Quantum Boltzmann equation solved by Monte Carlo method for nano-scale semiconductor devices simulation

A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.

FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.

Overview of High Voltage SiC Power Semiconductor Devices: Development and Application

Research on high voltage(HV)silicon carbide(SiC)power semiconductor devices has attracted much attention in recent years.This paper overviews the development and status of HV SiC devices.Meanwhile,benefits of HV SiC devices are presented.The technologies and challenges for HV SiC device application in converter design are discussed.The state-of-the-art applications of HV SiC devices are also reviewed.

Effect of NO annealing on charge traps in oxide insulator and transition layer for 4H-SiC metal–oxide–semiconductor devices

The effect of nitric oxide（NO） annealing on charge traps in the oxide insulator and transition layer in n-type4H–Si C metal–oxide–semiconductor（MOS） devices has been investigated using the time-dependent bias stress（TDBS）,capacitance–voltage（C–V）,and secondary ion mass spectroscopy（SIMS）.It is revealed that two main categories of charge traps,near interface oxide traps（Nniot） and oxide traps（Not）,have different responses to the TDBS and C–V characteristics in NO-annealed and Ar-annealed samples.The Nniotare mainly responsible for the hysteresis occurring in the bidirectional C–V characteristics,which are very close to the semiconductor interface and can readily exchange charges with the inner semiconductor.However,Not is mainly responsible for the TDBS induced C–V shifts.Electrons tunneling into the Not are hardly released quickly when suffering TDBS,resulting in the problem of the threshold voltage stability.Compared with the Ar-annealed sample,Nniotcan be significantly suppressed by the NO annealing,but there is little improvement of Not.SIMS results demonstrate that the Nniotare distributed within the transition layer,which correlated with the existence of the excess silicon.During the NO annealing process,the excess Si atoms incorporate into nitrogen in the transition layer,allowing better relaxation of the interface strain and effectively reducing the width of the transition layer and the density of Nniot.

Analysis of a two-grid method for semiconductor device problem

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

Infrastructure of Synchrotronic Biosensor Based on Semiconductor Device Fabrication for Tracking, Monitoring, Imaging, Measuring, Diagnosing and Detecting Cancer Cells

Copper Zinc Antimony Sulfide(CZAS)is derived from Copper Antimony Sulfide(CAS),a famatinite class of compound.In the current paper,the first step for using Copper,Zinc,Antimony and Sulfide as materials in manufacturing synchrotronic biosensor-namely increasing the sensitivity of biosensor through creating Copper Zinc Antimony Sulfide,CZAS(Cu1.18Zn0.40Sb1.90S7.2)semiconductor and using it instead of Copper Tin Sulfide,CTS(Cu2SnS3)for tracking,monitoring,imaging,measuring,diagnosing and detecting cancer cells,is evaluated.Further,optimization of tris(2,2'-bipyridyl)ruthenium(II)(Ru(bpy)32+)concentrations and Copper Zinc Antimony Sulfide,CZAS(Cu1.18Zn0.40Sb1.90S7.2)semiconductor as two main and effective materials in the intensity of synchrotron for tracking,monitoring,imaging,measuring,diagnosing and detecting cancer cells are considered so that the highest sensitivity obtains.In this regard,various concentrations of two materials were prepared and photon emission was investigated in the absence of cancer cells.On the other hand,ccancer diagnosis requires the analysis of images and attributes as well as collecting many clinical and mammography variables.In diagnosis of cancer,it is important to determine whether a tumor is benign or malignant.The information about cancer risk prediction along with the type of tumor are crucial for patients and effective medical decision making.An ideal diagnostic system could effectively distinguish between benign and malignant cells;however,such a system has not been created yet.In this study,a model is developed to improve the prediction probability of cancer.It is necessary to have such a prediction model as the survival probability of cancer is high when patients are diagnosed at early stages.

A Mixed-finite Volume Element Coupled with the Method of Characteristic Fractional Step Difference for Simulating Transient Behavior of Semiconductor Device of Heat Conductor And Its Numerical Analysis

The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.

GALERKIN ALTERNATING-DIRECTION METHODS FOR NONRECTANGULAR REGIONS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation，patch approximation, operator-splitting, characteristic method, symmetrical reflection,energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.

UPWIND FINITE VOLUME ELEMENT METHODS FOR ONE-DIMENSIONAL SEMICONDUCTOR DEVICE

This work is supported in part-by Shandong Province Natural Science Foundation under Grant No. ZR2010AQ010 and a Project of Shandong Province Higher Educational Science and Technology Program under Grant Nos. JllLA09 and J10LA01.

Multivariate rational regression and its application in semiconductor device modeling

Physics equation-based semiconductor device modeling is accurate but time and money consuming.The need for studying new material and devices is increasing so that there has to be an efficient and accurate device modeling method. In this paper, two methods based on multivariate rational regression（MRR） for device modeling are proposed. They are single-pole MRR and double-pole MRR. The two MRR methods are proved to be powerful in nonlinear curve fitting and have good numerical stability. Two methods are compared with OLS and LASSO by fitting the SMIC 40 nm MOS-FET I–V characteristic curve and the normalized mean square error of Single-pole MRR is 3.02 × 10^-8 which is 4 magnitudes less than an ordinary least square. The I–V characteristics of CNT-FET and performance indicators（noise factor, gain, power） of a low noise amplifier are also modeled by using MRR methods. The results show MRR methods are very powerful methods for semiconductor device modeling and have a strong nonlinear curve fitting ability.

MULTISTEP FINITE VOLUME APPROXIMATIONS TO THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE ON GENERAL 2D OR 3D MESHES

In this paper, we consider a hydrodynamic model of the semiconductor device. The approximate solutions are obtained by a mixed finite volume method for the potential equation and multistep upwind finite volume methods for the concentration equations. Error estimates in some discrete norms are derived under some regularity assumptions on the exact solutions.

Numerical simulation of shock wave phenomena in hydrodynamic model of semiconductor devices

We propose a finite element method to investigate the phenomena of shock wave and to simulate the hydrodynamic model in semiconductor devices. An introduction of this model is discussed first. Then some scaling factors and a relationship between the changing variables are discussed. And then, we use a finite element method （P1-iso-P2 element） to discrete the equations. Some boundary conditions are also discussed. Finally, a sub-micron n%＋-n-n^＋ silicon diode and Si MESFET device are simulated and the results are analyzed. Numerical results show that electronic fluids are transonic under some conditions.

Determination of capacitance-voltage characteristics of organic semiconductor devices by combined current-voltage and voltage decay measurements

We present in this paper a new method,based on measurements of conventional direct current-voltage(I-V) characteristics and transient voltage-time(V-t) characteristics during the discharge process,for determining capacitance-voltage(C-V) characteris-tics of organic semiconductor devices.Derivatives of I-V and V-t,dI/dV and dV/dt,are related with C by a simple formula C=-V(dI/dV)/(dV/dt)The validity of the method is confirmed by experimental data measured from a set of single-organic-layer devices with different layer thicknesses.

Recent progress on ambipolar 2D semiconductors in emergent reconfigurable electronics and optoelectronics

In these days,the increasing massive data are being produced and demanded to be processed with the rapid growth of information technology.It is difficult to rely solely on the shrinking of semiconductor devices and scale-up of the integrated circuits(ICs)again in the foreseeable future.Exploring new materials,new-principle semiconductor devices and new computing architectures is becoming an urgent topic in this field.Ambipolar two-dimensional(2D)semiconductors,possessing excellent electrostatic field controllability and flexibly modulated major charge carriers,offer a possibility to construct reconfigurable devices and enable the ICs with new functions,showing great potential in computing capacity,energy efficiency,time delay and cost.This review focuses on the recent significant advancements in reconfigurable electronic and optoelectronic devices of ambipolar 2D semiconductors,and demonstrates their potential approach towards ICs,like reconfigurable circuits and neuromorphic chips.It is expected to help readers understand the device design principle of ambipolar 2D semiconductors,and push forward exploring more new-principle devices and new-architecture computing circuits,and even their product applications.

Temperature Dependence of Performance of 6H-SiC Unipolar Power Devices

The temperature dependence of some performance of 6H SiC unipolar power devices is analyzed theoretically.By employing the temperature dependent ionization coefficient and mobility of a silicon carbide,the analytical expressions of the temperature dependent performance,such as breakdown characteristics and on resistance of 6H SiC unipolar power devices are derived in a closed form.The analytical results are compared with the experimental results,with good accordance found in the breakdown characteristics.

Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.

Black phosphorus-based field effect transistor devices for Ag ions detection

Black phosphorus （BP）, an attractive two-dimensional （2D） semiconductor, is widely used in the fields of optoelec- tronic devices, biomedicine, and chemical sensing. Silver ion （Ag＋）, a commonly used additive in food industry, can sterilize and keep food fresh. But excessive intake of Ag＋ will harm human health. Therefore, high sensitive, fast and simple Ag＋ detection method is significant. Here, a high-performance BP field effect transistor （FET） sensor is fabricated for Ag＋ detection with high sensitivity, rapid detection speed, and wide detection concentration range. The detection limit for Ag＋ is 10 l0 mol/L. Testing time for each sample by this method is 60 s. Besides, the mechanism of BP-FET sensor for Ag＋ detection is investigated systematically. The simple BP-FET sensor may inspire some relevant research and potential applications, such as providing an effective method for the actual detection of Ag＋, especially in wimessed inspections field of food.

A review of manufacturing technologies for silicon carbide superjunction devices

Superjunction technology is believed to reach the optimal specific on-resistance and breakdown voltage trade-off.It has become a mainstream technology in silicon high-voltage metal oxide semiconductor field effect transistor devices.Numerous efforts have been conducted to employ the same concept in silicon carbide devices.These works are summarized here.