Basic doubt about BETA of bipolar transistors (BJT)

Good morning,

Please, I have a basic question about BJT operation:

Consider a device Q1 (BJT), with base and collector terminals connected together, with a bias current: I_bias. This device has BETA (common-emitter current gain) equal to X.

Now, consider a second device Q2, another BJT that also has the base and collector terminals connected together, with the same bias current I_bias. However, Q2 has an emitter area 8 times larger than device Q1. In other words, there are 8 devices Q1 connected in parallel.

What is beta of transistor Q2?

I know that BETA of bipolar transistor is defined by 1/(Dp/DN)*(NA/Nd)*(W*Lp) + 0.5*(W^2/Dn*taub).

As the effective width of the base terminal does not change, I supposed that the BETA does not change too. But I`m not sure. Could somebody help me?

Where:
Dp: hole diffusivity in the emitter,
Dn: electron diffusivity in the base,
Lp: hole diffusion length in the emitter,
ND: doping concentration of the emitter,
NA: doping concentration of the base,
W: effective width of the base,
Tau: minority-carrier lifetime,

Thank you very much,
Best Regards,

Palmeiras,

At equal emitter current density the two assemblies will have
equal gain (mismatch aside). However all BJTs exhibit
a collector current dependence (beta vs Ic is a popular
chart, for good reason).

I wouldn't spend much time on the equations / definitions
as you show them. They don't appear to include either
low current or high current nonidealities, which are what you
most need to respect / avoid.