minority carrier life time? Why is it important for devices' switching speed. Why 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.