Coulomb Charging Energy Research Articles

Coulomb charging effect of holes in Ge quantum dots studied by deep level transient spectroscopy

The quantum confined energy levels in Ge quantum dots and the coulomb charging energy per added hole can be derived by deep level transient spectroscopy (DLTS). The number of holes captured by quantum dots can be controlled by varying the width of applied pulse voltage in the DLTS measurement. The Coulomb charging energy per added hole can be deduced from the energy step of the activation energy in the filling time dependent deep level transient spectra. The experiment results are confirmed by computer simulation.

Characterization and analysis of a novel hybrid magnetoelectronic device for magnetic field sensing

Structures in which magnetic and electronic materials are combined offer a variety of possibilities for realization of devices with improvement functionality or performance compared to conventional devices. We have designed, characterized, and analyzed a novel hybrid magnetoelectronic device: a monolithic field-effect-transistor-amplified magnetic field sensor in which a granular tunnel magnetoresistive (TMR) thin film, consisting of Co nanoparticles embedded in an insulating SiO2 matrix, is incorporated into the gate of a p-channel Si metal-oxide-semiconductor field-effect transistor. In this structure, current flow through the TMR film leads to a buildup of electronic charge within the gate due to the Coulomb charging energy of the Co nanoparticles, and consequently to a transistor threshold voltage shift that varies with applied external magnetic field. In a prototype demonstration device, the relative current change induced by application of a 6 kOe external magnetic field at room temperature was amplified from 5% for the current through the TMR film to 21% for the transistor subthreshold current. The absolute current response in the saturation regime increased by a factor of about 500 compared to that of the TMR film alone. A detailed analysis of the device operation and of methods for optimization of performance are presented. It is anticipated that substantially better performance should be achievable with relatively straightforward improvements in device design and processing. This device concept is shown to compare particularly favorably with Hall bar sensors and thus may be very beneficial in sensor applications for medium field ranges up to about 1 T.

Electron Transport in Nanocrystalline Si Based Single Electron Transistors

Electron transport has been studied by measurement and simulation of single electron transistors based on nanocrystalline silicon (nc-Si). Nanocrystalline silicon is formed in the gas phase of the SiH4 plasma cell by the coalescence of radicals. Digital chemical vapor deposition [CVD] technique using pulsed gas in the plasma is effective to obtain highly uniform Si quantum dots with an average size of 8 nm and dispersion of 1 nm. Single electron transistors have been successfully fabricated by deposition of nc-Si on top of heavily doped silicon nanoelectrodes with a gap of 15 nm which allows the study of electron transport through two or three nanocrystals. Coulomb blockade and Coulomb oscillations are observed in these devices at various temperatures, including room temperature. The observed Coulomb diamond structure is not as simple as in the case of metallic islands. With increasing gate voltage, the spacing between oscillation peaks decreases and the Coulomb diamonds reduce in size. These observations are explained on the basis of electron transport through a quantum dot with an energy gap between the highest occupied and the lowest unoccupied electron states. Modeling of such a system can reproduce measured electrical characteristics. The unequal spacing of gate oscillations and the reduced size of Coulomb diamonds are due to the interplay of Coulomb charging energy and the energy separation between the quantized energy levels.

Transport in split-gate silicon quantum dots

We report on the transport properties of novel Si quantum dot structures with controllable electron number through both top and side gates. Quantum dots were fabricated by a split-gate technique within a standard MOSFET process. Four-terminal dc electrical measurements were performed at 4.2 K in a liquid helium cryostat. Strong oscillations in the conductance through the dot are observed as a function of both the top gate bias and of the plunger bias. An overall monotonic and quasi-periodic movement of the peak conductance is observed which is believed to be associated with the bare level structure of the electronic states in the dot coupled with the Coulomb charging energy. Crossing behavior is observed as well, suggestive of either many-body effects or symmetry breaking of the dot states by the applied bias.

Conductances of ultrasmall tunnel junctions in the strong tunneling regime

We have calculated the conductance of a metallic tunnel junction with the junction conductance larger than the conductance quantum connected in series with a loading impedance. At sufficiently high temperatures, analytical forms have been derived that are found to coincide with the numerical results of the mean-field method as well as the experimental data. For the case when the Coulomb charging energy is much larger than the thermal energy, our results, obtained by using the full expression of the conductances evaluated with the help of the Monte Carlo simulations, are in good agreement with the experimental data but quantitatively different from the predictions of the mean-field approach. A simple approximative method to evaluate the conductances of the tunnel junctions has been discussed as well.

Single-electron tunnelling devices based on intrinsic Josephson junctions in Bi-2212

We fabricated submicron-sized intrinsic Josephson junctions of Bi-2212 by the focused-ion-beam (FIB) etching method. The main result was a reduction of the in-plane junction area to 0.3 µm2 by direct FIB etching with no degradation in the critical transition temperature (Tc). At the current (I)-voltage (V) characteristic of these stacks, the gap structure and the normal-state resistance are clearly observed by a reduction of the Joule heating. The critical current density is considerably suppressed, the hysteresis and multibranch structure are eliminated and a periodic structure of current peaks appears reproducibly on the I-V curves. The period V of the structure is consistent with the Coulomb charging energy of a single pair, V = e/C, where C is the effective capacitance of the stack. It is considered that this behaviour originates from the Coulomb blockade of intrinsic Josephson tunnelling in submicron Bi-2212 stacks. We demonstrated the junction operating up to 10 K for the stack with an in-plane size of 0.3 µm2 and an elementary junction number of 50.

CHARGING DYNAMICS OF Si-QUANTUM DOTS IN TUNNEL CAPACITOR

Using frequency-dependent capacitance spectroscopy, we investigate the charging dynamics of silicon quantum dots embedded in oxide matrix through a SiO2/Si-quantum dots/SiO2/Si-substrate tunnel capacitor. Two resonance peaks both for capacitance and conductance in the inversion region are observed at room temperature, being attributed to the direct tunneling between the condu ctance band ofSi-substrate and the one-and two-electron ground-state level of th e Si quantum dot. The Coulomb charging energy of the dots is extracted from the experimental results.

Electronic and optical properties of strained quantum dots modeled by 8-band k⋅p theory

We present a systematic investigation of the elastic, electronic, and linear optical properties of quantum dot double heterostructures in the frame of eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory. Numerical results for the model system of capped pyramid shaped InAs quantum dots in GaAs (001) with ${101}$ facets are presented. Electron and hole levels, dipole transition energies, oscillator strengths, and polarizations for both electron-hole and electron-electron transitions, as well as the exciton ground-state binding energy and the electron ground-state Coulomb charging energy are calculated. The dependence of all these properties on the dot size is investigated for base widths between 10 and $20$ nm. Results for two different approaches to model strain, continuum elasticity theory, and the Keatings valence force field model in the linearized version of Kane, are compared to each other.

Experimental evidence for Coulomb charging effects in submicron Bi-2212 stacks

We developed the focused ion beam (FIB) and ion milling techniques for a fabrication of the Bi_2Sr_2CaCu_2O_{8+\delta} (Bi-2212) stacked junctions with in-plane size L_{ab} from several microns down to the submicron scale without degradation of T_c. We found that behaviour of submicron junctions (L_{ab} < 1 {\mu}m) is quite different from the bigger ones. The critical current density is considerably suppressed, the hysteresis and multibranched structure of the IV characteristics are eliminated, the periodic structure of current peaks reproducibly appears on the IV curves at low temperatures. A period of the structure, {\Delta}V, is consistent with the Coulomb charging energy of a single pair, {\Delta}V = e/C with C the effective capacitance of the stack. We consider this behaviour to originate from the Coulomb blockade of the intrinsic Josephson tunneling in submicron Bi-2212 stacks.

Electrical characterization of InP/GaInP quantum dots by space charge spectroscopy

An investigation of coherently grown InP quantum dots embedded in Ga0.5In0.5P by conventional space charge spectroscopy methods is reported. Deep level transient spectroscopy (DLTS) is used to obtain quantitative information on the electron emission from the dots. The applied field is found to significantly enhance the electron emission rates as seen by shifts in the peaks towards lower temperatures with increased field. Taking the field induced barrier lowering into account, the emission energy for the one electron ground state of the dot is determined as 240±10 meV. The correlation between the measured signal and the observed electron accumulation in capacitance–voltage measurements is clearly demonstrated. Further, studies of the electron emission when the average electron population in the dots was varied show that the emission energies are modified by the coulomb charging energy. Admittance measurements as a function of temperature, bias and frequency were also performed, and the results are qualitatively explained in terms of response from the dots. These observations are consistent with the effect of the signal frequency on the measured carrier concentration profile. To complete the picture and in order to distinguish the DLTS signature of the dots from that of the deep levels in GaInP, electron traps in the barrier material were also characterized. Two main electron traps, one with an activation energy of about 950 meV and the other having an activation energy of 450 meV, were present in all the samples.

Coulomb effects on charged, buried metal disks at room temperature

Capacitance transients caused by capture and emission of electrons from buried metal disks are investigated. A single layer of tungsten disks, arranged in a square lattice, is introduced into GaAs by epitaxial overgrowth and a depleted layer is formed around the disks due to the metal–semiconductor Schottky barrier. The number of captured electrons on each disk is measured by the capacitance associated with the width of the depletion layer, whereas the capacitance transients reflect the changes in the number of excess electrons on the disks. By investigating the emission time constants for varying numbers of electrons in excess on the disks, the Coulomb effect is studied. In combination with a temperature-dependent capture, a Coulomb charging energy of only 4 meV is shown to shift the measured activation energies erroneously by hundreds of meV.

Comment on “Symmetry-breaking instabilities in symmetric coupled-quantum-dot structures”

In a recent paper [Phys. Rev. B 52, R17 005 (1995)] Tsukada, Gotoda, Nunoshita, and Nishino have investigated the effect of the Coulomb charging energy on the time evolution of the electron occupation probability in a coupled-dot system. At a small initial fluctuation around the equal distribution of the electron occupation probability to two quantum dots, they reported that the symmetry-breaking instabilities are induced for Coulomb charging energy larger than a certain threshold value. We claim that the symmetry-breaking instabilities are invalid for a negative coupling coefficient, which is the normal case for conduction band electrons. Numerical results for various initial conditions and the Coulomb charging energies are presented.

Shell-filling effects and Coulomb degeneracy in planar quantum-dot structures

We investigate the influence of electron-electron interactions on the electronic properties of quantum dots in a regime where the energy-level separation is comparable to or larger than the Coulomb charging energy at low temperature ${(e}^{2}/2C\ensuremath{\gg}{k}_{B}T).$ A self-consistent three-dimensional solution of Schr\"odinger and Poisson equation within the local-density approximation is implemented to study the formation of shell structure in highly symmetric quantum dots which is in good agreement with recent experimental results [Tarucha et al., Phys. Rev. Lett. 77, 3613 (1996)] For asymmetric quantum dots, we show that the shell structure disappears, and features due to electron-electron interaction lead to the accidental formation of an isolated electron shell called ``Coulomb degeneracy'' in the energy spectrum.

Possibility of a single electron tunneling diode and a controllable saturated tunneling current

A quantum theory of a degenerate p-n junction coupled to an external circuit shows that the combination of Coulomb blockade, and the intrinsic (constant–voltage bias) nonlinear I–V of the junction results in a new device with unique features. In the limit when the coulomb charging energy is larger than the energy width of the degeneracy on the P side, it is demonstrated that conduction is permitted in only one direction of voltage. It is also shown, that when the energy width of the degeneracy on the N side is much larger than that on the P side, then a controllable tunneling saturation current is possible.

Electron Interaction in a Quantum Dot with Hard Wall Confinement Potential

We have investigated the electron interaction energy in a circular quantum dot with hard confinement potential, using a renormalized perturbation series (RPS) approach which interpolates between the perturbation solutions in the weak interaction regime and the asymptotic solutions in the strong interaction regime. The RPS is based on the scaling property of the Hamiltonian, and the numerical procedure is not complicated even when the number of electrons in the dot is not very small. The accuracy of the RPS calculation has been tested with two electrons in a dot, where the RPS ground state energy agrees with the exact numerical solution within 1% relative error. We have performed the RPS calculation for three and four electrons in the dot, from which the Coulomb charging energy is derived. The results suggest the potential application of pillar-shaped quantum dots for single-electron tunneling transistors operating at higher temperatures.

Single electron charging and single electron tunneling in sub-micron [formula omitted] double barrier transistor structures

Transport phenomena in a specially optimized vertical asymmetric sub-micron Al 0.28Ga 0.72As GaAs double barrier structure with modulation-doped barriers is investigated by applying a bias to a special Schottky side gate, which allows the effective area of the conducting channel to be finely “tuned”. For a sufficiently small device, the electrical properties of the controllable quantum dot bounded by well defined heterostructure barriers and an adjustable side wall potential are expected to be governed by single electron charging, and single electron resonant tunneling. Single electron transistor (SET) operation is possible because the number of electrons in the dot, n, can be varied one-by-one with the side gate. The drain current flowing through the conducting channel in response to a small drain voltage is strongly modulated by the gate voltage close to “pinch-off” as n approaches zero, and oscillations in the drain current persist up to about 25 K. A gate modulated zero current region of Coulomb blockade, step-like features, and resonances exhibiting negative differential resistance are clearly observed at low bias. Although this technology is very promising for the realization of SET operation at temperatures well above 4.2 K, the temperature dependence of the Coulomb blockade is an important limitation. We describe the evolution of the conductance oscillations and the degradation of Coulomb blockade with temperature from 0.3 K up to 25 K, and propose that co-tunneling in a small system containing just a “few” electrons in which the zero-dimensional energy level spacing is significant and comparable to the Coulomb charging energy is important, and is likely to be more complex than that documented for large planar dot structures containing “ many” electrons.

Symmetry-breaking instabilities in symmetric coupled-quantum-dot structures.

The effect of the Coulomb charging energy on the time evolution of the electron occupation probability in a coupled-dot system is numerically investigated by use of nonlinear coupled equations derived from the Schr\"odinger equation. For the initial condition that the electron occupation probability is equally distributed to two quantum dots, a small initial fluctuation in the distribution of the electron occupation probability causes the symmetry-breaking instabilities of the distribution for Coulomb charging energies larger than a certain threshold value. The numerical analyses with various initial conditions are also discussed.

Deep level transient spectroscopy of InP quantum dots

We report on the application of deep level transient spectroscopy to the study of electron emission from quantum dots. The results are presented for coherently grown InP dots embedded in Ga0.5In0.5P. We determine an emission activation energy of 220 meV for the one electron ground state of the dots. With increased average electron occupation in the dots we observe a systematic shift of the DLTS peak towards lower temperatures. This we interpret as being due to Coulomb charging of the dots. We extract an average Coulomb charging energy of 8–12 meV per added electron in the dot in agreement with our estimated value of 9 meV.

Spectroscopy of quantum levels in charge-tunable InGaAs quantum dots.

Imbedding self-assembled lens-shaped InGaAs quantum dots in a suitably designed field-effect-type GaAs/AlAs heterostructure allows us to charge the lowest discrete quantum levels in the dots with single electrons. Because of their small diameters of about 20 nm the Coulomb charging energy is significantly smaller than the quantization energies. We extract energy spacings of about 41 meV between the $s$-like ground state and the first excited $p$-like state from capacitance as well as infrared transmission spectroscopy at low temperatures and under application of high magnetic fields.

Effect of Coulomb charging energy on electron oscillations in a coupled-quantum-dot structure.

The effect of the Coulomb charging energy on the time evolution of the electron wave packet in a coupled-quantum-dot structure is investigated by use of coupled equations derived from the Schr\odinger equation. As long as the Coulomb charging energy does not exceed a certain threshold energy (four times as much as the coupling energy between the dots), the electron wave packet, which was initially localized in one of the dots, is completely transferred to the other dot and oscillates back and forth between the two dots. If the Coulomb charging energy exceeds the threshold, the transfer rate of the wave packet becomes abruptly incomplete and is reduced to less than one-half. This effect may be called the Coulomb blockade of the resonant electron tunneling in coupled quantum dots. It should be stressed that the transfer period of the wave packet is remarkably increased at and near the threshold charging energy. The analysis presented here should provide a useful basis for the design and evaluation of mesoscopic devices operating with coupled quantum structures.