Mathematical Analysis

For a deep level state which is already occupied by an electron, there are two competing possibilities (processes). What are they ? The answer.

For a vacant deep state (unoccupied state), there are also two competing processes. What are they ? The answer.

Considering the two competing processes in each case, a given deep level state can be defined as an electron trap, a hole trap, a recombination center, or a generation center. These four names are related to the relative magnitude of the two competing processes (capture or emission) for the two possible states (occupied or vacant).

• electron trap: A normally empty deep state captures a CB electron (electron capture, cn) rather than the VB electron (hole emission, ep) => cn >> ep. Once occupied, it emits the captured electron into CB (en), not into VB (cp) => en >> cp.
• hole trap: A normally occupied deep state gives the electron to the VB (hole capture, cp), not to the CB (electron emission, en) => cp >> en.The vacated state gets an electron from the VB (hole emission, ep), not from the CB (electron capture, cn) => ep >> cn.
• recombination center: An empty deep state receives an electron from the CB (electron capture, cn) => cn >> ep. The captured electron falls into a VB state (hole capture, cp) => cp >> en.
• generation center: An empty deep state receives an electron from the VB by a thermal excitation (hole emission, ep) => ep >> cn.  This electron is thermally excited into the CB (electron emission, en) => en >> cp.

In summary, a given deep state is called as one of the following four types [C.T.Sah, Proc. IEEE 55, 654 (1967)]:

• electron trap, if cn >> ep and en >> cp.
• hole trap, if cp >> en and ep >> cn.
• recombination center, if cn >> ep and cp >> en.
• generation center, if ep >> cn and en >> cp.

An extended discussion follows on the emission and capture processes. The emission rates (en, ep) and capture rates (cn, cp) are defined as the probability per unit time, in units of [sec-1]. For example, a en = 0.1 sec-1 means that one out of 10 occupied deep states will emit the electron into CB within the next one second of time.

The emission processes are thermally excited. Therefore, the emission rates are

en ~ exp[ -(Ec - Et)/kT ], and

ep ~ exp[ -(Et - Ev)/kT ].

The capture of a mobile carrier occurs if this charge carrier comes within a certain physical interaction range of the deep level center.

cn = sn vn n, and

cp = sn vp p.

Where the sn and sp are the capture cross sections in units of [cm2] and vn and vp are the thermal velocities of carriers, obtainable from 1/2 m* vn2 = 3/2 kT. As was pointed out int the Introduction part, the magnitude of the capture cross-sections depend critically on the equilibrium charge state of the deep level center and the majority carrier type of the semiconductor.

Now because the name of the deep level center is determined by a relative size of capture and emission rates, the property depends on the charge state, deep level position, etc.

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