2,146 research outputs found
An Extra Electrostatic Energy in Semiconductors and its Impact in Nanostructures
This work revisits the classical concept of electric energy and suggests that
the common definition is likely to generate large errors when dealing with
nanostructures. For instance, deriving the electrostatic energy in
semiconductors using the traditional formula fails at giving the correct
electrostatic force between capacitor plates and reveals the existence of an
extra contribution to the standard electrostatic energy. This additional energy
is found to proceed from the generation of space charge regions which are
predicted when combining electrostatics laws with semiconductor statistics,
such as for accumulation and inversion layers. On the contrary, no such energy
exists when relying on electrostatics only, as for instance when adopting the
so-called full depletion approximation. The same holds for charged or neutral
insulators that are still consistent with the customary definition, but which
are in fact singular cases. In semiconductors, this additional free energy can
largely exceed the energy gained by the dipoles, thus becoming the dominant
term. Consequently, erroneous electrostatic forces in nanostructure systems
such as for MEMS and NEMS as well as incorrect energy calculations are expected
using the standard definition. This unexpected result clearly asks for a
generalization of electrostatic energy in matter in order to reconcile basic
concepts and to prevent flawed force evaluation in nanostructures with
electrical charges.Comment: 24 pages 8 figure
Assessing student reasoning in upper-division electricity and magnetism at Oregon State University
Standardized assessment tests that allow researchers to compare the
performance of students under various curricula are highly desirable. There are
several research-based conceptual tests that serve as instruments to assess and
identify students' difficulties in lower-division courses. At the
upper-division level, however, assessing students' difficulties is a more
challenging task. Although several research groups are currently working on
such tests, their reliability and validity are still under investigation. We
analyze the results of the Colorado Upper-Division Electrostatics diagnostic
from Oregon State University and compare it with data from University of
Colorado. In particular, we show potential shortcomings in the Oregon State
University curriculum regarding separation of variables and boundary
conditions, as well as uncover weaknesses of the rubric to the free response
version of the diagnostic. We also demonstrate that the diagnostic can be used
to obtain information about student learning during a gap in instruction. Our
work complements and extends the previous findings from the University of
Colorado by highlighting important differences in student learning that may be
related to the curriculum, illuminating difficulties with the rubric for
certain problems and verifying decay in post-test results over time.Comment: 11 pages, 12 figure
- …