3.9.1 Electron and Hole Density

The electron and hole concentration are respectively given by

$$\begin{array}{ll}\displaystyle n({\bf r},t) \ &\displaystyle... ...style = \ -i\hbar G^{<}({\bf r},t;{\bf r},t) \ , \end{array}$$ (3.77)

$$\begin{array}{ll}\displaystyle p({\bf r},t) \ &\displaystyle... ...style = \ +i\hbar G^{>}({\bf r},t;{\bf r},t) \ . \end{array}$$ (3.78)

Under steady-state condition (see Section 3.8.3) these relations can be written as [60]

$$\begin{array}{l}\displaystyle n({\bf r}) \ \displaystyle = \ -i \int \frac{dE}{2\pi} G^{<}({\bf r},E) \ . \end{array}$$ (3.79)

$$\begin{array}{l}\displaystyle p({\bf r}) \ \displaystyle = \ +i \int \frac{dE}{2\pi} G^{>} ({\bf r},E) \ . \end{array}$$ (3.80)

The total space charge density is given by

$$\begin{array}{l}\displaystyle \varrho({\bf r}) \ = \ q\left(p({\bf r}) - \ n({\bf r}) \right) \ . \end{array}$$ (3.81)

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors