An Analysis of Electron Direct Tunneling Current through a High-K MOS Capacitor by Including the Effect of a Trap between HfO[sub 2] and SiO[sub 2] Interfaces (original) (raw)
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2011
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Analytical modeling of tunneling current through Si O 2 -Hf O 2 stacks in metal oxide semiconductor structures Abstract. In this paper, we discuss the electron transmittance and tunneling current in high-k-based-MOS capacitors with trapping charge by including the off-diagonal effective-mass tensor elements and the effect of coupling between transverse and longitudinal energies represented by an electron velocity in the gate. The HfSiO x N/SiO 2 dual ultrathin layer is used as the gate oxide in an n + poly-Si/oxide/Si capacitor to replace SiO 2 . The main problem of using HfSiO x N is the charge trapping formed at the HfSiO x N/SiO 2 interface that can influence the performance of the device. Therefore, it is important to develop a model taking into account the presence of electron traps at the HfSiO x N/SiO 2 interface in the electron transmittance and tunneling current. The transmittance and tunneling current in n + poly-Si/HfSiO x N/trap/SiO2/Si(100) capacitors are calculated by using Airy wavefunctions and a transfer matrix method (TMM) as analytical and numerical approaches, respectively. The transmittance and tunneling current obtained from the Airy wavefunction are compared to those computed by the TMM. The effects of the electron velocity on the transmittance and tunneling current are also discussed.
Journal of Semiconductors, 2010
Analytical expressions of electron transmittance and tunneling current in an anisotropic TiN x /HfO 2 /SiO 2 /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 TiN x metal gate increases because the electron effective mass of TiN x 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.
Characterization and control of charge transfer in a tunnel junction
physica status solidi (b), 2017
Charge transfer in a tunnel junction is studied under dc and ac voltage bias using quantum shot noise. Under dc voltage bias V , spectral density of noise measured within a very large bandwidth enables to deduce the currentcurrent correlator in the time domain by Fourier transform. This correlator exhibits regular oscillations proving that electrons try to cross the junction regularly, every h/eV. Using harmonic and bi-harmonic ac voltage bias, we then show that quasiparticles excitations can be transferred through the junction in a controlled way. By measuring the reduction of the excess shot noise, we are able to determine the number of electron-hole pairs surrounding the injected electrons and demonstrate that bi-harmonic voltage pulses realize an on-demand electron source with a very small admixture of electron-hole pairs. A time-dependent voltage drive V (t) = V dc + Vac(t) applied to a contact with transmission T generates an incoming excitation giving rise to transmitted and reflected quasiparticles. The excess noise ∆SV = (I(t) 2 ac+dc − I(t) 2 dc)/∆f given by the difference between the noise measured with and without the ac excitation is measured by an ammeter with a bandwidth ∆f. It gives the number of electron-hole pairs surrounding the transmitted electrons: N e−h = h 2e 2 T ∆S V hν where ν is the repetition frequency of Vac.
Insights into Electron Transport in a Ferroelectric Tunnel Junction
Nanomaterials
The success of a ferroelectric tunnel junction (FTJ) depends on the asymmetry of electron tunneling as given by the tunneling electroresistance (TER) effect. This characteristic is mainly assessed considering three transport mechanisms: direct tunneling, thermionic emission, and Fowler-Nordheim tunneling. Here, by analyzing the effect of temperature on TER, we show that taking into account only these mechanisms may not be enough in order to fully characterize the performance of FTJ devices. We approach the electron tunneling in FTJ with the non-equilibrium Green function (NEGF) method, which is able to overcome the limitations affecting the three mechanisms mentioned above. We bring evidence that the performance of FTJs is also affected by temperature–in a non-trivial way–via resonance (Gamow-Siegert) states, which are present in the electron transmission probability and are usually situated above the barrier. Although the NEGF technique does not provide direct access to the wavefun...
Suppressed shot noise in trap-assisted tunneling of metal–oxide–semiconductor capacitors
Applied Physics Letters, 2000
We show that the tunneling current of a metal-oxide-semiconductor capacitor subjected to voltage stress exhibits suppressed shot noise with respect to the ''full'' shot noise level associated with the same current before stress. We provide experimental results exhibiting a suppression down to about 70% and a theoretical model for transport and noise in the stress induced leakage current regime based on trap assisted tunneling, which is able to reproduce such reduction. Numerical results from the model are compared with measurements.
Single electron tunneling rates in multijunction circuits
Zeitschrift f�r Physik B Condensed Matter, 1991
The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.