Chung-Kai Lin

Frequency domain analysis of the distribution function by small signal solution of the Boltzmann and Poisson equations

A method for solving the Boltzmann-Poisson system in the frequency domain has been developed. It is achieved by applying small signal analysis to the Spherical Harmonic expansion method of solving the Boltzmann equation. By solving this model in the frequency domain, we can investigate the frequency response of the entire momentum distribution function. A 0.05 /spl mu/m base BJT simulation in the frequency domain gives the results of the small signal distribution function response over the entire device in 4 minutes CPU time on an Alpha workstation.

Gate leakage current simulation by Boltzmann transport equation and its dependence on the gate oxide thickness

As device dimensions shrink toward 0.1 /spl mu/m, gate oxides are becoming so thin that MOSFET gate leakage current and oxide degradation are becoming limiting issues. We provide a more rigorous way to calculate gate leakage current. To achieve this we build upon the Spherical Harmonic Method of modeling, which deterministically solves the Boltzmann equation for an entire device. The method gives the distribution function and is 1000 times faster than MC. Once the distribution function is calculated, the tunneling probability is derived from the first principle WKB method. The barrier lowering effect is accounted for by the method of image charges. We calculate gate leakage current as a function of DC bias. The thermionic and tunneling components are compared at different DC bias points. The dependence of gate leakage current on gate oxide thickness is simulated.

A transient solution of the Boltzmann equation exposes energy overshoot in semiconductor devices

A method is developed to analyze the transient response of semiconductor devices in phase space. This is achieved by solving the space and time dependent electron Boltzmann transport equation self-consistently with the Poisson and transient hole-current-continuity equation. The result gives the details of the time evolution of the distribution function. The method is applied to analyze a bipolar junction transistor. The model predicts the limits in which the steady-state response approximation can be applied. The model exposes a transient overshoot in the high energy tail of the distribution function.

Spherical Harmonic Modeling of a 0.05 μmBase BJT: A Comparison with Monte Carloand Asymptotic Analysis

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.

2-D quantum transport device modeling by self-consistent solution of the Wigner and Poisson equations

A new approach for simulating quantum transport in nanoscale semiconductor devices is presented. The method is based on the self-consistent solution of the Poisson and Wigner equations within a device. The spherical harmonic approach is used to transform the Wigner equation into a tractable expression. The results provide the distribution function and its averages throughout the device. The method has been applied to a MOSFET and a BJT. Inclusion of quantum effects reduces carrier concentrations near potential energy barriers, leading to reduced terminal current.

Advances in spherical harmonic device modeling: calibration and nanoscale electron dynamics

Improvements in the Spherical Harmonic (SH) method for solving Boltzmann Transport Equation (BTE) are presented. The simulation results provide the same physical detail as analytical band Monte Carlo (MC) calculations, and are obtained approximately a thousand times faster. A new physical model for surface scattering has also been developed. As a result, the SHBTE model achieves calibration for a complete process of I-V characteristics and substrate current consistently for the first time.

Investigation of the optical spot position on the performance of metal–semiconductor–metal structures: novel application

Abstract The effect of the optical spot position relative to the electrodes in metal–semiconductor–metal (MSM) structures has been studied. Theoretically, we have found that the I–V characteristic depends strongly on the position and the intensity of the optical spot. Besides being very sensitive to the optical spot position, at zero applied bias, the MSM can be used as a current source where the magnitude and the direction of the output current depend on the position and the intensity of the optical spot. Being a planar structure with high signal-to-noise ratio makes the MSM a unique structure for these types of applications.

Extension of Spherical Harmonic Method to RF Transient Regime

The space and time dependent electron Boltzmann transport equation (BTE) is solved self-consistently with the Poisson and transient hole current-continuity equation. A transient Spherical Harmonic expansion method is used to solve the BTE. By this method we can efficiently solve the BTE in the RF regime to observe how the complete distribution function responds to a rapid transient. Calculations on a BJT, which give the time dependent distribution function over a large energy range 0–3eV, throughout the device, as well as average quantities, require only 40 minutes CPU time on an Alpha workstation.

The spherical harmonic method: corroboration with Monte Carlo and experiment

We show that the Spherical Harmonic method gives results for the space-dependent energy distribution function that agree with analytical band Monte Carlo simulations on a nanometer length scale, but are calculated approximately 1000 times faster. We also substantiate the Spherical Harmonic method by showing it gives values for MOSFET substrate current that agree with experiment without the use of fitting parameters. We explain the agreement through the use of asymptotic analysis.