|
|
| (12 intermediate revisions by the same user not shown) |
| Line 6: |
Line 6: |
|
| |
|
|
| |
|
| =Steady-State= | | =Small-signal analysis= |
| | | *[[Sinusoidal Steady State Analysis]] |
| =Transient=
| |
| | |
| | |
| =Frequency domain=
| |
| ==Sinusoidal Steady State Analysis==
| |
| Consider the symbolic representation of the 3 device equations: Poisson, electron and hole continuity equations.
| |
| | |
| [[File:Dev_eqn.png|200px]] | |
| | |
| The dot term represents the time derivative component of the electron and hole electron continuity equations.
| |
| Sinusoidal Steady State Analysis (S3A) solves the device equation system in the frequency domain as a steady state perturbed by an infinitesimal signal. The small signal assumption allows linearization of the device around the DC bias point. The corresponding Jacobian takes the symbolic form: | |
| | |
| [[File:matrix.png|300px]]
| |
| | |
| which is a 3Nx3N matrix (for 3 solution variables and N nodes). Notice the imaginary frequency dependent components in the electron and hole rows corresponding to the time derivative dot term in the continuity equation.
| |
| The matrix equation now takes a form slightly different to the steady-state form JX=B.
| |
| | |
| [[File:matrix_eqn.png|130px]]
| |
| | |
| where J remains the steady-state Jacobian at the desired DC-bias point, D is now a diagonal matrix with zeros for Poisson rows and ω=2πf for diagonal elements of continuity rows. Both are 3Nx3N matrices. X is solution vector and B is boundary condition vector.
| |
| For computational reasons(i.e. seperating real and imaginary terms), the matrix system takes the following 6Nx6N form
| |
| | |
| [[File:final_matrix_eqn.png|200px]]
| |
| | |
| where XR and XI are real and imaginary components of the solution variables.
| |
| | |
| ====Examples====
| |
| device
| |
| contact name=VSS voltage supply=$bias acreal
| |
| contact name=VSS voltage supply=0.0 acimag
| |
| device freq=100
| |
| | |
| ==== Set the band terms for each material (replace $Mat and <mat> for each) ====
| |
| #set Boltzmann and band diagram relations (ref. Taur)
| |
| solution add name=Ec solve $Mat const val = "(-(DevPsi)-($Chi_<mat>))";#match to variable above, eg. Chi_Si
| |
| solution add name=Ev solve $Mat const val = "(-(DevPsi)-($Chi_<mat>)-(Eg))"
| |
| solution add name=nQFL solve $Mat const val = "(Ec+($Vt)*log((Elec+1.0)/($Nc_<mat>)))";#log is approx
| |
| solution add name=pQFL solve $Mat const val = "(Ev-($Vt)*log((Hole+1.0)/($Nv_<mat>)))";#log is approx
| |