Comparison of tunneling currents in graphene nanoribbon tunnel field effect transistors calculated using Dirac-like equation and Schrodinger’s equation

The tunneling current in a graphene nanoribbon tunnel field effect transistor(GNR-TFET) has been quantum mechanically modeled. The tunneling current in the GNR-TFET was compared based on calculations of the Dirac-like equation and Schrodinger’s equation. To calculate the electron transmittance, a numerical approach-namely the transfer matrix method(TMM)-was employed and the Launder formula was used to compute the tunneling current. The results suggest that the tunneling currents that were calculated using both equations have similar characteristics for the same parameters, even though they have different values. The tunneling currents that were calculated by applying the Dirac-like equation were lower than those calculated using Schrodinger’s equation.     

Measurement of very low tunneling current density inSiO2 using the floating-gate technique

The floating-gate technique for measuring extremely low gate currents has been adapted to the measurement of Fowler-Nordheim tunneling currents in metal-oxide-semiconductor (MOS) capacitors. Using a special structure consisting of an MOS capacitor and a monitor transistor sharing a common-gate electrode, it has proved possible to measure tunneling current densities as low as 2×10^-13 A/cm². The Fowler-Nordheim tunneling relationship was found to be obeyed over the entire measurable range of current density     

Investigation of the Correlation Between Temperature and Enhancement of Electron Tunneling Current Through $hbox{HfO}_{bf 2}$ Gate Stacks

A model is established to describe the temperature dependence of the electron tunneling current through HfO₂ gate stacks based on analyzing the coupling between the longitudinal and transverse components of electron thermal energy caused by the difference of the effective electron mass between the HfO₂ gate stacks and silicon. By analyzing the three-dimensional Schrodinger equation for a MOS structure with HfO₂ gate stacks, a reduction in the barrier height is resulted from the large effective electron mass mismatch between the gate oxide and the gate (substrate). The calculated electron tunneling currents agree well with the experimental data over a wide temperature range. This coupling model can explain the temperature dependence of the electron tunneling current through HfO₂ gate stacks very well. The numerical results also demonstrate that the temperature dependence of the electron tunneling current strongly depends on the effective electron mass of HfO₂. This temperature sensitivity of the electron tunneling current can be proposed as a novel method to determine the effective electron mass of the gate oxide.     

场引晶体管理论:Ⅺ.双极电化电流(薄及厚、纯及不纯基体,单及双MOS栅极)

场引晶体管本质双极,包括电子和空穴表面和体积沟道和电流,一或多个外加横向控制电场.自1952年Shockley发明,55年来它被认为单极场引晶体管,因电子电流理论用多余内部和边界条件,不可避免忽略空穴电流.多余条件,诸如电中性和常空穴电化电势,导致仅用电子电流算内部和终端电学特性的错误解.当忽略的空穴电流与电子电流可比,可在亚阈值区和强反型区,错误解有巨大误差.本文描述普适理论,含有电子和空穴沟道和电流.用z轴宽度方向均匀的直角平行六面体(x,Y,z)晶体管,薄或厚、纯或杂基体,一或二块MOS栅极,描述两维效应及电势、电子空穴电化电势的正确内部和边界条件.没用多余条件,导出四种常用MOS晶体管,直流电流电压特性完备解析方程:半无限厚不纯基上一块栅极(传统的Bulk MOSFET),与体硅以氧化物绝缘的不纯硅薄层上一块栅极(SOI),在沉积到绝缘玻璃的不纯硅薄层上一块栅极(SOI TFT),和薄纯基上两块栅极(FinFETs).     

Full-Band Tunneling in High-κ Oxide MOS Structures

In this paper, we investigate the tunneling properties of ZrO₂ and HfO₂ high-k oxides, by applying quantum mechanical methods that include the full-band structure of Si and oxide materials. Semiempirical sp³s*d tight-binding parameters have been determined to reproduce ab-initio band dispersions. Transmission coefficients and tunneling currents have been calculated for Si/ZrO₂/Si and Si/HfO₂/Si MOS structures, showing a very low gate leakage current in comparison to SiO₂-based structures with the same equivalent oxide thickness. The complex band structures of ZrO₂ and HfO₂ have been calculated and used to develop an energy-dependent effective tunneling mass model. We show that effective mass calculations based on this model yield tunneling currents in close agreement with full-band results.     

基于密度梯度理论的MOS量子隧穿解析模型

提出了一种基于物理的MOS电容超薄氧化层量子隧穿解析模型,量子力学效应在应用奇异微扰法求解密度梯度方程时得以体现.将泊松方程和经量子修正的电子势方程同时求解,得出电子和静电势在垂直于沟道方向的分布.结果反映出量子效应明显不同于经典物理学的预测.对解析解结果和精确的数值模拟进行比较,结果表明,在栅极偏压和氧化层厚度的较大变化范围内,二者都能很好地吻合.     

利用FN振荡电流测量薄栅MOS结构栅氧化层中隧穿电子的有效质量

给出了一种利用 FN振荡电流的极值 ,测量电子在薄栅 MOS结构的栅氧化层中的平均有效质量方法 .利用波的干涉方法来处理电子隧穿势垒的过程 ,方便地获得了出现极值时外加电压和电子的有效质量之间的分析表达式 .用干涉方法计算所得到的隧穿电子在不同的 MOS结构的二氧化硅介质层中的有效质量表明 :它一般在自由电子质量的 0 .5 2— 0 .84倍的范围 .实验结果表明 :电子有效质量的值不随外加电压的变化而变化 ,并且对于相同的MOS结构 ,电子可能具有相同的有效质量     

场引晶体管理论:XI.双极电化电流（薄及厚、纯及不纯基体,单及双MOS栅极）

场引晶体管本质双极,包括电子和空穴表面和体积沟道和电流,一或多个外加横向控制电场．自1952年Shockley发明,55年来它被认为单极场引晶体管,因电子电流理论用多余内部和边界条件,不可避免忽略空穴电流．多余条件,诸如电中性和常空穴电化电势,导致仅用电子电流算内部和终端电学特性的错误解．当忽略的空穴电流与电子电流可比,可在亚阈值区和强反型区,错误解有巨大误差．本文描述普适理论,含有电子和空穴沟道和电流．用z轴宽度方向均匀的直角平行六面体（x,y,z）晶体管,薄或厚、纯或杂基体,一或二块MOS栅极,描述两维效应及电势、电子空穴电化电势的正确内部和边界条件．没用多余条件,导出四种常用MOS晶体管,直流电流电压特性完备解析方程：半无限厚不纯基上一块栅极（传统的Bulk MOSFET）,与体硅以氧化物绝缘的不纯硅薄层上一块栅极（SOI）,在沉积到绝缘玻璃的不纯硅薄层上一块栅极（SOI TFT）,和薄纯基上两块栅极（FinFETs）．     

Optical properties of blue light-emitting diodes in the InGaN/GaN system at high current densities

The current-voltage and brightness-voltage characteristics and the electroluminescence spectra of blue InGaN/GaN-based light-emitting diodes are studied to clarify the cause of the decrease in the emission efficiency at high current densities and high temperatures. It is found that the linear increase in the emission intensity with increasing injection current changes into a sublinear increase, resulting in a decrease in efficiency as the observed photon energy shifts from the mobility edge. The emission intensity decreases with increasing temperature when the photon energy approaches the mobility edge; this results in the reduction in efficiency on overheating. With increasing temperature, the peak of the electroluminescence spectrum shifts to lower photon energies because of the narrowing of the band gap. The results are interpreted taking into account the fact that the density-of-states tails in InGaN are filled not only via trapping of free charge carriers, but also via tunneling transitions into the tail states. The decrease in the emission efficiency at high currents is attributed to the suppression of tunneling injection and the enhancement of losses via the nonradiative recombination channel “under” the quantum well.     

总剂量辐照SiO2/6H-SiC引起的界面势垒变化

辐照会引起MOS器件电介质氧化物与半导体界面势垒变化,影响其工作性能和可靠性。测量了n型6H-SiC MOS电容辐照105rad(Si)剂量前后的I-V曲线,通过Fowler-Nordheim(F-N)隧道电流拟合,得到了界面势垒的大小,辐照前的为2.596 eV,辐照后降为1.492eV。界面势垒变化主要是由辐照产生的界面态引起的。     

Potentials and direct current in Si-(20 to 40 Å)SiO2-metal structures

The effects of oxide thickness and interface states on potentials in and direct currents through MOS structures with various metal contacts on 20–40 Å thick SiO₂ films and nondegenerate Si were investigated using a recently developed method of determining surface potential vs. bias and interface state vs. energy distributions of such structures from conventional admittance measurements. For Cr, Cu, and Mg contacts, the interface states are predominantly of acceptor type. The metal silicon work function differences are φ_MS = 0.91 V for Au, −0.04 for Cr, 0.18 for Cu, and −1.07 V for Mg. The forward device current consists mainly of majority carriers emitted over the Si barrier and tunneling through the oxide into the metal for depletion or weak inversion of Si, and of majority carriers tunneling from Si through the oxide into the metal for Si accumulation. Excess currents in forward and reverse direction are caused by carrier generation-recombination in interface states and tunneling through the oxide to and from the metal. The drooping of the forward current, deviating strongly from an ideal exponential characteristic, is mainly caused by the drop of a considerable part of the applied bias across the oxide layer.     

考虑量子力学效应的超薄栅氧nMOSFET's直接隧穿电流二维模型

研究了超薄栅氧MOS器件的直接隧穿(direct tunneling,DT)电流模型问题.利用修正的WKB近似方法(modified WKB,MWKB)得到电子隧穿栅氧的几率,利用修正的艾利函数(modified Airy function,MAF)方法计算得到在高电场条件下载流子的量子化能级,从而计算出在不同偏置条件下的DT电流.模型实现了nMOSFET's栅隧穿电流的二维模拟,可以模拟在不同栅漏偏置条件下的器件工作情况,具有较广泛的适用性.通过对比表明,本模型能够与实验结果很好地吻合,且速度明显优于数值方法.利用模型可很好地对深亚微米MOS器件的栅电流特性进行预测.     

Effect of SiO2/Si interface roughness on gate current

In many theoretical investigations of the electric-tunnel effect through an ultrathin oxide in metal-oxide-semiconductor (MOS) structure, it is commonly assumed that the oxide is of uniform thickness. One example of nonuniformity in oxides is interface roughness. Interface roughness effects on direct tunneling current in ultrathin MOS structures are investigated theoretically in this article. The roughness at SiO₂/Si interface is described in terms of Gauss distribution. It is shown that the transmission coefficient increases with root-mean-square (rms) roughness increasing, and the effect of rms roughness on the direct tunneling current decreases with the applied voltage increasing and increases with rms roughness increasing.     

Definition of curve fitting parameter to study tunneling and trapping of electrons in Si/ultra-thin SiO2/metal structures

The tunneling of electrons through metal–oxide–silicon (MOS) structures with ultra-thin oxide is modeled using a linear model for the electron potential energy, an approach which simplifies the computation of both the interface potential and the field penetration distance in the substrate. The one-particle quantum problem is split into finding the metastable states induced by the internal field penetration in the substrate and the running states in the gate region. The two states are assumed to be connected by the condition for the continuity of the probability density at the substrate–dielectric interface. The electron probability current and the total gate current density are obtained for different gate voltages. As the model yields excellent fittings with experimental current–voltage (I–V) data for MOS structures, it was further applied to constant current stressing analysis in order to obtain values for important electron trapping parameters in the oxide. The resultant estimates of the electron trapping cross-section fall in the range of other independent determinations in the literature.     

Direct tunneling at the front contact of amorphous silicon p-i-ndevices

The device physics behind hole direct tunneling currents at the front contact of a-Si:H p-i-n homojunction have been explored. In this paper, the dark I-V, the light I-V, and the QE characteristics of this structure with and without hole direct hole tunneling currents are evaluated and compared. The three differential equation systems of the Poisson's equation, the continuity equation for free electrons, and the continuity equation for free holes have been solved with allowances for direct tunneling currents. Hole direct tunneling currents at the front contact of a-Si:H p-i-n homojunctions give rise to a significant increase in the dark current level at high forward voltages and to an increase in the open-circuit voltage of the light I-V characteristic when the front electron barrier is low. The hole thermionic emission current and the hole direct tunneling current have been carefully compared to the front contact. Hole tunneling currents introduce important modifications to the carrier transport physics not only to the front contact but also in the bulk of the a-Si:H p-i-n homojunction     

Two-carrier conduction in MOS tunnel—Oxides II—Theory

Analytic expressions describing electron and hole current flow in the metal/tunnel—oxide/n-silicon structure are derived. In the particular approach that is taken, the tunneling barrier presented by the SiO₂ layer is treated using a “thick-oxide” MOS model; i.e. a trapezoidal tunneling barrier is used. Rather than assume a constant tunneling probability, the dependence of the tunneling barrier on applied bias and on the minority carrier density at the semiconductor surface is also included. Calculations based on the resultant equations are found to be in good agreement with experimental observations, and to correctly predict the “current-multiplication” effect that occurs under conditions of minority carrier injection to the Si---SiO₂ interface [1].

The derived equations are used to simulate device behaviour under various experimental conditions, including the effects of minority carrier injection, non-zero flatband voltage, and changes in substrate doping concentration and temperature. In addition, device parameters such as barrier height and carrier effective mass are also investigated with regard to their effect on the resultant electron and hole tunneling currents.     

Dielectric characteristics of gamma irradiated Au/SnO2/n-Si/Au (MOS) capacitor

The dielectric characteristics of gamma irradiated Au/SnO₂/n-Si/Au (MOS) capacitor were studied. The MOS capacitor was irradiated by a ⁶⁰Co gamma radiation source with a dose rate of 0.69 kGy/h. The dielectric parameters such as dielectric constant (ε′), dielectric loss (ε″), loss factor (tan δ) and ac electrical conductivity (σ_ac) were calculated from the capacitance–voltage (C–V) and conductance–voltage (G/ω–V) measurements. It is found that the C and G/ω values decrease with the increasing total dose due to the irradiation-induced defects at the interface. Also, the calculated values of ε′, ε″ and σ_ac are found to decrease with an increased radiation dose. This result indicates that the dielectric characteristics of the MOS capacitor are sensitive to gamma-ray dose.     

Current mechanism and band alignment of Al(Pt)/HfGdO/Ge capacitors

HfGdO high-k gate dielectric thin films were deposited on Ge substrates by radio-frequency magnetron sputtering. The current transport properties of Al(Pt)/HfGdO/Ge MOS structures were investigated at room temperature. The results show that the leakage currents are mainly induced by Frenkel-Poole emissions at a low electric field. At a high electric field, Fowler Nordheim tunneling dominates the current. The energy barriers were obtained by analyzing the Fowler Nordheim tunneling characteristics, which are 1.62 eV and 2.77 eV for Al/HfGdO and Pt/HfGdO, respectively. The energy band alignments for metal/HfGdO/Ge capacitors are summarized together with the results of current-voltage and the x-ray photoelectron spectroscopy.     

Tunneling leakage current in ultrathin (<4 nm) nitride/oxidestack dielectrics

The leakage current in high-quality ultrathin silicon nitride/oxide (N/O) stack dielectric is calculated based on a model of one-step electron tunneling through both the nitride and the oxide layers. The results show that the tunneling leakage current in the N/O stack is substantially lower than that in the oxide layer of the same equivalent oxide thickness (EOT). The theoretical leakage current in N/O stack has been found to be a strong function of the nitride/oxide EOT ratio: in the direct tunneling regime, the leakage current decreases monotonically as the M/O ratio increases, while in the Fowler-Nordheim regime the lowest leakage current is realized with a N/O EOT ratio of 1:1. Due to the asymmetry of the N/O barrier shape, the leakage current under substrate injection is higher than that under gate injection, although such a difference becomes smaller in the lower voltage regime. Experimental data obtained from high quality ultrathin N/O stack dielectrics agree well with calculated results     

Two-carrier conduction in MOS tunnel oxides—1 Experimental results

A novel device structure incorporating a p-channel MOSFET with a metal/tunnel-oxide/n-silicon device is proposed as a tool for separating electron and hole tunneling currents in ultra-thin silicon dioxide films. With this structure, the electron and hole tunneling currents can be independently measured at the substrate and source terminals, respectively. Furthermore, the injected minority carrier (hole) current which is supplied by the p-MOSFET can be varied independently of the tunnel-oxide bias. As expected, the injected hole current modulates the electron current and “current multiplication” was observed. By correlating experimental results for 22.5 Å SiO₂ films with theoretical calculations, the electron and hole barrier heights were determined to be 3.2 and 3.6 eV, respectively, where a trapezoidal tunneling barrier was assumed and a carrier effective mass of 0.5 m₀ was used.The tunnel-oxide quality and uniformity was evaluated by measuring I–V and C-V curves on two-terminal MOS capacitors of various areas. The results suggest that the oxide films are extremely uniform in thickness, and the measured interface trap density was determined to be less than 10¹¹ cm^?2eV^?1. For the reverse-biased tunnel-oxide, the electron/hole current ratio was found to be less than unity except for the condition when the injected hole current was very small compared to the electron current without any hole injection. In addition, this ratio was found to decrease rapidly with increasing oxide thickness and/or increasing hole injection level.