INTRODUCTION

Creation of the elemental base of vacuum microelectronics and high-current field emission cathodes (FECs) for devices for generating microwave and subterahertz signals is currently an urgent task, since devices become radiation-resistant and have ultra-high speed. However, their creation is hindered by several fundamental problems. They are associated, on the one hand, with obtaining a stable morphology of the surface of solids to the effects of strong electric fields and temperature gradients under technical vacuum conditions, and, on the other hand, with an increase in the transparency of potential barriers at the solid–vacuum interface, which is achieved by increasing the electric field amplification factors on the emitting protrusions of the FECs. Research in these areas follows from the practical experience of using FECs and the classical theory of Fowler and Nordheim. However, as experience and analysis of the results of numerous studies show, the solution to the problem associated with obtaining long-term and stable high-current field emission of electrons remains open. This indicates that traditional methods of research do not provide a cardinal solution to the problem. One of the most promising materials that can be used to obtain high-current FECs are nanocomposite carbon film structures [1–3].

It was shown in [4] that in low-dimensional carbon 2D heterostructures with different electron enrichment of layers, a decrease in the thickness of the depleted layer to a value comparable to the de Broglie wavelength enhances their rectifying properties and increases the field current density of cathode matrices based on them. An increase in field currents is achieved at a low steepness of the current–voltage characteristic (CVC) and sufficiently high emission activation thresholds. This limits the use of field sources of electrons in vacuum microelectronic devices in the microwave and subterahertz ranges.

Objective—To study and develop methods for increasing the transparency of potential barriers for non-dissipative transport in carbon 2D heterostructures of solid state and emission microelectronics in the microwave and subterahertz ranges.

1 EXPERIMENTAL TECHNIQUE AND RESULTS

Three-layer carbon heterostructures with different thicknesses and electron enrichment of the layers were obtained by deposition using a microwave plasma of low-pressure ethanol vapor [5]. Electron-enriched carbon films were used as the lower and upper layers of the heterostructure. The thickness of the base of the heterostructures was 0.2 μm, the thickness of the intermediate electron-depleted carbon layer in various heterostructures varied from 5 to 20 nm, and the thickness of the upper enriched layer was fixed at 120 nm. The connection of the heterostructure to the power source during static electrical measurements was carried out through nickel pads deposited by thermal evaporation in vacuum on the upper and lower enriched layers of the heterostructure. Field emission properties were studied under high vacuum conditions (10−6 Pa) on a diode structure capable of changing the distance between the electrodes with an accuracy of 1 μm according to the method described in [6]. The field emission activation thresholds were determined from the electric field strength in a 10 μs pulse at which the field currents were 5 μA.

Figures 1 and 2 show the results of static electrical measurements of the CVC of three-layer carbon structures at room temperature. For depleted layer thicknesses of 5 and 10 nm, the transverse currents in the heterostructures as the voltage increased from 0 to 10 V were significantly lower than for other thicknesses and in their absence. At high voltages, they increased rapidly. The strongest and fastest increase in current with increasing voltage above 10 V was observed for a thickness of 5 nm. At 20 V, this current exceeded by more than three times the current in the structure without a carbon layer depleted in carriers. At voltages of 30 and 50 V, the transverse currents have maxima at depletion layer thicknesses of 5 and 15 nm. The differences in transverse currents at direct and reverse voltage polarities, which characterize the rectifying properties of heterostructures, depend on the voltage between the drain and source and have a maximum at a depletion layer thickness of 5 nm. At a voltage of 50 V, the difference between the forward and reverse currents at a depletion layer thickness of 5 nm increased from 9 to 140 µA compared to a thickness of 100 nm, and at a voltage of 100 V, from 22 to 220 µA.

Fig. 1.
figure 1

CVC (a) in heterostructures with different thicknesses of depleted layers, nm: (1) 5; (2) 10; (3) 15; (4) 20; (5) 0; transverse currents (b) at voltages of 30 (1) and 50 V (2).

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Fig. 2.
figure 2

Dependence on the thickness of the depleted layer of the difference in transverse currents through heterostructures at direct and reverse voltage polarity of 50 V.

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Field current densities when using an intermediate tunnel-thin carbon layer depleted in charge carriers increase by 1.5–2.5 times (Figs. 3, 4). As with static measurements, the highest field current is observed for a depletion layer thickness of 5 nm. It is implemented at the lowest threshold for the onset of field emission and the highest CVC slope. With an increase in the thickness of the depleted layer, the thresholds for the onset of field emission increase, and the slope of the CVC decreases.

Fig. 3.
figure 3

Field CVCs of 2D carbon heterostructures at different depletion layer thicknesses, nm: 5 (1), 10 (2), 15 (3) and 0 (4).

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Fig. 4.
figure 4

Dependences on the thickness of the depleted layers of the carbon heterostructure: (a) field current densities (1) and emission activation thresholds (2), (b) the slope of the CVC (1) and intervals of permissible electric field strengths (2).

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In the heterostructures under consideration, tunnel thin layers of depleted carbon films, which are semimetals in nature, are smaller than the de Broglie wavelength at room temperature, which ranges from 25 to 100 nm for semiconductor structures, and an order of magnitude less for metals. In planar heterostructures with macrodimensional thicknesses of the upper and lower enriched layers, they represent typical quantum barriers (QBs). When electric fields are applied, this allows electrons to tunnel through the quantum-dimensional layers, transparency coefficient D which are higher, the smaller their thickness l [7]:

$$D \approx \exp \left[ { - \frac{2}{h}\int\limits_0^l {\sqrt {2m(U - W)} \,dx} } \right],$$
(1)

where h = 6.62 × 10–34 J s is Planck’s constant, m is the mass of the tunneling particle, U is the potential energy, and W is the energy of the electron incident on the barrier.

With an increase in the thickness of quantum-dimensional film layers, the zero energy levels of electrons E1 decreases inversely with its square. Estimates show that due to size quantization E1 in 2D structures with depleted layer thicknesses of 5, 10, and 15 nm, they are about 0.2, 0.05, and 0.02 eV, respectively. The highest tunneling coefficients in quantum-well structures are realized when the energy levels are close to the average kinetic energy of emitter electrons, which is about 0.025 eV at room temperature.

With an increase in the strength of the external field, the energies of the ground states of electrons in low-dimensional structures decrease, while the kinetic energy of electrons increases. When their values approach a value of the order k0T the currents through the heterostructures increase intensively. Due to the lower “geometric” tunneling transparency, the voltage dependence of the current at a layer thickness of 10 nm and low electric field strengths is weaker than for a thickness of 5 nm. As the voltage increases, the influence of the field increases and the current increases rapidly (Fig. 1a, curve 2).

At a quantum barrier width of 15 nm, the zero energy is close to the average kinetic energy of electrons. A condition arises that is close to resonant tunneling, under which the transverse current through the heterostructure increases almost linearly with increasing voltage (Fig. 1a, curve 3). For a depleted layer thickness of 20 nm or more, the size quantization effect is absent. This is evidenced by the relationship between current and voltage, close to Ohm’s law, with a significantly lower proportionality factor compared to a thickness of 15 nm, as well as a low transverse current, which is less than in a carbon heterostructure without a depleted layer.

During field emission in strong pulsed electric fields, the high zero energy of electrons in a heterostructure with a QB width of 5 nm increases their kinetic energy and transverse current, while the field emission onset threshold decreases and, in accordance with (1), the potential barrier (PB) transparency coefficient increases by the solid–vacuum boundary. An increase in transparency occurs due to a decrease in the difference between the height of the PB (electron work function) and the self-energy of the tunneling electron. Owing to the dissipative transport of electrons, the processes associated with the development of impact ionization of atoms in a carbon heterostructure slow down. With a small, compared with a single enriched layer, increase in the range of permissible strengths of the external electric field, the field current density and the slope of the CVC increase many times (Fig. 4).

With an increase in the thickness of the depleted layer, the transverse resistances of the heterostructures increase and the activation thresholds for field emission increase. Due to the decline in E1 the transparencies of the PB at the solid–vacuum interface decrease, the intervals of permissible electric field strengths increase, and the CVC slope decreases. An increase in the emission activation thresholds and admissible strengths of external fields at a lower PB transparency increases the electric field strength in the heterostructure and accelerates the development of impact ionization processes. For a depleted layer with a thickness of 10 nm, compared with a thickness of 5 nm, this leads to the destruction of the heterostructure at a lower field current density. Processes develop similarly at a QB width of 15 nm. The low zero energy of electrons reduces the transparency of the depleted layer and the vacuum gap, reduces the current component associated with non-dissipative electron transport in the heterostructure, and increases the emission activation threshold. The increased scattering of electrons by structural defects in comparison with smaller thicknesses of depleted layers slows down the rate of current rise and the rate of development of impact ionization of atoms in the near-surface carbon layer with an increase in the permissible external field strength. This allows, in comparison with the layer thickness of 10 nm, to increase the field current, but at a lower CVC slope.

CONCLUSIONS

In carbon heterostructures without the use of QBs in the form of tunnel-thin layers depleted in charge carriers, there are no mechanisms for non-dissipative transport and an increase in the transparency of the potential barrier at the solid–vacuum interface due to a “geometric” increase in the electron self-energy. Field emission is carried out only by reducing the height and thickness of the PB at the solid–vacuum interface for the tunneling of electrons with energies close to the stationary Fermi Sea. The strength of the external electric field for this, as is known, is 106–107 V/cm, which is very close to the electrical strength of bulk materials and, moreover, film structures based on them. These factors determine the low allowable ranges of external electric fields and field currents.

“Geometric” magnification of electron self-energy and the formation of resonant tunneling conditions in carbon heterostructures with a quantum-well depleted layer in strong microsecond pulsed electric fields increases transverse currents and increases the transparency of the potential barrier at the solid–vacuum interface without increasing the energy load on the field cathode material. This makes it possible to increase the field current density and the CVC slope by several times.