Tunneling Current Density Research Articles

Esaki tunnel diodes based on vertical Si-Ge nanowire heterojunctions

High performance Esaki tunnel diodes [L. Esaki, Phys. Rev. 109, 603 (1958)] based on small-diameter Ge/Si core/shell nanowires vertically grown on Si substrates are demonstrated. The devices exhibit pronounced negative differential resistance with peak-to-valley current ratio of 2.75, high peak current density of 2.4 kA/cm2, and high tunneling current density of 237 kA/cm2 at 1 V reverse bias, all obtained at room temperature. The peak current is found to increase with temperature and the data can be well explained with a band-to-band tunneling model. These results suggest that Si-Ge heterojunction with low defect density can be obtained for device applications such as tunnel diodes and tunnel field-effect transistors.

Analytical Modeling of Source-to-Drain Tunneling in Nanoscale Silicon MOSFET

Sub-10-nm bulk n-MOSFET (metal-oxide-semiconductor field effect transistor) direct source-todrain tunneling current density using WentzelKrammers-Brillouin (WKB) transmission tunneling theory has been simulated. The dependence of the source-to-drain tunneling current on channel length and barrier height is examined. Inversion layer quantization, band-gap narrowing, and drain induced barrier lowering effects have been included in the model. It has been observed that the leakage current density increases severely below 4 nm channel lengths, thus putting a limit to the scaling down of the MOSFETs. The results match closely with the numerical results already reported in literatures.

Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal—oxide—semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction approaches and a transfer matrix method

Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal—oxide—semiconductor (MOS) capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefunction approaches and the TMM at low electron energies. However, for high energies, only the transmittance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for all range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiNx metal gate increases because the electron effective mass of TiNx decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.

Nanogap electrodes formed at the exposed edge of Au/self-assembled monolayer/Al2O3/Au tunnel structures grown by atomic layer deposition

Atomic layer deposition of high quality Al2O3 thin films onto Au electrodes was enabled by surface modification with a self-assembled monolayer of –OH groups that react with a monolayer of trimethylaluminum gas source. Ar ion milling was then used to expose the edge of the Au/insulator/Au structure for molecular electrode contacts. The junctions are characterized by atomic force microscope and tunnel current properties. The Au/self-assembled monolayer/Al2O3/Au tunnel junction, with a very thin oxide insulator layer (15.4 Å), is stable and has a small tunneling current density of about 0.20–0.75 A/cm2 at 0.5 V.

Very High Room-Temperature Peak-to-Valley Current Ratio in Si Esaki Tunneling Diodes (March 2010)

Current density-voltage characteristics of Si p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -i-n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> Esaki tunneling diodes are presented, which are grown with low-temperature molecular beam epitaxy. The Esaki structures are realized without a postgrowth annealing step. A maximum peak-to-valley current ratio of more than 5 was obtained at room temperature. To the authors' knowledge, this result is the highest reported value for any pure Si tunnel diode. A temperature study of the current density-voltage characteristics separates all three forward current density components: 1) interband tunneling current density; 2) excess current density through defect-assisted tunneling; and 3) diffusion current density. The results show the high potential for the future development of Si Esaki tunneling diodes and predict an increase of the peak-to-valley current ratio up to 15 if the excess current density is suppressed.

Efficient III–V tunneling diodes with ErAs recombination centers

We report on recombination diodes containing monolayer depositions of ErAs between highly doped n- and p-layers in the (Al)GaAs and In(Al)GaAs material system. The ErAs material provides metallic states across the band gap of the host semiconductor that act as efficient recombination centers. Both electrons and holes can tunnel into the ErAs, resulting in extremely high tunneling current densities in the tens of kA cm−2 range. A device resistance area product of 1–2 × 10−5 Ω cm2 at low bias (±0.2 V) has been measured. Measurements on In(Al)GaAs and (Al)GaAs diodes will be compared to a simple theoretical model. Low band gap and high (p-) doping levels are identified as key parameters for achieving highest recombination currents. Compared to ErAs-free diodes, ErAs-enhanced recombination diodes provide orders of magnitude higher current densities at both moderate and low forward and reverse bias. This is attributed to the smaller and narrower tunnel barriers from the n- and p-layers into the ErAs compared to tunneling from the n- to the p-side through the whole depletion region.

Proposal for efficient generation of spin-polarized current in silicon

We propose a spin-dependent resonant tunneling structure to efficiently inject spin-polarized current into silicon. By means of a heavily doped polycrystalline Si between the ferromagnetic metal and Si, the Schottky barrier resistance is reduced and consequently the tunneling current density is raised. The small Fermi sea of the charge carriers in Si focuses the tunneling electrons to the resonant spin states within a small region of transverse momentum in the ferromagnet which creates the spin polarization of the current.

Model of a tunneling current in an anisotropic Si/Si1−xGex/Si heterostructure with a nanometer-thick barrier including the effect of parallel–perpendicular kinetic energy coupling

A theoretical model of an electron tunneling current in an anisotropic Si/Si1−xGex/Si heterostructure was developed. The parallel and perpendicular kinetic energies were coupled and the coupling was included in expressing the electron transmittance through the anisotropic heterostructure. The model was applied to the anisotropic Si(1 1 0)/Si0.5Ge0.5/Si(1 1 0) heterostructure with a 25 nm thick strained Si0.5Ge0.5 potential barrier, in which each layer of the heterostructure has three valleys (valleys 1, 2 and 3) with different inverse effective mass tensors and a conduction band discontinuity of 216 meV. The Si(1 1 0)/SiGe structure implies that only the four equivalent valleys (valleys 1 and 2) are considered in calculations. It was found that the transmittance for valley 1 is the same as that for valley 2 due to the same barrier height. The transmittance decreases as the electron phase velocity increases because the electron phase velocity enhances the barrier height. Moreover, the total tunneling current density for the phase velocity higher than 3 × 105 m s−1 differs significantly from that obtained without including the kinetic energy coupling. As the electron phase velocity gets higher, the total tunneling current density lowers. This implies that the coupling effect cannot be ignored for electrons with high phase velocity.

An Analytical Gate Tunneling Current Model for MOSFETs Having Ultrathin Gate Oxides

In this paper, we present a completely analytical model for the gate tunneling current, which can be used to get a first-order estimate of this parameter in present-generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. The model has been developed from first principles, and it does not use any empirical fitting and/or correction parameters. It takes into account the quantization of the electron energy levels within the inversion layer of a MOSFET, which behaves similar to a potential well. Several interesting simplifications regarding this well structure have been made, and all these assumptions have been rigorously justified, both based on physical arguments as well as through numerical quantifications. An extremely interesting and important outcome of this procedure is a nonzero value of the wavefunction at the semiconductor-insulator interface, which is physically justified, however, contrary to what other existing literatures in this area assume. This procedure also led to a closed-form analytical expression for the inversion layer thickness. The interface wavefunction was used, in association with the tunneling probability through the gate oxide, and the carriers in transit model in the gate metal, to find the resultant gate tunneling current density as a function of the applied gate-to-body voltage. The results obtained from our simple and completely analytical model were compared with the experimental results reported in the literature, and the match is found to be excellent for varying oxide thicknesses and substrate doping concentrations, which justifies the authenticity of the model developed in this work here.

An experimental study of the electronic structure of anodically grown films on an amorphous Ni78Si8B14 alloy

AbstractFilms of Ni(OH)2 and NiOOH grown on a rapidly solidified amorphous Ni78Si8B14 alloy by anodic polarisation were analysed with XPS and the results were compared with those of NiO and of films grown on polycrystalline Ni. SIMS performed on the polarised alloy showed enrichment of Ni at the outermost surface. Transmission electron microscopy (TEM) of cross‐sectional samples showed an absence of crystallinity. The Ni 2p shake up satellite and valence band spectra suggested that NiOOH is characterised by a more enhanced n‐type semi‐conducting behaviour compared to Ni(OH)2 in agreement with earlier tunnelling current density measurements performed with scanning tunnelling spectroscopy (STS). Copyright © 2008 John Wiley &amp; Sons, Ltd.

Reduction of gate-to-channel tunneling current in FinFET structures

In this work, the gate-to-channel leakage current in FinFET structures is experimentally studied in comparison with quasi-planar very wide-fin structures, and as a function of the fin width. Devices with both doped and undoped channels and different gate stacks are studied. Experimental evidence for the reduction of gate tunneling current density in narrow FinFET structures compared to their counterpart quasi-planar structures is reported for the first time. This gate current reduction is observed for both n-channel and p-channel devices and is found to be stronger for HfO 2 than for SiON. For a given gate dielectric, the above gate current improvement in FinFETs enhances with decreasing the fin width. For SiON with an equivalent oxide thickness of 1.6 nm in undoped n-channel devices, it varies from factor of 2.3–4.3, when the fin width decreases from 75 to 25 nm. The possible reasons for the observed effect are discussed.

Direct tunneling effective mass of electrons determined by intrinsic charge-up process

The electron effective mass for direct tunneling (EETM) in silicon dioxide (SiO 2) was determined by many authors using a high bias field for obtaining direct measurable direct tunneling current densities (TCDs), leaving some ambiguity to the electron kinetic energy at/within the SiO 2 barrier. A determination of the EETM by exploiting a long term intrinsic charge-up process of vacant defects adjacent to the SiO 2 barrier by capacitance–voltage ( CV) measurements is reported. The EETM is obtained by using the fixed charge sheet densities for iterating the TCD as a function of time. The zero bias field renders the average electron kinetic energy to converge on the thermal energy, leaving less ambiguity to the EETM. For an SiO 2 layer of d SiO 2 = 8.2 nm , an EETM of m eff = (0.3 ± 0.03) m 0 is obtained.

Rapid Melt Growth of Germanium Tunnel Junctions

A rapid melt growth process for forming interband Esaki tunnel junctions on Ge is shown. The process uses a phosphorus spin-on diffusant and rapid thermal annealing to form the side of the junction, while for the side, a deposited aluminum film serves both as an acceptor dopant source and a melt for epitaxial regrowth of . The current density in these junctions depends strongly on the peak temperature of the melt and ranges between a few to over . The use of a silicon nitride microcrucible improves the surface morphology by confining the melt. Record forward peak current density of and reverse interband tunnel current density of is achieved at a peak temperature of approximately .

Design Optimization of Metal Nanocrystal Memory—Part I: Nanocrystal Array Engineering

The three-dimensional (3D) electrostatics together with the modified Wentzel-Kramers-Brillouin tunneling model has been implemented to simulate the programming and retention characteristics of the metal nanocrystal (NC) memories. Good agreements with experimental data are first demonstrated to calibrate the transport parameters. In contrast to previous works, the 3D electrostatic effects investigated in this paper are proven very significant in the memory operations. Therefore, new design criteria of metal NC memories are investigated. Part I presents the physical model and the NC array design optimization. A sparse and large-size NC array, which is suitable for the one-dimensional narrow-channel memories, provides higher program/erase tunneling current density due to the field-enhancement effect and lower charging energy due to the large NC capacitance. On the other hand, to achieve a sufficient memory window, fast programming speed, and long retention time in the typical two-dimensional channel memories, a dense and large-size NC array is favorable while taking the tradeoff with the NC number density into account. Based on the same theoretical model, the authors continue in Part II to consider the design optimization when high-K dielectrics can be employed

Conserved flux in interband tunneling

A derivation of the interband tunneling transmission coefficient is given based on analytical solution of the two-band model and explicit account of the conservation of flux. The conventional estimate is obtained only in limiting cases. In general, the transmission is greater than this estimate, except for carrier energy near a band edge, in which case the transmission goes to zero. Analytical results are obtained for a corrected asymptotic transmission coefficient, and also for the tunneling current density using the conventional estimate of the transmission coefficient.

Hole tunnelling properties in resonant tunnelling diodes with Si/strained Si0.8Ge0.2 heterostructures grown on Si(1 0 0) by low-temperature ultraclean LPCVD

Hole resonant tunnelling diodes (RTDs) with Si/strained Si1–xGex heterostructures epitaxially grown on Si(1 0 0) were fabricated, and sharp current peaks have been reproducibly observed. From the quantum well width dependence of the current–voltage characteristics, at the peak voltage, heavy holes in the accumulation region resonantly tunnel through the estimated resonant states of a light hole and a heavy hole in a Si1–xGex quantum well. The top contact and mesa area dependence of the peak current shows that the tunnel current only flows under a top contact electrode, i.e. the leakage current at the sidewall is negligibly small. The resonant tunnelling current density reaches as high as 3.6 kA cm−2 at 0.19 V with 2 nm thick barriers. Moreover, the introduction of higher Ge fraction effectively suppresses the increase of the valley current and enables negative differential conductance at higher operation temperature.

Rigorous carrier dynamic model of electroluminescent metal-oxide-semiconductor silicon tunneling diodes

The carrier dynamics of electroluminescent metal-oxide-semiconductor silicon tunneling diodes is rigorously modeled in this study. Various tunneling and recombination current densities are formulated without using the Maxwell-Boltzmann approximation for the carrier concentrations. This model satisfactorily explains the current-voltage characteristics in strong accumulation using a self-consistent formulation. It also relates light emission efficiency to the interface-state density and the bulk-trap density in a straightforward manner. The internal radiative recombination efficiency in the bulk Si substrate is estimated to be in tens of percents. The model also explains clearly the strongly influenced small-signal light-current response time with respect to the injection current density. It enables the small-signal method to be useful in extracting the parameters of the interface-state density and the bulk-trap density.

$I$&amp;#8211;$V$Characterization of Tunnel Diodes and Multijunction Solar Cells

This paper discusses common difficulties in measuring tunnel diodes and sets a special focus on devices consisting of tunnel diodes and solar cells, such as multijunction solar cells. The resulting theoretical current-voltage (I-V) characteristics of tunnel diodes and solar cells when measured via four-wire techniques are calculated and compared with experimentally measured I-V curves. Solutions to overcome the measurement difficulties are provided, and a method to infer the maximum tunneling current density of tunnel diodes in a device with solar cells is discussed. This paper also describes how the elsewhere-observed ostensible hysteresis with multijunction solar cells is caused by the measurement setup or by large internal series resistances

Quantum-mechanical effects and gate leakage current of nanoscale n-type FinFETs: A 2d simulation study

This paper simulates a kind of new sub-50nm n-type double gate MOS nanotransistors by solving coupled Poisson–Schrödinger equations in a self-consistent manner with a finite element method, and presents a systematic simulation-based study on quantum-mechanical effects, gate leakage current of FinFETs. The simulation results indicate that the deviation from the classical model becomes more important as the gate oxide, gate length and Fin channel width becomes thinner and the Fin channel doping increases. Gate tunneling current density reduces with the body thickness decreasing. Excessive scaling increases the gate current below Fin thickness of 5nm. The gate current can be dramatically reduced beyond 1017cm−3 with the Fin body doping increasing. In order to understand the influence of electron confinement, quantum mechanical simulation results are also compared with the results from the classical approach. Our simulation results indicate that quantum mechanical simulation is essential for the realistic optimization of the FinFET structure.

Six-bandk∙pcalculation of spin-dependent interband tunneling in strained broken-gap heterostructures under a quantizing magnetic field

We investigate spin-dependent interband magnetotunneling processes in strained broken-gap resonant tunneling structures made from InAs, AlSb, and GaSb, which are promising materials for quantum devices. InAs/AlSb/GaSb/InAs/AlSb/GaSb double-barrier structures grown on both InAs and GaSb are considered. Transmission coefficients for interband tunneling processes from individual eigenstates in the InAs emitter as well as current-voltage characteristics were calculated using a six-band k center dot p model and the scattering matrix method. We predict that due to lattice-mismatch induced strain, the interband tunneling current density for the structure grown on InAs can be one or two orders of magnitude less than that for the structure grown on GaSb. Furthermore, as a consequence of interband magnetotunneling, structures grown on different substrates yield different spin polarization of the tunneling current. It is obtained that the current spin polarization can be greater than 90%. These resonant tunneling structures can be used as spin filters in the rapidly growing field of spintronics. (Less)