and T. González, Appl. Phys. Lett. 105, 113502(2014).

5 J. Torres, P. Nouvel, A. Penot, L. Varani, P. Sangare, B. Grimbert, M. Faucher, G. Ducournau, C. Gaquiere, I. Iniguez-de-la-Torre, J. Mateos, and T. Gonzalez, Semicond. Sci. Technol. 28, 125024 (2013).

6 A. Westlund, P. Sangaré, G. Ducournau, I. Iñiguez-de-la-Torre, P.-Ä Nilsson, C. Gaquiere, L. Desplanque, X. Wallart, J.F. Millithaler, T. González, J. Mateos, and J. Grahn, Solid-State Electronics 104, 79 (2015).

7 C. Balocco, S.R. Kasjoo, X.F. Lu, L.Q. Zhang, Y. Alimi, S. Winner, and A.M. Song, Appl. Phys. Lett. 98, 223501 (2011).

8 J. Mateos, B.G. Vasallo, D. Pardo, and T. González, Appl. Phys. Lett. 86, 212103 (2005).

9 C. Balocco, Y. Pan, S.R. Kasjoo, Y. Alimi, L.Q. Zhang, and A.M. Song, in THz imaging with broadband thermal sources: Proceedings of the IEEE 39th International Conference on Infrared, Millimeter, and Terahertz waves, Tucson, AZ, USA, September 14, 2014 (IRMMW-THz), pp. 53-54.

10 S.J. Byrnes, R. Blanchard, and F. Capasso, PNAS 111(11), 3927 (2014).

11 L. Mescia and A. Massaro, Adv. Mater. Sci. Eng. (2014) Article ID 252879.

12 M. Gallo, L. Mescia, O. Losito, M. Bozzetti, and F. Prudenzano, Energy 39, 27 (2012).

13 J.G. Consolmagno and Martha W. Schaefer, Worlds Apart: A Textbook in Planetary Sciences (Benjamin Cummings, 1994).

14 A.M. Song, M. Missous, P. Omling, A.R. Peaker, L. Samuelson, and W. Seifert, Appl. Phys. Lett. 83, 1881 (2003).

15 A.M Song, I. Maximov, M. Missousa, and W. Seifert, Physica E: Low-dimensional Systems and Nanostructures 21(2-4), 1116(2004).

16 G. Farhi, E. Saracco, J. Beerens, D. Morris, S.A. Charlebois, and J.-P. Raskin, Solid-State Electronics 51(9), 1245 (2007).

17 M.Y. Irshaid, C. Balocco, Y. Luo, P. Bao, C. Brox-Nilsen, and A.M. Song, Appl. Phys. Lett. 99, 092101 (2011).

18 J. Kettle, R.M. Perks, and R.T. Hoyle, Electronics Letters 45(1), 79 (2009).

19 F. Al-Dirini, F.M. Hossain, A. Nirmalathas, and E. Skafidas, Scientific Reports 4(3983), (2014).

20 F. Al-Dirini, F.M. Hossain, A. Nirmalathas, and E. Skafidas, Nanoscale 6, 7628 (2014).

21 A. Westlund, M. Winters, I.G. Ivanov, J. Hassan, P.-Ä Nilsson, E. Janzén, N. Rorsman, and J. Grahn, Appl. Phys. Lett. 106, 093116(2015).

22 Y. Pan, C.V. Powell, A.M. Song, and C. Balocco, Appl. Phys. Lett. 105, 253901 (2014).

23 K.-Y. Xu, G. Wang, and A.M. Song, Journal of Computational Electronics 6(1-3), 59 (2007).

24 A.K. Baraskar, M.A. Wistey, V. Jain, U. Singisetti, G. Burek, B.J. Thibeault, Y.J. Lee, A.C. Gossard, and M.J.W. Rodwell, J. Vac. Sci. Technol. B 27, 2036 (2009).

25 A. Sanchez, C.F. Davis, Jr., K.C. Liu, and A. Javan, J. Appl. Phys. 49, 5270 (1978).

26 J.A. Bean, A.W. , and G.D. Boreman, IEEE J. Quantum Electron. 47(1), 126 (2011).

27 M.N. Gadalla, M. Abdel-Rahman, and Atif Shamim, Scientific Reports 4(4270), (2014).

28 N. Alimardani, E.W. Cowell, J.F. Wager, J.F. Conley, Jr., D.R. Evans, M. Chin, S.J. Kilpatrick, and Madan Dubey, J. Vac. Sci. Technol. A 30, 01A113 (2012).

29 N. Alimardani and J.F. Conley, Jr., Appl. Phys. Lett. 102, 143501 (2013).

30 M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, in Solar spectrum rectification using nano-antennas and tunneling diodes: Proceedings of the XII Conference on Optoelectronic Integrated Circuits, San Francisco, California, USA, January 23 2010. edited by L. A Eldada and E.-H. Lee (SPIE 7605, 2010), pp. 76050E1 -76050E12.

31 T. González, A.M. Song, B.G. Vasallo, D. Pardo, and J. Mateos, in Transport and Noise in Ultrafast Unipolar Nanodiodes and Nanotransistors: Proceedings of the 14th International Conference, Chicago, USA, July 25, 2005. edited by M. Saraniti and U. Ravaioli (Springer Proceedings in Physics), pp. 109-113.

32 I. Iñiguez-de-la-Torre, J. Mateos, D. Pardo, and T. González, Appl. Phys. Lett. 103, 024502 (2008).

33 C. Balocco, S.R. Kasjoo, L.Q. Zhang, Y. Alimi, and A.M. Song, Appl. Phys. Lett. 99, 113511 (2011).