Investigation of the characteristics of GIDL current in 90nm CMOS technology

A specially designed experiment is performed for investigating gate-induced drain leakage (GIDL) current in 90nm CMOS technology using lightly-doped drain (LDD) NMOSFET. This paper shows that the drain bias $V_{\rm D}$ has a strong effect on GIDL current as compared with the gate bias $V_{\rm G}$ at the same drain--gate voltage $V_{\rm DG}$. It is found that the difference between $I_{\rm D}$ in the off-state $I_{\rm D}-V_{\rm G}$ characteristics and the corresponding one in the off-state $I_{\rm D}-V_{\rm D}$ characteristics, which is defined as $I_{\rm DIFF}$, versus $V_{\rm DG}$ shows a peak. The difference between the influences of $V_{\rm D}$ and $V_{\rm G}$ on GIDL current is shown quantitatively by $I_{\rm DIFF}$, especially in 90nm scale. The difference is due to different hole tunnellings. Furthermore, the maximum $I_{\rm DIFF }$($I_{\rm DIFF,MAX})$ varies linearly with $V_{\rm DG}$ in logarithmic coordinates and also $V_{\rm DG}$ at $I_{\rm DIFF,MAX}$ with $V_{\rm F}$ which is the characteristic voltage of $I_{\rm DIFF}$. The relations are studied and some related expressions are given.     

The research on suspended ZnO nanowire field-effect transistor

This paper reports that a novel type of suspended ZnO nanowire field-effect transistors (FETs) were successfully fabricated using a photolithography process, and their electrical properties were characterized by I--V measurements. Single-crystalline ZnO nanowires were synthesized by a hydrothermal method, they were used as a suspended ZnO nanowire channel of back-gate field-effect transistors (FET). The fabricated suspended nanowire FETs showed a p-channel depletion mode, exhibited high on--off current ratio of ～10⁵. When V_DS=2.5 V, the peak transconductances of the suspended FETs were 0.396 μS, the oxide capacitance was found to be 1.547 fF, the pinch-off voltage V_TH was about 0.6 V, the electron mobility was on average 50.17 cm²/Vs. The resistivity of the ZnO nanowire channel was estimated to be 0.96× 10²Ω cm at V_GS = 0 V. These characteristics revealed that the suspended nanowire FET fabricated by the photolithography process had excellent performance. Better contacts between the ZnO nanowire and metal electrodes could be improved through annealing and metal deposition using a focused ion beam.     

Degradation mechanisms of current gain in NPN transistors

An investigation of ionization and displacement damage in silicon NPN bipolar junction transistors (BJTs) is presented. The transistors were irradiated separately with 90-keV electrons, 3-MeV protons and 40-MeV Br ions. Key parameters were measured {\em in-situ} and the change in current gain of the NPN BJTS was obtained at a fixed collector current (I_{\rm c}=1~mA). To characterise the radiation damage of NPN BJTs, the ionizing dose D_{\i} and displacement dose D_{\d} as functions of chip depth in the NPN BJTs were calculated using the SRIM and Geant4 code for protons, electrons and Br ions, respectively. Based on the discussion of the radiation damage equation for current gain, it is clear that the current gain degradation of the NPN BJTs is sensitive to both ionization and displacement damage. The degradation mechanism of the current gain is related to the ratio of D_{\rm d}/(D_{\rm d}+D_{\rm i}) in the sensitive region given by charged particles. The irradiation particles leading to lower D_{\rm d}/(D_{\rm d}+D_{\rm i}) within the same chip depth at a given total dose would mainly produce ionization damage to the NPN BJTs. On the other hand, the charged particles causing larger D_{\rm d}/(D_{\rm d}+D_{\rm i}) at a given total dose would tend to generate displacement damage to the NPN BJTs. The Messenger--Spratt equation could be used to describe the experimental data for the latter case.     

Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1∑+g state of sodium dimer

The density functional theory (B3LYP, B3P86) and the quadratic configuration-interaction method including single and double substitutions (QCISD(T), QCISD) presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance $R_{\rm e}$, the dissociation energy $D_{\rm e }$ and the harmonic frequency $\omega _{\rm e}$ for the $X{}^{1}\Sigma^{ + }_{\rm g}$ state of sodium dimer in a number of basis sets. The conclusion is gained that the best $R_{\rm e}$, $D_{\rm e}$ and $\omega _{\rm e}$ results can be attained at the QCISD/6-311G(3df,3pd) level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0~nm and is fitted to the analytic Murrell--Sorbie function. The spectroscopic parameters $D_{\rm e}$, $D_{0}$, $R_{\rm e}$, $\omega _{\rm e}$, $\omega _{\rm e}\chi _{\rm e}$, $\alpha _{\rm e}$ and $B_{\rm e}$ are calculated to be 0.7219~eV, 0.7135~eV, 0.31813~nm, 151.63~cm$^{ - 1}$, 0.7288~cm$^{ - 1}$, 0.000729~cm$^{ - 1}$ and 0.1449~cm$^{ - 1}$, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G(3df,3pd) level of theory, a total of 63 vibrational states is found when $J=0$ by solving the radial Schr\"{o}dinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants ($D_{\upsilon }\, H_{\upsilon }$, $L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are reported for the first time for the first 31 vibrational states when $J=0$.     

Theoretica Study on defects associated with lead vacancies in PbWO4 crystals

The defects associated with lead vacancies(VPd)in lead tungstate crystals(PbWO4) are investigated by the relativistic self-consistent discrete variational embedded cluster method.We focus on the density of states and the effect of Vpb on surroundings,the results show that the existence of Vpb can diminish the bandwidth of WOr^2- group,however,it can neither produce O^- and Pb^3 ions nor result in absorptions at 350 and 420nm,The charge balance of VPb may be evenly compensated by the surrounding oxygen ions.     

Study on spectroscopic parameters and molecular constants of HCl(X~1Σ~+) molecule by using multireference configuration interaction approach

Equilibrium internuclear separations, harmonic frequencies and potential energy curves (PECs) of HCl($X^{1}\Sigma ^{ + })$ molecule are investigated by using the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with a series of correlation-consistent basis sets in the valence range. The PECs are all fitted to the Murrell--Sorbie function, and they are used to accurately derive the spectroscopic parameters ($D_{\rm e}$, $D_{0}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm e}$ and $B_{\rm e})$. Compared with the available measurements, the PEC obtained at the basis set, aug-cc-pV5Z, is selected to investigate the vibrational manifolds. The constants $D_{0}$, $D_{\rm e}$, $R_{\rm e}$, $\omega_{\rm e}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm e}$ and $B_{\rm e}$ at this basis set are 4.4006~eV, 4.5845~eV, 0.12757~nm, 2993.33~cm$^{ - 1}$, 52.6273~cm$^{ - 1}$, 0.2981~cm$^{ - 1}$ and 10.5841~cm$^{ - 1}$, respectively, which almost perfectly conform to the available experimental results. With the potential determined at the MRCI/aug-cc-pV5Z level of theory, by numerically solving the radial Schr\"{o}dinger equation of nuclear motion in the adiabatic approximation, a total of 21 vibrational levels are predicted. Complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reproduced, which are in excellent agreement with the available Rydberg--Klein--Rees data. Most of these theoretical vibrational manifolds are reported for the first time to the best of our knowledge.     

Effect of F doping on capacitance－voltage characteristics of SiCOH low-k films metal－insulator－semiconductor structure

This paper investigates the capacitance--voltage ($C$--$V$) characteristics of F doping SiCOH low dielectric constant films metal--insulator--semiconductor structure. The F doping SiCOH films are deposited by decamethylcyclopentasiloxane (DMCPS) and trifluromethane (CHF7755, 6855http://cpb.iphy.ac.cn/CN/10.1088/1674-1056/19/5/057701https://cpb.iphy.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=111779F-SiCOH, low-k dielectrics, capacitance--voltage characteristicProject supported by the National Natural Science Foundation of China (Grant No.~10575074).2/4/2009 12:00:00 AMThis paper investigates the capacitance--voltage ($C$--$V$) characteristics of F doping SiCOH low dielectric constant films metal--insulator--semiconductor structure. The F doping SiCOH films are deposited by decamethylcyclopentasiloxane (DMCPS) and trifluromethane (CHF$_{3})$ electron cyclotron resonance plasmas. With the CHF$_{3}$/DMCPS flow rate ratio from 0 to 0.52, the positive excursion of $C$--$V$ curves and the increase of flat-band voltage $V_{\rm FB}$ from $-6.1$~V to 32.2~V are obtained. The excursion of $C$--$V$ curves and the shift of $V_{\rm FB}$ are related to the change of defects density and type at the Si/SiCOH interface due to the decrease of Si and O concentrations, and the increase of F concentration. At the CHF$_{3}$/DMCPS flow rate ratio is 0.12, the compensation of F-bonding dangling bond to Si dangling bond leads to a small $V_{\rm FB}$ of 2.0~V.半导体结构;电压特性;电容电压;绝缘体;薄膜;金属;电子回旋共振等离子体;兴奋剂This paper investigates the capacitance-voltage （C-V） characteristics of F doping SiCOH low dielectric constant films metal-insulator-semiconductor structure. The F doping SiCOH films are deposited by decamethylcyclopentasilox-ane [DMCPS） and trifluromethane （CHF3） electron cyclotron resonance plasmas. With the CHF3/DMCPS flow rate ratio from 0 to 0.52, the positive excursion of C-V curves and the increase of fiat-band voltage VFB from -6.1 V to 32.2V are obtained. The excursion of C-V curves and the shift of VFB are related to the change of defects density and type at the Si/SiCOH interface due to the decrease of Si and O concentrations, and the increase of F concentration. At the CHF3/DMCPS flow rate ratio is 0.12, the compensation of F-bonding dangling bond to Si dangling bond leads to a small VFB of 2.0V.     

Parameter extraction for a Ti/4H-SiC Schottky diode

Based on the MIS model, a simple method to extract parameters of SiC Schottky diodes is presented using the $I$-$V$ characteristics. The interface oxide capacitance $C_\i$ is extracted for the first time, as far as we know. Parameters of 4H-SiC Schottky diodes fabricated for testing in this paper are: the ideality factor $n$, the series resistance $R_{\rm s}$, the zero-field barrier height $\phi_{\rm B0}$, the interface state density $D_{\rm it}$, the interface oxide capacitance $C_\i$ and the neutral level of interface states $\phi_0$.     

Quantum coherent effects in multi-Zeeman-sublevel atomic systems

This paper reports the experimental results on electromagnetically induced absorption （EIA） spectra observed in the system which does not satisfy completely the conditions given by Lezama et al [1999 Phys. Rev. A 59 4732]. EIA signals on the transitions in the Cs D2 line are able to be observed, where Fg ←→ Fe = Fg-1 as open systems. Theoretical model of Lezama et al is good for the case Fg ←→ Fc = Fg ＋ 1, considering spontaneous transfer of atomic coherences or populations this model is not able to explain our experimental results obtained in the case Fg ←→ Fe = Fg - 1. This paper offers a theoretical model which is able to well explain the case Fg ←→ Fc = Fg - 1. It also uses this theoretical model to explain the split and shift of EIA peaks, which have been obtained in experiments.     

Improved 4H-SiC UMOSFET with super-junction shield region

This article investigates an improved 4H-SiC trench gate metal-oxide-semiconductor field-effect transistor (MOSFET) (UMOSFET) fitted with a super-junction (SJ) shielded region. The modified structure is composed of two n-type conductive pillars, three p-type conductive pillars, an oxide trench under the gate, and a light n-type current spreading layer (NCSL) under the p-body. The n-type conductive pillars and the light n-type current spreading layer provide two paths to and promote the diffusion of a transverse current in the epitaxial layer, thus improving the specific on-resistance ($R_{\rm on,sp}$). There are three p-type pillars in the modified structure, with the p-type pillars on both sides playing the same role. The p-type conductive pillars relieve the electric field ($E$-field) in the corner of the trench bottom. Two-dimensional simulation (silvaco TCAD) indicates that $R_{\rm on,sp }$ of the modified structure, and breakdown voltage ($V_{\rm BR}$) are improved by 22.2% and 21.1% respectively, while the maximum figure of merit (${\rm FOM}=V^{2}_{\rm BR}/R_{\rm on,sp}$) is improved by 79.0%. Furthermore, the improved structure achieves a light smaller low gate-to-drain charge ($Q_{\rm gd}$) and when compared with the conventional UMOSFET (conventional-UMOS), it displays great advantages for reducing the switching energy loss. These advantages are due to the fact that the p-type conductive pillars and n-type conductive pillars configured under the gate provide a substantial charge balance, which also enables the charge carriers to be extracted quickly. In the end, under the condition of the same total charge quantity, the simulation comparison of gate charge and OFF-state characteristics between Gauss-doped structure and uniform-doped structure shows that Gauss-doped structure increases the $V_{\rm BR}$ of the device without degradation of dynamic performance.     

Ab initio calculations on the α^3∑u^＋ state properties of dimer ^7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometry of the α^3∑u^＋ state for ^7Li2 is made at numerous basis sets such as 6-311＋＋G（2df）, cc-PVTZ, 6-311＋＋G（2df, p）, 6-311G（3df,3pd）, 6-311＋＋G（2df,2pd）, D95（3df,3pd）, 6-311＋＋G, DGDZVP, 6-311＋＋G（3df,2pd）, 6-311G（2df,2pd）, D95V＋＋, CEP-121G, 6-311＋＋G（d,p）, 6-311＋＋G（2df, pd） and 6-311＋＋G（3df,3pd） in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction （SAC/SAC=CI） method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at those sets over a wide internuclear distance range from about 3.0α0 to 37.0α0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at ccopVTZ, the spectroscopic data （Te, De, D0, ωe,ωeХe, αe and Be） are computed and they are 1.006 eV, 338.71 cm^-1, 307.12 cm^-1, 64.88 cm^-1, 3.41 cm^-1, 0.0187 cm^-1 and 0.279 cm^-1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant （By） and six centrifugal distortion constants （Dr Hv, Lv, My, Nv, and Ov） are calculated. The scattering length is calculated to be -27.138α0, which is in good accord with the experimental data.     

New aspects of HCI test for ultra-short channel n-MOSFET devices

Hot carriers injection (HCI) tests for ultra-short channel n-MOSFET devices were studied. The experimental data of short channel devices (75--90\,nm), which does not fit formal degradation power law well, will bring severe error in lifetime prediction. This phenomenon usually happens under high drain voltage ($V_{\rm d}$) stress condition. A new model was presented to fit the degradation curve better. It was observed that the peak of the substrate current under low drain voltage stress cannot be found in ultra-short channel device. Devices with different channel lengths were studied under different $V_{\rm d}$ stresses in order to understand the relations between peak of substrate current ($I_{\rm sub}$) and channel length/stress voltage.     

Accurate studies of dissociation energies and vibrational energies on alkali metals

This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares （LS） fitting and an algebraic method （AM） proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that： （1） although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; （2） the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.     

A 4H-SiC trench MOSFET structure with wrap N-type pillar for low oxide field and enhanced switching performance

An optimized silicon carbide (SiC) trench metal-oxide-semiconductor field-effect transistor (MOSFET) structure with side-wall p-type pillar (p-pillar) and wrap n-type pillar (n-pillar) in the n-drain was investigated by utilizing Silvaco TCAD simulations. The optimized structure mainly includes a p$+$ buried region, a light n-type current spreading layer (CSL), a p-type pillar region, and a wrapping n-type pillar region at the right and bottom of the p-pillar. The improved structure is named as SNPPT-MOS. The side-wall p-pillar region could better relieve the high electric field around the p$+$ shielding region and the gate oxide in the off-state mode. The wrapping n-pillar region and CSL can also effectively reduce the specific on-resistance ($R_{\rm on,sp}$). As a result, the SNPPT-MOS structure exhibits that the figure of merit (FoM) related to the breakdown voltage ($V_{\rm BR}$) and $R_{\rm on,sp}$ ($V_{\rm BR}^{2}R_{\rm on,sp}$) of the SNPPT-MOS is improved by 44.5%, in comparison to that of the conventional trench gate SJ MOSFET (full-SJ-MOS). In addition, the SNPPT-MOS structure achieves a much faster-witching speed than the full-SJ-MOS, and the result indicates an appreciable reduction in the switching energy loss.     

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD（χ^2П） radical

Interaction potential of the SiD(X2Π) radical is constructed by using the CCSD(T) theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the valence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present D0, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm-1, 0.07799 cm-1 and 3.8717 cm-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J=0 by solving the radial Schro¨dinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J=0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0×10-11–1.0×10-3 a.u. when the two atoms approach each other along the SiD(X2Π) potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10-5, 4.0×10-5, 6.45×10-5 and 5.5×10-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.     

First principle study of nitrogen vacancy in aluminium nitride

In the framework of density functional theory, using the plane-wave pseudopotential method, the nitrogen vacancy ($V_{\rm N})$ in both wurtzite and zinc-blende AlN is studied by the supercell approach. The atom configuration, density of states, and formation energies of various charge states are calculated. Two defect states are introduced by the defect, which are a doubly occupied single state above the valance band maximum (VBM) and a singly occupied triple state below the conduction band minimum (CBM) for wurtzite AlN and above the CBM for zinc-blende AlN. So $V_{\rm N}$ acts as a deep donor in wurtzite AlN and a shallow donor in zinc-blende AlN. A thermodynamic transition level $E({3 + } \mathord{\left/ {\vphantom {{3 + } + }} \right. \kern-\nulldelimiterspace} + )$ with very low formation energy appears at 0.7 and 0.6eV above the VBM in wurtzite and zinc-blende structure respectively, which may have a wide shift to the low energy side if atoms surrounding the defect are not fully relaxed. Several other transition levels appear in the upper part of the bandgap. The number of these levels decreases with the structure relaxation. However, these levels are unimportant to AlN properties because of their high formation energy.     

The splitting of low-lying states for hydroxyl molecule under spin--orbit coupling

The splitting of potential energy curves for the states $X^{2}\Pi _{3/2}$, $^{2}\Pi _{1/2}$ and $A^{2}\Sigma ^{ +}$ of hydroxyl OH under spin--orbit coupling (SOC) has been calculated by using the SO multi-configuration quasi-degenerate perturbation theory (SO-MCQDPT). Their Murrell--Sorbie (M--S) potential functions have been derived, then, the spectroscopic constants for $X^{2}\Pi _{3/2}$,$^{ 2}\Pi _{1/2}$ and $A^{2}\Sigma ^{ + }$ have been derived from the M--S function. The calculated dissociation energies for the three states are $D_{0}$[OH($X^{2}\Pi _{3/2})$]=34966.632cm$^{-1}$, $D_{0}$[OH($^{2}\Pi _{1/2})$]=34922.802cm$^{-1}$, and $D_{0}$[OH($A^{2}\Sigma ^{ + })$]=17469.794cm$^{-1}$, respectively. The vertical excitation energy $\nu [ {{ }^2\Pi _{1/2} ( {\nu = 0} ) \to {X}{ }^2\Pi _{3/2} ( {\nu = 0} )} ] = 139.6{\rm cm}^{-{\rm 1}}$. All the spectroscopic data for the $X^{2}\Pi _{3/2}$ and $^{2}\Pi _{1/2 }$ are given for the first time except the dissociation energy of $X^{2}\Pi _{3/2}$.     

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.     

A novel Si-rich SiN bilayer passivation with thin-barrier AlGaN/GaN HEMTs for high performance millimeter-wave applications

We demonstrate a novel Si-rich SiN bilayer passivation technology for AlGaN/GaN high electron mobility transistors (HEMTs) with thin-barrier to minimize surface leakage current to enhance the breakdown voltage. The bilayer SiN with 20-nm Si-rich SiN and 100-nm Si$_{3}$N$_{4}$ was deposited by plasma-enhanced chemical vapor deposition (PECVD) after removing 20-nm SiO$_{2}$ pre-deposition layer. Compared to traditional Si$_{3}$N$_{4}$ passivation for thin-barrier AlGaN/GaN HEMTs, Si-rich SiN bilayer passivation can suppress the current collapse ratio from 18.54% to 8.40%. However, Si-rich bilayer passivation leads to a severer surface leakage current, so that it has a low breakdown voltage. The 20-nm SiO$_{2}$ pre-deposition layer can protect the surface of HEMTs in fabrication process and decrease Ga-O bonds, resulting in a lower surface leakage current. In contrast to passivating Si-rich SiN directly, devices with the novel Si-rich SiN bilayer passivation increase the breakdown voltage from 29 V to 85 V. Radio frequency (RF) small-signal characteristics show that HEMTs with the novel bilayer SiN passivation leads to $f_{\rm T}/f_{\rm max}$ of 68 GHz/102 GHz. At 30 GHz and $V_{\rm DS} = 20$ V, devices achieve a maximum $P_{\rm out}$ of 5.2 W/mm and a peak power-added efficiency (PAE) of 42.2%. These results indicate that HEMTs with the novel bilayer SiN passivation can have potential applications in the millimeter-wave range.     

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method (ATMM) is applied to calculating the critical radius $r_{\rm c}$ and the dipole polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen atom and the Hulth\'{e}n potential. We find that there exists a linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$ for a fixed angular quantum number $l$, moreover, the three bounds of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$, $\alpha_{\rm d}^{U}$) satisfy an inequality: $\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.