6.2 Minority Carrier Lifetime

Consider what happens when an n-type semiconductor is uniformly illuminated with appropriate wavelength light to photogenerate electron-hole pairs（EHPs）. We will now define thermal equilibrium majority and minority carrier concentrations in a extrinsic semiconductor. In general，the subscript “n” or “p” is used to denote the type of semiconductor，and “o”to refer to thermal equilibrium in the dark.

In an n-type semiconductor，electrons are the majority carriersand holes are the minority carriers .

nn0 is defined as the majority carrier concentration（electron concentration in an n-type semiconductor）in thermal equilibrium in the dark. These electrons constituting the majority carriers，are thermally ionized from the donors.

pn0 is defined as the minority carrier concentration（hole concentration in an n-type semiconductor）in thermal equilibrium in the dark.

When we illuminate the semiconductor，we create excess EHPs by photogeneration. Suppose that the electron and hole concentrations at any instant are denoted by nn and pn，which are defined as the instantaneous majority（electron）and minority（hole）concentrations，respectively. At any instant and at any location in the semiconductors，we define the departure from the equilibrium by excess concentrations as follows：

Δnn is the excess electron concentration：Δnn=nn-nn0

Δpn is the excess hole concentration：Δpn=pn-pn0

Fig.6.6 shows a pictorial view of what is happening inside an n-type semiconductor when light is switched on at a certain time and then later switched off again. Obviously when the light is switched off，the condition pn=Δpn（state B in Fig.6.6）must eventually revert back the dark case（state A）where pn=pn0. In other words，the excess minority carriers Δpn and excess majority carriers Δnn must be removed. This removal occurs by recombination. Excess hole recombine with the electrons available and disappear. This，however，takes time because the electrons and holes have to find each other. In order to describe the rate of recombination，we introduce a temporal quantity，denoted by τ and called the minority carrier lifetime（mean recombination time），which is defined as follows：τ is the average time a hole exists from its generation to its recombination，that is，the mean time the hole is free before recombining with an electron. An alternative and equivalent definition is that 1/τ is the average probability per unit time that a hole will recombine with an electron. We must remember that the recombination process occurs through recombination centers，so the recombination time τ will depend on the concentration of these centers and their effectiveness in capturing the minority carriers. Once a minority carrier has been captured by a recombination center，there are many majority carriers available to recombine with it，so τ in an indirect process is independent of the majority carrier concentration. This is the reason for defining the recombination time as a minority carrier lifetime.

Fig.6.6 illumination of an n-type semiconductor results in excess electron and hole concentrations. After the illumination，the recombination process restores equilibrium；the excess electrons and holes simply recombine.

We should note that the recombination time τ depends on the semiconductor material，impurities，crystal defects，temperature，and so forth，and there is no typical value to quote. It can be anywhere from nanoseconds to seconds. Later it will be shown that certain applications require a short τ，as in fast switching of pn junctions，whereas others require a long τ，for example，persistent luminescence.