3.9.1 Electron and Hole Density

The electron and hole concentration are respectively given by

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

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

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

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

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

The total space charge density is given by

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

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