I am trying to get my head around why would a silicon engineer care about the minority life time carrier and how does the minority carrier affect the switching speed of PN junction. Why is it so much about minority life time and not majority carriers?
Considering a diode in series with a resistance R connected to a voltage source \$V_i\$.
Once the diode is turned on and has reached a steady state condition, the forward current is \$I_f = V_i/R\$. Now the input voltage is suddenly reversed. In particular the current applied to the diode is suddenly reversed to \$I_r\$. You will note that although the applied current reverses at the same time as the input voltage \$V_i\$, the diode voltage does not. This occurs because the minority carriers that were established in the junction region with \$I_f\$ must first be swept out (recombined with opposite polarity charge), much as one would first have to discharge a capacitor to zero charge and voltage before one could recharge it with the opposite polarity.
This effect gives rise to the storage delay time \$t_s\$ (see: Revere recovery time). The storage time occurs whenever a diode is switched from forward conduction to reverse bias, and is a consequence of the storage of excess minority carriers in the neutral regions of the diode. The storage delay time can be reduced by removing the stored carriers faster, which is effected either by reducing the lifetime τ or by increasing the reverse current \$I_r\$.
The rise-time/fall-time of the switching increases with storage time \$t_s\$, which depends on τ. Or the switching speed depends on minority carrier life time. And that is why minority carrier life time is important in switching applications.
See the article, Recombination time in semiconductor diodes also.
When a diode is reverse-biased, there is a "neutral" layer around the PN junction, due to the diffusion of electrons from the N-doped side into holes on the P-doped side (which can also be regarded as holes diffusing into the N side). Electrons from the N side become minority carriers on the P side, and holes from the P side are minority carriers on the N side.
The neutral region is key to reverse bias because it "looks" like an undoped crystal: a nonconductor rather than a semiconductor: it has no excess electrons or holes, making movement of charge difficult.
When you switch a diode from forward to reverse bias, it has to return to this state before it actually stops conducting.
The lifetime of a minority carrier is the average time that it can spend in the opposite-doped crystal before combining: how long an electron can "bounce around" in a P doped semiconductor before falling into a hole, or how long a hole can persist in an N doped semiconductor before being filled with an extra electron.
The longer this time the longer it takes to form the neutral region of the reverse bias, because while the minority carriers are still bouncing around, they carry current.
This is why minority carriers are important: they are the "oposite type" carriers on the opposite side of the junction that create the "virtually undoped" section that looks like a nonconductive piece of silicon, once they recombine with a majority carrier.
The majority carriers don't matter because they are passive: they are considered to just "sit there" in the lattice waiting for the minority carrier.
Why minority carriers have a lifetime is that the lattice is not fully doped. Only some small fraction of the atoms have a hole, or surplus electron. So consider a hole moving around in N-doped crystal. While it bounces around inside silicon atoms that have a complete valence shell, it cannot settle down. A hole on one of these atoms is a high energy, unstable state. The hole has to find an arsenic atom that has a surplus electron to create that stable shell of eight. Finding that atom isn't instantaneous; it takes time. Similarly, an extra electron has to find a hole to "fall into": a Gallium atom.