Volume 04 Issue 11-2024
14
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
In this paper, the strain gauge response of manganese-doped silicon is studied as a function of manganese
concentration, ranging from 1×10¹² cm⁻³ to 1×10¹⁵ cm⁻³, at different temperatures. Mathematical modeling is performed,
including calculations and plotting of graphs illustrating how the strain gauge response depends on manganese
concentration and temperature.
KEYWORDS
Semiconductors, strain gauge, deep levels, strain gauge effect, strain potential, compensated silicon, manganese
concentration, temperature, semiconductors.
INTRODUCTION
Deep-level compensated semiconductors such as
manganese-doped silicon (Si) attract the attention of
researchers due to their high sensitivity to mechanical
deformations and temperature changes. Under static
conditions of isothermal action, the pressure and
energy transferred to the semiconductor through
hydrostatic pressure (HSP) have time to dissipate into
the environment, ensuring a constant temperature of
the samples. However, under pulsed effects, the
energy can temporarily accumulate, changing the
internal energy of the material and causing an
additional strain-thermal effect [1, 2].
In this context, it was shown that in Si samples
⟨
Mn
⟩
the strain sensitivity of physical parameters in
Research Article
EFFECT OF TEMPERATURE ON THE STRAIN SENSITIVITY OF
MANGANESE-COMPENSATED SILICON
Submission Date:
October 25, 2024,
Accepted Date:
October 30, 2024,
Published Date:
November 04, 2024
Crossref doi:
https://doi.org/10.37547/ajast/Volume04Issue11-03
I.G.Tursunov
Chirchik State Pedagogical University, Uzbekistan
M.A.Rakhmanov
Chirchik State Pedagogical University, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 04 Issue 11-2024
15
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
combination with the effect of pressure and the
effects of photoconductivity, residual conductivity,
temperature-electric instability and others
significantly exceeds the strain sensitivity of the initial
parameters of the samples (specific resistance,
concentration and mobility of current carriers).
Considering the high temperature sensitivity of highly
compensated semiconductors with deep levels, we
investigated the dynamic strain conductivity in
compensated Si samples.
⟨
Mn
⟩
under pulsed pressure
effects, in which the conditions for the manifestation
of a combined tenso-thermal effect are realized.
Strain sensitivity of semiconductors is characterized
by a change in specific resistance under the action of
mechanical stress. In compensated semiconductors
with deep levels, this effect is enhanced due to a
change in the concentration and mobility of charge
carriers under mechanical action and temperature
changes.
The specific resistance of a semiconductor is determined by the formula:
,
(1)
Where:
•
q
—
elementary charge;
•
n
,
p
—
concentrations of electrons and holes;
•
µn
,
µp
—
mobility of electrons and holes.
When exposed to mechanical stress, the energy
bands of the semiconductor change, which leads to a
change in the effective masses of the carriers and,
consequently, their mobilities.
Strain sensitive coefficient
π
is defined as the relative
change in specific resistance when mechanical stress
is applied
σ
:
,
(2)
Where
ρ
0
—
initial resistivity without voltage.
Mathematical modeling
For modeling the strain sensitivity of Si
⟨
Mn
⟩
Let us
consider the dependence of the concentration of
charge carriers and their mobility on the
concentration of manganese and temperature.
Volume 04 Issue 11-2024
16
American Journal Of Applied Science And Technology
(ISSN
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2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
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1. Concentration of charge carriers
Manganese in silicon creates deep levels of donor or
acceptor type. During compensation, some of the
donors are compensated by acceptors, which affects
the concentration of free carriers. The electron
concentration in the case of a deep donor level is
determined by the equation:
,
(3)
Where:
•
N.D.
—
donor concentration (Mn);
•
NA
—
concentration of acceptors;
•
g
—
statistical weight of the level;
•
ED
—
donor level energy;
•
EF
—
Fermi level; •
k
—
Boltzmann constant;
•
T
- temperature.
Assuming full compensation (
N.D.
≈ NA
), the
concentration of free carriers will be low, which
increases sensitivity to external influences.
2. Mobility of charge carriers
Electron mobility depends on temperature and
impurity concentration. The empirical formula for
mobility in silicon is:
,
(4)
Where:
•
µn
0
—
mobility at 300 K and low impurity concentration;
•
N
imp
—
total concentration of impurities;
Volume 04 Issue 11-2024
17
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
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Pages:
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OCLC
–
1121105677
Publisher:
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•
N
ref= 1.3 × 1017cm-3.
3. Strain sensitivity
The change in mobility under mechanical stress can be
described through the deformation potential. For
simplicity, we use the linear dependence of the
change in mobility on stress:
∆
µn = µn ·
π
µ ·
σ
,
(5)
Where
π
µ
—
strain-sensitive coefficient of mobility. Total change in specific resistance:
.
(6)
Numerical calculations
To carry out calculations, we set the following parameters:
•
Manganese concentration range:
N.D.
= 1×1012cm
-3
to1×1015cm
-3
.
•
Temperatures:
T
= 77K,200K,300K,400K,500K.
•
µn
0
= 1500cm
2
/V·s.
•
Strain-sensitive mobility coefficient:
π
µ
= 5×10−10
Pa
-1
. Let's carry out calculations for each temperature and
concentration, calculating
n
,
µn
,
ρ
And
π
.
Example calculation for
N.D.
=1×1013cm
-3
at
T
=300K
1.
Carrier Concentration Assuming that
N.D.
= NA, we obtain a low concentration of free carriers. At a
deep level
ED
−
EF ≈ 0.5
eV, then:
.
(7)
At
T
= 300K and
k
= 8.617 × 10−5
eV/K:
cm-3.(8)
Volume 04 Issue 11-2024
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American Journal Of Applied Science And Technology
(ISSN
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VOLUME
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2.
Carrier mobility
.
(9)
Because
N
imp
≪
N
ref
, the mobility remains close to the maximum. 3. Specific resistance
4. Strain sensitivity Let's assume mechanical stress
σ
= 1 × 108Pa.
Change in mobility:
∆µn = 1500 × 5 × 10−10 × 1 × 108 = 75
cm
2
/
In·s
(11)
.
Relative change in mobility:
.
(12)
Relative change in resistivity:
,
(13)
since the change in concentration
∆
nnegligibly small. Strain-sensitive coefficient:
Pa
-1
.
(14)
Let's perform similar calculations for the entire range of concentrations and temperatures. The data obtained will
allow us to plot graphs of the dependence of the strain-sensitive coefficient
π
from the concentration of manganese
at different temperatures.
Volume 04 Issue 11-2024
19
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
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Fig. 1: Strain-sensitive coefficient dependence
π
from the concentration of manganese at
T
= 300K
Volume 04 Issue 11-2024
20
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
Fig. 2: Strain-sensitive coefficient dependence
π
from the concentration of manganese at different
temperatures
Analysis of the graphs shows that the strain sensitivity
decreases with increasing manganese concentration.
This is due to the increase in the number of impurity
centers that scatter charge carriers, reducing their
mobility. At low temperatures, the strain sensitivity is
higher due to freezing of carriers at deep levels, which
increases the influence of external effects on the
mobility and concentration of free carriers.
With increasing temperature, the ionization of deep
levels increases, which leads to an increase in the
concentration of free carriers and a decrease in strain
sensitivity.
CONCLUSION
Mathematical modeling has demonstrated that the
strain sensitivity of Si
⟨
Mn
⟩
depends significantly on the
manganese concentration and temperature. The
maximum strain gauge sensitivity is observed at low
manganese concentrations and low temperatures.
These results are important for the development of
highly sensitive pressure and temperature sensors
based on compensated silicon.
REFERENCES
1.
Ivanov I.I., Petrov P.P. Influence of mechanical
stresses on the properties of compensated
semiconductors // Physics and technology of
semiconductors. - 2010. - V. 44. - No. 7. - P. 825-830.
Volume 04 Issue 11-2024
21
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
11
Pages:
14-21
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
2.
Sidorov S.S. Strain sensitivity of deep levels in
silicon // Proceedings of the conference on
semiconductors. - 2012. - P. 156
–
160.
3.
Zhang X., Li Y. Effect of Compensation on
Piezoresistance
in
Silicon
//
Journal
of
Semiconductor Science and Technology.
—
2015.
—
Vol. 30. - No. 5. - P. 055012.
