Terahertz devices based on
laser-assisted quantum tunneling
Statement of the problem
Spectroscopy and imaging with radiation at terahertz frequencies show promise for applications in security (detecting explosives and biological agents), medicine (rapid in vivo detection of cancer), and industrial processing (characterization of pharmaceuticals). However, the progress in each of these areas is impeded by the limited output power and tunable bandwidth of the terahertz sources that are presently available. State-of-the-art supercomputers and high-speed communications systems have already achieved Tb/s data rates by massive paralleling of solid state systems but terahertz clock rates must follow when better terahertz technology is available.
Our innovation—laser-assisted field emission
We pioneered in the analysis and fast (sub-microsecond) measurements of laser-assisted field emission, a form of quantum tunneling. This included the modeling, design, and testing of ultrafast optoelectronic devices based on this effect. Whereas others use semiconductors and non-linear optical media to obtain terahertz radiation with lasers, we use the durable clean surface of a nanoscale tip made of a polyvalent refractory metal in vacuum during field emission as the optical medium.
In field emission, a strong applied static field, typically 5V/nm, bends the potential barrier at the surface of the nanoscale tip so that electrons are emitted by quantum tunneling. The apex of the tip is much smaller than the laser wavelengths so that quasistatic conditions prevail. Thus, the potential barrier at the tip rises and falls to follow each cycle of the total electric field formed by superimposing the laser radiation on the static potential barrier.
Field emission current follows the instantaneous electric field with a delay (t) of less than 2 fs, and the non-linear current-voltage relation in field emission causes the emitted current to follow the envelope of the radiation from a mode-locked ultrafast laser or to have a tunable difference frequency with two lasers. Thus, signals from DC to over 500 THz (1/t) may be generated.
Laser-assisted field emission using refractory metals has the potential advantage of providing much greater output power, greater tunable bandwidth, higher terahertz frequencies, and resistance to environmental temperature, ionizing radiation, and electrostatic discharge (ESD), as well as reduced cost. We have also discovered a resonance in laser-assisted field emission that causes a further increase in the output power.
In field emission, a strong applied static field, typically 5V/nm, bends the potential barrier at the surface of the nanoscale tip so that electrons are emitted by quantum tunneling. The apex of the tip is much smaller than the laser wavelengths so that quasistatic conditions prevail. Thus, the potential barrier at the tip rises and falls to follow each cycle of the total electric field formed by superimposing the laser radiation on the static potential barrier.
Field emission current follows the instantaneous electric field with a delay (t) of less than 2 fs, and the non-linear current-voltage relation in field emission causes the emitted current to follow the envelope of the radiation from a mode-locked ultrafast laser or to have a tunable difference frequency with two lasers. Thus, signals from DC to over 500 THz (1/t) may be generated.
Laser-assisted field emission using refractory metals has the potential advantage of providing much greater output power, greater tunable bandwidth, higher terahertz frequencies, and resistance to environmental temperature, ionizing radiation, and electrostatic discharge (ESD), as well as reduced cost. We have also discovered a resonance in laser-assisted field emission that causes a further increase in the output power.
Specific examples of innovation
1. X-band prototype: We have modeled several methods for coupling the signals directly from the tip in order to avoid the effects of the electrode capacitance and dispersion of bunching of the electrons during transit to the anode; these are described in the references and patents at the end of this section. Figure 1 shows our first microwave prototype for X-band (7 to 12 GHz). Microwave current generated at the tip is transmitted by transverse-magnetic surface waves to a conical horn transition with a 50 Ω coaxial SMA connector.
Fig. 1. First microwave prototype coupling energy from the tip by surface waves.
2. Unique characteristics of carbon nanotubes (CNT) for laser-assisted field emission: CNT offer many advantages when compared to metal tips as field emitters for generating microwave and terahertz radiation by laser-assisted field emission. CNT are excellent field emitters, having a high current density with a relatively low applied static field, and they may be used in a poor vacuum. Single-walled CNT can be used as transmission lines, and because of their kinetic inductance, they have an unusually high characteristic impedance of approximately 30 k-Ohms. The current oscillations that are generated by laser-assisted field emission act as a constant current source, so the power that may be coupled to a CNT transmission line is increased because of the high characteristic impedance. Furthermore, when a large number of CNT have a common junction it is possible to cause a broad-band impedance match to the output. For example, if 600 CNT are used the microwave power from all of them is combined at a 50 Ohm load.
3. Robust nanoscale field emission diodes operating in air: We have made robust self-healing nanoscale field emission diodes which operate in air with emission currents up to 1 µA. This was possible by fabricating Ir/IrO2 tips because the natural oxide of iridium is electrically conductive and has a lower work function than the metal itself. The oxide coating is self-healing so that when a tube designed to operate with a bias of 10 V was subjected to 200 V DC, after a few seconds it recovered and was usable with the typical voltage/current characteristics. The tip-anode spacing in these diodes was 100 nm. They were mounted on miniature terahertz antennas but have not yet been tested for laser-assisted field emission.
4. Extremely high currents by field emission with capacitive ballasting: We have designed field emitters to provide extremely high currents by using capacitive ballasting to achieve a constant current density over a large surface, but these devices have not yet been built or tested. Analysis suggests that the high density of conduction band electrons in metals could support field emission current densities as high as 1016 A/m2. However, the current density is usually much less than this because of instabilities caused by heating, but values as high as 1015 A/m2 are obtained with emitters smaller than 4 nm because this is less than the mean-free path for electron-phonon scattering.
By contrast, field emission tips of refractory metals such as tungsten, with a radius of approximately 100 nm have an upper limit of 109 A/m2 in sustained operation at room temperature. The maximum emitted current does not increase in proportion to the area of the emitter, because field emission is not uniform over the tip, but is limited to a small number of sites where contaminants reduce the work function or asperities enhance the local electric field. We have studied the large data base for diamond field emitters having areas from 10-15 to 10-4 m2 to determine that the emitted current is proportional to the 0.25 power of the area of the emitter. We attribute this effect to the lack of uniform emission over large surfaces.
When resistive ballasting is used to even the distribution of the field emission current density it is possible to increase the total current, but this causes considerable power loss in the ballast resistors so it would be ineffective to scale up that procedure to obtain extremely high currents. We have studied the possibility of using distributed capacitive ballasting with a system of nanoparticle field emitters as shown in Fig. 2.
3. Robust nanoscale field emission diodes operating in air: We have made robust self-healing nanoscale field emission diodes which operate in air with emission currents up to 1 µA. This was possible by fabricating Ir/IrO2 tips because the natural oxide of iridium is electrically conductive and has a lower work function than the metal itself. The oxide coating is self-healing so that when a tube designed to operate with a bias of 10 V was subjected to 200 V DC, after a few seconds it recovered and was usable with the typical voltage/current characteristics. The tip-anode spacing in these diodes was 100 nm. They were mounted on miniature terahertz antennas but have not yet been tested for laser-assisted field emission.
4. Extremely high currents by field emission with capacitive ballasting: We have designed field emitters to provide extremely high currents by using capacitive ballasting to achieve a constant current density over a large surface, but these devices have not yet been built or tested. Analysis suggests that the high density of conduction band electrons in metals could support field emission current densities as high as 1016 A/m2. However, the current density is usually much less than this because of instabilities caused by heating, but values as high as 1015 A/m2 are obtained with emitters smaller than 4 nm because this is less than the mean-free path for electron-phonon scattering.
By contrast, field emission tips of refractory metals such as tungsten, with a radius of approximately 100 nm have an upper limit of 109 A/m2 in sustained operation at room temperature. The maximum emitted current does not increase in proportion to the area of the emitter, because field emission is not uniform over the tip, but is limited to a small number of sites where contaminants reduce the work function or asperities enhance the local electric field. We have studied the large data base for diamond field emitters having areas from 10-15 to 10-4 m2 to determine that the emitted current is proportional to the 0.25 power of the area of the emitter. We attribute this effect to the lack of uniform emission over large surfaces.
When resistive ballasting is used to even the distribution of the field emission current density it is possible to increase the total current, but this causes considerable power loss in the ballast resistors so it would be ineffective to scale up that procedure to obtain extremely high currents. We have studied the possibility of using distributed capacitive ballasting with a system of nanoparticle field emitters as shown in Fig. 2.
Fig. 2. Symmetric capacitively-ballasted field Emitter fed by a high-frequency generator.
Figure 2 illustrates the concept of using a high-frequency generator to cause a displacement current in each dielectric layer, which then causes the nano-particle field emitters (semicircles) to emit and accept electrons back and forth between the two conductive layers. However, a more interesting application would be that shown in Fig. 3 where this system may be driven by a pulsed laser focused on the nano-particle emitters. The dipole antenna may be used to couple the resulting high-power microwave energy to other devices. These devices have been modeled but no devices were fabricated or tested.
Fig. 3. Symmetric capacitively-ballasted field emitter with Dipole antenna to couple radiation to and/or from the device.