{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105928"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105928","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Thermomechanical behavior of single crystal silicon microbeams under bending at elevated temperatures","abstract":"Understanding the deformation mechanisms of materials at high temperature at the micro/nanoscale became important with the increasing miniaturization of electronic and mechanical devices. Silicon is the most commonly used material in these devices. Bulk silicon is brittle at room temperature, but is ductile at 550 ºC - a phenomenon known as brittle-to-ductile transition (BDT). Recently, there has been a speculation in the literature that BDT is size dependent - smaller the size, lower is the BDT temperature. This led to a controversy: some studies report ductility at room temperature, others reported brittle behavior. This thesis challenges the notion of a precise BDT temperature in single crystal silicon, unlike Curie temperature in ferromagnetic materials when phase change occurs. We hypothesize that brittleness or ductility in silicon is the outcome of a competition between cleavage or plastic deformation due to presence of flaws and nucleation of dislocation. At any temperature, dislocations may nucleate at high enough stress, τn, if flaw induced fracture can be avoided, and as long as τn < τc, the cleavage stress of silicon. However, τn is temperature dependent. It increases with decrease in temperature. On the other hand, flaw probability decreases with sample size (increased flaw tolerance) or the size of the high stress zone. This gives access to high stress in small samples and hence an apparent size dependence of BDT temperature. We tested the hypothesis by carrying out experiments with single crystal silicon micro beams under near pure bending which limits the high stress region to a small volume of the material near the surface and the support. We developed a novel method using microfabrication to carry out these experiments. The method involves a silicon MEMS stage that allows to test silicon samples under bending at high temperature (up to 450°C) in-situ in SEM. The stage performance was first tested by measuring the elastic modulus of SCS micro-beams oriented along [0 1 1] and by comparing the measured value with that in the literature. We found that the strength of silicon increases compared to the uniaxial tension test results. Second, specimens with thicknesses 2-5 µm exhibited BDT at 400 ºC, much less than the bulk value of 550ºC. Third, we studied stress relaxation behavior in silicon after initiation of ductility at 400 ºC. Here, silicon deforms with time while stress decreases. We also revealed the detailed mechanism of stress relaxation using a combined SEM, TEM and AFM analysis. We find, at peak stress of about 3.2 GPa, multiple dislocation sites nucleate simultaneously. Dislocations begin to initiate from these sites with time mediating plastic deformation and stress relaxation. We developed a simple mechanistic model to correlate dislocations activities, nucleation and glide, with changes in load during stress relaxation. The model takes into consideration the effect of stress gradient and predicts the plastic zone size along the beam thickness.","abstract_html":"Understanding the deformation mechanisms of materials at high temperature at the micro/nanoscale became important with the increasing miniaturization of electronic and mechanical devices. Silicon is the most commonly used material in these devices. Bulk silicon is brittle at room temperature, but is ductile at 550 ºC - a phenomenon known as brittle-to-ductile transition (BDT). Recently, there has been a speculation in the literature that BDT is size dependent - smaller the size, lower is the BDT temperature. This led to a controversy: some studies report ductility at room temperature, others reported brittle behavior. This thesis challenges the notion of a precise BDT temperature in single crystal silicon, unlike Curie temperature in ferromagnetic materials when phase change occurs. We hypothesize that brittleness or ductility in silicon is the outcome of a competition between cleavage or plastic deformation due to presence of flaws and nucleation of dislocation. At any temperature, dislocations may nucleate at high enough stress, τn, if flaw induced fracture can be avoided, and as long as τn &lt; τc, the cleavage stress of silicon. However, τn is temperature dependent. It increases with decrease in temperature. On the other hand, flaw probability decreases with sample size (increased flaw tolerance) or the size of the high stress zone. This gives access to high stress in small samples and hence an apparent size dependence of BDT temperature. We tested the hypothesis by carrying out experiments with single crystal silicon micro beams under near pure bending which limits the high stress region to a small volume of the material near the surface and the support. We developed a novel method using microfabrication to carry out these experiments. The method involves a silicon MEMS stage that allows to test silicon samples under bending at high temperature (up to 450°C) in-situ in SEM. The stage performance was first tested by measuring the elastic modulus of SCS micro-beams oriented along [0 1 1] and by comparing the measured value with that in the literature. We found that the strength of silicon increases compared to the uniaxial tension test results. Second, specimens with thicknesses 2-5 µm exhibited BDT at 400 ºC, much less than the bulk value of 550ºC. Third, we studied stress relaxation behavior in silicon after initiation of ductility at 400 ºC. Here, silicon deforms with time while stress decreases. We also revealed the detailed mechanism of stress relaxation using a combined SEM, TEM and AFM analysis. We find, at peak stress of about 3.2 GPa, multiple dislocation sites nucleate simultaneously. Dislocations begin to initiate from these sites with time mediating plastic deformation and stress relaxation. We developed a simple mechanistic model to correlate dislocations activities, nucleation and glide, with changes in load during stress relaxation. The model takes into consideration the effect of stress gradient and predicts the plastic zone size along the beam thickness.","abstract_has_math":false,"creators":["Elhebeary, Mohamed Mohamed Rashad Ibrahim"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Saif, Taher","Sehitoglu, Huseyin","Krogstad, Jessica","Tawfick, Sameh"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:59:44Z","date_published":"2019-11-26T20:59:44Z","updated_at":"2026-07-22T22:24:45Z","subjects":["Silicon, stress relaxation, plasticity, bending, MEMS, insitu SEM"],"languages":["en"],"rights":["Copyright 2019 by Mohamed Elhebeary"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105928","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Saif, Taher","Sehitoglu, Huseyin","Krogstad, Jessica","Tawfick, Sameh"]},{"key":"dc:creator","label":"Author","values":["Elhebeary, Mohamed Mohamed Rashad Ibrahim"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:59:44Z","2021-12-13T10:15:25Z","2019-07-11","2019-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Silicon, stress relaxation, plasticity, bending, MEMS, insitu SEM"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 by Mohamed Elhebeary"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105928"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Understanding the deformation mechanisms of materials at high temperature at the micro/nanoscale became important with the increasing miniaturization of electronic and mechanical devices. Silicon is the most commonly used material in these devices. Bulk silicon is brittle at room temperature, but is ductile at 550 ºC - a phenomenon known as brittle-to-ductile transition (BDT). Recently, there has been a speculation in the literature that BDT is size dependent - smaller the size, lower is the BDT temperature. This led to a controversy: some studies report ductility at room temperature, others reported brittle behavior. This thesis challenges the notion of a precise BDT temperature in single crystal silicon, unlike Curie temperature in ferromagnetic materials when phase change occurs. We hypothesize that brittleness or ductility in silicon is the outcome of a competition between cleavage or plastic deformation due to presence of flaws and nucleation of dislocation. At any temperature, dislocations may nucleate at high enough stress, τn, if flaw induced fracture can be avoided, and as long as τn < τc, the cleavage stress of silicon. However, τn is temperature dependent. It increases with decrease in temperature. On the other hand, flaw probability decreases with sample size (increased flaw tolerance) or the size of the high stress zone. This gives access to high stress in small samples and hence an apparent size dependence of BDT temperature. We tested the hypothesis by carrying out experiments with single crystal silicon micro beams under near pure bending which limits the high stress region to a small volume of the material near the surface and the support. We developed a novel method using microfabrication to carry out these experiments. The method involves a silicon MEMS stage that allows to test silicon samples under bending at high temperature (up to 450°C) in-situ in SEM. The stage performance was first tested by measuring the elastic modulus of SCS micro-beams oriented along [0 1 1] and by comparing the measured value with that in the literature. We found that the strength of silicon increases compared to the uniaxial tension test results. Second, specimens with thicknesses 2-5 µm exhibited BDT at 400 ºC, much less than the bulk value of 550ºC. Third, we studied stress relaxation behavior in silicon after initiation of ductility at 400 ºC. Here, silicon deforms with time while stress decreases. We also revealed the detailed mechanism of stress relaxation using a combined SEM, TEM and AFM analysis. We find, at peak stress of about 3.2 GPa, multiple dislocation sites nucleate simultaneously. Dislocations begin to initiate from these sites with time mediating plastic deformation and stress relaxation. We developed a simple mechanistic model to correlate dislocations activities, nucleation and glide, with changes in load during stress relaxation. The model takes into consideration the effect of stress gradient and predicts the plastic zone size along the beam thickness.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Mohamed Elhebeary, accepted the attached license on 2019-07-10 at 12:20.","The student, Mohamed Elhebeary, submitted this Dissertation for approval on 2019-07-10 at 15:15.","This Dissertation was approved for publication on 2019-07-11 at 16:55.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14244 on 2019-11-26 at 14:03:36","Made available in DSpace on 2019-11-26T20:59:44Z (GMT). No. of bitstreams: 3 ELHEBEARY-DISSERTATION-2019.pdf: 4866621 bytes, checksum: 895abb082d804056533b9f35dd0aa508 (MD5) Thesis Elhebeary.docx: 19323756 bytes, checksum: b985d8e5a0d913a04679a84753964c11 (MD5) LICENSE.txt: 4214 bytes, checksum: 815d411d7a4877c6d76c745c4a8122f0 (MD5) Previous issue date: 2019-07-11","Embargo set by: Seth Robbins for item 113075 Lift date: 2021-11-26T20:59:54Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","U of I Only Restriction set for Item 113075 on 2019-12-13T19:56:01Z with date 2021-12-13 by astein@illinois.edu.","U of I Only Restriction set for Item 113075 on 2019-12-13T19:56:08Z with date 2021-12-13 by astein@illinois.edu.","U of I Only Restriction Lifted for Item 113075 on 2021-12-13T10:15:25Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Thermomechanical behavior of single crystal silicon microbeams under bending at elevated temperatures"]}]}],"canonical_facts":{"dc:contributor":["Saif, Taher","Sehitoglu, Huseyin","Krogstad, Jessica","Tawfick, Sameh"],"dc:creator":["Elhebeary, Mohamed Mohamed Rashad Ibrahim"],"dc:date":["2019-11-26T20:59:44Z","2021-12-13T10:15:25Z","2019-07-11","2019-08"],"dc:description":["Understanding the deformation mechanisms of materials at high temperature at the micro/nanoscale became important with the increasing miniaturization of electronic and mechanical devices. Silicon is the most commonly used material in these devices. Bulk silicon is brittle at room temperature, but is ductile at 550 ºC - a phenomenon known as brittle-to-ductile transition (BDT). Recently, there has been a speculation in the literature that BDT is size dependent - smaller the size, lower is the BDT temperature. This led to a controversy: some studies report ductility at room temperature, others reported brittle behavior. This thesis challenges the notion of a precise BDT temperature in single crystal silicon, unlike Curie temperature in ferromagnetic materials when phase change occurs. We hypothesize that brittleness or ductility in silicon is the outcome of a competition between cleavage or plastic deformation due to presence of flaws and nucleation of dislocation. At any temperature, dislocations may nucleate at high enough stress, τn, if flaw induced fracture can be avoided, and as long as τn < τc, the cleavage stress of silicon. However, τn is temperature dependent. It increases with decrease in temperature. On the other hand, flaw probability decreases with sample size (increased flaw tolerance) or the size of the high stress zone. This gives access to high stress in small samples and hence an apparent size dependence of BDT temperature. We tested the hypothesis by carrying out experiments with single crystal silicon micro beams under near pure bending which limits the high stress region to a small volume of the material near the surface and the support. We developed a novel method using microfabrication to carry out these experiments. The method involves a silicon MEMS stage that allows to test silicon samples under bending at high temperature (up to 450°C) in-situ in SEM. The stage performance was first tested by measuring the elastic modulus of SCS micro-beams oriented along [0 1 1] and by comparing the measured value with that in the literature. We found that the strength of silicon increases compared to the uniaxial tension test results. Second, specimens with thicknesses 2-5 µm exhibited BDT at 400 ºC, much less than the bulk value of 550ºC. Third, we studied stress relaxation behavior in silicon after initiation of ductility at 400 ºC. Here, silicon deforms with time while stress decreases. We also revealed the detailed mechanism of stress relaxation using a combined SEM, TEM and AFM analysis. We find, at peak stress of about 3.2 GPa, multiple dislocation sites nucleate simultaneously. Dislocations begin to initiate from these sites with time mediating plastic deformation and stress relaxation. We developed a simple mechanistic model to correlate dislocations activities, nucleation and glide, with changes in load during stress relaxation. The model takes into consideration the effect of stress gradient and predicts the plastic zone size along the beam thickness.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Mohamed Elhebeary, accepted the attached license on 2019-07-10 at 12:20.","The student, Mohamed Elhebeary, submitted this Dissertation for approval on 2019-07-10 at 15:15.","This Dissertation was approved for publication on 2019-07-11 at 16:55.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14244 on 2019-11-26 at 14:03:36","Made available in DSpace on 2019-11-26T20:59:44Z (GMT). No. of bitstreams: 3 ELHEBEARY-DISSERTATION-2019.pdf: 4866621 bytes, checksum: 895abb082d804056533b9f35dd0aa508 (MD5) Thesis Elhebeary.docx: 19323756 bytes, checksum: b985d8e5a0d913a04679a84753964c11 (MD5) LICENSE.txt: 4214 bytes, checksum: 815d411d7a4877c6d76c745c4a8122f0 (MD5) Previous issue date: 2019-07-11","Embargo set by: Seth Robbins for item 113075 Lift date: 2021-11-26T20:59:54Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","U of I Only Restriction set for Item 113075 on 2019-12-13T19:56:01Z with date 2021-12-13 by astein@illinois.edu.","U of I Only Restriction set for Item 113075 on 2019-12-13T19:56:08Z with date 2021-12-13 by astein@illinois.edu.","U of I Only Restriction Lifted for Item 113075 on 2021-12-13T10:15:25Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/105928"],"dc:language":["en"],"dc:rights":["Copyright 2019 by Mohamed Elhebeary"],"dc:subject":["Silicon, stress relaxation, plasticity, bending, MEMS, insitu SEM"],"dc:title":["Thermomechanical behavior of single crystal silicon microbeams under bending at elevated temperatures"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:45Z"}