Theoretical consideration of charge transport through the nanoindentor/GaAs junction
The process of indentation of GaAs single crystal by the conductive nanoindentor has been analyzed theoretically. The diode formed by the nanoindentor tip and small area of GaAs platelet has been considered. The evolution of local mechanical stress during the nanoindentation cycle and an appropri...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2008
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| Цитувати: | Theoretical consideration of charge transport through the nanoindentor/GaAs junction / A. O. Kosogor, R. Nowak, D. Chrobak, V. A. L'vov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 3. — С. 217-220. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-1189032017-06-02T03:04:16Z Theoretical consideration of charge transport through the nanoindentor/GaAs junction Kosogor, A.O. Nowak, R. Chrobak, D. L’vov, V.A. The process of indentation of GaAs single crystal by the conductive nanoindentor has been analyzed theoretically. The diode formed by the nanoindentor tip and small area of GaAs platelet has been considered. The evolution of local mechanical stress during the nanoindentation cycle and an appropriate transformation of electric potential difference inherent in tip/GaAs junction are described qualitatively. The nonmonotone variation of the mechanical stress and electric potential difference during the indentation cycle has been disclosed. The current spike experimentally registered in the moment of abrupt penetration of indentor tip into the GaAs platelet has been attributed to the non-monotone variation of potential difference during the indentation cycle. 2008 Article Theoretical consideration of charge transport through the nanoindentor/GaAs junction / A. O. Kosogor, R. Nowak, D. Chrobak, V. A. L'vov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 3. — С. 217-220. — Бібліогр.: 6 назв. — англ. 1560-8034 PACS 07.10.Pz, 72.80.Ey, 73.40.-c, 62.40.+i http://dspace.nbuv.gov.ua/handle/123456789/118903 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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The process of indentation of GaAs single crystal by the conductive
nanoindentor has been analyzed theoretically. The diode formed by the nanoindentor tip
and small area of GaAs platelet has been considered. The evolution of local mechanical
stress during the nanoindentation cycle and an appropriate transformation of electric
potential difference inherent in tip/GaAs junction are described qualitatively. The nonmonotone
variation of the mechanical stress and electric potential difference during the
indentation cycle has been disclosed. The current spike experimentally registered in the
moment of abrupt penetration of indentor tip into the GaAs platelet has been attributed to
the non-monotone variation of potential difference during the indentation cycle. |
| format |
Article |
| author |
Kosogor, A.O. Nowak, R. Chrobak, D. L’vov, V.A. |
| spellingShingle |
Kosogor, A.O. Nowak, R. Chrobak, D. L’vov, V.A. Theoretical consideration of charge transport through the nanoindentor/GaAs junction Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kosogor, A.O. Nowak, R. Chrobak, D. L’vov, V.A. |
| author_sort |
Kosogor, A.O. |
| title |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction |
| title_short |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction |
| title_full |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction |
| title_fullStr |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction |
| title_full_unstemmed |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction |
| title_sort |
theoretical consideration of charge transport through the nanoindentor/gaas junction |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118903 |
| citation_txt |
Theoretical consideration of charge transport through the nanoindentor/GaAs junction / A. O. Kosogor, R. Nowak, D. Chrobak, V. A. L'vov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 3. — С. 217-220. — Бібліогр.: 6 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT kosogorao theoreticalconsiderationofchargetransportthroughthenanoindentorgaasjunction AT nowakr theoreticalconsiderationofchargetransportthroughthenanoindentorgaasjunction AT chrobakd theoreticalconsiderationofchargetransportthroughthenanoindentorgaasjunction AT lvovva theoreticalconsiderationofchargetransportthroughthenanoindentorgaasjunction |
| first_indexed |
2025-07-08T14:52:08Z |
| last_indexed |
2025-07-08T14:52:08Z |
| _version_ |
1837090817254096896 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N3. P. 217-220.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
217
PACS 07.10.Pz, 72.80.Ey, 73.40.-c, 62.40.+i
Theoretical consideration of charge transport
through the nanoindentor/GaAs junction
A.O. Kosogor1, R. Nowak2, D. Chrobak2, and V.A. L’vov1
1Taras Shevchenko Kyiv National University, Radiophysics Department, Ukraine
2Nordic Hysitron Laboratory, Helsinki University of Technology, Finland
E-mail: emera@ukr.net
Abstract. The process of indentation of GaAs single crystal by the conductive
nanoindentor has been analyzed theoretically. The diode formed by the nanoindentor tip
and small area of GaAs platelet has been considered. The evolution of local mechanical
stress during the nanoindentation cycle and an appropriate transformation of electric
potential difference inherent in tip/GaAs junction are described qualitatively. The non-
monotone variation of the mechanical stress and electric potential difference during the
indentation cycle has been disclosed. The current spike experimentally registered in the
moment of abrupt penetration of indentor tip into the GaAs platelet has been attributed to
the non-monotone variation of potential difference during the indentation cycle.
Keywords: nanoindentor, GaAs single crystal, charge transport.
Manuscript received 27.05.08; accepted for publication 20.06.08; published online 15.09.08.
1. Introduction
A nanoindentation technique is widely used for the local
mechanical stressing of solid and determination of its
microhardness [1]. The nanoindentor is a small probe
with the sharp hard tip. During the nanoindentation cycle
the tip is pressed into the solid-state specimen by an
increasing mechanical force (see Fig. 1). At the first
stage of the cycle, the tip moves down smoothly and
elastically deforms the specimen of solid. When the
pressing force reaches certain critical value, the tip
abruptly penetrates into the specimen. This effect is
called a “pop-in event”.
The manufacturing of different elements in
nanoelectronics is accompanied by the appearance of
mechanical stresses inside these elements. These
technological stresses vary in nanometer scale. The
sharply variable/local stresses also exist in the systems
with quantum dots, which attract common attention now.
The experimental study of the influence of these local
stresses on physical properties of semiconductor
structures is a topical but very complicate problem. The
possible approach to the problem solution is the
modeling of technological local stresses by the stress,
which is induced by a nanoindentor probe: a compre-
hensive study of physical effects that accompany nano-
indentation cycle can help to foresee the consequences
of technological stressing.
In the experimental work [2], a 1 µm epitaxial
GaAs layer with Si dopant concentration ND =1016 cm–3
has been grown by the molecular beam epitaxy on
350 µm thick GaAs (100) substrate. A conductive
nanoindentation system has been used to study an
electric response of doped GaAs epilayer on a local
mechanical stressing. The experimental technique used
in Ref. [2] involves the standard nanoindentation
hardware, conductive indentor probe, electric voltage
source, and nanoammeter. This technique enables the
study of correlation between the force acting on GaAs
specimen, displacement of nanoindentor, and electrical
current flow through the nanoindentor tip/GaAs
junction. During the nanoindentation test, the constant
voltage and increasing mechanical force have been
applied to the tip/GaAs contact, and the magnitude of
current running through this contact has been monitored.
In this way, a sharp current spike was registered just
before the pop-in event [2].
In the present article, the theoretical study of diode
properties of tip/GaAs junction is carried out, and the
explanation of current spikes arising in the course of
nanoindentation cycle is proposed.
2. Diode properties of nanoindentor tip/GaAs
junction
To study the variation of diode properties of tip/GaAs
junction during the nanoindentation cycle, the evolution
of electron energy bands under the axial compressive
stress was considered using the set of programs PWscf.
The computations showed the linear increase of the
energy gap between the valence and conductivity bands
in Γ-point during the compression cycle:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N3. P. 217-220.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
218
hκ h
Indentor tip
Ga As specimen
S = 2πRhκ
Fig. 1. Nanoindentor acting on GaAs platelet (schematically).
σα+=σ ΓΓΓ )0()( EE , (1)
where σ is an absolute stress value, )0(ΓE = 1.43 eV [3],
αΓ ≈ 0.045 eV/GPa is a computed value. This value is
rather close to the value 0.055 eV/GPa reported in the
early work [4]. In contrast to this, the energy gap in X-
point decreases during the axial stressing as
σα−=σ XXX )0()( EE , (2)
where EX(0) = 1.9 eV [3], Xα ≈ 0.083 eV/GPa is a com-
puted value. As a consequence, the inequality
)()(X σ<σ ΓEE (3)
is valid when GPa 7.3>σ .
In the simplest approach to the problem solution
the axial stress may be related to the applied force F(h)
by the simple formula
)()2()( 1 hFhRh −κπ=σ , (4)
where R ≈ 234 nm is the radius of indentor tip, h is the
displacement of tip during the nanoindentation cycle,
and κ is a dimensionless adjusted parameter introduced
in view of the misfit between the shapes of indentor tip
and specimen surface (see Fig. 1). Thus, the value hκ is
the depth of penetration of tip into the specimen and
)(2)( hhRhS κπ= is the area of tip/GaAs contact.
Let κ = κ1 before the pop-in event. Fig. 1 and
elementary calculation shows that after the event
s
s
hh
hh
/1
/1
2 ∆+
∆+κ
=κ , (5)
where ∆h = hf – hs, the values hs and hf correspond to the
start and finish of the pop-in event. In the case when the
area S(h) of nanoindentor-semiconductor contact varies
linearly in the interval hs < h < hf , the expression
hhhh s ∆−κ−κ+κ≡κ /))(()( 121 (6)
is valid.
4 6 8 10 12 14 16 18
20
40
60
80
100
120
140
160
180
200 (a)
Fo
rc
e
F,
µ
N
Tip displacement h, nm
4 6 8 10 12 14 16 18
6
8
10
12
14
16
18
(b)
κ
1
= 0.767
κ
1
= 0.4152
St
re
ss
σ
, G
Pa
Tip displacement h, nm
Fig. 2. Reported in Ref. [2] experimental values of the force
applied to the specimen (a), and the correspondent values of
the mechanical stress (b) computed from Eqs. (4)-(6).
Fig. 2a shows the monotonous dependences of the
compressive force on the tip displacement measured in
Ref. [2] during the nanoindentation cycle for doped
specimen with ND =1016 cm–3. The experimental points
shown in Fig. 2a and Eqs. (4)-(6) enabled the compu-
tation of the mechanical stress versus tip displacement.
The graphs of stresses created by the nanoindentor tip
are shown in Fig. 2b for two different values of the
parameter κ. The choice of κ values shown in Fig. 2b
will be explained below.
The graphs presented in Fig. 2b exhibit the non-
monotonous variation of stress versus the tip displace-
ment. The non-monotony appears because the tip/GaAs
junction area κπ= hRS 2 arises during the nanoinden-
tation cycle: the stress increases first because the force
increases quicker then the area, but decreases when
because the graph of force reaches the “plateau” (see
Fig. 2a). It is seen from Fig. 2b that the pop-in event
takes place at the maximal stress value. If κ = 0.767, this
event is accompanied by the 15 % stress relaxation. The
reduction of an unknown κ value results in the increase
of stress values computed from the experimental values
of the force and makes the stress relaxation more
pronounced.
The indentor tip and contiguous spatial domain of
the semiconductor platelet form a Schottky barrier diode.
For the reverse bias voltage the current flows through
the diode are
),/||(exp)()(
),/||(exp)()(
BX0X
B0
TkehSjhJ
TkehSjhJ
ϕ−=
ϕ−= ΓΓ (7)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N3. P. 217-220.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
219
4 6 8 10 12 14 16 18
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
ϕ
Γ
ϕXP
ot
en
tia
l b
ar
rie
r,
eV
Tip displacement h, nm
Fig. 3. Potential barriers versus tip displacement computed for
the GaAs specimen using the couples of values κ1 = 0.767,
ϕ0 = 0.86 eV (triangles) and κ1 = 0.4152, ϕ0 = 0.2 eV (circles).
where the subscripts Γ and Χ mark the current flows
created by the carriers corresponding to Γ- and Χ-points
of the Brillouin zone, j0 is the saturation current density,
e is the electron charge, T is temperature, and kB is the
Boltzmann constant [5].
The non-monotonous dependence of stresses
causes the non-monotonous variation of potential
barriers inherent to the diode structure
X,0X,X, ΓΓΓ ϕ∆−ϕ−=ϕ E , (8)
where 0ϕ is a potential induced by the surface charges,
∆φ = (| e | E / 4π εS )1/ 2 (9)
is the potential barrier reduction caused by the Schottky
effect, and the parameter E that have the dimension of
electric field is introduced as
E = [2ND (| e |U + | e |Ubi – kB T )] 1/ 2 εS
-1/ 2 (10)
where ND is the silicon concentration, U is the bias
voltage, | e |Ubi is the built-in electric potential, εS = 12ε0
is the dielectric constant of GaAs [5], ε0 is the dielectric
constant of vacuum.
The potential barriers Γϕ and Xϕ computed from
Eq. (8) are shown in Fig. 3. The computations were
carried out for j0 = 1010 A/m2, T = 300 K, Ubi = 0.591 V
[3] and the reverse bias voltage U = 3 V, which was
maintained in the course of experiments. Two different
couples of values κ1, φ0 were used for computations. The
choice of 0ϕ will be explained below. It is of impor-
tance that Γϕ is substantially higher than Xϕ in the
high-pressure range, and therefore, in this range the
current flow ΓJ can be disregarded.
3. Explanation of the electric current spikes observed
during nanoindentation of the GaAs specimen
To explain the experimentally observed spikes of
electrical current, the theoretical dependences of current
flow XJ on the tip displacement were computed from
the Eqs. (4)-(10). These dependences are presented in
Fig. 4. The current values were computed for the
discrete collection of tip displacements shown in
Figs. 2, 3. The computations were carried out for
maximal and minimal values of the potential (φ0 =
0.53 ± 0.33 eV [5]). The curves were plotted using the
“spline” tool involved in standard MathSoft Apps. The
amplitudes of theoretical spikes were equalized to the
experimental one by the adjustment of parameter κ1
values.
Fig. 4 illustrates a satisfactory agreement between
the theoretical current values and experimental spike
obtained in Ref. [2]. Therefore, the stress relaxation
accompanying the pop-in event is sufficient for the
substantial reduction of current flow and formation of
the spike at the J(h) curve. However, the additional
reasons for the abrupt current reduction after the pop-in
event may exist, and we can point out two of them now.
First, the pop-in event may be accompanied by the
substantial changes in the parameters involved in the
Eqs. (1), (2), because in the case under consideration this
event is caused by the jump-like transformation of the
crystal lattice [6]. Second, the experimentally observed
during pop-in event deflection at the F(h) curve may be
less pronounced than the real one due to the apparatus
effects. The latter statement is supported by the
computer experiments carried out in Ref. [6].
4. Discussion and summary
It may be summarized that the spikes observed in the
course of measuring the current flow through the
junction formed by the indentor tip and thin GaAs
platelet is caused by superposition of two physical
effects: i) the linear decrease of the energy gap in X-
point of the Brillouin zone; ii) the non-monotonous
dependence of the mechanical stress induced during the
nanoindentation cycle on the tip displacement. These
effects result in the non-monotonous variation of the
6 8 10 12 14 16 18
0
10
20
30
40
50 Experimental values
κ
1
= 0.4152, ϕ0= 0.2
κ
1
= 0.767, ϕ0= 0.86
C
ur
re
nt
J
, n
A
Tip displacement h, nm
Fig. 4. Theoretical (triangles and crosses) and experimental
(closed circles) values of current flow obtained for GaAs
specimens with ND = 1016 cm−3.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N3. P. 217-220.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
220
electric potential barrier inherent to the tip/GaAs
junction. As far as the barrier value is involved in the
exponential describing the variation of current flow (see
Eq. (7)), the current spike appears.
It should be emphasized that the current spikes are
described above in the frame of simplest theoretical
approach. Additional physical mechanisms of the affect
of the pop-in event on the current flow may also be
present; among them the reconstruction of crystal lattice
accompanied by the radical change of the electron band
structure should be mentioned.
The experimentally observed correlation between
the appearance of the current spike and presence of
epilayer doped by silicon points to the diffusive nature
of current, because in this case the saturation current
density is proportional to 2/1
DN .
The affect of mechanical nanostressing on the
charge transport in semiconductors is an intriguing
problem. The theoretical aspect of the problem may be
subdivided into the “electronic” and “mechanical” parts.
The electronic part includes (i) the theoretical study of
the energy band structure of semiconductor both before
and after the transformation of crystal lattice caused by
the pop-in event; (ii) the elucidation of physical peculia-
rities of the current flow through the tip/specimen
junction. The point (i) means that the parameters EΓ,Χ(0)
and X,Γα , which are involved in the Eqs. (1), (2), must
be computed not only for the elastically deformed cubic
lattice but also for the lattice that is transformed by the
indentor tip. The point (ii) is topical because the charge
transport through the junction with diode-like
characteristic drastically depends on the structural,
physical and chemical features of the junction and its
material.
Acknowledgements
The authors are grateful to Dr. A.G. Shkavro and
Dr. V.V. Ilchenko for the helpful discussion.
References
1. W.C. Oliver and G.M. Pharr, Measurement of hard-
ness and elastic modulus by instrumented indenta-
tion: Advances in understanding and refinements to
methodology // J. Mater. Res. 19 (3) (2004).
2. R. Nowak, D. Chrobak, S. Nagao, D. Vodnick,
M. Berg, A. Tukiainen, M. Pessa, Electric current
spike phenomenon linked to nanoscale plasticity (in
press).
3. Semiconductors: Group 5 Elements and 3-5 Com-
pounds, ed. O. Madelung, In: Data in Science and
Technology. Springer, Berlin, 1991.
4. F. Pollak, M. Cardona, K. Shaklee, Piezo-electro-
reflectance in GaAs // Phys. Rev. Lett. 16(21),
p. 942-990 (1966).
5. S.M. Sze, Physics of Semiconductor Devices.
Willey-Interscience Publ., New York, 1981.
6. D. Chrobak, K. Nordlund, and R. Nowak, Nondis-
location origin of GaAs nanoindentation pop-in
event // Phys. Rev. B 98, 045502 (2007).
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