「$adddiffusivedope」：修訂間差異

於 2023年4月25日 (二) 15:23 的修訂

$adddiffusivedope is the command to put diffusive dopant distribution in the device. The doping density decay can be either exponential decay or Gaussian distribution. The command is

$adddiffusivedope
N_region
type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top  $L_{x}$  解析失敗 (語法錯誤): {\displaystyle L__y}
  
type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top  $L_{x}$   $L_{y}$   
...
...
Nth_type ....

type: Can be 1, 11, 111, 101. Please see below
regionID:  The region No to use the diffusive doping
Ndope: Na pr Nd  Posive is for n-type, negative is for p-type
 $a l p h a x$  and  $a l p h a y$  is the diffusion length in x and y direction. The unit is  $μ m$

For type = 1, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d, a} = N d o p e$ 
x < x_left    :  $N_{d, a} = N_{d, a} + N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
x > x_right   :  $N_{d, a} = N_{d, a} + N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
y < y_bottom  :  $N_{d, a} = N_{d, a} + N d o p e * e x p (- 1 / L_{y} * (| y - y_{b o t t o m} |))$  
y > y_top     :  $N_{d, a} = N_{d, a} + N d o p e * e x p (- 1 / L_{y} * (| y - y_{t o p} |))$ 
For type = 11, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d, a} = N d o p e$ 
x < x_left    :  $N_{d, a} = N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
x > x_right   :  $N_{d, a} = N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
y < y_bottom  :  $N_{d, a} = N d o p e * e x p (- 1 / L_{y} * (| y - y_{b o t t o m} |))$  
y > y_top     :  $N_{d, a} = N d o p e * e x p (- 1 / L_{y} * (| y - y_{t o p} |))$

For type = 101, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d, a} = N d o p e$ 
x < x_left    :  $N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
x > x_right   :  $N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
y < y_bottom  :  $N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 1 / L_{y} * (| y - y_{b o t t o m} |))$  
y > y_top     :  $N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 1 / L_{y} * (| y - y_{t o p} |))$ 
For type = 111, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d, a} = N d o p e$ 
x < x_left    :  $N_{i m p u r i t y} = N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
x > x_right   :  $N_{i m p u r i t y} = N d o p e * e x p (- 1 / L_{x} * (| x - x_{l e f t} |))$  
y < y_bottom  :  $N_{i m p u r i t y} = N d o p e * e x p (- 1 / L_{y} * (| y - y_{b o t t o m} |))$  
y > y_top     :  $N_{i m p u r i t y} = N d o p e * e x p (- 1 / L_{y} * (| y - y_{t o p} |))$

@@ 第3行： / 第3行： @@
   $adddiffusivedope
   N_region
-  type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top <math>\alpha_x</math> <math>\alpha_y</math>
+  type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top <math>L_x</math> <math>L__y</math>
-  type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top <math>\alpha_x</math> <math>\alpha_y</math>
+  type  regionID Ndope  activation_energy  x_left  y_bottom  x_right y_top <math>L_x</math> <math>L_y</math>
   ...
   ...
   Nth_type ....
-  type: Can be 1, 11, 111, 2, 12, 112. Please see below
+  type: Can be 1, 11, 111, 101. Please see below
   regionID:  The region No to use the diffusive doping
   Ndope: Na pr Nd  Posive is for n-type, negative is for p-type
   <math>alphax</math> and <math>alphay</math> is the diffusion length in x and y direction. The unit is <math>\mu m </math>
-  For type = 1
+  For type = 1, inside regionID
   x_left < x < x_right  y_bottom < y < y_top :  <math>  N_{d,a} = Ndope </math>
-  x < x_left    : <math>  N_{d,a} = Ndope * exp(-\alpha_{x}(|x-x_{left}|)) </math>
+ x < x_left    : <math>  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-  x > x_right   : <math>  N_{d,a} = Ndope * exp(-\alpha_{x}(|x-x_{left}|)) </math>
+ x > x_right   : <math>  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-  y < y_bottom  : <math>  N_{d,a} = Ndope * exp(-\alpha_{y}(|y-y_{bottom}|)) </math>
+ y < y_bottom  : <math>  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
-  y > y_top     : <math>  N_{d,a} = Ndope * exp(-\alpha_{y}(|y-y_{top}|)) </math>
+ y > y_top     : <math>  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+ For type = 11, inside regionID
+ x_left < x < x_right  y_bottom < y < y_top :  <math>  N_{d,a} = Ndope </math>
+  x < x_left    : <math>  N_{d,a} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+  x > x_right   : <math>  N_{d,a} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+  y < y_bottom  : <math>  N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+  y > y_top     : <math>  N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+ For type = 101, inside regionID
+ x_left < x < x_right  y_bottom < y < y_top :  <math>  N_{d,a} = Ndope </math>
+ x < x_left    : <math>  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+ x > x_right   : <math>  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+ y < y_bottom  : <math>  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+ y > y_top     : <math>  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+ For type = 111, inside regionID
+ x_left < x < x_right  y_bottom < y < y_top :  <math>  N_{d,a} = Ndope </math>
+ x < x_left    : <math>  N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+ x > x_right   : <math>  N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+ y < y_bottom  : <math>  N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+ y > y_top     : <math>  N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>

「$adddiffusivedope」：修訂間差異

於 2023年4月25日 (二) 15:23 的修訂

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