"$1Daddefmas" 修訂間的差異

出自 DDCC TCAD TOOL Manual
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行 10： 行 10：
 
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_{valley}..</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_{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_{valley}~~m_{e,z,2nd valley} ~~ m_{e,x,2nd valley}~~ m_{hh,y,2nd valley}~~ N_{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_{valley}~~m_{e,z,2nd valley} ~~ m_{e,x,2nd valley}~~ m_{hh,y,2nd valley}~~ N_{valley}..</math>
  +
  +
Note: type 2 is under testing.
   
 
z is the calculation direction of 1D program. If there is a QW, z is the confined direction in the 1D program. <math>N_{valley}</math> is the valley number of electrons
  
z is the calculation direction of 1D program. If there is a QW, z is the confined direction in the 1D program. <math>N_{valley}</math> is the valley number of electrons
行 17： 行 19：
 
$1Daddefmas
  
$1Daddefmas
 
1
 
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
−
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
−
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
 
.... to N layers
  
.... 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
+
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 0.3 in the growth direction and 0.1 in the x,y direction with 3 valleys, we set
 
$1Daddefmas
  
$1Daddefmas
 
1
 
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 0.3 0.1 0.1 3
−
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 0.3 0.1 0.1 3
−
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 0.3 0.1 0.1 3
 
.... to N layers
  
.... to N layers
   
行 44： 行 46：
 
<math> m_{2d,dos}^{*} = ( m_{x} m_{y} ) ^{1/2} </math>
  
<math> m_{2d,dos}^{*} = ( m_{x} m_{y} ) ^{1/2} </math>
 
<math> N_{DOS}(E) = \frac{m_{2d,dos}^{*}}{\pi\hbar^{2}}</math>
  
<math> N_{DOS}(E) = \frac{m_{2d,dos}^{*}}{\pi\hbar^{2}}</math>
  +
  +
For structures like Si, it may have some problems when Schrodinger solver is used. Since Si has six valleys with effective masses in different directions (<math>m_{l}=0.98 m_{0}, m_{l}=0.19 m_{0}</math>, if we do not solve the Schrodinger equations, we can simply use m_e =1.08 m0 in the $1Dparameter. Or here, we can set
  +
$1Daddefmas
  +
1
  +
0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 6
  +
  +
For the Schrodinger solver, after quesnum confine effects, we can expect 2 confinement in the electron effective mass, the lower valleys are z valleys with mz=0.98, N=2. We can neglect the high valleys and only 2 valleys are left as ground states. The setting would be
  +
  +
$1Daddefmas
  +
1
  +
0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 2
  +
  +
If we want to use type 2, we can set
  +
  +
$1Daddefmas
  +
2
  +
0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 2 0.19 0.98 0.19 4
  +
  +
Note: type 2 is under testing.

於 2023年2月27日 (一) 15:23 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_{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_{valley}..
 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_{valley}..
... 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_{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_{valley}..
For I_effective_type= 2,  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_{valley}~~m_{e,z,2nd valley} ~~ m_{e,x,2nd valley}~~ m_{hh,y,2nd valley}~~ N_{valley}..

Note: type 2 is under testing. 

z is the calculation direction of 1D program. If there is a QW, z is the confined direction in the 1D program. N_{valley} is the valley number of electrons

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
 1.8 1.8 1.8 0.17 0.17 0.17 0.21 0.2 0.2 1
 1.8 1.8 1.8 0.17 0.17 0.17 0.21 0.2 0.2 1 
 .... 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 0.3 in the growth direction and 0.1 in the x,y direction with 3 valleys, we set 

 $1Daddefmas
 1 
 1.4 0.7 0.9 0.17 0.17 0.17 0.3 0.1 0.1 3
 1.4 0.7 0.9 0.17 0.17 0.17 0.3 0.1 0.1 3
 1.4 0.7 0.9 0.17 0.17 0.17 0.3 0.1 0.1 3 
 .... 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_{dos}^{*} = (N_{valley})^{2/3} ( m_x m_y m_z)^{1/3} 

For the valence band 
   m_{HH, dos}^{*} = ( m_{hh,x} m_{hh,y} m_{hh,z})^{1/3}  
   m_{LH, dos}^{*} = ( m_{lh,x} m_{lh,y} m_{lh,z})^{1/3}  
   m_{p, dos}^{*} = ( m_{hh,dos}^{3/2}+ m_{hh,dos}^{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 } \psi = E \psi

The for the n2d calculation, the density of state effective mass in the 2D structures is 

   m_{2d,dos}^{*} = ( m_{x} m_{y} ) ^{1/2} 
   N_{DOS}(E) = \frac{m_{2d,dos}^{*}}{\pi\hbar^{2}}

For structures like Si, it may have some problems when Schrodinger solver is used. Since Si has six valleys with effective masses in different directions (m_{l}=0.98 m_{0}, m_{l}=0.19 m_{0}, if we do not solve the Schrodinger equations, we can simply use m_e =1.08 m0 in the $1Dparameter. Or here, we can set 

 $1Daddefmas
 1 
 0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 6

For the Schrodinger solver, after quesnum confine effects, we can expect 2 confinement in the electron effective mass, the lower valleys are z valleys with mz=0.98, N=2. We can neglect the high valleys and only 2 valleys are left as ground states. The setting would be 

 $1Daddefmas
 1 
 0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 2

If we want to use type 2, we can set 

 $1Daddefmas
 2 
 0.49 0.49 0.49 0.16 0.16 0.16 0.98 0.19 0.19 2 0.19 0.98 0.19 4

 Note: type 2 is under testing.
取自 "http://yrwu-wk.ee.ntu.edu.tw/mediawiki/index.php?title=$1Daddefmas&oldid=2662"