Yutao Ma

Effective density-of-states approach to QM correction in MOS structures

Abstract MOS structure threshold voltage shift due to quantum mechanical effects (QMEs) has a substantial influence on deep-submicron MOSFET characteristics. However, its physical nature has not been thoroughly investigated and an analytical model is absent. In this paper, a numerical solution of the Schrodinger equation with parabolic potential well and an analytical solution with triangular well are compared, and the validity of the triangular well approximation is verified. Based on the calculation of the subband structure in the quantized region in a weak inversion regime, the concepts of surface layer effective density-of-states (SLEDOS) is proposed. Carrier distribution in subbands is then analyzed and physical base of MOSFETs Vth shift due to QMEs are discussed. The single subband occupation approximation used in earlier works is proved to be invalid and a new analytical threshold voltage (Vth) shift model due to QMEs including multisubband occupation is derived based on the concept of SLEDOS. The model reveals the physical nature of QMEs on Vth shift and gives consistent results with experiments and self-consistent calculation.

Validity and applicability of triangular potential well approximation in modeling of MOS structure inversion and accumulation layer

Two methods are presented to calculate the carrier distribution in MOS inversion and accumulation layer by self-consistent solution of Schrodinger and Poisson equations. One is the fully numerical solution of Schrodinger equation by finite difference method and the other is the analytical solution of Schrodinger equation under triangular potential well approximation. The effective electric field used in the analytical solution is properly determined. Results show that both carrier sheet density and surface potential in inversion layer and accumulation layer can be determined by analytical solution under triangular potential well approximation with sufficiently high accuracy. However, the carrier distribution profile and centroid of mobile charge layer, as well as the behavior at the flat-band region, have a large deviation from the numerical results.

Analytical charge-control and I-V model for submicrometer and deep-submicrometer MOSFETs fully comprising quantum mechanical effects

A new analytical current-voltage (I-V) model for submicrometer and deep-submicrometer metal-oxide-semiconductor field-effect transistors (MOSFETs) is developed based on a newly developed charge-control model for the metal-oxide-semiconductor structure. Threshold-voltage shift due to quantum mechanical effects, finite inversion layer thickness effects (inversion layer capacitance), as well as increased depletion layer charge density after the strong inversion point are incorporated in the model. Inversion layer charge density with respect to the gate voltage from depletion through weak inversion to strong inversion regions with smooth transition between different regions is given by one expression. Two-dimensional short channel effects such as channel length modulation, drain-induced barrier lowering, mobility degradation, and carrier velocity saturation, as well as polysilicon depletion effects are included in the I-V model. Model results are compared with both numerical results of carrier sheet density and surface potential in the channel, and experimental results of I-V data for submicrometer and deep-submicrometer MOSFETs down to 0.09-/spl mu/m effective gate length and the accuracy of the model are demonstrated.

Modified Airy function method for modeling of direct tunneling current in metal–oxide–semiconductor structures

Using a modified Airy function (MAF) to solve the Schrodinger equation in the whole metal–oxide–semiconductor structure, a fully quantum-mechanical model of direct tunneling current from an inverted p-Si substrate through ultrathin oxides is presented. The effects of tunneling on the electrostatic potential and the distribution of electrons are also included when self-consistently solving the Schrodinger and Poisson equations in silicon. Due to the semianalytical nature of the MAF method, the model has high efficiency. Model results are compared with experimental data and show excellent agreement. Moreover, an approximately linear relationship between the logarithm of the direct tunneling current and oxide thickness is found out.

A new charge model including quantum mechanical effects in MOS structure inversion layer

Abstract Based on the analysis of the distribution of inversion layer carriers in MOS structure, the concept of surface layer effective density-of-states (SLEDOS) is proposed. Then a new charge control model suitable for both semi-classical and quantum mechanical theory is established in which the effects of inversion layer carrier distribution on surface potential are included. In this model, a newly developed efficient iteration method is introduced, which has high efficiency and satisfied stability. Based on the model, the effects of quantum mechanical effects (QMEs) on inversion layer charge density both in weak and strong inversion regions and the surface potential are studied. Model results are compared with the self-consistent solutions of Schrodinger and Poisson equations, which proves the high accuracy of the new model.

Characterization and modeling of threshold voltage shift due to quantum mechanical effects in pMOSFET

Abstract The threshold voltage shift due to quantum mechanical effects (QMEs) has substantial influences on modern pMOSFET characteristics. Investigations of QMEs in a pMOSFET are classified into two approaches: full-band calculation and effective mass approximation. In this paper, formulation of carrier distribution in the pMOSFET inversion layer in the threshold region based on the effective mass approximation is presented, and a new method to calculate the threshold voltage shift due to QMEs is developed. The results with the effective mass approximation are compared with the full-band calculation and show satisfactory coincidence. Based on the present model, the subband structure of the hole inversion layer and the carrier distribution characteristics are investigated. The quantum mechanical and semi-classical two-dimensional density of states (2D DOS) are calculated and compared. The dependence of the threshold voltage shift due to QMEs on substrate doping concentration is then analyzed from the DOS point of view.

Comprehensive analytical physical model of quantized inversion layer in MOS structure

Abstract A new analytical charge model in quantized inversion layer in MOS structure is developed by comprehensively considering the quantum mechanical effects. The model is based on the newly proposed concept of space charge capacitance. Explicit expressions of surface potential and inversion layer carrier density are given which have smooth transition characteristics from depletion to weak to strong inversion regions. Threshold voltage shift, finite inversion layer thickness and the increment of depletion charge after strong inversion are properly modeled. Model results are compared with numerical data by self-consistent solution of Schrodinger and Poisson equation and the high accuracy of the model is demonstrated.

Thorough analysis of quantum mechanical effects on MOS structure characteristics in threshold region

Threshold voltage shift due to quantum mechanical effects (QMEs) are studied for both n- and p-MOS structure in the paper. Subband structure and carrier distribution are formulated for both type of MOS structure in effective mass approximation. QMEs on threshold voltage shift are thoroughly analyzed based on the model. Carrier distribution in subbands for both n-MOS and p-MOS are calculated and analyzed from density-of-states point of view. Model results for n- and p-MOS structure are compared with experimental and full-band self-consistent calculation results and show good coincidence. It is proved that at least in threshold region, effective mass approximation has similar accuracy as the full-band self-consistent method to predict the influence of QMEs MOS structure characteristics.

Simplified method to investigate quantum mechanical effects in MOS structure inversion layer

A simplified method to calculate the band bending and subband energies is employed to investigate quantum mechanical effects (QMEs) in MOS structure inversion layer. The subband structure and the two-dimensional (2-D) density-of-states in semi-classical and quantum mechanical cases are then calculated. The well-known band-gap widening model is analyzed through a density-of-states point of view and a new scheme to analyse and model QMEs in an MOS inversion layer is proposed.

A discussion on the universality of inversion layer mobility in MOSFET's

An obvious discrepancy exists in published research results concerning the universality of MOS inversion layer electron mobility in nonuniform substrate doping profile cases. By thorough analysis of the data and the parameter extraction method, it is demonstrated that the discrepancy is simply due to the different definition of depletion layer charge and the invalid extraction of parameters from experimental data. Studies in this work show that inversion layer carrier mobility experiences the same universality feature in nonuniform doping substrates as in uniform ones.