... devices^2.1

In semiconductor devices the characteristic dimensions are much smaller than the wavelength $\lambda$ associated with the operating frequency $f$ by $\lambda = c / f$, where c is the velocity of propagation in the semiconductor defined by $c = c_0 / \sqrt{\varepsilon_r \, \mu_r}$. $c_0$ is the speed of light in vacuum, $\varepsilon_r$ and $\mu_r$ are the relative permittivity and permeability, respectively, and have values of $\varepsilon_r = 11.9$ [5, p.849] and $\mu_r = 1$ for silicon. Thus for a frequency of $f = 100 \, \mathrm{GHz}$ the wavelength evaluates to $\lambda = 877 \, \mu \mathrm{m}$ which is much bigger that the typical device dimension of semiconductor devices which is in the order of $1 \, \mu \mathrm{m}$ [6, p.14] [7, p.110].

... conduction^2.2

In the literature this current is sometimes referred to as convection current [9, p.31] in analogy to thermodynamics since the current is caused by moving particles. On the other hand the transport happens in a solid medium which in thermodynamics is only capable to conduct the (heat) current. However the important point in this context is to distinguish between the current caused by moving carriers (which will in this text be called conduction current) and the current caused by a time variation of the electric displacement vector $\ensuremath{\boldsymbol{\mathrm{D}}}$ which is uniformly called displacement current. The displacement current appears as $\ensuremath{\partial_{t} \, \ensuremath{\boldsymbol{\mathrm{D}}}}$ in eqn. (2.3).

... semiconductors^2.3

Strictly speaking the conductivity $\sigma$ is a scalar only in isotropic materials. Semiconductors are due to their crystal structure in principle anisotropic. However, due to symmetry properties, especially in the case of Germanium and Silicon, the anisotropicity of the conductivity is very small and can be neglected in many cases.

...-space^2.4

Physically correct would be to integrate over the first BRILLOUIN zone (sometimes also termed WIGNER-SEITZ cell). However, since the effective mass of an electron is assumed to be constant in this text, and since the decay of the distribution function is of exponential order, the error is negligible.

... mass^2.5

In literature the effective mass is often denoted by $m^*$. For a clearer notation in combination with powers of $m^*$ this text will use just $m$.

... assumed^2.6

A first order approximation for a non-parabolic energy band can be written as $\mathcal{E}\, (1 + \alpha \, \mathcal{E}) = \hbar^2 \, k^2 / (2 \, m)$ with $\alpha$ being the non-parabolicity correction factor [19]. However, inclusion of non-parabolic effects considerably complicates the formulation of adequate transport equations since no closed form solutions exist even for this simple first order approximation.

... isotropic^2.7

The assumption of an isotropic distribution function can be justified due to the strong scattering of the carriers inside the semiconductor. Nevertheless, as will be seen in Chapter 5, this assumption is worth a detailed investigation as it can lead to erroneous results.

... kinetic^2.8

In literature this term is also called convective term [22, p.157] [23, p.232]. As the expression convection is already quite mixed up in conjunction with the current density (see footnote on page ), the expression kinetic will be used here.

... model^2.9

Nomenclature in literature again is ambiguous. Sometimes the model presented in this text under the term energy transport model, which neglects the term in the current relation, which is nonlinear in $\ensuremath{\boldsymbol{\mathrm{J}}}$, is also called hydrodynamic model, sometimes it is referred to as energy balance model. However, the important point is to distinguish between including and neglecting the term nonlinear in $\ensuremath{\boldsymbol{\mathrm{J}}}$.

... mobility^2.10

Various different models have been developed. Examples can be found for instance in [32] [33] [34].

...#tex2html_wrap_inline26003#
^2.11

Note: The implementation in MINIMOS-NT uses $\Theta$ instead of $\beta$

... holds^2.12

In the time variant case a conservation equation for the trapped charge has to be added to the transport model $\ensuremath{\partial_{t} \, n_t} = (R_n - G_n) - (R_p - G_p)$.

... term^2.13

For example comparing the RHS of eqn. (2.76) with the first term of the corresponding SRH contribution yields

$$\frac{\mbox{LHS}}{m} = - \Bigl( \frac{1}{\tau_m} + \frac{1 - f_t}... ... \Bigr) \, \ensuremath{\langle \ensuremath{\boldsymbol{\mathrm{v}}} \rangle}\ ,$$

where the term containing $\tau_n$ can be neglected since the lifetime is much larger than the momentum relaxation time, $\tau_n \gg \tau_m$.

...D0068^3.1

Due to the early date of this article (1953) it is especially entertaining to read. Beside proposing the box integration method the author also shows its application using electrical circuits with "physically realizable" electrical resistors to solve a system of partial differential equations.

...VORONOI^3.2

Control volume and WIGNER-SEITZ cell are also common terms used in literature.

... criterion^3.3

An entertaining Java applet where a DELAUNAY triangulation and its VORONOI diagram together with the circumcircles can be drawn manually is found at http://www.cs.cornell.edu/Info/People/chew/Delaunay.html. The vertices of the VORONOI region associated with each node can be regarded as the circumcenters of the triangle formed by the nodes.

... density^3.4

Such a rectangle-hierarchy is sometimes termed quad-tree

... measurements^4.1

In [56] the authors report on a slight decrease of the drain current for a p-MOSFET. However, it seems that this decrease occurs due to self-heating since it vanishes if the drain voltage is swept faster. Anyway, even if such an effect can occur in a real SOI device, the energy transport model tends to overestimate the effect considerably.