Semiconductor Device Modelling







This work limits to pn-junction/mosfet and all material properties is assumed.






Analytical vs Numerical


Boundary Condition


Vmax = 1.0; % max voltage for voltage sweep
Vmin = 0.0;



Drift-Diffusion Model



Non-linear Poisson's Equation


- Neglecting Magnetci Filed



Continuity Equations



Current Density Equations




Solving Poisson's Equation


- Finite Difference

- Finite Element (used in this work)


Galerkin Method: 1D Poisson's Equation [3]



Numerical Integration: Gaussian Quadrature



Gummel's Iteration Method


Gummel's method [2] solves the coupled set of semiconductor equations together with the
Poisson equation via a decoupled procedure. If we choose the quasi-Fermi level formulation, we
solve first a nonlinear Poisson's equation. The potential obtained from this solution is substituted
into the continuity equations, which are now linear, and are solved directly to conclude the
iteration step. The result in terms of quasi-Fermi levels is then substituted back into Poisson's
equation and the process repeated until convergence is reached. In order to check for
convergence, one can calculate the residuals obtained by positioning all the terms to the left hand
side of the equations and substituting the variables with the iteration values. For the exact
solution the residuals should be zero. Convergence is assumed when the residuals are smaller
than a set tolerance.




Simulation Parameters

ni = 1.45e10; % intrinsic concentration (cm^-3)
Na = 5e17; % concentration of acceptor atoms (cm^-3)
Nd = 1e17;
mu_n = 1400; % electron mobility
mu_p = 450; % hole mobility (cm^2 V^-1 s^-1)
D_n = ft * mu_n; % electron diffussion coefficient
D_p = ft * mu_p; % hole diffussion coefficient



Results of Simulation


Voltage Sweep and Potential Profile





Current-Voltage Characteristics



stepsize = 0.01



Electron/Holes Concentration



Fermi Potential







Device Structure




Current Concentration







- Steady state analysis (no-transient)






Electrical Charactrizatino




Conductors - material propery (carrier concentraion, band-gap, fermi-level



Self-consistent ensemble Monte Carlo


Commertially available software Sentaurus Device [1]








Device Modeling and Simulation of sub-micron press-fit MOS Transistor





Parts - Conductor (Au?,Al), Insulator (SiO2), Semiconductor (Si, n-Si, p-Si)


Back-End Simulation of Bricks Fabrication


Simulating physical stress, oxidation and dopant diffusion.


Oxidation and Boron Diffussion








Next, stress vs Boron diffusion


Electrical Properties


Deriving electrical properties: Carrier concentration, mobility, conductivity.


IV/CV measurement of press-fit metal-semiconductor junction, p-n junction and MOS capacitor.



(Note: Fabricatin - Deposition and lift-off, Doping - Ion Implant and Annealing)



1 -

2 -






Project (Old Idea)