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Radiative Recombination Constant B

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: SiLENSe
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: 2023-12-04
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The default value for the radiative recombination constant is kept constant for many years in all versions of SiLENSe. Let me
explain how it works.

From basic physical considerations, the radiation recombination constant is proportional to T^(-3/2). So, it is useful to express
B as
B(T) = B(300K) * (300/T)^(3/2)
However, this works only for 3D carriers. For carriers localized in quantum wells the theory predicts that B ~ 1/T. Besides, there
are some experimental data on temperature dependence of B for InGaN which give neither B ~ T^(-3/2) nor B ~ 1/T. So, we want to
provide end-users to modify the temperature dependence of B.

In version 5.14 and all previous versions, the database includes the value for B at 300 K, and for alloys a linear interpolation
of B over the composition was used. Separately, user can specify a temperature power factor f for B in global physical parameters,
and result for thermal dependence of B was as
B(T) = B(300K) * (T/300)^f
where default value was f=-1.5 .
On the other hand, users might specify B as a user-defined function. In this way, solver first calculated function and then
multiplied the result by (T/300)^f, that was a little it counter-intuitive.

In version 6.3 and next versions, the default setting for B is function, which works exactly as old model
- set values for B(300K) for binary materials
- make linear interpolation for alloys
- multiply by (T/300)^(-3/2)

> Q1. The typical value is "B_300_GaN = 2.4e-11"?

Yes.

> Q2. "B_300_InN = 6.6e-12" is not needed to modify?
> or is there any configuration(In composition or other factors) to be modified?

It depends on what you want to do. I have explained how the function works above.

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