$RandomizedR

$RandomizedR is a special command to setup the random alloy structures. The format is

$RandomizedR
Region_Number_used Random_type location_N_used seeding_num
location_1 location_2 ...... location_N
Region_1 method P1 P2 P3 P4 P5  .... 
Region_2 method P1 P2 P3 P4 P5 P6 P7  .... 
...
Region_N method  P1 P2 P3 P4 P5  .... 

Random_type is not used at this moment
Method=0 Don't use it
Method=1 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$  
Method=2 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$  
Method=3 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ 

If method ==11 12 13, the format would be

$RandomizedR
Region_Number_used Random_type location_N_used seeding_num
location_1 location_2 ...... location_N
Region_1 method P1=Region_ini  P2=Region_fin P3 P4 P5 P6 P7  .... 
Region_2 method P1=Region_ini  P2=Region_fin P3 P4 P5 P6 P7  .... 
...
Region_N method P1=Region_ini  P2=Region_fin P3 P4 P5 P6 P7  .... 

Method=11 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ 
Method=12 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ 
Method=13 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ 

The difference between (1,2,3) and (11,12,13) is that 11-13 allows us to choose the virtual region range.  
Method=0 fully random number
Method=1 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method=2 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method=3 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method=11 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method=12 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method=13 region_start region_end ${\delta }_r$(um) $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ R1-R6(useless) 
Method 1 or (11): Use all coefficients in the virtual regions.
Method 2 or (12): Use the original trap-related coefficients, nonradiative lifetime, doping, impurity, and generation rate in the original region
Method 3 or (13): Use the original polarization, trap-related coefficients, nonradiative lifetime, doping, impurity, and generation in the original region

The idea is to generate virtual regions. The region number is "location_N_used" 
The second line defines the ID of virtual regions (location_N_used). For example location_N_used=10
13 14 15 16 17 18 19 20 21 22 23    means these regions are virtual regions
P1 is the lattice size. Typically 2.83e-4 um. 
P2=average_com of this QW. For example, 0.15 is 15% average indium composition
P3=sigma  -> broaden factor of averaging local indium composition. Typically, 2-4 lattice size. Unit is um. 
P4=indium_low  define indium composition of virtual region 1. 
P5=delta-In%   defines the composition difference of each virtual region. It should be linear.

Note that no matter which method is used, the mobility, B, and C will use the original region setting.

Example:

$RandomizedR
7 1 20 -10       #total 20 regions as virtual region
13 14 15 16 17 18 19 20 21 22 23 .... 32     # The region id of 20 virtual region 
3 0                                       （QW location)
4 0
7  1  2.83e-4  0.15  9.8e-4 0.01 0.02
8  2  2.83e-4  0.15  9.8e-4 0.01 0.02         # use the original lifetime, doping, , impurity, traps, and generation of the original region.
9  3  2.83e-4  0.15  9.8e-4 0.01 0.02         # use the original polarization, lifetime, doping, , impurity, traps, and generation of the original region.
10 11  1  10   2.83e-4  0.15  9.8e-4 0.01 0.02   # use virtual region 1-10 as 1% to 19%  if composition smaller than 1%, it would be 1%. If > 19% it would be 19%
12 11  11 20   2.83e-4  0.40  9.8e-4 0.21 0.02    # use virtual region 11-20 as 21% to 39%  if composition smaller than 21%, it would be 21%. If > 39% it would be 39%

Note that random alloy fluctuations will generate random atoms inside the region. It assumes that the atomic composition is zero outside the region and uses a Gaussian weighting method to determine the composition. It may not be enough for condtion that the barrier is not 0% composition. Even for AlGaN barrier condition, it might be with higher composition. To solve this problem. We expand the command set to be

Method 301, 302, and 303 and Method 311, 312, and 313.

 Method=301 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ $com{p}_{top}$ $com{p}_{bottom}$ $com{p}_{left}$ $com{p}_{right}$ 
 Method=302 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$  $com{p}_{top}$ $com{p}_{bottom}$ $com{p}_{left}$ $com{p}_{right}$ 
 Method=303 ${\delta }_r$ $com{p}_{ave}$ $\sigma$ $com{p}_{min}$ ${\delta }_{comp}$ $com{p}_{top}$ $com{p}_{bottom}$ $com{p}_{left}$ $com{p}_{right}$

The definition of 301 is the same as 1. 302 is equal to 2, and 303 is equal to 3. But there are 4 additional parameters defining the neighboring compositions. They are, sequentially, top, bottom, left, and right. By the same way, 311 = 11, 312=12, and 313=13.