Weifu Fang

Modeling and analysis of laser-beam-induced current images in semiconductors

A mathematical model is developed for the new nondestructive optical technique called laser-beam–induced currents (LBIC), which can be used to detect electrically active regions and defects in semiconductors. The wellposedness of the model equations is shown, and an approximate model that simplifies the numerical implementation of the identification problem is obtained. Some numerical results are presented to show that the approximate model preserves the significant features that the LBIC technique has been experimentally shown to possess.

PARAMETER IDENTIFICATION FOR SEMICONDUCTOR DIODES BY LBIC IMAGING

Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of parameters from the LBIC image by least-squares formulation. Numerical examples are presented to illustrate the success of identifying parameters such as junction depth, diffusion length, and equilibrium potential of an abrupt p-n junction diode from its LBIC image. The differentiability of the image with respect to the parameters also is established.

Reconstruction of semiconductor doping profile from laser-beam-induced current image

In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional algorithm supplemented with a correction from the other spatial direction to establish an alternate direction iteration algorithm for reconstruction of the two-dimensional equilibrium potential. The authors also present some numerical examples to illustrate the reconstruction results by these algorithms.

Identifiability of semiconductor defects from LBIC images

The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.

EXISTENCE OF STATIONARY SOLUTIONS TO AN ENERGY DRIFT-DIFFUSION MODEL FOR SEMICONDUCTOR DEVICES

We analyze a mathematical model for semiconductors derived from the hydrodynamic model under the massless assumption. This model augments the classical drift-diffusion model by including temperature as a dependent variable. We establish the existence of stationary solutions near the equilibrium state.

Identification of contact regions in semiconductor transistors by level-set methods

In this paper we present the formulation of level-set methods for the inverse problem of identifying an interface in the coefficient of an elliptic equation from a boundary measurement. This problem arises from the modeling of the identification of contact regions by boundary measurements for semiconductor transistors. We propose the Gauss-Newton direction as the interface velocity, and implement the scheme for a parameterized class of interfaces.

Investigation of laser beam-induced current techniques for heterojunction photodiode characterization

A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P‐n HgCdTe heterojunction photodiode structures. In particular, the question of correctly identifying erroneous device structures formed during the fabrication process is addressed, and experimental measurements are presented to support the simulation results.

LBIC imaging of semiconductor arrays: the cross-sectional model

Laser beam induced current (LBIC)/nondestructive technique that has been used for a number of years to qualitatively examine large arrays of p-n junctions, especially in HgCdTe infrared focal plane arrays. In this paper, we quantitatively study the application of the LBIC imaging technique to semiconductor arrays Based on a previous mathematical model for LBIC applied to individual devices, we employ the homogenization method to derive approximations of the LBIC images of large arrays. Such approximations reduce the computational burden in simulations of these LBIC bouges. We then illustrate the application of our approximations for the purpose of recovering array parameters from the LBIC images.

On the inhomogeneous system of isentropic gas dynamics by the viscosity method

The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L ∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed

Energy estimates for a one-dimensional hydrodynamic model of semiconductors

Abstract Energy functions are introduced for the weak solutions to a one-dimensional hydrodynamic model for semiconductors, and are shown to be continous and nonincreasing in time.