「$adddiffusivedope」：修訂間差異

於 2025年10月19日 (日) 04:34 的修訂

$adddiffusivedope is the command that puts 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  $L_{x}$   $L_{y}$   
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
 $L_{x}$  and  $L_{y}$  is the diffusion length in x and y direction. The unit is  $μ m$

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

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

As shown in the above equation, the difference between 11 and 1 is that the diffusive dopant is additional to the region. For example, in parameters, you already set the doping density to be -1.0e19. If you use 1, Ndope = 2.0e19. Then, the final doping density in this region is 2e19-1e19 = 1.0e19. If you use 11, the doping density becomes 2e19

For 101 and 111, it is applied in impurity. The difference between N_impuriy and N_{d,a} is that N_impuriy is 100% activated.

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

type: Can be 2, 12, 112, 102. with is decay like Gaussian broadening. 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
 $L_{x}$  and  $L_{y}$  is the Gaussian broading width in x and y direction. The unit is  $μ m$

For type = 2, inside regionID
  $x_{l e f t} < x < x_{r i g h t} y_{b o t t o m} < y < y_{t o p} : N_{d, a} = N_{d, a} + N d o p e$ 
 $x < x_{l e f t} : N_{d, a} = N_{d, a} + N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{l e f t} |)^{2})$  
 $x > x_{r i g h t} : N_{d, a} = N_{d, a} + N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{r i g h t} |)^{2})$  
 $y < y_{b o t t o m} : N_{d, a} = N_{d, a} + N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{b o t t o m} |)^{2})$  
 $y > y_{t o p} : N_{d, a} = N_{d, a} + N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{t o p} |)^{2})$

For type = 12, inside regionID
  $x_{l e f t} < x < x_{r i g h t} y_{b o t t o m} < y < y_{t o p} : N_{d, a} = N d o p e$ 
 $x < x_{l e f t} : N_{d, a} = N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{l e f t} |)^{2})$  
 $x > x_{r i g h t} : N_{d, a} = N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{r i g h t} |)^{2})$  
 $y < y_{b o t t o m} : N_{d, a} = N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{b o t t o m} |)^{2})$  
 $y > y_{t o p} : N_{d, a} = N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{t o p} |)^{2})$

As shown in the above equation, the difference between 11 and 1 is that the diffusive dopant is additional to the region. For example, in parameters, you already set the doping density to be -1.0e19. If you use 1, Ndope = 2.0e19. Then, the final doping density in this region is 2e19-1e19 = 1.0e19. If you use 11, the doping density becomes 2e19

For 102 and 112, it is applied in impurity. The difference between N_impuriy and N_{d,a} is that N_impuriy is 100% activated.

For type = 102, inside regionID
  $x_{l e f t} < x < x_{r i g h t} y_{b o t t o m} < y < y_{t o p} : N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e$ 
 $x < x_{l e f t} : N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{l e f t} |)^{2})$  
 $x > x_{r i g h t} : N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{r i g h t} |)^{2})$  
 $y < y_{b o t t o m} : N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{b o t t o m} |)^{2})$  
 $y > y_{t o p} : N_{i m p u r i t y} = N_{i m p u r i t y} + N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{t o p} |)^{2})$ 
For type = 112, inside regionID
  $x_{l e f t} < x < x_{r i g h t} y_{b o t t o m} < y < y_{t o p} : N_{i m p u r i t y} = N d o p e$ 
 $x < x_{l e f t} : N_{i m p u r i t y} = N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{l e f t} |)^{2})$  
 $x > x_{r i g h t} : N_{i m p u r i t y} = N d o p e * e x p (- 0.5 / L_{x}^{2} * (| x - x_{r i g h t} |)^{2})$  
 $y < y_{b o t t o m} : N_{i m p u r i t y} = N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{b o t t o m} |)^{2})$  
 $y > y_{t o p} : N_{i m p u r i t y} = N d o p e * e x p (- 0.5 / L_{y}^{2} * (| y - y_{t o p} |)^{2})$

The $adddiffusivedope setting in GUI interface is here
Press Additional Function, check the box for Functional Dope and fill in these fields as needed!

@@ 第16行： / 第16行： @@
   For type = 1, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :    N_{d,a} =N_{d,a}+ Ndope </math>
-   <math>x < x_{left}    :  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+   <math>x < x_{left}~~~  :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-   <math>x > x_{right}   :  N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
+   <math>x > x_{right}~~  :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
-   <math>y < y_{bottom}  :   N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+   <math>y < y_{bottom}~  :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
-   <math>y > y_{top}     :   N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+   <math>y > y_{top}~~~~  :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
 <br><br>
   For type = 11, inside regionID
   <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :    N_{d,a} = Ndope </math>
-   <math>x < x_{left}    :  N_{d,a} =  Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+   <math>x < x_{left}~~~  :  ~N_{d,a} =  Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-   <math>x > x_{right}   :  N_{d,a} =  Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
+   <math>x > x_{right}~~   :  ~N_{d,a} =  Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
-   <math>y < y_{bottom}  :   N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+   <math>y < y_{bottom}~  :   ~N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
-   <math>y > y_{top}     :   N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+   <math>y > y_{top}~~~~ :   ~N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
   As shown in the above equation, the difference between 11 and 1 is that the diffusive dopant is additional to the region. For example, in parameters, you already set the doping density to be -1.0e19. If you use 1, Ndope = 2.0e19. Then, the final doping density in this region is 2e19-1e19 = 1.0e19. If you use 11, the doping density becomes 2e19
@@ 第34行： / 第34行： @@
   For type = 101, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :   N_{impurity} =N_{impurity}+ Ndope </math>
-  <math>x < x_{left}    :  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+  <math>x < x_{left}~~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-  <math>x > x_{right}   :  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
+  <math>x > x_{right}~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
-  <math>y < y_{bottom}  :  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+  <math>y < y_{bottom}~  :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
-  <math>y > y_{top}     :  N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+  <math>y > y_{top}~~~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
   For type = 111, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :   N_{impurity} = Ndope </math>
-  <math>x < x_{left}    :  N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
+  <math>x < x_{left}~~~ :  ~N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|)) </math>
-  <math>x > x_{right}   :  N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
+  <math>x > x_{right}~~ :  ~N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{right}|)) </math>
-  <math>y < y_{bottom}  :  N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
+  <math>y < y_{bottom}~  :  ~N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|)) </math>
-  <math>y > y_{top}     :  N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
+  <math>y > y_{top}~~~~     :  ~N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{top}|)) </math>
@@ 第54行： / 第54行： @@
   For type = 2, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :  N_{d,a} = N_{d,a}+Ndope </math>
-  <math>x < x_{left}    :  N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
+  <math>x < x_{left}~~~ :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
-  <math>x > x_{right}   :  N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
+  <math>x > x_{right}~~ :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
-  <math>y < y_{bottom}  :  N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
+  <math>y < y_{bottom}~  :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
-  <math>y > y_{top}     :  N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
+  <math>y > y_{top}~~~~ :  ~N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
   For type = 12, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :   N_{d,a} = Ndope </math>
-  <math>x < x_{left}    :  N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
+  <math>x < x_{left}~~~ :  ~N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
-  <math>x > x_{right}   :  N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
+  <math>x > x_{right}~~ :  ~N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
-  <math>y < y_{bottom}  :  N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
+  <math>y < y_{bottom}~  :  ~N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
-  <math>y > y_{top}     :  N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
+  <math>y > y_{top}~~~~ :  ~N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
   As shown in the above equation, the difference between 11 and 1 is that the diffusive dopant is additional to the region. For example, in parameters, you already set the doping density to be -1.0e19. If you use 1, Ndope = 2.0e19. Then, the final doping density in this region is 2e19-1e19 = 1.0e19. If you use 11, the doping density becomes 2e19
@@ 第72行： / 第72行： @@
   For type = 102, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :   N_{impurity} =  N_{impurity} +Ndope </math>
-  <math>x < x_{left}    :  N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
+  <math>x < x_{left}~~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
-  <math>x > x_{right}   :  N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
+  <math>x > x_{right}~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
-  <math>y < y_{bottom}  :  N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
+  <math>y < y_{bottom}~  :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
-  <math>y > y_{top}     :  N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
+  <math>y > y_{top}~~~~ :  ~N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
   For type = 112, inside regionID
    <math>x_{left} < x < x_{right} ~~ y_{bottom} < y < y_{top} :   N_{impurity} = Ndope </math>
-  <math>x < x_{left}    :  N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
+  <math>x < x_{left}~~~ :  ~N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2}) </math>
-  <math>x > x_{right}   :  N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
+  <math>x > x_{right}~~ :  ~N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{right}|)^{2}) </math>
-  <math>y < y_{bottom}  :  N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
+  <math>y < y_{bottom}~  :  ~N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2}) </math>
-  <math>y > y_{top}     :  N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
+  <math>y > y_{top}~~~~ :  ~N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2}) </math>
 <br>'''<big><big>The $adddiffusivedope setting in GUI interface is here</big></big>''' <br>
 Press '''Additional Function''', check the box for '''Functional Dope''' and fill in these fields as needed!<br>
 [[檔案:2D_adddiffusivedope_fig1.jpg|1200px]]

「$adddiffusivedope」：修訂間差異

於 2025年10月19日 (日) 04:34 的修訂

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