The role of hydrogen in hydrogenated microcrystalline silicon film and in deposition process with VHF-PECVD technique

The role of hydrogen in hydrogenated microcrystalline silicon ($\mu $c-Si:H) thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition (VHF-PECVD) technique have been investigated in this paper. With \textit{in situ} optical emission spectroscopy (OES) diagnosis during the fabrication of $\mu $c-Si:H thin films under different plasma excitation frequency $\nu _{\rm e }$ (60MHz--90MHz), the characteristic peak intensities ($I_{{\rm SiH}^*}$, $I_{{\rm H}\alpha^*}$ and $I_{{\rm H}\beta ^*}$) in SiHVHF-PECVD技术 氢化微晶硅 光发射光谱 薄膜学VHF-PECVD technique, hydrogenated microcrystalline silicon, role of hydrogen, optical emission spectroscopyProject supported by the Natural Science Foundation of Guangdong Province, China (Grant No 05300378), the State Key Development Program for Basic Research of China (Grant Nos G2000028202 and G2000028203) and the Program on Natural Science of Jinan University, Guangzhou, China (Grant No 51204056).2005-11-252005-11-252006-01-05The role of hydrogen in hydrogenated microcrystalline silicon （μc-Si：H） thin films in deposition processes with very high frequency plasma-enhanced chemical vapour deposition （VHF-PECVD） technique have been investigated in this paper. With in situ optical emission spectroscopy （OES） diagnosis during the fabrication of μc-Si：H thin films under different plasma excitation frequency Ve （60MHz-90MHz）, the characteristic peak intensities （IsiH＊, IHα＊ and IHβ＊ ） in SiH4＋H2 plasma and the ratio of （IHα＊ ＋ IHβ＊ ） to IsiH＊ were measured; all the characteristic peak intensities and the ratio （IHα＊ ＋ IHβ＊ ）/IsiH＊ are increased with plasma excitation frequency. It is identified that high plasma excitation frequency is favourable to promote the decomposition of SiH4＋H2 to produce atomic hydrogen and SiHx radicals. The influences of atomic hydrogen on structural properties and that of SiHx radicals on deposition rate of μc-Si：H thin films have been studied through Raman spectra and thickness measurements, respectively. It can be concluded that both the crystalline volume fraction and deposition rate are enhanced with the increase of plasma excitation frequency, which is in good accord with the OES results. By means of FTIR measurements, hydrogen contents of μc-Si：H thin films deposited at different plasma excitation frequency have been evaluated from the integrated intensity of wagging mode near 640 cm^-1. The hydrogen contents vary from 4% to 5%, which are much lower than those of μc-Si：H films deposited with RF-PECVD technique. This implies that μc-Si：H thin films deposited with VHF-PECVD technique usually have good stability under light-soaking.     

Influence of the total gas flow rate on high rate growth microcrystalline silicon films and solar cells

This paper reports that high-rate-deposition of microcrystalline silicon solar cells was performed by very-high-frequency plasma-enhanced chemical vapor deposition. These solar cells, whose intrinsic μ c-Si:H layers were prepared by using a different total gas flow rate (F_total), behave much differently in performance, although their intrinsic layers have similar crystalline volume fraction, opto-electronic properties and a deposition rate of ～ 1.0~nm/s. The influence of F_total on the micro-structural properties was analyzed by Raman and Fourier transformed infrared measurements. The results showed that the vertical uniformity and the compact degree of μ c-Si:H thin films were improved with increasing F_total. The variation of the microstructure was regarded as the main reason for the difference of the J--V parameters. Combined with optical emission spectroscopy, we found that the gas temperature plays an important role in determining the microstructure of thin films. With F_total of 300~sccm, a conversion efficiency of 8.11% has been obtained for the intrinsic layer deposited at 8.5~\AA/s (1~\AA=0.1\,nm).     

The effect of initial discharge conditions on the properties of microcrystalline silicon thin films and solar cells

This paper studies the effects of silane back diffusion in the initial plasma ignition stage on the properties of microcrystalline silicon ($\mu $c-Si:H) films by Raman spectroscopy and spectroscopic ellipsometry, through delaying the injection of SiH7280N, 7830G, 8115Hhttp://cpb.iphy.ac.cn/CN/10.1088/1674-1056/19/5/057205https://cpb.iphy.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=111771back diffusion, microcrystalline silicon, thin film, Raman crystallinityProject supported by the State Key Development Program for Basic Research of China (Grant No.~2006CB202601).This paper studies the effects of silane back diffusion in the initial plasma ignition stage on the properties of microcrystalline silicon ($\mu $c-Si:H) films by Raman spectroscopy and spectroscopic ellipsometry, through delaying the injection of SiH$_{4}$ gas to the reactor before plasma ignition. By comparing with standard discharge condition, delayed SiH$_{4}$ gas condition could prevent the back diffusion of SiH$_{4}$ from the reactor to the deposition region effectively, which induced the formation of a thick amorphous incubation layer in the interface between bulk film and glass substrate. Applying this method, it obtains the improvement of spectral response in the middle and long wavelength region by combining this method with solar cell fabrication. Finally, results are explained by modifying zero-order analytical model, and a good agreement is found between model and experiments concerning the optimum delayed injection time.back;diffusion;microcrystalline;silicon;thin;film;Raman;crystallinityThis paper studies the effects of silane back diffusion in the initial plasma ignition stage on the properties of microcrystalline silicon(μc-Si:H) films by Raman spectroscopy and spectroscopic ellipsometry,through delaying the injection of SiH4 gas to the reactor before plasma ignition.Compared with standard discharge condition,delayed SiH4 gas condition could prevent the back diffusion of SiH4 from the reactor to the deposition region effectively,which induced the formation of a thick amorphous incubation layer in the interface between bulk film and glass substrate.Applying this method,it obtains the improvement of spectral response in the middle and long wavelength region by combining this method with solar cell fabrication.Finally,results are explained by modifying zero-order analytical model,and a good agreement is found between the model and experiments concerning the optimum delayed injection time.     

The high deposition of microcrystalline silicon thin film by very high frequency plasma enhanced chemical vapour deposition and the fabrication of solar cells

This paper reports that the intrinsic microcrystalline silicon ($\mu $c-Si:H) films are prepared with plasma enhanced chemical vapour deposition from silane/hydrogen mixtures at 200\du\ with the aim to increase the deposition rate. An increase of the deposition rate to 0.88\,nm/s is obtained by using a plasma excitation frequency of 75\,MHz. This increase is obtained by the combination of a higher deposition pressure, an increased silane concentration, and higher discharge powers. In addition, the transient behaviour, which can decrease the film crystallinity, could be prevented by filling the background gas with Hchemical vapour deposition, plasma deposition, solar cells, crystallinityProgram supported by the State Key Development Program for Basic Research of China (Grant No 2006CB202601), and Basic Research Project of Henan Province in China (Grant No 072300410140).7280N, 7830G, 8115HThis paper reports that the intrinsic microcrystalline silicon ($\mu $c-Si:H) films are prepared with plasma enhanced chemical vapour deposition from silane/hydrogen mixtures at 200\du\ with the aim to increase the deposition rate. An increase of the deposition rate to 0.88\,nm/s is obtained by using a plasma excitation frequency of 75\,MHz. This increase is obtained by the combination of a higher deposition pressure, an increased silane concentration, and higher discharge powers. In addition, the transient behaviour, which can decrease the film crystallinity, could be prevented by filling the background gas with Hchemical vapour deposition, plasma deposition, solar cells, crystallinityProgram supported by the State Key Development Program for Basic Research of China (Grant No 2006CB202601), and Basic Research Project of Henan Province in China (Grant No 072300410140).7280N, 7830G, 8115HThis paper reports that the intrinsic microcrystalline silicon ($\mu $c-Si:H) films are prepared with plasma enhanced chemical vapour deposition from silane/hydrogen mixtures at 200\du\ with the aim to increase the deposition rate. An increase of the deposition rate to 0.88\,nm/s is obtained by using a plasma excitation frequency of 75\,MHz. This increase is obtained by the combination of a higher deposition pressure, an increased silane concentration, and higher discharge powers. In addition, the transient behaviour, which can decrease the film crystallinity, could be prevented by filling the background gas with Hchemical vapour deposition, plasma deposition, solar cells, crystallinityProgram supported by the State Key Development Program for Basic Research of China (Grant No 2006CB202601), and Basic Research Project of Henan Province in China (Grant No 072300410140).7280N, 7830G, 8115HThis paper reports that the intrinsic microcrystalline silicon ($\mu $c-Si:H) films are prepared with plasma enhanced chemical vapour deposition from silane/hydrogen mixtures at 200\du\ with the aim to increase the deposition rate. An increase of the deposition rate to 0.88\,nm/s is obtained by using a plasma excitation frequency of 75\,MHz. This increase is obtained by the combination of a higher deposition pressure, an increased silane concentration, and higher discharge powers. In addition, the transient behaviour, which can decrease the film crystallinity, could be prevented by filling the background gas with Hchemical vapour deposition, plasma deposition, solar cells, crystallinityProgram supported by the State Key Development Program for Basic Research of China (Grant No 2006CB202601), and Basic Research Project of Henan Province in China (Grant No 072300410140).7280N, 7830G, 8115HThis paper reports that the intrinsic microcrystalline silicon ($\mu $c-Si:H) films are prepared with plasma enhanced chemical vapour deposition from silane/hydrogen mixtures at 200\du\ with the aim to increase the deposition rate. An increase of the deposition rate to 0.88\,nm/s is obtained by using a plasma excitation frequency of 75\,MHz. This increase is obtained by the combination of a higher deposition pressure, an increased silane concentration, and higher discharge powers. In addition, the transient behaviour, which can decrease the film crystallinity, could be prevented by filling the background gas with H$_{2}$ prior to plasma ignition, and selecting proper discharging time after silane flow injection. Material prepared under these conditions at a deposition rate of 0.78\,nm/s maintains higher crystallinity and fine electronic properties. By H-plasma treatment before i-layer deposition, single junction $\mu $c-Si:H solar cells with 5.5{\%} efficiency are fabricated.     

The study of a new n/p tunnel recombination junction and its application in a-Si：H/μc-Si：H tandem solar cells

This paper reports that a double N layer (a-Si:H/μc-Si:H) is used to substitute the single microcrystalline silicon n layer (n-μc-Si:H) in n/p tunnel recombination junction between subcells in a-Si:H/μc-Si:H tandem solar cells. The electrical transport and optical properties of these tunnel recombination junctions are investigated by current-voltage measurement and transmission measurement. The new n/p tunnel recombination junction shows a better ohmic contact. In addition, the n/p interface is exposed to the air to examine the effect of oxidation on the tunnel recombination junction performance. The open circuit voltage and FF of a-Si:H/μc-Si:H tandem solar cell are all improved and the current leakage of the subcells can be effectively prevented efficiently when the new n/p junction is implemented as tunnel recombination junction.     

Influence of air pressure on mechanical effect of laser plasma shock wave

The influence of air pressure on mechanical effect of laser plasma shock wave in a vacuum chamber produced by a Nd:YAG laser has been studied. The laser pulses with pulse width of 10ns and pulse energy of about 320mJ at 1.06$\mu $m wavelength is focused on the aluminium target mounted on a ballistic pendulum, and the air pressure in the chamber changes from $2.8\times 10^{3}$ to 1.01$\times $10$^{5 }$Pa. The experimental results show that the impulse coupling coefficient changes as the air pressure and the distance of the target from focus change. The mechanical effects of the plasma shock wave on the target are analysed at different distances from focus and the air pressure.     

Power dissipation characteristics of great power and super high speed semiconductor switch

The power dissipation characteristics of pulsed power switch reversely switched dynistors （RSDs） are investigated in this paper. According to the expressions of voltage on RSD, derived from the plasma bipolar drift model and the RLC circuit equations of RSD main loop, the simulation waveforms of current and voltage on RSD are acquired through iterative calculation by using the fourth order Runge-Kutta method, then the curve of transient power on RSD versus time is obtained. The result shows that the total dissipation on RSD is trivial compared with the pulse discharge energy and the commutation dissipation can be nearly ignored compared with the quasi-static dissipation. These characteristics can make the repetitive frequency of RSD increase largely. The experimental results prove the validity of simulation calculations. The influence factors on power dissipation are discussed. The power dissipation increases with the increase of the peak current and the n-base width and with the decrease of n-base doping concentration. In order to keep a low power dissipation, it is suggested that the n-base width should be smaller than 320μm when doping concentration is 1.0×10^14cm^-3 while the doping concentration should be higher than 5.8×10^13cm^-3 when n-base width is 270μm.     

Effect of substrate temperature on the growth and properties of boron-doped microcrystalline silicon films

Highly conductive boron-doped hydrogenated microcrystalline silicon (\mu c-Si:H) films are prepared by very high frequency plasma enhanced chemical vapour deposition (VHF PECVD) at the substrate temperatures $T_{\rm S})$ ranging from 90$^\circ$C to 270$^\circ$C. The effects of $T_{\rm S}$ on the growth and properties of the films are investigated. Results indicate that the growth rate, the electrical (dark conductivity, carrier concentration and Hall mobility) and structural (crystallinity and grain size) properties are all strongly dependent on $T_{\rm S}$. As $T_{\rm S}$ increases, it is observed that 1) the growth rate initially increases and then arrives at a maximum value of 13.3 nm/min at $T_{\rm S}$=210$^\circ$C, 2) the crystalline volume fraction ($X_{\rm c})$ and the grain size increase initially, then reach their maximum values at $T_{\rm S}$=140$^\circ$C, and finally decrease, 3) the dark conductivity ($\sigma _{\rm d})$, carrier concentration and Hall mobility have a similar dependence on $T_{\rm S}$ and arrive at their maximum values at $T_{\rm S}$=190$^\circ$C. In addition, it is also observed that at a lower substrate temperature $T_{\rm S}$, a higher dopant concentration is required in order to obtain a maximum $\sigma _{\rm d}$.     

Judd-Oflet analysis of spectrum and laser performance of Ho：YAP crystal end-pumped by 1.91μm Tm：YLF laser

The Ho:YAP crystal is grown by the Czochralski technique.The room temperature polarized absorption spectra of Ho:YAP crystal was measured on a c cut sample with 1 at% holmium.According to the obtained Judd-Ofelt intensity parameters Ω2 = 1.42 × 10-20 cm2,Ω4 = 2.92 × 10-20 cm2,and Ω6 = 1.71 × 10-20 cm2,this paper calculated the fluorescence lifetime to be 6 ms for 5I7 →5 I8 transition,and the integrated emission cross section to be 2.24×10-18 cm2.It investigates the room temperature Ho:YAP laser end pumped by a 1.91 μm Tm:YLF laser.The maximum output power was 4.1 W when the incident 1.91 μm pump power was 14.4 W.The slope efficiency is 40.8%,corresponding to an optical to optical conversion efficiency of 28.4%.The Ho:YAP output wavelength was centred at 2118 nm with full width at half maximum of about 0.8 nm.     

用H-W-ECR CVD系统实现氢化非晶硅薄膜在氢气环境下同时进行化学热退火和光诱导退火的研究

为了研究氢化非晶硅薄膜的稳定性，我们设计了一个在原子氢气氛中热退火的同时进行光诱导退火的实验(TLAH)。实验装置是由传统的微波电子回旋共振化学气相沉积系统改造而成为热丝辅助微波电子回旋共振化学气相沉积系统。为了对这一退火方法进行比较，对样品还进行了热退火、热退火同时进行光诱导退火。同时，为了定量地分析光电导衰退，我们假设光电导衰退遵循扩展指数规律：1/σph=1/σs-(1/σs-1/σ0)exp[-(t/τ)β]，这里扩展指数参数β 和时间常数 τ 可从与 lnt 的线性关系中截距和斜率得到, 式中光电导饱和值σs可以通过在对数坐标系中表示的光电导和光照时间关系进行高斯拟合得到。实验结果显示：TLAH 方法可以提高氢化非晶硅薄膜的稳定性、改善其微结构和光电特性，同时还发现，光学带隙明显减小、荧光光谱显著地朝着低能方向移动。     

Synthesis and high temperature thermoelectric transport properties of Si-based type-I clathrates

N-type Si-based type-I clathrates with different Ga content were synthesized by combining the solid-state reaction method, melting method and spark plasma sintering (SPS) method. The effects of Ga composition on high temperature thermoelectric transport properties were investigated. The results show that at room temperature, the carrier concentration decreases, while the carrier mobility increases slightly with increasing Ga content. The Seebeck coefficient increases with increasing Ga content. Among all the samples, Ba_7.93Ga_17.13Si_28.72 exhibits higher Seebeck coefficient than the others and reaches -135~μ V.K^-1 at 1000 K. The sample prepared by this method exhibits very high electrical conductivity, and reaches 1.95× 10⁵S.m^-1 for Ba_8.01Ga_16.61Si_28.93 at room temperature. The thermal conductivity of all samples is almost temperature independent in the temperature range of 300--1000~K, indicating the behaviour of a typical metal. The maximum {ZT} value of 0.75 is obtained at 1000~K for the compound Ba_7.93Ga_17.13Si_28.72.     

Judd--Ofelt analysis of spectra and experimental evaluation of laser performance of Tm3+ doped Lu2SiO5 crystal

This paper reports that the Tm^3＋：Lu2SiO5 （Tm：LSO） crystal is grown by Czochralski technique. The roomtemperature absorption spectra of Tm：LSO crystal are measured on a b-cut sample with 4 at.% thulium. According to the obtained Judd-Ofelt intensity parameters Ω2=9.3155×10^-20 cm^2, Ω4=8.4103×10^-20 cm^2, Ω6=1.5908×10^-20 cm^2, the fluorescence lifetime is calculated to be 2.03 ms for ^3F4 → ^3H6 transition, and the integrated emission cross section is 5.81×10^-18 cm^2. Room-temperature laser action near 2μm under diode pumping is experimentally evaluated in Tm：LSO. An optical-optical conversion efficiency of 9.1% and a slope efficiency of 16.2% are obtained with continuouswave maximum output power of 0.67 W. The emission wavelengths of Tm：LSO laser are centred around 2.06μm with spectral bandwidth of -13.6 nm.     

激光二极管端面抽运的高效率1.34μm Nd:YVO4 平凹腔型激光器

理论方面分析了端面抽运的1.34mm Nd:YVO4平凹腔型激光器的各项参数；文中的分析可为同类激光器的设计提供参考。实验方面实现了LD端面抽运的1.34mm Nd:YVO4平凹腔型激光器的运转；在输入泵浦功率为9.0W时，获得了1.34mm 激光输出功率3.51W，光－光转换效率为39.0%。     

A CVD diamond film detector for pulsed proton detection

A chemical vapour deposition （CVD） diamond film detector was prepared and the main characteristics for pulsed proton detection were studied at Beijing Tandem Accelerator. The result shows that the charge collection efficiency of the detector increases with increasing electric field intensity and reaches to 9.44% at 5 V/μm with the charge collection distance of 15.9 μm. The relationship between the sensitivity of the detector and proton energy is consistent with the Monte Carlo （MC） simulation result. Its plasma time for a pulse with 4.85×10^5 protons is 1l.2ns. The dose threshold for onset of damage under 9MeV proton irradiation in the detector is about 10^13 cm^-2. All of the results show that a CVD diamond detector has fast time response and high radiation hardness, and can be used in pulsed proton detection.     

Effects of preparation parameters on growth and properties of β-Ga2O3 film

The Ga$_{2}$O$_{3}$ films are deposited on the Si and quartz substrates by magnetron sputtering, and annealing. The effects of preparation parameters (such as argon-oxygen flow ratio, sputtering power, sputtering time and annealing temperature) on the growth and properties ($e.g.$, surface morphology, crystal structure, optical and electrical properties of the films) are studied by x-ray diffractometer (XRD), scanning electron microscope (SEM), and ultraviolet-visible spectrophotometer (UV-Vis). The results show that the thickness, crystallization quality and surface roughness of the $\beta $-Ga$_{2}$O$_{3}$ film are influenced by those parameters. All $\beta $-Ga$_{2}$O$_{3 }$films show good optical properties. Moreover, the value of bandgap increases with the enlarge of the percentage of oxygen increasing, and decreases with the increase of sputtering power and annealing temperature, indicating that the bandgap is related to the quality of the film and affected by the number of oxygen vacancy defects. The $I$-$V$ curves show that the Ohmic behavior between metal and $\beta $-Ga$_{2}$O$_{3}$ films is obtained at 900 ${^\circ}$C. Those results will be helpful for the further research of $\beta $-Ga$_{2}$O$_{3}$ photoelectric semiconductor.     

Plasma characterization on carbon fiber cathode by spectroscopic diagnostics

This paper mainly investigates plasma characterization on carbon fiber cathodes with and without cesium iodide (CsI) coating powered by a ～300~ns, ～ 200~kV accelerating pulse. It was found that the CsI layers can not only improve the diode voltage, but also maintain a stable perveance. This indicates a slowly changed diode gap or a low cathode plasma expansion velocity. By spectroscopic diagnostics, in the vicinity of the cathode surface the average plasma density and temperature were found to be ～ 3× 10¹⁴~cm^-3 and ～ 5~eV, respectively, for an electron current density of ～ 40~A/cm². Furthermore, there exists a multicomponent plasma expansion toward the anode. The plasma expansion velocity, corresponding to the carbon and hydrogen ions, is estimated to be ～ 1.5~cm/μ s. Most notably, Cs spectroscopic line was obtained only at the distance ≤ 0.5~mm from the cathode surface. Carbon and hydrogen ions are obtained up to the distance of 2.5~mm from the cathode surface. Cs ions almost remain at the vicinity of the cathode surface. These results show that the addition of CsI enables a slow cathode plasma expansion toward the anode, providing a positive prospect for developing long-pulse electron beam sources.     

Microwave properties and surface topography of softmagnetic films with high resistivity

A single layer of CoFeB and a multilayer of CoFeB--MgO films are prepared by means of DC/RF magnetron sputter deposition. The excellent microwave properties and high electrical resistivity are simultaneously achieved in the discontinuous multilayer structure of [Co₄₄Fe₄₄B₁₂(0.7nm)/MgO(0.4nm)]_{40} film. This film has a high permeability ({μ \prime }) (larger than 100 below 2.1GHz), a high magnetic loss (μ') (larger than 100 in a range from 1.5 to 3.3GHz), a resistivity of 3.3× 10^*     

Anisotropic properties of TaS2

The anisotropic properties of 1T- and 2H-TaS2 axe investigated by the density functional theory within the framework of full-potential linearized augmented plane wave method. The band structures of 1T- and 2H-TaS2 exhibit anisotropic properties and the calculated electronic specific-heat coefficient γ of 2H-TaS2 accords well with the existing experimental value. The anisotropic frequency-dependent dielectric functions including the effect of the Drude term are analysed, where the ε^xx（ω） spectra corresponding to the electric field E perpendicular to the z axis show excellent agreement with the measured results except for the ε1^xx（ω） of 1T-TaS2 below the energy level of 2.6 eV which is due to the lack of the enough CDW information for reference in our calculation. Furthermore, based on the values of optical effective mass ratio P of 1T and 2H phases it is found that the anisotropy in 2H-TaS2 is stronger than that in 1T-TaS2.     

Enhanced interface properties of diamond MOSFETs with Al_2O_3 gate dielectric deposited via ALD at a high temperature

The interface state of hydrogen-terminated(C–H) diamond metal–oxide–semiconductor field-effect transistor(MOSFET) is critical for device performance. In this paper, we investigate the fixed charges and interface trap states in C–H diamond MOSFETs by using different gate dielectric processes. The devices use Al_2O_3 as gate dielectrics that are deposited via atomic layer deposition(ALD) at 80℃ and 300℃, respectively, and their C–V and I–V characteristics are comparatively investigated. Mott–Schottky plots(1/C~2–VG) suggest that positive and negative fixed charges with low density of about 1011 cm~(-2) are located in the 80-℃-and 300-℃ deposition Al_2O_3 films, respectively. The analyses of direct current(DC)/pulsed I–V and frequency-dependent conductance show that the shallow interface traps(0.46 e V–0.52 e V and0.53 e V–0.56 e V above the valence band of diamond for the 80-℃ and 300-℃ deposition conditions, respectively) with distinct density(7.8 × 10~(13) e V~(-1)·cm~(-2)–8.5 × 10~(13) e V-1·cm~(-2) and 2.2 × 1013 e V~(-1)·cm~(-2)–5.1 × 10~(13) e V~(-1)·cm~(-2) for the80-℃-and 300-℃-deposition conditions, respectively) are present at the Al_2O_3/C–H diamond interface. Dynamic pulsed I–V and capacitance dispersion results indicate that the ALD Al_2O_3 technique with 300-℃ deposition temperature has higher stability for C–H diamond MOSFETs.     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.