「$Withionmove」：修訂間差異

於 2019年8月18日 (日) 03:20 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.

 $\frac{\partial M_{i o n}}{\partial t} = \nabla ((q_{s i g n}) e μ M_{i o n} \vec{E} - q D_{M} \nabla M_{i o n})$

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
 $N_{s} w e e p$   $N_{o} u t p u t$ 
 $T_{1, s t o p}$    $d t_{1}$   $T_{2, s t o p}$    $d t_{2}$  ...  $T_{N_{s w e e p}, s t o p}$    $d T_{M_{s w e e p}}$ 
 $N_{i o n s} q_{s i g n, 1} q_{s i g n, 2} q_{s i g n, 3} . . . . q_{s i g n, N_{i o n s}}$ 
 $P_{t y p e, 1} M_{i o n s, 1} μ$  p3 p4 Parameters of the 1 layer
 $P_{t y p e, 2} M_{i o n s, 2} μ$  p3 p4 Parameters of the 2 layer
 $P_{t y p e, 3} M_{i o n s, 3} μ$  p3 p4 Parameters of the 3 layer
 ....
 .....
 $P_{t y p e, N} M_{i o n s, N} μ$  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

 $P_{t y p e, 1}$  is the parameter type:  it depends on ion number  $N_{i o n s}$ 
1:  $M_{i o n s, 1} μ$ ,  $M_{i o n s, 2} μ$ ,........  $M_{i o n s, N_{i o n s}}, μ_{N_{i o n s}}$ 
2:  $M_{i o n s, 1} μ D_{M}$ ,  $M_{i o n s, 2} μ D_{M}$ ,........  $M_{i o n s, N_{i o n s}}, μ_{N_{i o n s}} D_{M}$

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

  $D_{M} = μ k_{B} T / q$

@@ 第8行： / 第8行： @@
   <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> Parameter_{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> Parameter_{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> Parameter_{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
    ....
-  <math> Parameter_{type,N} ~~ M_{ions,N} \mu </math> p3 p4 Parameters of the [[$totalregion]] layer
+  .....
+  <math> P_{type,N} ~~ M_{ions,N} \mu </math> p3 p4 Parameters of the [[$totalregion]] layer
@@ 第26行： / 第27行： @@
 1.0e17 1.0e-11  2.0e17 1.0e-12
-  <math>Parameter_{type,1}</math>:  it depends on ion number <math> N_{ions}</math>
+  <math>P_{type,1}</math> is the parameter type:  it depends on ion number <math> N_{ions}</math>
 : <math> M_{ions,1} ~~~\mu </math>, <math> M_{ions,2} ~~~\mu </math>,........ <math> M_{ions,N_{ions}}, ~~~\mu_{N_{ions}}</math>
 : <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>

「$Withionmove」：修訂間差異

於 2019年8月18日 (日) 03:20 的修訂

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