Physics of Discrete Impurities under the Framework of Device Simulations for Nanostructure Devices

Abstract

Localized impurities doped in the semiconductor substrate of nanostructure devices play an essential role in understanding and resolving transport and variability issues in device characteristics. Modeling discrete impurities under the framework of device simulations is, therefore, an urgent need for reliable prediction of device performance via device simulations. In the present paper, we discuss the details of the physics associated with localized impurities in nanostructure devices, which are inherent, yet nontrivial, to any device simulation schemes: The physical interpretation and the role of electrostatic Coulomb potential in device simulations are clarified. We then show that a naive introduction of localized impurities into the Poisson equation leads to a logical inconsistency within the framework of the drift-diffusion simulations. We describe a systematic methodology for how to treat the Coulomb potential consistently with both the Poisson and current-continuity (transport) equations. The methodology is extended to the case of nanostructure devices so that the effects of the interface between different materials are taken into account.

Evaluation of Low-Frequency Noise in MOSFETs Used as a Key Component in Semiconductor Memory Devices

“…Figure 9 shows the Gumbel plot of the RTN amplitude for MOSFETs with varying channel doping [51]. The channel percolation is accelerated by increasing channel doping concentration [46][47][48]. This figure shows that the probability of the number of MOSFETs with large amplitude increases with doping concentration.…”

“…This is caused by the increase in the number of channel electrons as IDS increases. However, the amplitude and TF of some samples did not exhibit monotony, which is due to the percolation channel effect [46][47][48][49]. The distance between the channel and trap changes as IDS (VGS) changes because of the formation of the percolation channel.…”

“…In this experiment, I DS was constant at 1.0 µA, and this means that the number of electrons was almost the same for each V BS . Increasing V BS caused channel percolation [46][47][48][49], making the channel thickness narrow and percolated and increasing electron energy [50]. The probability is increased by channel percolation [46,47], and the varying electron energy modulates the time constants.…”

Quantum Kinetic Equation for the Wigner Equation and Reduction to the Boltzmann Transport Equation under Discrete Impurities

“…However, such theoretical approaches based on the BTE are incomplete in some respects, especially when taking into account the discrete nature of impurities. For instance, electrostatic Hartree potential determined by Poisson's equation represents the potential under the long-wavelength limit [5] and impurity scattering in the collision integral is evaluated under the implicit assumption of self-averaging over all possible impurity configurations [3][4][5][6][7][8]. We would also like to mention that the collision integral in the BTE is introduced by the reasoning that the rate of change of the electron distribution function must be balanced between drift and scattering processes [9][10][11].…”

Special Issue: Nanowire Field-Effect Transistor (FET)

“…The effect of the impurities in the NW-FETs was also analysed in two articles. Sano et al [4] focused their work on the physics associated with localized impurities inside the device, describing a systematic methodology on how to treat Coulomb interaction in many body-systems when using drift-diffusion simulations. Sady et al [5], on the other hand, studied the effect of various scattering mechanisms and nanowire cross-section shapes on electron mobility in nanoscale Si NW-FETs.…”