Fowler-Nordheim Regime Research Articles

Transitions between field emission and vacuum breakdown in nanoscale gaps

The continuing reduction in device size motivates a more fundamental understanding of breakdown and electron emission for nanoscale gaps. While prior experiments have separately studied breakdown and electron emission in vacuum gaps, no study has comprehensively examined the transitions between these mechanisms. In this study, we measure the current-voltage (I−V) curves for electrodes with different emitter widths for 20–800 nm gaps at vacuum (∼1 μTorr) to measure breakdown voltage and assess electron emission behavior. The breakdown voltage Vb increases linearly with increasing gap distance from ∼15 V at 20 nm to ∼220 V at 300 nm and remains nearly constant for larger gaps; Vb does not depend strongly on the emitter width. Breakdown can proceed directly from the field emission regime. Nexus theory, which predicts transitions between space-charge limited current (SCLC) and field emission (FE), shows that the experimental conditions are in the Fowler–Nordheim regime and within a factor of 0.7 to the FE-SCLC transition. We also present the results of electrode damage by emission current-induced heating to explain the flattening of Vb at larger gaps that was absent in previous experiments for similar gap distances at atmospheric pressure.

Vectorial, non-destructive magnetic imaging with scanning tunneling microscopy in the field emission regime

When a scanning tunneling microscope is operated at tip-target distances ranging from few nanometers to few tens of nanometers (Fowler-Nordheim or field emission regime), a new electronic system appears, consisting of electrons that escape the tip-target junction. If the target is ferromagnetic, this electronic system is spin polarized. Here, we use these spin polarized electrons to image magnetic domains in thin films. As two components of the spin polarization vector are detected simultaneously, the imaging of the local magnetization has vectorial character. The tip is nonmagnetic, i.e., the magnetic state of the target is not perturbed by the act of probing. We expect this spin polarized technology, which scales down scanning electron microscopy with polarization analysis by bringing the source of primary electrons in close proximity to the target, to find its main applications in the imaging of noncollinear, weakly stable spin excitations.

Scanning Field Emission Microscopy with Polarization Analysis (SFEMPA)

In the Fowler-Nordheim regime of Scanning Tunneling Microscopy (STM) the tip-target distance is few nanometers to few tens of nanometers. In this situation the tunneling between tip and target is completely suppressed. Instead, electrons can be field-emitted from the tip and their impact with the target might excite electrons off the surface. Under certain circumstances, the excited electrons escape the tip-target junction and build a new electronic system, absent in the tunneling regime of STM. A recent experiment discovered that this electronic system is spin polarized at nanoscale tip-target distances. Here we provide a comprehensive review of all strategies that have been adopted to perform the spin polarized experiments in the Fowler-Nordheim regime of STM. We also present new data that complement the proof of spin polarization and specifically underline the magnetic imaging potential of this new technology, which we call Scanning Field Emission Microscopy with Polarization Analysis (SFEMPA).

Effect of the presence of trap states in oxides in modeling gate leakage current in advanced MOSFET with multi-oxide stack

Abstract A model of trap assisted tunneling due to the presence of trap states distributed over the oxide and at the interface has been introduced to develop a complete analytical model for gate tunneling current in advanced nano-scale MOSFET in addition to the ideal direct tunneling current with double layer silicon oxide-Hafnium Oxide stack used as gate dielectric. Trapping-detrapping of charge carriers is mostly subjected to multiphonon transitions and thus is dependent on temperature, gate bias and the distribution of trap states across oxide. Relative contribution of the direct tunneling and trap-assisted tunneling has been estimated even in the Fowler-Nordheim regime. The assumption of simplified parabolic energy band dispersion with proper boundary conditions in Wentzel-Kramers-Brillouin (WKB) effective mass approximation is employed to determine the probability density of electrons at different materials throughout the MOS structure. It is then modulated by the tunneling probability to estimate the total amount of tunneling current as a function of effective oxide thickness and gate-biasing.

Current-Fluctuation Mechanism of Field Emitters Using Metallic Single-Walled Carbon Nanotubes with High Crystallinity

Field emitters can be used as a cathode electrode in a cathodoluminescence device, and single-walled carbon nanotubes (SWCNTs) that are synthesized by arc discharge are expected to exhibit good field emission (FE) properties. However, a cathodoluminescence device that uses field emitters radiates rays whose intensity considerably fluctuates at a low frequency, and the radiant fluctuation is caused by FE current fluctuation. To solve this problem, is very important to obtain a stable output for field emitters in a cathodoluminescence device. The authors consider that the electron-emission fluctuation is caused by Fowler–Nordheim electron tunneling and that the electrons in the Fowler–Nordheim regime pass through an inelastic potential barrier. We attempted to develop a theoretical model to analyze the power spectrum of the FE current fluctuation using metallic SWCNTs as field emitters, owing to their electrical conductivity by determining their FE properties. Field emitters that use metallic SWCNTs with high crystallinity were successfully developed to achieve a fluctuating FE current from field emitters at a low frequency by employing inelastic electron tunneling. This paper is the first report of the successful development of an inelastic-electron-tunneling model with a Wentzel–Kramers–Brillouin approximation for metallic SWCNTs based on the evaluation of FE properties.

Tuning contact transport mechanisms in bilayer MoSe2 transistors up to Fowler–Nordheim regime

Atomically thin molybdenum diselenide (MoSe2) is an emerging two-dimensional (2D) semiconductor with significant potential for electronic, optoelectronic, spintronic applications and a common platform for their possible integration. Tuning interface charge transport between such new 2D materials and metallic electrodes is a key issue in 2D device physics and engineering. Here, we report tunable interface charge transport in bilayer MoSe2 field effect transistors with Ti/Au contacts showing high on/off ratio up to 107 at room temperature. Our experiments reveal a detailed map of transport mechanisms obtained by controlling the interface band bending profile via temperature, gate and source-drain bias voltages. This comprehensive investigation leads to demarcating regimes and tuning in transport mechanisms while controlling the interface barrier profile. The careful analysis allows us to identify thermally activated regime at low carrier density, and Schottky barrier driven mechanisms at higher carrier density demonstrating the transition from low-field direct tunneling/ thermionic emission to high-field Fowler–Nordheim tunneling. Furthermore, we show that the transition voltage Vtrans to Fowler–Nordheim correlates directly to the difference between the chemical potential of the metal electrode and the conduction band minimum in the 2D semiconductor, which opens up opportunities for new theoretical and experimental investigations. Our approach being generic can be extended to other 2D materials, and the possibility of tuning contact transport regimes is promising for designing MoSe2 device applications.

Evidence of Gumbel distributions of conductance fluctuations in bacteriorhodopsin thin films

By considering a set of experiments carried out on bacteriorhodopsin in vitro by Casuso et al (2007 Phys. Rev. E 76 041919), we extract the conductance as function of the applied voltage. The microscopic interpretation of experiments shows that charge transfer is ruled by a direct tunneling (DT) mechanism at low bias and by a Fowler–Nordheim (FN) tunneling mechanism at high bias. A nucleation region at the cross-over between the DT and FN regimes can be identified. A theoretical analysis of conductance fluctuations is performed by calculating the corresponding variance and the probability density functions (PDFs): these constitute a powerful indicator in order to understand the internal dynamics of the system. Conductance fluctuations are non-Gaussian and follow well the standard generalized Gumbel distributions G(a). In particular, at low bias, the PDFs are bimodal and can be resolved in at least a couple of G(a) functions with different values of the shape parameter a. The nucleation region is characterized by a single Gumbel distribution, G(1). At increasing bias, the G(1) distribution turns in a bimodal distribution. We discuss possible correlations between the voltage dependence of the G(a) and the microscopic mechanisms that determine the electrical response of the system.

Quantum-Mechanical Charge Distribution in Cylindrical Gate-All-Around MOS Devices

We present a self-consistent 2-D quantum-mechanical model for charge distribution in cylindrical gate-all-around devices with computation of the gate tunneling current. The validity of 1-D approximations for the charge and the gate current is discussed, assessing the validity of a previously proposed analytical approximation for the tunneling current in the Fowler-Nordheim regime.

Scanning probe nanolithography on calixarene

The direct patterning of molecular resist materials using scanning probes as local nano-toolbox represents an interesting alternative to radiation-based lithography circumventing proximity effects and development-related problems. Here, we demonstrate the development-less patterning of 10-40nm thick, spin-coated C-Methylcalix[4]resorcinarene molecular resist in a positive-tone. The lithography was performed with a modified STM operated in constant-current Fowler-Nordheim regime at ambient conditions. Thereby, wide process latitude from sub-10nm up to the @mm-size was achieved by variation of the line dose and bias voltage. The reproducible and reliable tip-based patterning of calixarene has also been demonstrated on Silicon substrates with low electron line dose values of 10nC/cm corresponding to 40pA set-point and [email protected]/s tip speed.

Effect of high temperature annealing on the performance of MANOS charge trapping memory

We have investigated the effect of post deposition annealing (PDA) temperature of Al2O3 blocking layer on the performance of charge trapping memory capacitors. Two splits of PDA were performed in N2 ambient at 850°C/60 s and 1050°C/60 s, respectively. The 1050°C annealed capacitor could be programmed and erased normally by using Fowler-Nordheim (FN) injection. In contrast, the 850°C annealed device could not be erased, even though it could be programmed properly. By measuring the gate leakage current and the flatband voltage shift, we found the erase failure in the 850°C annealed device was due to a larger gate back-injection leakage current at V g<0. The trend of gate leakage current was further verified in two Al/Al2O3/SiO2/p-Si control capacitors with the same PDA splits. In addition, constant voltage stress measurements on control capacitors in the FN regime showed that the change of gate leakage current followed an empirical Curie-von Schweidler law at V g<0. The data pointed out the importance to further study the relation between PDA conditions and the defect generation properties in Al2O3 blocking layer.

Scanning proximal probe lithography for sub-10 nm resolution on calix[4]resorcinarene

The use of molecular resist in scanning proximal probe lithography (SPPL) offers a novel and promising maskless lithographic method with sub-10 nm resolution. Here, the authors present their investigation of the patterning capabilities of C-Methylcalix[4]resorcinarene at ambient conditions using SPPL. The STM-based setup operates in constant-current Fowler–Nordheim regime and results in positive-tone self-developing phenomena. The lithographic operation is performed at currents in the range of pico-ampere, writing speeds of 1–10 μm/s, and bias voltages ranging from 20 up to 70 V. Currently, the authors have achieved feature sizes from 7 nm to micrometers depending on the applied exposure parameters. The direct patterning process shows high reproducibility and reliability over this large feature range.

Impact of temperature increments on tunneling barrier height and effective electron mass for plasma nitrided thin SiO2 layer on a large wafer area

Thermally grown SiO2 layers were treated by a plasma nitridation process realized in a vertical furnace. The combination of a pulsed-low frequency plasma and a microwave remote plasma with N2/NH3/He feed gas mixture was used to nitride the thermally grown SiO2 gate dielectrics of MIS structures. Temperature dependency of effective masses and the barrier heights for electrons in pure thermally grown SiO2 as well as plasma nitrided SiO2 in high electric field by means of Fowler–Nordheim regime was determined. It is frequently seen from the literature that either effective electron mass or barrier height (generally effective electron mass) is assumed to be a constant and, as a result, the second parameter is calculated under the chosen assumption. However, in contrast to general attitude of previous studies, this work does not make any such assumptions for the calculation of neither of these two important parameters of an oxide at temperature ranges from 23 to 110 °C for SiO2, and 23 to 130 °C for nitrided oxide. It is also shown here that both parameters are affected from the temperature changes; respectively, the barrier height decreases while the effective mass increases as a result of elevated temperature in both pure SiO2 and plasma nitrided SiO2. Therefore, one parameter could be miscalculated if the other parameter, i.e., effective mass of electron, was assumed to be a constant with respect to variable physical conditions like changing temperature. Additionally, the barrier heights were calculated just by taking constant effective masses for both types of oxides to be able to compare our results to common literature values.

Physical Modeling for Programming of TANOS Memories in the Fowler–Nordheim Regime

This paper presents a physics-based model that is able to describe the TANOS memory programming transients in the Fowler-Nordheim uniform tunneling regime across the bottom-oxide layer. The model carefully takes into consideration the trapping/detrapping processes in the nitride, the limited number of traps available for charge storage, and their spatial and energetic distribution. Results are in good agreement with experimental data on TANOS devices with different gate-stack compositions, considering a quite extended range of gate biases and times. The reduced gate-bias sensitivity of the programming transients with respect to the floating-gate cell is explained in terms of a finite number of nitride traps and a thinner extension of the nitride trapping region as the gate bias is increased. The model represents a valid contribution for the investigation of the achievable performances of the TANOS technology.

EOT Measurement of Ultra-Thin Gate Dielectrics using the Tunneling Current Regime

Presented in this work is a measurement method to obtain the Equivalent Oxide Thickness (EOT) using the tunneling current regime for ultra-thin gate dielectrics ranging from 1.5 to 16 nm. With the aid of the I-V characteristic of MOS capacitors in a low electric-field range (5-7 MV/cm), EOT was obtained from the slope of the ln(I/Vox2) versus 1/Vox graph for direct or Fowler-Nordheim tunneling current regimes. The average EOT uniformity was obtained for representative populations of tested MOS capacitors (at least a hundred per wafer) and, comparing with the results obtained from C-V measurements, the method was validated.

Impact of wafer charging on hot carrier reliability and optimization of latent damage detection methodology in advanced CMOS technologies

We have studied the possibility to use hot carrier stresses to reveal the latent damage due to Wafer Charging during plasma process steps in 0.18 μm and 0.6 μm CMOS technologies. We have investigated various hot carrier conditions in N- and PMOSFETs and compared the results to classical parametric studies and short electron injections under high electric field in Fowler–Nordheim regime, using a sensitivity factor defined as the relative shift towards a reference protected device. The most accurate monitor remains the threshold voltage and the most sensitive configuration is found to be short hot electron injections in PMOSFET’s. The ability of very short hot electron injections to reveal charging damage is even more evidenced in thinner oxides and the better sensitivity of PMOSFET is explained in terms of conditions encountered by the device during the charging process step.

Fabrication and characterization of sub-3 nm gaps for single-cluster andsingle-molecule experiments

We describe a simple process for preparing sub-3 nm gaps by means ofcontrollable breaking of gold wires lithographed on a SiO2/Sisubstrate at low temperature (4.2 K). We show that the mechanism involvedis thermally assisted electromigration. We investigate the effect of thehigh electric field developed at the final stage of the breaking of thenanowire and observe that the current–voltage characteristics (I–V)of the resulting electrodes are stable up to ∼5 V. Thishigh-electric-field stability gives access to the well-known Fowler–Nordheim regime (eV > Φ0) in theI–Vcharacteristic, thus allowing an accurate characterization of the gap size. The sizeof the gap is found to be between 1 and 2 nm. We validate this characterization byfabricating single-electron tunnelling devices based on alkylthiol capped goldnanoparticles.

Reply to “Comment on ‘Unified compact theory of tunneling gate current in metal-oxide-semiconductor structures: Quantum and image force barrier lowering’ [J. Appl. Phys. 92, 3724 (2002)

Our transparency factor, Peff using the effective triangular approximation is shown to practically match PWKB given in the comment. It indicates that Peff can model the effect of image force lowering (if it exists) on the gate current (Ig) in the Fowler–Nordheim regime as accurately as the Wentzel–Kramers–Brillouin method. The experimentally extracted value of α≈0 indicates that PWKB incorporating the image potential still overestimates Ig. Additionally, physics underlying the image force lowering in metal-oxide-silicon systems is briefly discussed in light of the wave nature of electrons and other reported experimental data.

Optical and electrical transport mechanisms in Si-nanocrystal-based LEDs

In this work, we present photoluminescence (PL) and electroluminescence studies on thermal SiO 2 Si-implanted light-emitting devices (LEDs) containing crystallites of size 3 nm . The PL measurements reveal a bulk-type behavior of nc-Si-associated PL confirming that the PL obtained at ∼1.6 eV is closely related to Q-confined nc-Si. Analysis of electrical transport mechanisms confirms that the current is related to a tunneling process as expected and not to Fowler–Nordheim regime. Finally, threshold electric field for light emission obtained was as low as 5 MV/cm , confirming the real potential of a such Si-implanted material for LEDs based on Si.

Quantum partition noise in field emission currents

A quantum partition noise with spectral density significantly smaller than the Schottkyvalue 2qI (withq the elementarycharge and Ithe mean current) is predicted to occur in nanoscale electron emitters under theaction of strong applied electric fields. The noise suppression effect appearswhenever the transmission probabilities for highly occupied states are not smallwith respect to 1. We show that in two limiting cases: the Fowler–Nordheimregime and the Richardson–Laue–Dushman regime of electron emission,the noise recovers the full Schottky noise without the suppression effect.

Si – SiO 2 barrier height and its temperature dependence in metal-oxide-semiconductor structures with ultrathin gate oxide

The potential distribution across n+ polycristalline silicon (poly-Si)/SiO2/Si(p) structures, with an oxide layer thinner than 4 nm, was determined using a full quantum self-consistent model. When applied to capacitance–voltage measurements, it allows an accurate determination of the oxide thickness tox to be made. When applied to current–voltage measurements, in the Fowler–Nordheim regime, it leads to an accurate determination of the barrier height Φ at the interface between the emitting poly-Si gate electrode and the oxide, over a temperature range 20–250 °C. The results show a constant Φ(0 K) for 3 nm&amp;lt;tox⩽9 nm. However, the temperature sensitivity |dΦ/dT| increases from 0.35 to 0.7 meV/K with tox reduction.