「$1Daddefmas」：修訂間差異

於 2023年2月27日 (一) 07:07 的修訂

$1Daddefmas   is the function to add additional effective mass information for electron and holes. In some cases, the electron's (holes) effective mass in different directions are different. Hence the new functions is to put additional information for the program to calculate.

$1Daddefmas
I_effective_type 
 $m_{h h, z} m_{h h, x} m_{h h, y} m_{l h, z} m_{l h, x} m_{l h, y} m_{e, z} m_{e, x} m_{h h, y} N_{e}_{v} a l l e y . .$ 
 $m_{h h, z} m_{h h, x} m_{h h, y} m_{l h, z} m_{l h, x} m_{l h, y} m_{e, z} m_{e, x} m_{h h, y} N_{e}_{v} a l l e y . .$ 
... to N layers

I_effective_type is the input type. The default should be 1. The typical semiconductor material has heavy hole, light hole, and electron effective mass of direct band. The type 1 is used. 
For I_effective_type= 1,  $m_{h h, z} m_{h h, x} m_{h h, y} m_{l h, z} m_{l h, x} m_{l h, y} m_{e, z} m_{e, x} m_{h h, y} N_{e}_{v} a l l e y . .$ 
For I_effective_type= 2,  $m_{h h, z} m_{h h, x} m_{h h, y} m_{l h, z} m_{l h, x} m_{l h, y} m_{e, z} m_{e, x} m_{h h, y} N_{e}_{v} a l l e y m_{e, z, 2 n d v a l l e y} m_{e, x, 2 n d v a l l e y} m_{h h, y, 2 n d v a l l e y} N_{e}_{v} a l l e y 2 . .$

z is the calculation direction of 1D program. If there is a QW, z is the confined direction in the 1D program.

For example, for a material like GaN effective mass for HH is 1.8, LH=0.17, and the electron is 0.21 in the growth direction and 0.2 in the x,y direction. We set

 $1Daddefmas
 1 
 1.8 1.8 1.8 0.17 0.17 0.17 0.21 0.2 0.2
 1.8 1.8 1.8 0.17 0.17 0.17 0.21 0.2 0.2
 1.8 1.8 1.8 0.17 0.17 0.17 0.21 0.2 0.2 
 .... to N layers

For example, for a material effective mass for HH_growth direction is 1.4 in the other two directions are 0.7 and 0.9, LH=0.17, and electron is 0.21 in the growth direction and 0.2 in the x,y direction, we set

 $1Daddefmas
 1 
 1.4 0.7 0.9 0.17 0.17 0.17 0.21 0.2 0.2
 1.4 0.7 0.9 0.17 0.17 0.17 0.21 0.2 0.2
 1.4 0.7 0.9 0.17 0.17 0.17 0.21 0.2 0.2 
 .... to N layers

Actually, the simulation program, it mainly uses the density of state effective mass. The different direction's effective mass will be put together as

For conduction band:
 $m_{d o s}^{*} = (N_{v a l l e y})^{2 / 3} (m_{x} m_{y} m_{z})^{1 / 3}$

For the valence band 
  $m_{H H, d o s}^{*} = (m_{h h, x} m_{h h, y} m_{h h, z})^{1 / 3}$ 
  $m_{L H, d o s}^{*} = (m_{l h, x} m_{l h, y} m_{l h, z})^{1 / 3}$ 
  $m_{p, d o s}^{*} = (m_{h h, d o s}^{3 / 2} + m_{h h, d o s}^{3 / 2})^{2 / 3}$

For the Schrodinger solver, it will use m_z to calculate the quantum confinement effects. The equation will solve

 $- \nabla \frac{1}{m_{z}} \nabla + V ψ = E ψ$

@@ 第3行： / 第3行： @@
   $1Daddefmas
   I_effective_type
-  <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y} ..</math>
+  <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y} N_e_valley..</math>
-  <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y} ..</math>
+  <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y} N_e_valley..</math>
   ... to N layers
   I_effective_type is the input type. The default should be 1. The typical semiconductor material has heavy hole, light hole, and electron effective mass of direct band. The type 1 is used.
-  For I_effective_type= 1, <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y} ..</math>
+  For I_effective_type= 1, <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y}~~ N_e_valley..</math>
-  For I_effective_type= 2, <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y}  ~~m_{e,z,2nd valley} ~~ m_{e,x,2nd valley}~~ m_{hh,y,2nd valley} ..</math>
+  For I_effective_type= 2, <math> m_{hh,z} ~~ m_{hh,x}~~ m_{hh,y}~~m_{lh,z} ~~ m_{lh,x}~~ m_{lh,y} ~~m_{e,z} ~~ m_{e,x}~~ m_{hh,y}~~ N_e_valley~~m_{e,z,2nd valley} ~~ m_{e,x,2nd valley}~~ m_{hh,y,2nd valley}~~ N_e_valley2..</math>
   z is the calculation direction of 1D program. If there is a QW, z is the confined direction in the 1D program.
@@ 第32行： / 第32行： @@
 Actually, the simulation program, it mainly uses the density of state effective mass. The different direction's effective mass will be put together as
   For conduction band:
-  <math>  m_{dos}^{*} = ( m_x m_y m_z)^{1/3} </math>
+  <math>  m_{dos}^{*} = (N_{valley})^{2/3} ( m_x m_y m_z)^{1/3} </math>
   For the valence band
@@ 第38行： / 第38行： @@
    <math>  m_{LH, dos}^{*} = ( m_{lh,x} m_{lh,y} m_{lh,z})^{1/3}  </math>
    <math>  m_{p, dos}^{*} = ( m_{hh,dos}^{3/2}+ m_{hh,dos}^{3/2} ) ^{2/3} </math>
+For the Schrodinger solver, it will use m_z to calculate the quantum confinement effects. The equation will solve
+ <math> {- \nabla \frac{1}{m_{z}} \nabla + V } \psi = E \psi </math>

「$1Daddefmas」：修訂間差異

於 2023年2月27日 (一) 07:07 的修訂

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