"$adddiffusivedope" 修訂間的差異

於 2024年4月28日 (日) 11:49 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  $L_x$   $L_y$   
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  $\mu m$

For type = 1, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d,a} = Ndope$ 
x < x_left    :  $N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
x > x_right   :  $N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
y < y_bottom  :  $N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|))$  
y > y_top     :  $N_{d,a} = N_{d,a}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|))$ 
For type = 11, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d,a} = Ndope$ 
x < x_left    :  $N_{d,a} = Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
x > x_right   :  $N_{d,a} = Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
y < y_bottom  :  $N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|))$  
y > y_top     :  $N_{d,a} = Ndope * exp(-1/L_{y}*(|y-y_{top}|))$

As shown in above equation, the difference between 11 and 1 is that for, the diffusive dopant is additional to the regionID. For example, in parameters, you already set 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_left < x < x_right  y_bottom < y < y_top :   $N_{impurity} = Ndope$ 
x < x_left    :  $N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
x > x_right   :  $N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
y < y_bottom  :  $N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{bottom}|))$  
y > y_top     :  $N_{impurity} = N_{impurity}+ Ndope * exp(-1/L_{y}*(|y-y_{top}|))$ 
For type = 111, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{impurity} = Ndope$ 
x < x_left    :  $N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
x > x_right   :  $N_{impurity} = Ndope * exp(-1/L_{x}*(|x-x_{left}|))$  
y < y_bottom  :  $N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{bottom}|))$  
y > y_top     :  $N_{impurity} = Ndope * exp(-1/L_{y}*(|y-y_{top}|))$

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  $\mu m$

For type = 2, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d,a} = Ndope$ 
x < x_left    :  $N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
x > x_right   :  $N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
y < y_bottom  :  $N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2})$  
y > y_top     :  $N_{d,a} = N_{d,a}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2})$ 
For type = 12, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{d,a} = Ndope$ 
x < x_left    :  $N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
x > x_right   :  $N_{d,a} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
y < y_bottom  :  $N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2})$  
y > y_top     :  $N_{d,a} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2})$

As shown in above equation, the difference between 11 and 1 is that for, the diffusive dopant is additional to the regionID. For example, in parameters, you already set 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_left < x < x_right  y_bottom < y < y_top :   $N_{impurity} = Ndope$ 
x < x_left    :  $N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
x > x_right   :  $N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
y < y_bottom  :  $N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2})$  
y > y_top     :  $N_{impurity} = N_{impurity}+ Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2})$ 
For type = 112, inside regionID
x_left < x < x_right  y_bottom < y < y_top :   $N_{impurity} = Ndope$ 
x < x_left    :  $N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
x > x_right   :  $N_{impurity} = Ndope * exp(-0.5/L_{x}^{2}*(|x-x_{left}|)^{2})$  
y < y_bottom  :  $N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{bottom}|)^{2})$  
y > y_top     :  $N_{impurity} = Ndope * exp(-0.5/L_{y}^{2}*(|y-y_{top}|)^{2})$

"$adddiffusivedope" 修訂間的差異

於 2024年4月28日 (日) 11:49 的修訂

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