Collaborator: K. Gärtner
Cooperation with: R. Richter (Halbleiterlabor (Semiconductor Laboratory),
Max-Planck-Institut für Physik, München, und Max-Planck-Institut
für extra-terrestrische Physik, Garching)
The main goal is the development of improved algorithms for the numerical solution
of degenerate systems of elliptic and parabolic partial differential equations
based on discretizations, fulfilling qualitative stability properties, known
from the analytic equations, too.
The semiconductor device equations
can be seen as an example out of a much
larger class of problems, but they are well understood in many respects,
sufficiently hard to solve and of practical interest--hence a good candidate
to deal with.
The interest starts with grid generation, includes properties of the equations
and their discretization, effective algorithms for the solution, and ends with
solving some selected real-world problems.
The present status of the work is roughly characterized by:
The present results are:
- A basic level of the models (for recombination, transport phenomena, etc.);
- A general geometry and boundary descriptions using tetrahedral
- Three different Newton methods based on different decoupling techniques together
with the use of iterative and direct simulation methods (PARDISO,
see page ) to solve the stationary
equations and to compare their efficiency and robustness;
- The use (expansion) of 2D numerically given doping profiles is possible
To illustrate the status from the application point of view, a summary
of the device function is given: the DEPFET combines detection and
amplification within one device, .
A p-channel MOSFET or JFET (junction field effect transistor, contacts SOURCE,
GATE, DRAIN) is integrated onto a silicon detector substrate,
which becomes fully depleted by the application of a sufficiently high
to a backside p+ contact (BACK). By means of sideward depletion, a potential
minimum is formed which is shifted
directly underneath the transistor channel at a depth of about 1 m
below the GATE contact.
Incident photons and particles generate electron-hole pairs within the
fully depleted bulk.
While the holes drift into the back contact, electrons are accumulated
in the potential minimum, called the
internal gate. The resulting change of the JFET current is a measure of
the collected amount of charge and the deposited energy, respectively.
- A 3D prototype code (SMP parallel in the essential parts, using a completely
weak formulation of the finite volume discretization) for discussing and
investigating some issues of interest in the more general pdelib2
(see page ) design,
including basic algorithms;
- The transfer of specific algorithms to
- And some contribution by ``insight'' into computed potential and density
distributions to the design of a DEPFET sensor at the Semiconductor
Laboratory in Munich.
The readout of the device is non-destructive and can be repeated several
times. For removing signal electrons
and thermally generated charges from the internal gate, a clear structure
is integrated into the device (contacts CLEAR and CLEAR-GATE). The efficiency
of the clear process determines the readout noise essentially.
Understanding this process is the point where 3D device simulations enter.
Due to the very low input capacitance the inherent noise
during amplification becomes very low. Equivalent noise charges
of about two electrons were measured at room temperature on recently
DEPFET detectors can be applied for XRAY spectroscopy, e.g., in space or
biomedical experiments (, )
as well as for particle detection, for instance, in vertex detectors
The pictures (generated by
show the electron and hole
density (log10) in a section of a sensor element.
The grid is highly anisotropic and has a resolution of
order 10 nm close to the contacts. The computational domain of
18x28x50 m3 size is discretized by 156000 nodes. The numerical challenges
are introduced by the floating regions and the very small recombination,
resulting in density variations of 25 orders of magnitude.
The I-V curves show some properties of the detector for different
boundary and doping conditions. The device performance depends strongly on
doping concentration, geometric parameters, and boundary conditions.
Numerical challenges for the future are, for instance, faster algorithms to allow
higher resolution and time-dependent computations on better grids
(TetGen, see page ).
Investigations of the interaction of two or more pixel sensor elements may
be another task introducing a new level of complexity.
- J. KEMMER, G. LUTZ,
New semiconductor detector concepts,
Nucl. Instr. & Meth., A253 (1987), pp. 365-377.
- G. LUTZ, R.H. RICHTER, L. STRÜDER,
New novel pixel detectors for X-ray astronomy and other applications,
Nucl. Instr. & Meth., A461 (2001), pp. 393-404.
- W. NEESER ET AL.,
The DEPFET pixel BIOSCOPE,
IEEE Trans. Nucl. Sci., 47 (2000), pp. 1246-1250.
- R.H. RICHTER ET AL.,
Design and technology of DEPFET pixel sensors for linear collider
Nucl. Instr. & Meth., A511 (2003), pp. 250-256.
I-V curves (top),
log10 of the electron (middle) and hole densities (bottom) at
the top and a
vertical cut (cut at
y = 14 m, grey relief) of the detector.
(The contact areas on top of the device can be identified by the following
codes (e, h: color), where e denotes the electron density and h the holes
density pictures above: CLEAR (e: red),
CLEAR-GATE (e, h: light blue),
DRAIN (in the cut of region),
GATE (h: orange),
SOURCE (h: red),
floating region (h: yellow).)
LaTeX typesetting by I. Bremer