ISSN 10637397, Russian Microelectronics, 2012, Vol. 41, No. 4, pp. 278–284. © Pleiades Publishing, Ltd., 2012.
Original Russian Text © A.S. Puzanov, S.V. Obolensky, 2012, published in Mikroelektronika, 2012, Vol. 41, No. 4, pp. 304–312.
As microelectronics progresses to ever smaller
device dimensions, engineers are faced with the issue
of strong and highly nonuniform electric fields arising
in active regions. When the electric field varies on a
length scale shorter than the energy relaxation length
of the electron–hole gas (100–300 nm), the energy of
an electron or a hole at a point cannot be considered a
function of the electric field at the point . In fact,
the same is true of other properties of the electron–
hole gas, such as mean velocity, mean energy, and dif
fusion coefficient . A need thus arises for mathe
matical models that would allow for a nonlocal char
acter of the relationship between the behavior of an
electron–hole gas and the variation of an electric field
to which it is exposed.
An excellent example of a nonlocal relationship
between the electricfield strength
and the mean
is provided by avalanche multi
plication in silicon
junctions with a depletion
layer so thin that electrons mostly cross its highfield
region before they can reach an energy level high
enough to cause impact ionization .
The problem of carrier transport in high electric
fields subject to impact ionization was solved in a
quasihydrodynamic approximation by Maiorov et al.
. To this end, they deduced the impactionization
from a measured function
and an analytical relation
obtained for a uniform
However, the quasihydrodynamic approximation
does not allow one to derive basic equations rigorously
without assuming the Maxwellian electron energy dis
tribution, which implies a fixed number of particles
. This assumption appears to be among the major
factors that reduce the accuracy of the quasihydrody
namic treatment . Monte Carlo simulation may
therefore represent a viable alternative.
When a semiconductor crystal is exposed to high
energy photons, fast electrons are generated by photo
ionization, Compton scattering, and electron–
positron production. As they lose their kinetic energy
in traveling through the crystal, the electrons produce
collective plasma oscillations known as bulk plasmons
[7–9]. These decay to form electron–hole pairs with
an energy greatly different from an equilibrium value,
leading to distortion of the carrier energy distribution
function. The the change in the impactionization rate
is due to a difference between the fast electrons and
equilibrium carriers in the probability of attaining an
energy level high enough to cause impact ionization.
junctions in thin semiconductor struc
tures, the electronhole gas in the depletion layer is
therefore heated by two agents: the applied electric
field and the photogenerated carriers. As will be seen,
impact ionization should
with an increase in
radiation intensity when the applied field is not too
strong; otherwise, impact ionization should
The reason is that if the velocity of a hot free electron
is originally aligned with the field, the latter will tend
to invert the former; otherwise, the velocity should
only be increased in magnitude.
Our previous study addressed the development of
an avalancheinduced thermal breakdown in a non
junction under ionizing irradia
tion when the depletionlayer thickness is greater than
the energy relaxation length; the velocity
of hot electrons generated by high
energy photons within the depletion layer were shown
to vary according to electron point of origin .
The present paper employs the Monte Carlo
method to further investigate electron transport sub
ject to a highly nonuniform strong electric field and
highenergy photons in the context of a semiconduc
tor structure smaller than the electron energy relax
ation length, allowing for impact ionization.
Electron Transport in ThinBase Transistor Structures
Exposed to HighEnergy Photons
A. S. Puzanov and S. V. Obolensky
Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
Received December 16, 2011
—Monte Carlo simulations are run to investigate the electron transport in thinbase BJT structures
exposed to highenergy photons. The radiationinduced distortion of the electron energy distribution func
tion is shown to be capable of changing, in either direction, the rate of impact ionization in the collector
depletion layer to a great extent.