From Fowler-Nordheim Research Articles

Theoretical analysis of the transition from field emission to space-charge-limited emission in liquids and gases

Discharge formation and breakdown in liquids have critical implications for water purification, medicine, and combustion, thereby motivating characterization of liquid behavior under high voltages. While several experiments with dielectric liquids have demonstrated that current transitions from Fowler–Nordheim (FN) scaling for field emission to Mott–Gurney (MG) scaling for space-charge-limited emission (SCLE) with increasing voltage, there is no common model linking electron emission from the liquid to gas phase. We show that applying a theory unifying FN, MG, and the Child–Langmuir law (CL) for SCLE at vacuum as a function of electron mobility and gap distance [Darr et al., Appl. Phys. Lett. 114, 014103 (2019)] yields excellent agreement with dielectric liquid emission experiments [Dotoku et al., J. Chem. Phys. 69, 1121 (1978)]. Specifically, current follows FN scaling at lower voltages before space charge contributions dominate, although none of the dielectric liquids considered achieve MG scaling in the experimental regime of interest. Considering a higher mobility representative of a vapor in the theory demonstrates the feasibility of achieving CL scaling for the gaps of the size considered experimentally at reasonably achievable applied voltages. Increasing the gap distance by an order of magnitude eliminates the contribution of space charge; decreasing gap distance by an order of magnitude causes a transition to MG. The implications of these results on electron emission in liquids and during a phase change to vapor and gas will be discussed.

Incorporating Resistance Into the Transition From Field Emission to Space Charge Limited Emission With Collisions

Field emitters and microplasmas often use series resistors to mitigate the rapid increase in current density that reduces device stability. This paper investigates the impact of external resistance on the transition of electron emission mechanism as a function of applied voltage Vapp, gap distance D, and electron mobility μ. For low μ (high gas pressure), the circuit transitions from Fowler-Nordheim (FN) to space charge limited emission by Mott-Gurney (MG) and Child-Langmuir (CL) before reaching Ohm's law (OL). At higher μ, a triple point arises where the asymptotic solutions for FN, MG, and CL intersect. This triple point is uniquely defined by D, μ, or gap voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> while also defining a specific gap impedance Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tp</sub> . When R ≤ Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tp</sub> , the electron emission transitions from FN to MG to CL to OL with increasing V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">app</sub> while MG and CL are bypassed at higher R. For a given R, increasing the applied voltage or emission current causes the gap to appear as a short.

Locally Resolved Electron Emission Area and Unified View of Field Emission from Ultrananocrystalline Diamond Films.

In this paper, we study the effect of the actual, locally resolved, field emission area on electron emission characteristics of uniform planar conductive nitrogen-incorporated ultrananocrystalline diamond ((N)UNCD) field emitters. High resolution imaging experiments were carried out in a field emission microscope with a specialty imaging anode screen such that electron emission micrographs were taken concurrently with measurements of I-V characteristics. An automated image processing algorithm was applied to process the extensive imaging data sets and calculate the emission area per image. It was routinely found that field emission from as-grown planar (N)UNCD films was always confined to a counted number of discrete emitting centers across the surface, which varied in size and electron emissivity. It was established that the actual field emission area critically depends on the applied electric field and that the field emission area and overall electron emissivity improve with the sp2-fraction present in the film, irrespective of the original substrate roughness or morphology. Most importantly, when as-measured I-E characteristics were normalized by the electric field-dependent emission area, the resulting j-E curves demonstrated a strong kink and departed from the Fowler-Nordheim law, finally saturating at a value on the order of 100 mA/cm2. This value was nearly identical for all studied films regardless of substrate. It was concluded that the saturation value is specific to the intrinsic fundamental properties of (N)UNCD.

Endurance degradation and lifetime model of p-channel floating gate flash memory device with 2T structure

The endurance degradation mechanisms of p-channel floating gate flash memory device with two-transistor (2T) structure are investigated in detail in this work. With the help of charge pumping (CP) measurements and Sentaurus TCAD simulations, the damages in the drain overlap region along the tunnel oxide interface caused by band-to-band (BTB) tunneling programming and the damages in the channel region resulted from Fowler-Nordheim (FN) tunneling erasure are verified respectively. Furthermore, the lifetime model of endurance characteristic is extracted, which can extrapolate the endurance degradation tendency and predict the lifetime of the device.

Characterization of Electron Emission from High Density Self-Aligned Si-Based Quantum Dots by Conducting-Probe Atomic Force Microscopy

Nanometer-scale silicon structures have been attracted much attention because their novel functionalities such as multiple-valued charge storage [1], single-electron transfer [2], electroluminescence (EL) [3], and electron emission [4]. Recently, we have succeeded in stacking Si quantum dots (Si-QDs) self-aligned by a selective growth technique focusing on the 2nd formation of Si-QDs on pre-grown Si-QDs [3], and demonstrated stable near-infrared EL from the self-aligned Si-QDs in a diode structure with semitransparent Au top electrode and n-Si(100) substrate under forward bias conditions over a threshold voltage as low as +1.2 V [3]. In this work, to get an insight into ballistical electron transport through self-aligned Si-QDs, we extended our research work to the spatially-resolved characterization of electron emission from self-aligned Si-QDs formed on ultrathin SiO2/n-Si(100) by using a conductive cantilever. Self-aligned Si-QDs with an areal density as high as ~1011 cm-2 were fabricated on ~1.0nm-thick SiO2 by process steps consisting of the first formation of Si-QDs by controlling low-pressure chemical vapor deposition (LPCVD) using pure SiH4, selective Ge-LPCVD from GeH4diluted with He, in-situ surface oxidation of the dots, thermal desorption of Ge oxide and subsequent 2nd formation of the Si-QDs. After the slight oxidation of the dot surface and boundaries between the 1st and the 2nd formed Si-QDs at 850°C, semitransparent Au top electrodes and the Al back contact to n-Si(100) were formed by thermal evaporation. The self-aligned formation of the Si-QDs with an areal as high as ~1011 cm-2and an average size of ~20 nm in diameter was confirmed by comparing topographic images taken just after the 1st Si-QDs formation and the 2nd one. TEM images also confirm the formation of ~1nm-thick oxide layer in-between self-aligned Si-QDs after the slight oxidation. In spatially-resolved characterization of electron emission from the align-dots through the Au top electrodes, current images were taken by using AFM in a non-contact mode keeping a distance of ~200nm from the sample surface by using a Au-coated Si cantilever with DC negative bias application to the Al back contact with respect to the grounded Au top electrode at room temperature in the atmosphere. With DC bias application over -7V, non-uniform image contrast due to electron emission from localized area being almost the same size of Si-QDs, emerged and was enhanced exponentially with an increase in the applied bias. From Fowler-Nordheim (FN) plots of observed field emission with an estimation of the potential drop in the topmost oxide on the self-aligned Si-QD, the emission current is likely to be limited by FN tunneling (Fig. 1). Considering the work function difference between n-Si(100) and Au-top electrode, the quantized energy states of the aligned dots can be placed at energies higher than the vacuum level of the top electrode when the DC biases over -7 V is applied as shown in the inset of Fig. 1. In tunneling from bottom to top dots, electrons can gain their kinetic energies efficiently as a result of reduced inelastic scattering.. Therefore, the observed electron emission is likely to be promoted by quasi-ballistic transport through aligned-dots structure. AcknowledgementsThis work was supported in part by Grant-in Aids for Scientific Research (A) No. 24246054 and Young Scientists (A) No. 25709023 from the Ministry of Education, Culture, Sports, Science and Technology, Japan and by JSPS Core-to-Core Program of International Collaborative Research Center on Atomically Controlled Processing for Ultralarge Scale Integration. In addition, the author deeply appreciates that the samples were fabricated successfully by utilizing the clean room facilities of Hiroshima Univ.

Enhanced field emission properties of doped graphene nanosheets with layered SnS2

We report here our experimental investigations on p-doped graphene using tin sulfide (SnS2), which shows enhanced field emission properties. The turn on field required to draw an emission current density of 1 μA/cm2 is significantly low (almost half the value) for the SnS2/reduced graphene oxide (RGO) nanocomposite (2.65 V/μm) compared to pristine SnS2 (4.8 V/μm) nanosheets. The field enhancement factor β (∼3200 for the SnS2 and ∼3700 for SnS2/RGO composite) was calculated from Fowler-Nordheim (F-N) plots, which indicates that the emission is from the nanometric geometry of the emitter. The field emission current versus time plot shows overall good emission stability for the SnS2/RGO emitter. The magnitude of work function of SnS2 and a SnS2/graphene composite has been calculated from first principles density functional theory (DFT) and is found to be 6.89 eV and 5.42 eV, respectively. The DFT calculations clearly reveal that the enhanced field emission properties of SnS2/RGO are due to a substantial lowering of the work function of SnS2 when supported by graphene, which is in response to p-type doping of graphene.

Experimental investigation of transition from Fowler–Nordheim field emission to space-charge-limited flows in a nanogap

An experimental investigation of the transition from Fowler–Nordheim (FN) field emission to space-charge-limited (SCL) flows in a nanogap is presented. Electrodes with gap size D∼30–70 nm corresponding to D/λo up to a maximum of ∼2×103, where λo is the de Broglie wavelength of the space-charge-electrons, are experimented. The transition from the FN field emission to the classical SCL flow is a function of the applied bias and lies in the range 5–15 V. The equilibrium transmitted current density for the 50 nm sample indicates a transition from the FN to the quantum SCL flow at ∼0.4 V with D/λo of ∼35 and then gradually to the classical SCL behavior as the voltage is increased beyond ∼9 V. The experiments indicate no sharp demarcation between the different regimes.

Investigation of the Electron-Injection Spread in Barrier-Engineered NAND Flash Memories

This letter investigates the threshold voltage statistical spread induced by the electron-injection process during programming of barrier-engineered floating-gate NAND Flash memories. The spread is shown to be independent of the tunnel-dielectric stack composition for low amplitudes of the programming staircase, for which the granular electron injection follows the Poisson statistics. Differences in the spread arise instead for large staircase step amplitudes, as in this regime the sub-Poissonian nature of the electron-injection process strictly depends on the steepness of the tunnel-dielectric current-voltage characteristics. This steepness can be modified by changing the electron-injection regime from Fowler-Nordheim (FN) to direct tunneling (DT) to modified FN (MFN): MFN is shown to allow a reduction of the electron-injection spread with respect to FN tunneling, while the DT regime gives rise to a large increase of the spread.

Extraction of emission area from Fowler–Nordheim plots

The process of deriving emission-area estimates from Fowler–Nordheim (FN) plots is investigated, using emission-area extraction functions and an iterative procedure suggested earlier [R. G. Forbes, J. Vac. Sci. Technol. B 17, 526 (1999)]. Simulated FN-plot data have been prepared using free-electron theory and three different tunneling-barrier models (elementary triangular barrier, image-rounded “Schottky–Nordheim” barrier, and a quadratically enhanced barrier). These have been analyzed using two area-extraction spreadsheets with different models (elementary triangular barrier and Schottky–Nordheim barrier) embedded in them. It is confirmed that significant errors in the area estimate may occur if the emission model used to analyze the FN-plot data does not correspond well with the model/physics responsible for generating the data. It is also concluded that parameters used in the area-extraction process should correspond to emission variables in the midrange of the FN-plot data.

Analysis of thin gate oxide degradation during fabrication of advanced CMOS ULSI circuits

The electrical characteristics uniquely associated with the thin gate oxide degradation of the advanced CMOS technology in manufacturing were determined for the first time. They were different from Fowler-Nordheim (F-N) stress, and therefore, cannot be simulated by the F-N stress. The p/sup +/ thin gate oxides were found to be inherently more susceptible to gate oxide degradation than the n/sup +/ gate oxides. The p/sup +/ oxide degradation is caused by a combination of the process-induced defect and plasma charging. The nature of the defect and its formation were identified by electrical and physical analysis. The defect formation was modeled. The p-channel gate oxide degradation will be worse with gate oxide scaling, and may limit the device scaling.