A Numerical Analysis of Heterojunction Bipolar Devices.

Numerical simulation plays an important role in the design, analysis and fabrication of semiconductor devices. In this work, a computer program is developed to obtain a one-dimensional steady-state constant temperature current-voltage characteristics of diodes and bipolar transistors fabricated from materials having position dependent material properties such as band-gap, electron affinity, permittivity and the density of states functions. The general formulation of the problem allows for an unambiguous choice of reference potential. The modular form of the program allows for the choice of appropriate recombination processes for each of the materials used in the structure. The program can adjust the step sizes automatically during the calculations. This reduces the convergence problem significantly and increases the application of the program to a wider variety of device structures and bias voltages. The automatic step selection process was found to take up an excessive amount of the computer CPU time. Hence, an alternate step selection process was also employed that retains many of the benefits of the variable step size selection but requires considerably less CPU time. A finite-difference method through quasi-linearization technique is employed to numerically solve the three second-order non-linear partial differential equations describing the behavior of semiconductor devices. The computer program can handle a large variation in the device size and has no restrictions in the impurity doping profile other than the Boltzmann approximation. The program is applied to a variety of homo and heterostructure diodes and bipolar transistors. The individual electron and hole current densities are computed with position in the device along with carrier densities and potentials. Structures with abrupt and graded heterostructure interfaces are considered. The results obtained from this program compare well with those of others reported in the literature