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Next: 3.5.2 Carrier Transport and Up: 3.5 Quantum Mechanical Aspects Previous: 3.5 Quantum Mechanical Aspects

3.5.1 Carrier Distribution

As stated, in typically 10-20 nm wide quantum wells the distribution of the energy levels is modified as the geometric width is smaller than the de Broglie wave length. This results in quantized subbands in the channel and leads to the formation of a two-dimensional electron gas. For the carrier concentration in the channel the most obvious difference between the classical three-dimensional and the quantum mechanical two-dimensional gas is the local distribution of the carriers. In the classical case the concentration increases towards the interfaces, while for the quantum mechanical solution the peak of the electron concentration is located in the middle of the channel. However, the mean of the charge density is similar [220], so that the capacitances can be modeled correctly in the classical case.