A Further Complication Hole Trapping

Until now, it has been considered that all donors or acceptors, whether intrinsic or extrinsic, are fully ionized. As the temperature is lowered, however, those centers particularly of extrinsic origin tend to trap electrons or holes. Once electronic carriers are fully trapped, the defect-sensitive properties are often altered appreciably, and at low temperatures in particular 7,8]. This trapping effect may be utilized ingeniously when designing the composition of actual material for special functions. 

For example, when considering hole trapping by fixed-valent acceptor impurities (e.g., AVi). when hole trapping is no longer negligible - and hence, the concentration of the trapped holes (e.g., [A ]) is of concern, then one more equilibrium condition can be added to Eqs. (3)-(6). This is the internal equilibrium condition with respect to hole trapping or ionization equilibrium condition of the acceptors. 

The charge neutrality equation, however, remains the same or as Eq. (18), because the trapped holes make the acceptor centers only neutral (A ) in the present case. Otherwise, it would have to be modified to include the acceptors with different effective charges due to hole trapping. 

Two extreme cases may be distinguished. When x T the concentration hierarchy will be such that 

As aoj increases further, the trapped centers come to overwhelm the acceptor impurities, or 

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