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George Pau

How do I derive the 2D electron density used in nano MOSFET calculations?

In nanomos-2.5, the density of charge is obtained by multiplying the square of the wavefunction by a prefactor: with semiclassical method, that prefactor is given by

  1. 2*(sqrt(mx*my)*m_e*k_B*Temp)/(2*pi1.5*h_bar2)

while in the full ballistic transport, it is given by


Could someone tell me how these two factors are derived or a good reference?

Thank you.


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    Yang Liu

    Hello George,

    To answer your question in brief, you can find the expression for the ballistic quantum model on page 52 of Zhiben Ren’s thesis throught the link below:

    The charge density is calculated with local density of states in the transport direction first and then integrate in the transverse direction by summing up all the transverse modes.

    The 2D charge in the ballistic semi-classical model is calculated by integrating the 2D density of states( sqrt(mx*my)*kT/pi/hbar^2)) times the fermi function, and that is the second expression in your question.

    Hope this helps your understanding.


    Yang Liu

    NCN@Purdue University

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