Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena
The mechanisms of directional motion of highly mobile charged point defects in semiconductor structures under the non-thermal action of microwave radiation have been considered. The effects of particle drift along the direction of the electric field of a homogeneous electromagnetic wave and in the d...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2020
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| Cite this: | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena / G.V. Milenin, R.A. Redko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2020. — Т. 23, № 1. — С. 46-51. — Бібліогр.: 15 назв. — англ. |
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| citation_txt | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena / G.V. Milenin, R.A. Redko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2020. — Т. 23, № 1. — С. 46-51. — Бібліогр.: 15 назв. — англ. |
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| description | The mechanisms of directional motion of highly mobile charged point defects in semiconductor structures under the non-thermal action of microwave radiation have been considered. The effects of particle drift along the direction of the electric field of a homogeneous electromagnetic wave and in the direction of its propagation, as well as the appearance of a gradient ponderomotive force in an inhomogeneous wave, have been analyzed. The features of the appearance of an electric force acting on charged point defects as a result of the formation of electron-hole junctions around charged dislocations have been studied. Analytical relationships describing the dynamics of impurity ions in semiconductor structures exposed to microwave radiation have been presented.
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2020. V. 23, N 1. P. 46-51.
© 2020, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
46
Semiconductor physics
Transformation of defects in semiconductor structures under
the influence of microwave electromagnetic radiation,
which is stimulated by drift phenomena
G.V. Milenin
1
, R.A. Redko
1,2
1
V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine,
41, prospect Nauky, 03680 Kyiv, Ukraine
2
State University of Telecommunications, 7, Solomenska str., 03680 Kyiv, Ukraine
E-mail: milenin.gv@gmail.com; redko.rom@gmail.com
Abstract. The mechanisms of directional motion of highly mobile charged point defects in
semiconductor structures under the non-thermal action of microwave radiation have been
considered. The effects of particle drift along the direction of the electric field of a
homogeneous electromagnetic wave and in the direction of its propagation, as well as the
appearance of a gradient ponderomotive force in an inhomogeneous wave have been
analyzed. The features of the appearance of an electric force acting on charged point defects
as a result of formation of electron-hole junctions around charged dislocations have been
studied. Analytical relationships describing the dynamics of impurity ions in semiconductor
structures exposed to microwave radiation have been presented.
Keywords: microwave radiation, charged defect, particle drift, ponderomotive force.
https://doi.org/10.15407/spqeo23.01.46
PACS 72.30.+q, 72.90.+y
Manuscript received 10.12.19; revised version received 22.01.20; accepted for publication
18.03.19; published online 23.03.19.
1. Introduction
In [1–4], the mechanisms of transformation of charged
defects in semiconductor structures under the non-
thermal action of electromagnetic radiation of the
microwave range, which were based on resonant
(vibrational) phenomena, were discussed. Their essence
was the coincidence of frequency inherent to this
radiation with the intrinsic and ion-plasma frequencies of
vibrations typical to dislocations and clusters of
impurity-defect complexes. At a resonant frequency, due
to a sharp increase in the amplitude of oscillations,
dislocations detach and subsequently move under the
influence of a mosaic of internal mechanical stresses of
the crystal, as well as impurity-defect complexes decay
and diffusion of decay products occur. At the same time,
it should be noted that in addition to the above, other
mechanisms providing evolution of defects under the
influence of microwave radiation are not excluded. They
are based on the idea that in a microwave electro-
magnetic field, a charged defect not only oscillates, but
also drifts. For example, in [5, 6], the ponderomotive
effect arising as a result of nonlinear interaction of the
electric component of microwave electromagnetic field
with charged point defects in the near-surface region of
ionic crystals was experimentally investigated and
theoretically substantiated.
This article is devoted to studying the drift
mechanisms for highly mobile charged point defects in
semiconductor crystals under the influence of microwave
radiation.
2. Drift of charged point defects inside semiconductor
structures exposed to homogeneous microwave
electromagnetic field
During propagation of a microwave electromagnetic
wave inside a semiconductor crystal, its attenuation is
observed. If the latter can be neglected, then the micro-
wave field in the crystal can be considered as homo-
geneous. Otherwise, if extinction cannot be neglected,
the corresponding microwave electromagnetic field
should be considered as inhomogeneous. Let us first
analyze the features of the drift of charged point defects
in a homogeneous microwave field.
SPQEO, 2020. V. 23, N 1. P. 46-51.
Milenin G.V., Redko R.A. Transformation of defects in semiconductor structures under the influence of microwave …
47
In [7, 8], it was shown that a free charged particle
with the mass m and charge e in an electromagnetic field
with an electric component ( )tiE ωexp0 not only
oscillates but also performs a systematic drift in parallel
to the direction of this electric field. The velocity of this
directional movement υ1 can be defined as in [7]:
ω
ϕ
−=υ
m
eE sin0
1 , (1)
where E0 is the amplitude of the electric field, ϕ – phase
of the field at the initial time, ω – circular frequency of
the field.
As it follows from (1), systematic motion is absent
only at 0sin =ϕ , and for all other values of the phase ϕ,
the charged particle systematically moves along the
electric field, and depending on the values ϕ, the particle
drifts in mutually opposite directions [7, 8].
It is quite natural that for an arbitrary phase value ϕ
over a finite period of time t, the particle will travel over
the distance l1 equal to:
t
m
eE
l
ω
ϕ
−=
sin0
1 . (2)
It should be noted that for the entire set of charged
particles, the initial phase ϕ is a random value that obeys
a continuous uniform distribution. In turn, since all
values of the initial phase are equally probable, the drift
velocity averaged over ϕ is equal to zero [7]. It means
that, along with the systematic drift of individual charged
particles as a whole, directional movement of the entire
set of particles is absent.
In addition to drift along the electric vector of the
wave, the particle systematically drifts in the direction of
wave propagation with the velocity υ2 [8, 9]:
( )
cm
Ee
22
2
0
2
2
4
22cos
ω
+ϕ
=υ , (3)
where c is the speed of light.
Accordingly, the expression for the distance l2, over
which the charged particle moves due to action of
electromagnetic radiation, has the form:
( )
t
cm
Ee
l
22
2
0
2
2
4
22cos
ω
+ϕ
= . (4)
Therefore, the charged particle in the field of
electromagnetic wave drifts both in the direction of the
electric field and in the direction of the wave vector of
the latter, the sign of the drift velocity in the direction of
wave propagation is always the same, and its value
depends on the initial phase [8].
In the expressions (1) to (4), the mass of free
charged particles defines as m. However, impurity ions in
semiconductor crystals are not free, since they have to
overcome potential barriers with height Ea when moving.
This feature of motion of charged point defects can be
taken into account, if, in the indicated expressions, by the
mass of a singly charged particle we mean some effective
mass of an impurity ion:
=
kT
E
mm a
eff exp , (5)
where m is the mass of free ion, k – Boltzmann constant,
T – absolute temperature.
3. Drift of charged point defects inside the
semiconductor structure exposed to the
inhomogeneous microwave electromagnetic field
The Gaponov–Miller force, which is proportional to the
gradient from the square of the absolute electric field
value at a given point, acts on a free charged particle in
an inhomogeneous microwave field ( ) ( )tizyxE ωexp,,
[8, 10]:
( )
2
2
2
,,grad
4
zyxE
m
e
F
ω
−=
→
. (6)
We assume that the electric field of an
electromagnetic wave has only one component along the
axis y perpendicular to the direction of propagation along
the axis x. Then the wave is homogeneous along the axis
y and inhomogeneous along the axis x. In this case, for
the value of the ponderomotive force (6) in any point x
we have:
( )
( )
x
xE
m
e
xF
∂
∂
ω
−=
2
2
2
4
. (7)
When the electromagnetic microwave radiation acts
on the semiconductor structure, the inhomogeneity of the
wave occurs due to attenuation, since it propagates in the
crystal. The law of variation of the amplitude along the
propagation axis has the form [11]:
( ) ( )xExE β−= exp0 ,
where E0 is the amplitude of oscillations of the electric
component of the electromagnetic wave on the surface of
semiconductor, β is the extinction coefficient of the
electromagnetic wave. Then the expression for the force
acting on a singly charged point defect is written in the
form:
( ) ( )x
m
Ee
xF
eff
β−
ω
β
= 2exp
2 2
2
0
2
. (8)
The dynamics of behavior inherent to a charged
point defect is described by the following equation:
SPQEO, 2020. V. 23, N 1. P. 46-51.
Milenin G.V., Redko R.A. Transformation of defects in semiconductor structures under the influence of microwave …
48
( )xF
dt
xd
meff =
2
2
. (9)
Let us represent the acceleration in the following
way:
dx
d
dt
dx
dx
d
dt
d
dt
xd 3
3
33
2
2 υ
υ=
υ
=
υ
= . (10)
Then for (9), we have:
( )xF
dx
d
meff =
υ
υ 3
3 . (11)
Integrating (11) with account of (8) within the
ranges [ ]x,0 and [ ]3,0 υ , we obtain that the drift velocity
of impurity ions equals:
( )[ ] 2
10
3 2exp1
2
x
m
eE
eff
β−−
ω
=υ . (12)
Based on (10) and (12), we find that the change in
the velocity of the impurity ion in time obeys the
equation:
dt
d
β−=
υ−υ
υ
2
0
2
3 , (13)
where ω=υ effmeE 200 .
Integrating (13), we obtain:
( )
( )t
t
0
0
03
2exp1
2exp1
βυ−+
βυ−−
υ=υ . (14)
Let us consider the case of short durations of
exposure to microwave radiation (non-thermal effect) on
the semiconductor structure, at which 12 0 <<βυ t .
Taking into account that under this exposure
( ) tt 00 212exp βυ−=βυ− , for υ3 we have:
22
2
0
2
3
2 ω
β
=υ
effm
tEe
. (15)
Therefore, an impurity ion, the initial velocity of
which is zero, under the influence of microwave radiation
moving uniformly accelerated, over time t will move the
distance l3:
22
22
0
2
0
33
4 ω
β
=υ=∫
eff
t
m
tEe
dtl . (16)
When using (15) and (16) for calculations, it is
necessary to have an idea of the parameter β. The
extinction coefficient β depends on the prevailing
mechanism of electromagnetic radiation absorption
inside semiconductor crystals. In the microwave range,
absorption is caused by free charge carriers. If in the
microwave frequency range the condition 1<<ωτ is
satisfied (which takes place in experiments on the
influence of microwave processing on semiconductor
structures), then the corresponding expression for the
absorption coefficient by free charge carriers α has the
form [11]:
nc 0ε
σ
=α , (17)
where em nnµ=τ is the relaxation time, nenµ=σ –
specific electrical conductivity of semiconductor, mn –
effective mass of electrons in a crystal, µn – electron
mobility, n – concentration of free electrons in a
semiconductor crystal, n – real part of the complex
refraction index, ε0 – electric constant of vacuum.
The coefficients β and α are related by the relation
[11]:
2
α
=β . (18)
Using (17) involves knowledge of the numerical
value n . It is known that the real n and imaginary χ
parts of the complex refractive index are determined by
the expressions [11]:
ε+χ= 22n , (19)
ωε
σ
=χ
02n
, (20)
where ε is the permittivity of a semiconductor crystal.
As a result of solving the system of equations (19)
and (20) with respect to n , we have:
εωε
σ
++
ε
=
2
0
11
2
n . (21)
Substituting (21) into (17) and taking into account
(18), one can obtain the values of β.
Let us consider two practically important particular
cases. If ( ) 10 >>εωεσ , then
2
1
02
ωε
σ
=n . (22)
SPQEO, 2020. V. 23, N 1. P. 46-51.
Milenin G.V., Redko R.A. Transformation of defects in semiconductor structures under the influence of microwave …
49
Then, in accordance with (17) and (18),
2
1
02
1
ε
σω
=β
c
, (23)
that is sδ=β−1 , where ( ) 2
1
02 σωε=δ cs is the
thickness of the skin layer [12].
If ( ) 10 <<εωεσ , then
( ) 2
1
ε=n (24)
and
2
1
02 εε
σ
=β
c
. (25)
In conclusion, we formulate a criterion for weak
and strong attenuation of electromagnetic waves incident
onto a semiconductor structure (characterized by
homogeneity or inhomogeneity of a microwave field in a
crystal). Let us assume that for the thickness d of the
semiconductor crystal and the extinction coefficient β,
the following condition is satisfied: 1−β<<d , i.e.,
attenuation is absent. Otherwise, attenuation becomes
significant, and when 1−β≥d there is a strong
attenuation of electromagnetic waves.
4. The effect of charged dislocations on the drift of
charged point defects in semiconductor structures
under action of microwave radiation
Dangling bonds in the nuclei of edge dislocations can act
as acceptors or donors of electrons [13]. If free electron is
captured by a dangling bond, then the dislocation
becomes negatively charged. Such a negatively charged
line repulses free electrons and induces formation of a
tube of a positive charge around the dislocation [13]. For
sufficiently large values of the charge of dislocation in an
n-type semiconductor, around this dislocation formation
of an inversion layer becomes possible [13] and,
consequently, formation of a p-n junction. The effect of
rectification of currents due to the formation of an
electron-hole junction around a dislocation was
experimentally observed in [14]. It was noted that the
current-voltage characteristic of a dislocation diode in
n-type silicon is non-linear and asymmetric, moreover,
direct and reverse currents are different by hundred times
[14]. The p-n junction thus formed during oscillations of
one of the half-waves of alternating electric field of the
electromagnetic wave is switched on in the forward
direction, and in the opposite direction – during the other.
In the closed state, in the dislocation diode the width of
the space charge region of the p-n junction increases with
increasing voltage, and ionic impurities localized near the
dislocations fall into this area. Under the influence of the
built-in electric field, highly mobile charged point defects
gain the ability to move.
In particular, for a symmetrical stepwise p-n
junction in the state of thermal equilibrium, the width of
the depletion area W is [15]:
2
1
04
εϕε
=
N
W , (26)
in which the following relation takes place:
in
N
e
kT
ln
2
=ϕ , (27)
where ϕ is the contact potential difference, N –
concentration of impurities in the n- and p-areas of the
junction (it is assumed that all donors and acceptors are
ionized), ni – intrinsic concentration of carriers.
For this junction, the maximum width of the
depletion region Wmax under the action of microwave
radiation can be found by solving the equation:
( ) 2
1
max00
max
4
+ϕεε
=
N
WE
W , (28)
and it is:
2
1
0
22
2
0
22
000
max
442
εϕε
+
εε
+
εε
=
eNNe
E
eN
E
W . (29)
Let it be: E is the average (over the period of
oscillations) value of the electric component of
electromagnetic wave corresponding to being of the
dislocation diode in the closed state and is equal to:
( )
π
=ωω
π
= ∫
π
0
0
0 sin
2
1 E
tdtEE . (30)
Then, on average during a period of electromagnetic
oscillations, a force acts on a singly charged impurity ion
in the space charge region of the p-n junction:
ϕ
+=
W
EeF , (31)
where W is determined from (29) with replacing E0
by E .
The average displacement of a point defect with a
zero initial velocity under action of a given force during
the period of microwave radiation presence is:
( ) ( )[ ] 202
4
22
t
m
WEe
t
m
F
l
effeff
ϕ+π
== , (32)
at that Wl ≤4 .
SPQEO, 2020. V. 23, N 1. P. 46-51.
Milenin G.V., Redko R.A. Transformation of defects in semiconductor structures under the influence of microwave …
50
5. Calculation of parameters describing the drift of
defects in semiconductor structures under action of
microwave radiation
Let us estimate the values of drift parameters υ1 and l1
for rapidly diffusing singly-charged copper ions in
epitaxial semiconductor structures under the influence
of a homogeneous microwave field. Let the frequency
of electromagnetic radiation is 2.45·10
9
Hz, and
E0 = 1.5·10
3
V/m. Taking into account that the mass of
free copper ions m = 1.055·10
–25
kg, then at Ea = 0.4 eV,
ϕ = –π/2, T = 300 K and t = 5 s, the calculation according
to formulas (1), (2) and (5) gives the following values
for the drift parameters: υ1 = 0.28·10
–7
m/s and
l1 = 1.4·10
–7
m. At Ea = 0.45 eV and unchanged values
of the remaining parameters, one can obtain:
υ1 = 0.41·10
–8
m/s and l1 = 2.1·10
–8
m. As one can see,
the drift parameters, ceteris paribus, are characterized by
a strong sensitivity to Ea. Thus, drift effects under action
of microwave radiation are most pronounced in relation
to defects with high mobility.
6. Conclusions
Transformation of the subsystem of highly mobile
charged point defects in semiconductor structures during
non-thermal microwave processing may be caused by the
directional movement of the latter under the influence of
an electromagnetic wave. If attenuation of electro-
magnetic waves incident on a semiconductor crystal can
be neglected, then in such a homogeneous microwave
field there is a drift of impurity ions both along the
direction of the electric field of the wave and in the
direction of its wave vector. In the first case, the drift
velocity is proportional to the amplitude of oscillations of
the electric field and inversely proportional to the
frequency of the microwave radiation, as well as to the
effective mass of ion. In the second case, these
dependences are squared in respect to the corresponding
quantities. The consequence of attenuation of the incident
electromagnetic waves in the semiconductor structure is
that for the corresponding inhomogeneous microwave
field, the charged point defects are affected by the
Gaponov–Miller force proportional to the gradient of the
square of the electric field modulus.
The value of this gradient force is determined by the
extinction coefficient of the electromagnetic wave in the
semiconductor crystal, the oscillation amplitude of the
electric component of the latter on the surface of
semiconductor, the radiation frequency and effective
mass of the defect.
Impurity ions localized in the vicinity of
dislocations under conditions of microwave radiation are
subjected to an electric force, the cause of appearance of
which is formation of an electron-hole junction around
the charged dislocation, in other words, formation of a
dislocation diode. This force is proportional to the
amplitude of oscillations of the electric field.
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Authors and CV
Milenin G.V. PhD “Solid-State
Physics”, Senior Researcher at Labo-
ratory of Physical and Technological
Problems of Solid-State Microwave
Electronics at the V. Lashkaryov
Institute of Semiconductor Physics,
NAS of Ukraine. Authored more than
80 scientific publications and 5 pa-
tents. The areas of scientific interests
are semiconductor physics and solid-
state electronics.
Redko R.A. PhD “Solid-State Phy-
sics”, Associate Professor, Senior Re-
searcher at Laboratory of Physical and
Technological Problems of Solid-
State Microwave Electronics at the
V. Lashkaryov Institute of Semicon-
ductor Physics, NAS of Ukraine.
Authored more than 30 scientific pub-
lications and 4 patents. The areas of
scientific interests are semiconductor
physics and solid-state electronics.
|
| id | nasplib_isofts_kiev_ua-123456789-215663 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-26T19:16:26Z |
| publishDate | 2020 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Milenin, G.V. Redko, R.A. 2026-03-24T12:21:32Z 2020 Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena / G.V. Milenin, R.A. Redko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2020. — Т. 23, № 1. — С. 46-51. — Бібліогр.: 15 назв. — англ. 1560-8034 PACS: 72.30.+q, 72.90.+y https://nasplib.isofts.kiev.ua/handle/123456789/215663 https://doi.org/10.15407/spqeo23.01.046 The mechanisms of directional motion of highly mobile charged point defects in semiconductor structures under the non-thermal action of microwave radiation have been considered. The effects of particle drift along the direction of the electric field of a homogeneous electromagnetic wave and in the direction of its propagation, as well as the appearance of a gradient ponderomotive force in an inhomogeneous wave, have been analyzed. The features of the appearance of an electric force acting on charged point defects as a result of the formation of electron-hole junctions around charged dislocations have been studied. Analytical relationships describing the dynamics of impurity ions in semiconductor structures exposed to microwave radiation have been presented. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor Physics Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena Article published earlier |
| spellingShingle | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena Milenin, G.V. Redko, R.A. Semiconductor Physics |
| title | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| title_full | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| title_fullStr | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| title_full_unstemmed | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| title_short | Transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| title_sort | transformation of defects in semiconductor structures under the influence of microwave electromagnetic radiation, which is stimulated by drift phenomena |
| topic | Semiconductor Physics |
| topic_facet | Semiconductor Physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215663 |
| work_keys_str_mv | AT mileningv transformationofdefectsinsemiconductorstructuresundertheinfluenceofmicrowaveelectromagneticradiationwhichisstimulatedbydriftphenomena AT redkora transformationofdefectsinsemiconductorstructuresundertheinfluenceofmicrowaveelectromagneticradiationwhichisstimulatedbydriftphenomena |