檢視 $Withionmove 的原始碼

When the system has ion to perform as drift-diffusion equations, we solve the time dependent drift-diffusion for slow ion move simulation. Since the ion moves may not be governed fermi-level concept. We simply treat is a tradiational drift-diffusion equations. 
<br>
 <math> \frac{\partial M_{ion}}{\partial t} = \nabla \left( (q_{sign}) e\mu M_{ion} \vec{E} - q D_{M} \nabla M_{ion} \right)</math>

Ideally, the ion density is given by initial setting. The total ion number should be fixed. The program is aim to model multi-ions drift-diffusion. The command is as following. 
 $Withionmove
 <math> N_sweep </math> <math> N_{output}</math>
 <math>T_{1,stop}</math>  <math>dt_{1}</math> <math>T_{2,stop}</math>  <math>dt_{2}</math> ... <math>T_{N_{sweep},stop}</math>  <math>dT_{M_{sweep}}</math>
 <math> N_{ions} ~~ q_{sign,1} ~~ q_{sign,2} ~~ q_{sign,3}  ....~~ q_{sign,N_{ions}} </math>
 <math> P_{type,1} ~~ M_{ions,1} \mu </math> p3 p4 Parameters of the 1 layer
 <math> P_{type,2} ~~ M_{ions,2} \mu </math> p3 p4 Parameters of the 2 layer
 <math> P_{type,3} ~~ M_{ions,3} \mu </math> p3 p4 Parameters of the 3 layer
  ....
  .....
 <math> P_{type,N} ~~ M_{ions,N} \mu </math> p3 p4 Parameters of the [[$totalregion]] layer


For example: Consider 2 ions, 1st is negative charges, 2nd is positive charges, total 5 Regions we can
 $Withionmove
 1 1000
 1.00  1.0d-4 
 2 -1.0 1.0
 1 0.0e17 0.0      0.0e17 0.0   
 1 1.0e17 1.0e-11  2.0e17 1.0e-12
 1 1.0e17 1.0e-11  2.0e17 1.0e-12
 1 1.0e17 1.0e-11  2.0e17 1.0e-12
 1 1.0e17 1.0e-11  2.0e17 1.0e-12

 <math>P_{type,1}</math> is the parameter type:  it depends on ion number <math> N_{ions}</math>
 1: <math> M_{ions,1} ~~~\mu </math>, <math> M_{ions,2} ~~~\mu </math>,........ <math> M_{ions,N_{ions}}, ~~~\mu_{N_{ions}}</math>
 2: <math> M_{ions,1} ~~~\mu ~ D_{M}</math>, <math> M_{ions,2} ~~~\mu~~D_{M} </math>,........ <math> M_{ions,N_{ions}}, ~~~\mu_{N_{ions}}~~ D_{M}</math>

When type 1 is chosen, we only put mobility <math> \mu </math>, and the diffusion coefficient <math> D_{M} </math> is calculated with Einstein relation, where 
 
  <math> D_{M} = \mu k_{B} T / q</math>