Doping profile and Ge-dose optimization for silicon–germanium heterojunction bipolar transistors

Abstract

The speed of silicon-germanium (SiGe) heterojunction bipolar transistors (HBTs) has been dramatically increased. It is known that the speed of HBTs is dominated by the base transit time, which could be influenced by the doping profile in the base region and the Ge concentration. In this study, the design of the doping profile and Ge-dose concentration for SiGe HBTs are mathematically formulated and solved by a technique of geometric programming (GP). The solution calculated by the GP method is guaranteed to be a global optimal. The accuracy of the adopted numerical optimization technique is first confirmed by comparing with two-dimensional device simulation. The result of this study shows that a 23% Ge fraction may maximize the current gain; furthermore, a 12.5% Ge may maximize the cutoff frequency for the explored device, where a 254 GHz cutoff frequency is achieved.

Optimal Channel Doping Profile of Two-Dimensional Metal-Oxide-Semiconductor Field-Effect Transistors via Geometric Programming

“…By integrating the z-direction for the triple integral in (35) and discretizating this integral based on the technique in (10)-(11), we can approximate (35) by the summation:…”

“…Various applications of GP, such as space optimization [23], optimal condenser in chemical reaction [24], and solving the marketing-mix strategy [25] were reported. In recent years, circuit and layout optimizations [26][27][28][29][30][31], communication system design [32][33], and semiconductor design [34][35][36] in the related fileds of electrical engineering have been explored by proper transformation to GP formulation. A solution method by using interior-point algorithm was advanced to solve large-scale GP problems in convex form [18][19].…”

“…This is computationally efficient and reliable method which can significantly accelerate applications of GP in real-world problems. In our earlier work, the GP approach has been utilized to optimize the Ge-dose concentration and silicon doping profile in SiGe HBTs for high frequency characteristic and 1D MOS problem [34][35][36]. However, seeking optimal channel doping profile via GP approach in 2D MOSFETs has not been investigated yet.…”

Geometric programming approach to doping profile design optimization of metal-oxide-semiconductor devices

“…Problems with a GP form could be solved using an interior-point based algorithm in a computationally costeffective manner [14]. GP was applied in designs of BJT devices and electronic circuits [15][16][17][18][19], except its diverse applications in management and engineering (see, for instance, [12,13] and references therein).…”