What is the error in the boltzmann approximation

Reference no: EM131320842

What is the error in the Boltzmann approximation if the crystal size is not infinite but contains 10², 10³, 10⁴, 10⁵, 10⁶, 10⁹ atoms? This is a very real situation in submicron transistors In which an active region has a very small volume and one must choose a smaller differential volume dxdydz In order to give many volume elements in a finite difference analysis of the problem.

For example, in an Si volume of 0.1x1x1μm³=10⁷A³ =10^-17cm³, such as the base of a BIT or channel of a MOST, there are only 10^-17x2x10²²=2x10⁵ Si atoms.

This base or channel layer must be partitioned into 10² or more volume elements in order to accurately calculate the transistor characteristics using numerical techniques. Then, each volume would have only 2000 Si atoms.

Reference no: EM131320842

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