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2
DOI: 10.21122/2220-9506-2023-14-4-277-283
Influence of Temperature from 20 to 100 °C on Specific Surface Energy and Fracture Toughness of Silicon Wafers
V.A. Lapitskaya1,2, T.A. Kuznetsova12, S.A. Chizhik1,2
1A.V. Luikov Heat and Mass Transfer Institute ofNAS of Belarus, P. Brovki str., 15, Minsk 220072, Belarus 2Belarusian National Technical University, Nezavisimosty Ave., 65, Minsk 220013, Belarus
Received 18.10.2023
Accepted for publication 27.11.2023
Abstract
The influence of temperature in the range from 20 to 100 °C on the specific surface energy and fracture toughness of standard silicon wafers of three orientations (100), (110) and (111) was studied. Silicon wafers were heated on a special thermal platform with an autonomous heating controller, which was installed under the samples. At each temperature, the samples were kept for 10 min. The specific surface energy y after exposure to temperature was determined by atomic force microscopy (AFM). Fracture toughness during and after exposure to temperature was determined by indentation followed by visualization of the deformation region using AFM. It has been established that the specific surface energy Y of Si wafers with orientation (100) and (111) increases with increasing temperature from 20 to 100 °C, and for orientation (110) it increases at temperatures from 20 to 80 °C, and then decreases. The diagonal length d of indentation marks, performed both during the heating process and after heating, decreases by increasing the temperature from 20 to 100 °C. The crack length c decreases on silicon wafers during indentation during heating from 20 to 100 °C, and after exposure to temperature, the length increases. When the plates are exposed to temperature, the fracture toughness KIC increases with increasing temperature: for orientation (100) - up to 1.61±0.08 MPam1/2, for (110) - up to 1.60±0.08 MPam1/2 and for
1/2
(111) - up to 1.66±0.04 MPa m . A direct correlation was established between KIC, measured during exposure to temperature, and an inverse correlation between KIC measured after exposure to temperature and specific surface energy for the (100) and (111) orientations. An inverse correlation was obtained by KIC at the (110) orientation when exposed to temperatures of 20-40 and 80-100 °C, and after exposure, a direct correlation was obtained. At 60 °C there is no correlation. The results obtained can be used to improve the mechanical properties of silicon wafers used in solar cells and microelectromechanical systems (operating at temperatures up to 100 °C).
Keywords: silicon wafers, temperature, fracture toughness, indentation method, atomic force microscopy
Адрес для переписки:
Лапицкая В.А.
Институт тепло- и массообмена им. А.В. Лыкова НАНБеларуси, ул. П. Бровки, 15, г. Минск 220072, Беларусь e-mail: vasilinka.92@mail.ru
Для цитирования:
V.A. Lapitskaya, T.A. Kuznetsova, S.A. Chizhik.
Influence of Temperature from 20 to 100 °C on Specific Surface
Energy and Fracture Toughness of Silicon Wafers.
Приборы и методы измерений.
2023. Т. 14. № 4. С. 277-283.
DOI: 10.21122/2220-9506-2023-14-4-277-283
Address for correspondence:
Lapitskaya V.A.
A.V. Luikov Heat and Mass Transfer Institute of NAS ofBelarus, P. Brovki str., 15, Minsk 220072, Belarus e-mail: vasilinka.92@mail.ru
For citation:
Lapitskaya VA, | Kuznetsova TA, | Chizhik SA.
Influence of Temperature from 20 to 100 °C on Specific Surface
Energy and Fracture Toughness of Silicon Wafers.
Devices and Methods of Measurements. 2023;14(4):277-283.
DOI: 10.21122/2220-9506-2023-14-4-277-283
Б01: 10.21122/2220-9506-2023-14-4-277-283
Влияние температуры от 20 до 100 °С на удельную поверхностную энергию и вязкость разрушения пластин кремния
12 12 12 В.А. Лапицкая ' , Т.А. Кузнецова ' , С.А. Чижик '
1 Институт тепло- и массообмена имени А.В. Лыкова НАНБеларуси, ул. П. Бровки, 15, г. Минск 220072, Беларусь 2Белорусский национальный технический университет, пр-т Независимости, 65, г. Минск 220013, Беларусь
Поступила 18.10.2023 Принята к печати 27.11.2023
Проведены исследования влияния температуры в диапазоне от 20 до 100 °С на удельную поверхностную энергию и вязкость разрушения стандартных пластин кремния трёх ориентаций (100), (110) и (111). Пластины кремния нагревали на специальной термоплатформе с автономным контроллером нагрева, которую устанавливали под образцы. При каждой температуре образцы выдерживали в течении 10 мин. Удельная поверхностная энергия у после воздействия температуры определялась методом атомно-силовой микроскопии (АСМ). Вязкость разрушения во время и после воздействия температуры определялась методом индентирования с последующей визуализацией области деформации методом АСМ. Установлено, что удельная поверхностная энергия у пластин кремния ориентации (100) и (111) увеличивается с увеличением температуры от 20 до 100 °С, у ориентации (110) - увеличивается при температурах от 20 до 80 °С, а затем снижается. Длина диагонали d отпечатков индентирования, выполняемых как в процессе нагрева, так и после нагрева, уменьшается с увеличением температуры от 20 до 100 °С. Длина трещин c уменьшается на пластинах кремния при индентировании во время нагрева от 20 до 100 °С, а после воздействия температуры длина увеличивается. Во время воздействия температуры на пластины вязкость разрушения KIC увеличивается с увеличением температуры: для ориентации (100) - 1,61±0,08 МПам12, для (110) - до 1,60±0,08 МПам12 и для (111) - до 1,66±0,04 МПам12. Установлена прямая корреляция KIC, измеренной во время воздействия температуры, и обратная корреляция KIC, измеренной после воздействия температуры, c удельной поверхностной энергией для ориентаций (100) и (111). Обратная корреляция KIC с у получена на ориентации (110) при воздействии температур 20-40 и 80-100 °С, а после воздействия - прямая корреляция. При 60 °С корреляции нет. Полученные результаты могут быть использованы для улучшения механических свойств кремниевых пластин, используемых в солнечных элементах и микроэлектромеханических системах (работающих при температурах до 100 °С).
Ключевые слова: пластины кремния, температура, вязкость разрушения, метод индентирования, атомно-силовая микроскопия
Адрес для переписки:
Лапицкая В.А.
Институт тепло- и массообмена им. А.В. Лыкова НАН Беларуси, ул. П. Бровки, 15, г. Минск 220072, Беларусь e-mail: vasilinka.92@mail.ru
Для цитирования:
V.A. Lapitskaya, \ T.A. Kuznetsova, S.A. Chizhik.
Influence of Temperature from 20 to 100 °C on Specific Surface
Energy and Fracture Toughness of Silicon Wafers.
Приборы и методы измерений.
2023. Т. 14. № 4. С. 277-283.
DOI: 10.21122/2220-9506-2023-14-4-277-283
Address for correspondence:
Lapitskaya V.A.
A.V. Luikov Heat and Mass Transfer Institute of NAS of Belarus, P. Brovki str, 15, Minsk 220072, Belarus e-mail: vasilinka.92@mail.ru
For citation:
Lapitskaya VA, | Kuznetsova TA, | Chizhik SA.
Influence of Temperature from 20 to 100 °C on Specific Surface
Energy and Fracture Toughness of Silicon Wafers.
Devices and Methods of Measurements. 2023;14(4):277-283.
DOI: 10.21122/2220-9506-2023-14-4-277-283
Introduction
Recently, there has been great interest in the thermomechanical properties of silicon wafers [1] due to their application in the production of solar cells and MEMS operating at elevated temperatures [2]. Under such operating conditions, the formation of cracks, dislocations, and deterioration of the characteristics of semiconductor devices can occur [3]. Elastic-plastic transitions occur when exposed to temperature in silicon [2, 4, 5]. In this case, a change occurs from low-energy brittle fracture to high-energy plastic fracture, which leads to a direct dependence of the mechanical properties of single-crystal silicon on temperature changes [2, 4, 5].
One of the important mechanical properties characterizing the strength and resistance to cracking in a material is the fracture toughness KIC [6]. The fracture toughness of single-crystalline silicon, depending on the orientation, can vary significantly [710] - from 0.60 to 3.30 MPam1/2. In addition to orientation, the influence of temperature on the KIC of single-crystal silicon was established in [5, 8]. Thus, in [5], a change in temperature from 25 to 300 °C leads to an increase in the fracture toughness of (001)-oriented silicon from 0.67 to 3.29 MPam1/2. In addition to orientation and temperature, fracture toughness depends on the specific surface energy of the material [11, 12].
The purpose of the work was to study the effect of temperature from 20 to 100 °C on the fracture toughness and specific surface energy of silicon wafers with (100), (110) and (111) orientations, as well as to establish a correlation between fracture toughness and specific surface energy.
Materials and methods of research
Standard single-crystalline silicon wafers with (100), (110), and (111) orientations were used. The plates were manufactured at the "Kamerton" (branch of INTEGRAL OJSC, Belarus). Plate dimensions: 0100 mm and thickness 0.5 mm.
Silicon wafers were heated on a special thermal platform with an autonomous heating controller (Microtest Machines ODO, Belarus), which was installed under the samples. The temperatures for the study were as follows: 20, 40, 60, 80 and 100 °C. At each temperature, the samples were kept for 10 min. During exposure to each temperature, indentation was performed using a PMT-3M microhardness tester (LOMO, Russia). A Vickers type tip (GOST
9377-81) was used as an indenter. The load on the indenter was 0.5 N. Five indentations were made on each sample. Indentation was also additionally carried out at the same load after the samples had completely cooled.
Studies of the silicon wafers surface, the indentation imprints morphology, determination of roughness and adhesion force were carried out on a Dimension FastScan atomic force microscope (Bruker, USA) in PeakForce QNM mode using standard silicon cantilevers MPP-12120-10 (Bruker, USA) with a cantilever stiffness of 5.7 N/m. Surface roughness was determined according to GOST R 8.700-20101. After visualizing the indentation imprints, the diagonal length of the indentations d and the cracks length from the center of the indentation c were quantified.
Fracture toughness KIC was determined using the formulas given in [13]. The choice of formula depends on the value of c/a (crack length to the length of the indent semi-diagonal) and the type of cracks formed (median or Palmquist) [14, 15].
The specific surface energy (adhesion work) was determined according to the formula [16]:
Y =
F
1 ad
2 nR'
(1)
where Fad is the force of adhesive interaction between the tip of the AFM probe and the surface, N; R is the radius of the probe tip curvature, m.
The radius of the probe tip curvature R was estimated using the reference sample RS-12M - a poly-crystalline titanium roughness sample.
Specific surface energy y was determined on all plates before and after exposure to temperatures in the range from 20 to 100 °C by AFM on several fields of size: 1x 1, 3x3, 5x5, 10x 10, 20x20 and 30x30 ^m2. First, the adhesion force was determined, and then the specific surface energy was calculated using Formula (1).
Results and discussion
The roughness (Figure 1) of the silicon wafers surface varies in the range: from 0.3 to 2.5 nm for the
1 Государственная система обеспечения единства измерений. Методика измерений эффективной высоты шероховатости поверхности с помощью сканирующего зондового атомно-силового микроскопа: ГОСТ 8.700-2010. - Введ. 01.11.2010. - Москва: Национальный стандарт Российской Федерации, 2010. -
12 с.
(100) orientation, from 0.3 to 1.6 nm for the (110) orientation, and from 0.3 to 3.6 nm for the (111) orientation. The specific surface energy y of the surface of the (100) and (111) orientation plates increases with increasing temperature from 20 to 100 °C (Figure 1a, c). In this case, y for the (100) orientation varies in the range from 0.276±0.018 to
0.409±0.033 N/m (Figure 1a), and for the (111) orientation - from 0.254±0.016 to 0.273±0.007 N/m (Figure 1c). For the (110) orientation, y of the surface has a maximum at a temperature of 80 °C and is 0.296±0.017 N/m, and at temperatures of 20 and 100 °C y is almost the same and is 0.247±0.017 N/m and 0.257±0.005 N/m, respectively (Figure 1b).
d
a
0.290 I
0.270
^ 0.250 0.230
4.5 i
20 40 60 80
Temperature, °C
100
120
S
с
г/Г 1 0 -
'Г,
DJ
С
4=
OU 3 1.5 -
О
Pi
0.0
20 40 60 80
Temperature, °C
f
100
120
Figure 1 - Dependence of specific surface energy (a-c) and surface roughness (d-f) of silicon wafers before and after exposure to temperature in the range from 20 to 100 °C: a, d- Si wafer with (100) orientation; b, e - Si plate with (110) orientation; c, f - Si plate orientation (111)
c
After visualization and quantitative determination of the indentation parameters (diagonals length and cracks length), it was found that with an increase in temperature from 20 to 100 °C, the length of the indentation imprints diagonal, performed both during the heating process and after heating, decreases
(Figure 2a, d). During heating, the values of the diagonal length d decrease from 10.21-10.57 ^m to 9.85-10.07 ^m when the temperature changes from 20 to 40 °C. Further, the values practically do not change and are in the range of 9.96-10.04 ^m (Figure 2a).
a
b
e
c
Figure 2 - Dependences of the diagonal length (a, b), crack length from the center of the indentation imprint (b, e) and the c/a ratio (c, f) during (a, b, c) and after (d, e, f) exposure to temperature
The diagonal of the indentation imprints after heating decreases from 10.21-10.57 ^m to 10.2110.38 ^m when the temperature changes from 20 to 40 °C (Figure 2d). In the temperature range of 40-80 °C it remains practically unchanged, and at 100 °C it decreases to 9.77-10.04 ^m (Figure 2d).
The crack length c decreases on silicon wafers upon indentation during heating from 20 to 100 °C (Figure 2b). The c values for all silicon orientations at 20 °C are in the range of 11.78-12.71 ^m (Figure 2b). Exposure to temperature causes the range to decrease to 11.00-11.25 ^m. The length c on silicon wafers of orientation (110) and (111) after heating increases at 100 °C to 12.13 and 13.71 ^m (Figure 2e),
and on the (100) wafer it decreases to 11.25 ^m compared to the value of 12.71 ^m at 20 °C.
The c/a ratio for all samples is above 2 (Figure 2c, f). For samples that were indented during temperature exposure, c/a is in the range of 2.302.45 at 20 °C and decreases to 2.20-2.26 at 100 °C (Figure 2c). The c/a ratio for samples after exposure to temperature increases from 2.30-2.45 at 20 °C to 2.40-2.75 at 100 °C (Figure 2d).
The fracture toughness KIC increases with increasing temperature from 20 to 100 °C while the plates are exposed to temperature (Figure 3a). For the (100) orientation plate, KIC changes from 1.46±0.07 MPam12 to 1.61±0.08 MPa m1/2, for
(110) - from 1.53±0.05 MPam172 to 1.60±0.08 MPam1/2 and for (111) - from 1.52±0.03 MPam1/2 to 1.66±0.04 MPam12 (Figure 3a). After exposure to temperature, fracture toughness decreases with increasing temperature (Figure 3b): for the (100) orientation plate from 1.46±0.07 MPam1/2 to 1.34±0.03 MPam1/2, for (110) - from 1.53±0.05 MPam172
—•—Si(100) -•—Si(l 10) —•— Si( 111)
1.8 и
0 20 40 60 80 100 120
Temperature, °C
a
(100) (110) (111) during exposure to temperature
Y 1.0 -0.1 0.8
The correlation coefficients Ccorr between fracture toughness and specific surface energy of silicon wafers with temperature changes are given in Table. A direct correlation was established (Table) KIC, measured during exposure to temperature, and specific surface energy for wafers (100) and (111) -Ccorr, respectively are equal to 1.0 and 0.8.
The fracture toughness KIC measured after temperature exposure is inversely correlated with the specific surface energy of the (100) and (111) orientation plates. If we determine Ccorr over the entire temperature range from 20 to 100 °C for a (110) orientation plate, then there is practically no correlation between KIC (both during and after exposure to temperature) and y (Table). However, if we consider the ranges before and after 60 °C, then Ccorr is equal to -1.0 (when exposed to temperature) and Ccorr = 1.0 (after exposure).
The presence of a difference in the values of specific surface energy and KIC at a temperature of 60 °C
to 1.39±0.05 MPam12 and for (111) - from 1.52±0.03 MPa m12 to 1.22±0.04 MPam1/2.
The KIC largely depends on the crack length [15, 16]. It should also be noted that the KIC value is influenced by the energy of crack propagation, which in turn is related to the specific surface energy of the material [11, 12].
—•—Si(100) -•—Si(l 10) -•—Si(lll)
1.7 -1
1.1 -I-1-1-1-1-1-1
0 20 40 60 80 100 120
Temperature, °C b
Table
kic_
(100) (110) (111)
after exposure to temperature -0.8 -0.1 -0.9
may be associated with the appearance of an elastic-plastic transition, the appearance of dislocations in the lattice instead of cracks [17].
Conclusion
The specific surface energy and fracture toughness of silicon wafers of three orientations (100), (110) and (111) were studied during and after exposure to temperatures in the range from 20 to 100 °C using atomic force microscopy and the indentation method.
Determined that the specific surface energy y of the surface of the (100) and (111) orientation plates increases with increasing temperature from 20 to 100 °C. The diagonal length of the indentation marks (performed both during the heating process and after heating) decreases by increasing the temperature from 20 to 100 °C. The length of cracks on silicon wafers decreases during indentation during heating
Figure 3 - Dependences of KIC during (a) and after (b) exposure to temperature
Correlation coefficients between fracture toughness KIC and specific surface energy y
from 20 to 100 °C, and after cooling, the length increases.
The fracture toughness KIC behaves similarly. When the plates are exposed to temperature, the fracture toughness KIC increases with increasing temperature: for orientation (100) - 1.61±0.08 MPam1/2,
for (110) - up to 1.60±0.08 MPa m12 and for (111) -
1/2
up to 1.66±0.04 MPam . A direct correlation was established between KIC, measured during exposure to temperature, and the specific surface energy for the (100) and (111) orientations. KIC measured after temperature exposure is inversely correlated with the specific surface energy of the (100) and (111) orientations. An inverse correlation was obtained by KIC at the (110) orientation when exposed to temperatures of 20-40 and 80-100 °C, and after exposure, a direct correlation was obtained. At 60 °C there is no correlation. The results obtained can be used to improve the mechanical properties of silicon wafers used in solar cells and microelectromechanical systems (operating at temperatures up to 100 °C).
Acknowledgments
This research was supported by the grant of Be-larusian Republican Foundation for Fundamental Research BRFFR No. Т22М-006 и Т23МЕ-010, as part of the assignment No. 2.3 SPSR "Energy and nuclear processes and technologies".
References
1. Tilli M, Paulasto-Krockel M, Petzold M, The-uss H, Motooka T, Lindroos V. Handbook of Silicon Based MEMS Materials and Technologies. Elsevier, 2020.636 p.
2. Masolin A, Bouchard PO, Martini R, Bernacki M. Thermo-mechanical and fracture properties in single-crystal silicon, Journal of Materials Science. 2013;48: 979-988. DOI: 10.1007/s10853-012-6713-7
3. Hashimov AM, Hasanli ShM. Influence the heat treatment on the mechanical characteristics of silicon plates, Fizika. 2004;CILD X №4:71-73.
4. Courtney TH. Mechanical Behavior of Materials: Second Edition. Waveland Press;2005. 733 p.
5. Lauener CM, Petho L, Chen M, Xiao Y, Michler J, Wheeler JM. Fracture of Silicon: Influence of rate, positioning accuracy, FIB machining, and elevated temperatures on toughness measured by pillar indentation splitting. Materials & Design. 2018;142:340-349.
DOI: 10.1016/j.matdes.2018.01.015
6. Gdoutos EE. Fracture Mechanics. Cham: Springer. 2020; XIX, 477 p. DOI: 10.1007/1-4020-3153-X
7. McLaughlin JC, Willoughby AFW. Fracture of silicon wafers. Journal of Crystal Growth. 1987;85:83-90. DOI: 10.1016/0022-0248(87)90207-7
8. Mohamed Cherif Ben Romdhane, Hatem Mrad, Fouad Erchiqui, Ridha Ben Mrad. Thermomechanical Study and Fracture Properties of Silicon Wafer under Effect of Crystal Orientation. IOP Conf. Series: Materials Science and Engineering. 2019;521, article № 012004. DOI: doi:10.1088/1757-899X/521/1/012004
9. Tanaka M, Higashida K, Nakashima H, Takagi H, Fujiwara M. Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon. International Journal of Fracture. 2006;139:383-394.
DOI: 10.1007/s10704-006-0021-7
10. Ebrahimi F, Kalwani L. Fracture anisotropy in silicon single crystal. Materials Science and Engineering: A. 1999;268:116-126.
DOI: 10.1016/S0921-5093(99)00077-5
11. Tanaka M, Higashida K, Nakashima H, Takagi H, Fujiwara M. Fracture toughness evaluated by indentation methods and its relation to surface energy in silicon single crystals. Materials Transactions. 2003;44(4):681-684. DOI: 10.2320/matertrans.44.681
12. Yang C, Pham J. On the Fracture Toughness Measurement of Thin Film Coated Silicon Wafers. Silicon. 2015;7:27-30.
DOI: 10.1007/s12633-014-9215-1
13. Lapitskaya VA, Kuznetsova TA, Chizhik SA, Warcholinski B. Methods for Accuracy Increasing of Solid Brittle Materials Fracture Toughness Determining. Devices and Methods of Measurements. 2022;13(1):40-49. DOI: 10.21122/2220-9506-2022-13-1-40-49
14. Lapitskaya VA, Kuznetsova TA, Khudoley AL, Khabarava AV, Chizhik SA, Aizikovich SM, Sady-rin EV. Influence of polishing technique on crack resistance of quartz plates. International Journal of Fracture. 2021;231(1):61-77.
DOI: 10.1007/s10704-021-00564-5
15. Lapitskaya VA, Kuznetsova TA, Khabarava AV, Chizhik SA, Aizikovich SM, Sadyrin EV, Mitrin BI, Wei-fu Sun. The use of AFM in assessing the crack resistance of silicon wafers of various orientations. Engineering Fracture Mechanics. 2022;259, Article №. 107926. DOI: 10.1016/j.engfracmech.2021.107926
16. Wang QJ, Chung YW. Encyclopedia of Tribol-ogy. Boston: Springer. 2013. 4192 p.
DOI: 10.1007/978-0-387-92897-5
17. Shigeki Nakao, Taeko Ando, Mitsuhiro Shikida, Kazuo Sato. Effect of temperature on fracture toughness in a single-crystal-silicon film and transition in its fracture mode. Journal of micromechanics and microengineering. 2008;18, article № 015026 (7 pp).
DOI: 10.1088/0960-1317/18/1/015026
