Exhibit 31.1

Certifications

Certification pursuant to Section 302
of the Sarbanes-Oxley Act of 2002

I, Timothy E. Brog, certify that:

| | 1. | I have reviewed this Annual Report on Form 10-K/A of Rubicon Technology, Inc. (the “registrant”);
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| | 2. | Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact
necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with
respect to the period covered by this report;
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| | 3. | Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in
all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods
presented in this report;
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| | 4. | The registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls
and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined
in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:
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| | a) | designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our
supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known
to us by others within those entities, particularly during the period in which this report is being prepared;
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| | b) | designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed
under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of
financial statements for external purposes in accordance with generally accepted accounting principles;
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| | c) | evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions
about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on
such evaluation; and
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| | d) | disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during
the registrant’s most recent fiscal quarter (the registrant’s fourth fiscal quarter in the case of an annual report)
that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial
reporting; and
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| | 5. | The registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control
over financial reporting, to the registrant’s auditors and the audit committee of the registrant’s board of directors
(or persons performing the equivalent functions):
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| | a) | all significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting
which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize and report financial
information; and
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| | b) | any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s
internal control over financial reporting.
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|                     |     |                                      
|-------------------- | --- | -------------------------------------
|Date: April 29, 2020 | By: | /s/ Timothy E. Brog                  
|                     |     | Timothy E. Brog                      
|                     |     | President and Chief Executive Officer