previous up next Dissertation Enzo Ungersboeck contents
 Previous: Intervalley Scattering   Up: 5.3 The Monte Carlo Method   Next: Acoustic Intravalley Scattering

5.3.2 Scattering Mechanisms in the 2DEG

In analogy with the 3D case, the scattering rates for electrons residing in subband $ n$ of valley $ v$ are obtained from an integration over all possible two-dimensional $ \mathitbf{k'}$ states after scattering

$\displaystyle S_{n}^v({\ensuremath{\mathitbf{k}}}) = \frac{A}{4\pi^2} \int_{\ma...
...'} S_{n',n}^{v',v}({\ensuremath{\mathitbf{k'}}},{\ensuremath{\mathitbf{k}}})\ .$ (5.22)

Here, $ A$ denotes the area, and a summation over all subbands $ n'$ and valleys $ v'$ after scattering is performed. The density of states per spin for the 2DEG is obtained as

$\displaystyle g_{n}\left(E\right)=\frac{1}{(2\pi)^{2}}\int\delta[E-E_{n}({\ensuremath{\mathitbf{k}}})]\,\mathrm{d}^2k\ .$ (5.23)

As in the three dimensional case the energy subband dispersion $ E_{n}^v({\ensuremath{\mathitbf{k}}})$ of subband $ n$ in a valley $ v$ can be approximated close to its minimum using a nonparabolic relation [Ando82,Laux88]

$\displaystyle E(1 + \alpha_n^v E) = \frac{\hbar^2}{2}\left ( \frac{k_1^2}{m_{\shortparallel,1}^v} + \frac{k_2^2}{m_{\shortparallel,2}^v}\right )\ ,$ (5.24)

where $ E=E_{n}^v({\ensuremath{\mathitbf{k}}}) - E_{n,0}^v$ denotes the energy with respect to the subband minimum $ E_{n,0}^v$, and $ \alpha_n^v$ is the nonparabolicity coefficient. The integration over the energy in (5.23) can be performed analytically yielding

$\displaystyle g_{n}^v\left(E\right) = \frac{\{m_\mathrm{dos}\}_n^v}{2\pi \hbar^2} (1+2\alpha_n^v E) \Theta[E]\ ,$ (5.25)

for the density of states of the subband $ n$ of valley $ v$. Here, $ \Theta$ denotes the Heaviside step function, and $ \{m_\mathrm{dos}\}^v =
\sqrt{m_{\shortparallel,1}^v m_{\shortparallel,2}^v}$ is the density of states mass. In Si the subband dispersion is frequently assumed to be independent of the subband index $ n$ [Jungemann93,Fischetti02,Roldan96]. The masses $ m_{\shortparallel,1}^v$ and $ m_{\shortparallel,2}^v$ for three substrate orientations of Si are listed in Table 4.1.

The bulk phonon scattering model for the six valleys along $ \Delta $ has been adapted for the 2DEG following the treatment of Price [Price81]. The well accepted model for the bulk phonon spectrum of Jacoboni [Jacoboni83] can be used for the Si inversion layer.


Subsections


previous up next   contents
 Previous: Intervalley Scattering   Up: 5.3 The Monte Carlo Method   Next: Acoustic Intravalley Scattering
E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology