"$Withionmove" 修訂間的差異

於 2023年10月1日 (日) 11:34 的修訂

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.

 $\frac{\partial M_{ion}}{\partial t} = \nabla \left( (q_{sign}) e\mu M_{ion} \vec{E} - q D_{M} \nabla M_{ion} \right)$

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
 $N_{sweep}$   $N_{output}$ 
Sweep_type_1   $T_{1,stop}$    $dt_{1}$  P1 P2 P3 P4 P5 ...
Sweep_type_1   $T_{2,stop}$    $dt_{2}$  P1 P2 P3 P4 P5 .. 
 ... 
 ...
Sweep_type_N_{sweep   $T_{N_{sweep},stop}$    $dT_{M_{sweep}}$   P1 P2 P3 P4 P5 ..
 $N_{ions} ~~ q_{sign,1} ~~ q_{sign,2} ~~ q_{sign,3} ....~~ q_{sign,N_{ions}}$ 
 $P_{type,1} ~~ M_{ions,1}~~ \mu$  p3 p4 Parameters of the 1 layer
 $P_{type,2} ~~ M_{ions,2}~~ \mu$  p3 p4 Parameters of the 2 layer
 $P_{type,3} ~~ M_{ions,3}~~ \mu$  p3 p4 Parameters of the 3 layer
 ....
 .....
 $P_{type,N} ~~ M_{ions,N} \mu$  p3 p4 Parameters of the $totalregion layer

 $N_{sweep}$ : The number of runs for the time step
 $N_{output}$ : The number of output results for each run
Sweep_type:
1: constant voltage, P1 to P5 is not used
2: Sweep Vg during this time period P1=Vgstart, P2=Vgend, P3=swdt of each step  (step Number=   $T_{1,stop}/swdt$ 
3: Sweep Vd during this time period P1=Vdstart, P2=Vdend, P3=swdt of each step 
4,5,6.... leave for future use
 $T_{1,stop}$  : The time for the first run.  $T_{2,stop}$ The time for the 2nd run. 
 $dt_{1}$  is the  $\delta t$  for each sweep. 
 $N_{ions}$  How many ions are considered. If we only want to consider 1 negative ion,we can put 1
 $q_{sign}$  The sign of ions. only accept  $\pm 1.0$

For example: Consider 2 ions, 1st is negative charges, 2nd is positive charges, total 5 Regions we can

$Withionmove
3 1000
1 1.00  1.0d-4 
3 1.00  1.0d-4 0.0 1.0 0.02  
1 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

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

When type 1 is chosen, we only put mobility $\mu$ , and the diffusion coefficient $D_{M}$ is calculated with Einstein relation, where

  $D_{M} = \mu k_{B} T / q$

See related commands

Related commands: $Withionmove $IonMovewithPoisson *.time_ion

@@ 行 12： / 行 12： @@
  Sweep_type_N_{sweep  <math>T_{N_{sweep},stop}</math>  <math>dT_{M_{sweep}}</math>  P1 P2 P3 P4 P5 ..
  <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,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,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,3} ~~ M_{ions,3}~~  \mu </math> p3 p4 Parameters of the 3 layer
   ....
   .....

"$Withionmove" 修訂間的差異

於 2023年10月1日 (日) 11:34 的修訂

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