Theory Of Photon-assisted Tunneling Research Articles

Optical Rectenna Arrays Using Carbon Nanotubes: From Fundamental Understanding to Next Generation Devices

Optical rectennas have emerged as promising devices for high frequency optoelectronic applications such as infrared and optical sensing and energy conversion. We achieve optical rectification using vertical multiwall carbon nanotube (CNT) arrays. The CNT nanoantennas absorb electromagnetic waves and ultrafast metal-insulator-metal tunnel diodes fabricated at the CNT tips convert the resulting terahertz AC current into DC electricity. Since the first demonstration in 2015, considerable progress to CNT optical rectennas has been made. The latest generation of CNT rectenna uses an innovative multi-insulator structure to provide exceptional diode properties and enable air stable materials. We applied photon-assisted tunneling theory to model our device’s optical-frequency behavior. Comparing the rectenna model to our optical experiments through a range of wavelengths (404–1064 nm) has yielded a better fundamental understanding that will guide future device design. The model provides strong evidence that the CNT antennas behave as dipole antennas and implicates a 780 THz diode cutoff frequency that reveals room for performance improvement. We report ongoing research developing a novel flexible CNT rectenna device structure. We use polydimethylsiloxane (PDMS) to infiltrate the CNT array and create a mechanically flexible substrate and planarized diode surface. This structure enables transparent, conductive top electrodes with PEDOT:PSS. Our recent efforts greatly enhance the commercial development of efficient, low cost, and application tunable CNT rectennas.

Photon-Assisted Tunneling in Carbon Nanotube Optical Rectennas: Characterization and Modeling

We present optical characterization and modeling of carbon nanotube (CNT) rectennas featuring multi-insulator, metal–insulator–metal tunneling diodes. The diodes use four layers of Al2O3 and ZrO2 dielectrics to obtain strong nonlinearity and highly asymmetric current density at low turn-on voltage. The CNT rectenna devices show energy conversion in the full optical spectrum (404–980 nm). We introduce the theory of photon-assisted tunneling (PAT) to model the optical behavior based on unilluminated diode characteristics. Our model shows agreement between PAT and our experimental results, and fitting suggests a wavelength-dependent optical voltage. We discuss the impact of rectenna parameters and elucidate performance limits to our CNT rectenna device.

Steps of the Giant Terahertz Photoconductance of a Tunneling Point Contact

The photoresponse of the conductance of a tunneling quantum point contact to irradiation in the frequency range of 0.5–1.7 THz has been simulated within the theory of photon-assisted tunneling. The simulation has shown that the dependences of the conductance on the Fermi energy exhibit steps corresponding to transitions with the absorption of one, two, or three photons to channels near the top of the tunnel barrier. Under experimentally achievable conditions, the ratio of the photoconductance to the dark value on these steps can reach several orders of magnitude.

Simple Figure of Merit for Diodes in Optical Rectennas

Harvesting infrared and visible light energy using optical rectennas—diode-coupled optical antennas—is strongly dependent on the diode current–voltage characteristics. Predicting the conversion efficiency is an arduous procedure that involves calculating the efficiency by solving the nonlinear diode circuit using the theory of photon-assisted tunneling (PAT). Because of the complexity of the calculations, many rectenna diodes have been reported without indications of how well these diodes will actually function in a rectenna. To provide a quick assessment of the diodes’ usefulness in optical rectennas, we provide a figure of merit ( FOM ) that incorporates the diodes’ current–voltage and capacitance, the antenna radiation resistance, and the illumination parameters.

Efficiency limits of rectenna solar cells: Theory of broadband photon-assisted tunneling

Because rectifiers can convert a wide range of frequencies to dc it was thought that rectenna solar cells–antennas coupled to ultra-high speed diodes–could efficiently harvest the entire solar spectrum and exceed the Shockley-Queisser limit. We show that there are efficiency limits to broadband optical conversion and provide a quantitative analysis using the theory of photon-assisted tunneling. This quantum-based approach differs from classical rectification in lower frequency rectennas. The conversion efficiency approaches 100% for monochromatic illumination. For broadband illumination at terrestrial solar intensities, the diode operating voltage plays the role that bandgap plays in conventional solar cells.

Theory of photon-assisted tunneling through quantum dot

Based on the two-channel Anderson Hamiltonian with the non-equilibrium electron distribution under an external electric field, we develop the theory of stationary photon-assisted tunneling current via strongly correlated energy levels in a quantum dot. The non-equilibrium (Mahanthappa–Baksi–Keldysh) Green function formalism is employed to study the Kondo effect and Coulomb blockade phenomenon in the presence of an external field. The Coulomb interaction is treated within the second order perturbation in the self-energy. The change of electron distribution function in the quantum dot due to emission and absorption of photons is taken into account and is found to play a very important role for the suppression of the Kondo effect. We show that an opening of new tunneling channel through photon side band accounts for a Coulomb staircase in the electric current.

Theory of Photon-Assisted Tunneling in the Transition between the Quantum Mechanical and Classical Limits

We report unpublished experimental results of Photon-Assisted Tunneling (PAT) in the transition region between the quantum mechanical and classical limits. Using these results, we show that there is a discrepancy between the Tien-Gordon theory of Quasiparticle Photon-Assisted Tunneling and experiment in this region. Finally, we show that the modified Tien-Gordon theory is also valid in this region.

Theory of Photon-Assisted Tunneling in the Transition between the Quantum Mechanical and Classical Limits

We report unpublished experimental results of Photon-Assisted Tunneling (PAT) in the transition region between the quantum mechanical and classical limits. Using these results, we show that there is a discrepancy between the Tien-Gordon theory of Quasiparticle Photon-Assisted Tunneling and experiment in this region. Finally, we show that the modified Tien-Gordon theory is also valid in this region.

Development of a tunnelling model of charge-density-wve depinning

The tunneling model of transport by charge-density waves in quasi-one-dimensional metals has been developed from a close interaction between theory and experiment. Depinning by coherent Zener tunneling of electrons in the CDW condensate in many parallel chains, first applied to NbSe 3,and TaS 3, was suggested by the field dependence of the dc current. In 1981, a program initiated at Illinois to study detection, mixing and harmonic generation was successful in showing that photon-assisted tunneling theory accounts for a wide range phenomena. The only inputs are a scaling parameter and the dc I-V characteristic. Recent measurements by Grüner, Reagor baret al. of ϑ(ω) in the range 1–100 Ghz suggested a modification to account for CDW metals with high pinning frequencies, such as (TaSe 4) 2I and the alloys Ta 1−xNb xS 3. The dc and low-frequency ac response can be derived from parameters measured at high frequencies. The theory accounts for the “narrow band” noise that accompanies dc current flow and the subharmonic steps of constant current in the dc I-V characteristic measured in the presence of an applied ac.

Relation of stimulated and spontaneous transitions in tunneling structures to the elastic current-voltage characteristic

The stimulated emission and absorption of surface plasma modes by inelastic scattering of tunneling electrons is considered. It is shown that the net absorption rate is proportional to the current difference between points ±ℏω/e about the bias point on the elastic current-voltage characteristic. In particular, this can be negative implying the possibility of net stimulated emission over a large bandwidth. The relationship to photon assisted tunneling theory is considered.

Conversion gain in millimeter wave quasi-particle heterodyne mixers

The physical mechanisms which give rise to conversion gain in SIS quasi-particle mixers are studied. It is shown that the S -shape tunneling structure at the gap voltage of the I- V curve is essential in achieving conversion gain. In the development of SIS quasi-particle mixers, a new approach is used to analyze the embedding network of the mixing experiment. The method described in this paper has the advantage over conventional methods that no separate measurements are necessary. In order to obtain a complete picture of the performance of SIS quasi-particle mixers, the photon-assisted tunneling theory used by Tucker to describe quasi-particle mixing is extended here to include pair current contribution. Based on this complete quantum theory, the effects of the Josephson noise on SIS quasi-particle mixing is discussed and an upper frequency limit of SIS quasi-particle mixing is estimated.

Computer simulations of the performance of quasiparticle heterodyne mixers

Heterodyne mixers for millimeter wavelengths which have conversion gain and noise comparable to the quantum limit can be made using the non-linearity of the quasi-particle I-V curve of SIS or SIN tunnel junctions. When the voltage range of the non-linearity becomes small compared with hω/e, classical device theory breaks down and photon assisted tunneling theory must be used to understand mixer performance. In this paper we describe detailed computer simulations of SIS and SIN quasiparticle mixers. Predictions for conversion efficiency and noise are given for both devices as a function of operating frequency, bias voltage, RF source conductance and local oscillator power. A novel type of SIN harmonic mixer is proposed for which gain is also predicted.

Superconductive devices for millimeter wave detection, mixing, and amplification

Single-particle (quasi-particle) tunneling through an insulating barrier between two superconductors or between a superconductor and a normal conductor is being used to make very-low-noise detectors and mixers for millimeter wavelengths. The nonlinearity of the I-V curve obtained from tunneling between two superconductors can be so strong that classical theory breaks down and photon-assisted tunneling theory must be used to understand device performance. Quantum theory predicts that a quasi-particle tunnel junction can be operated as a microwave photon detector with quantum efficiency close to unity or as a heterodyne mixer with conversion gain and with mixer noise temperature comparable with the quantum noise limit T_{M} =\bar{h}\omega/k . Both of these predictions have been experimentally realized at 36 GHz using superconductor-insulator-superconductor (SIS) junctions. It appears probable that these quasi-particle detectors and mixers will supercede the corresponding Josephson-effect devices at millimeter wavelengths.

Superconductor-insulator-superconductor quasiparticle junctions as microwave photon detectors

The strong nonlinearity of the quasiparticle tunneling current in superconductor-insulator-superconductor junctions near the full-gap voltage 2Δ/e can be used for direct detection of microwave signals. Measurements at 36 GHz yielded a current responsivity of 3500 A/W, which is within a factor of 2 of the quantum-limited value e/∇ω. The measured NEP of 2.6±0.8×10−16 W/,Hz1/2 is the lowest value reported to date and can probably be improved significantly. The experimental results are compared with both the standard classical analysis and photon-assisted tunneling theory.

Predicted conversion gain in superconductor-insulator-superconductor quasiparticle mixers

A computer simulation is constructed to describe the performance of superconductor-insulator-superconductor (SIS) quasiparticle heterodyne receivers in terms of photon-assisted tunneling theory. The results predict that conversion efficiencies greater than unity can be realized at millimeter wave frequencies, with noise temperatures approaching the fundamental quantum limit. The nonlinearity responsible for the mixing is the extremely rapid onset of quasiparticle tunneling current in SIS junctions near the full gap voltage 2Δ/e, and is independent of the Josephson pair currents. Substantial gain is expected under a variety of conditions and for a wide range of source and load impedances.

Theory of photon-assisted tunneling with radiation-activated barrier impurities

The addition of a new term in the conventional Hamiltonian is used to study photon-assisted tunneling for superconducting junctions containing active barrier impurities. For a sufficiently sharp molecular resonance, the impingent radiation can cause a large enhancement of the $n=1$ Dayem and Martin current step or a significant alteration of the dc Josephson current. The important mechanism is capture of a photon by a molecule followed by electron tunneling through the barrier.

Theory of Photon-Assisted Tunneling in Superconducting Junctions with Active Barrier Impurities

Theory of Photon-Assisted Tunneling in Superconducting Junctions with Active Barrier Impurities

Rf-Induced Effects in Superconducting Tunnel Junctions

Arguments are presented to resolve experimental discrepancies with the theory of photon-assisted tunneling. A standing-wave model is suggested as a more realistic picture of the rf fields in a thin-film tunnel junction. By including the effects of this model in the theories of Tien and Gordon and of Werthamer, we obtain qualitative agreement with data on both the Josephson effects and the photon-assisted tunneling effects in the same junction. In an experiment with a junction sufficiently small to maintain a uniform rf field, we find excellent agreement with the unmodified theory. The low-frequency equivalence of the photon-assisted tunneling phenomenon and classical rf detection is also pointed out and used to demonstrate that the magnitude of the rf voltage appears correctly in the theory. We conclude that the Werthamer theory of rf-induced effects in superconducting tunnel junctions is on very firm experimental ground.

Radiative Tunneling in GaAs Abrupt Asymmetrical Junctions

A representative number of abrupt GaAs junctions, asymmetrically doped, have been studied to delineate quantitatively the properties of spectra (called shifting-peak spectra) whose peak energy approximately equals the applied voltage V, and shifts in position and intensity with V. The free-electron concentration n on the more lightly doped side was varied from 3×1017 cm−3 to 8×1018 cm−3, the voltage range was ∼1.0 to ∼1.5 V, and the temperature was varied from 12° to 255°K. Because the active region width is 600 Å or less, and the spectral shape agrees in all details with Morgan's theory of photon-assisted tunneling, these shifting-peak spectra have been identified as radiative tunneling. It is shown here that no adjustable parameters are needed to calculate the experimental spectral shape when only T, V, and n are specified. This means that for any given temperature, n alone represents the influence of the junction on the spectral shape, while the independent parameter in terms of excitation is the voltage and not the current, as usually stated. The agreement between the calculated and experimental spectra includes the logarithmic slope of the low energy tail, and the difference between V and the energy of the peak-emission intensity hvp: eV0=eV-hvp. This agreement emphasizes the necessity of including the parabolic junction potential as obtained from Poisson's equation when calculating the tunneling-hole and electron-wave functions. The usual simplifying assumption of a linear potential is inadequate. To clarify previous observations of one or two types of shifting-peak spectra, linear-graded and abrupt-asymmetrical junctions were made from adjacent wafers of the same crystal, and the resulting shifting-peak spectra were compared. Only band-to-band radiative tunneling was observed for the abrupt junction, but for the linear-graded junction two shifting-peak spectra were observed. In the low excitation region for linear-graded junctions, the shifting-peak spectra may be described by band-to-impurity radiative tunneling that results in a narrow active-region width, while at higher bias the emission becomes band-to-band radiative tunneling with a wider active region. These results demonstrate that shifting-peak spectra previously attributed to band filling may be described in terms of photon-assisted tunneling.

Recombination by Tunneling in Electroluminescent Diodes

The theory of photon-assisted tunneling in the presence of an electric field is developed and used to obtain quantitative expressions for the line shape and intensity of light emitted by forward-biased electroluminescent diodes in the "peak-shift" region. Recombination of tunneling electrons and holes through one or more intermediate states is also considered and shown to produce an "excess" current which varies as the nth root of the "peak shift" intensity, where $n\ensuremath{\approx}2$ for processes involving one intermediate state and $n>2$ for more than one. Auger recombination through these same states is shown to provide an explanation for the high-energy emission ($h\ensuremath{\nu}\ensuremath{-}\mathrm{eV}\ensuremath{\gg}\mathrm{kT}$), which varies as the square of the current and is frequently observed at low currents in electroluminescent diodes.