Exhibit 4.1

Amendment No. 2 to Rights Agreement, dated as of September 18, 2012,

between Ramtron International Corporation and Computershare Trust Company, LLC, as Rights Agent.

This Amendment No. 2 to Rights Agreement (this “Amendment”) is effective as of September 18, 2012, and is by and between Computershare Trust Company, N.A., a Delaware corporation (“Agent”), having its principal place of business at 250 Royall Street, Canton, Massachusetts, 02021; and Ramtron International Corporation, a Delaware corporation (“Ramtron” or the “Company”), having its principal place of business at 1850 Ramtron Drive, Colorado Springs, CO 80921. Ramtron and/or Agent may be referred to herein as a “Party” or the “Parties,” as the case may require.

WITNESSETH:

WHEREAS, Ramtron and the original Rights Agent entered into the Rights Agreement dated as of April 19, 2001 (as amended, the “Rights Agreement”);

WHEREAS, Ramtron and Agent entered into the Assumption of Rights Agreement effective July 1, 2007, pursuant to which Agent became the successor Rights Agent under and pursuant to the Rights Agreement;

WHEREAS, Ramtron and Agent entered into Amendment No. 1 to Rights Agreement effective March 2, 2011;

WHEREAS, the Board of Directors of the Company (the “Board”) has determined that it is in the best interests of the Company and its stockholders to amend the Rights Agreement as set forth herein immediately prior to and in connection with the execution of the Agreement and Plan of Merger, dated as of September 18, 2012 (as amended, modified or supplemented, from time to time, the “Merger Agreement”), by and among Cypress Semiconductor Corporation, a Delaware corporation (“Parent”), Rain Acquisition Corp., a Delaware corporation and wholly-owned subsidiary of Parent (“Purchaser”), and the Company;

WHEREAS, the Company desires to amend the Rights Agreement pursuant to Section 27 of the Rights Agreement, immediately prior to entering into the Merger Agreement, to facilitate the transactions contemplated by the Merger Agreement; and

WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company has delivered to the Agent a certificate signed by an appropriate officer of the Company which states that this Amendment is in compliance with the terms of Section 27 of the Rights Agreement; and

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements herein set forth, the parties hereby agree as follows:

SECTION 1. Amendment to Section 1

a. The definition of “Acquiring Person” in Section 1(a) of the Rights Agreement is hereby amended by adding the following sentence to the end of said definition:

“Notwithstanding anything in this Agreement to the contrary, none of Parent, Purchaser or any of their respective Affiliates or Associates shall be or become an Acquiring Person, and the term “Acquiring Person” shall not include any of Parent, Purchaser or any of their respective Affiliates or Associates, solely by reason of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the public announcement, commencement or consummation of the Offer, Merger or Top-Up Option, (iii) the public announcement, commencement or consummation of any of the other transactions contemplated by the Merger Agreement, or (iv) the acceptance for payment and purchase or exchange of the Rights pursuant to the Merger Agreement, including, without limitation, in connection with the Offer, the Merger or the exercise of the Top-Up Option.”

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b. The definition of “Stock Acquisition Date” in Section 1(ee) of the Rights Agreement is hereby amended by adding the following sentence to the end of said definition:

“Notwithstanding anything in this Agreement to the contrary, no Stock Acquisition Date shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the public announcement, commencement or consummation of the Offer, Merger or Top-Up Option, (iii) the public announcement, commencement or consummation of any of the other transactions contemplated by the Merger Agreement, or (iv) the acceptance for payment and purchase or exchange of the Rights pursuant to the Merger Agreement, including, without limitation, in connection with the Offer, the Merger or the exercise of the Top-Up Option.”

c. The definition of “Triggering Event” in Section 1(jj) of the Rights Agreement is hereby amended by adding the following sentence to the end of said definition:

“Notwithstanding anything in this Agreement to the contrary, no Triggering Event shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the public announcement, commencement or consummation of the Offer, Merger or Top-Up Option, (iii) the public announcement, commencement or consummation of any of the other transactions contemplated by the Merger Agreement, or (iv) the acceptance for payment and purchase or exchange of the Rights pursuant to the Merger Agreement, including, without limitation, in connection with the Offer, the Merger or the exercise of the Top-Up Option.”

d. Section 1 of the Rights Agreement is hereby amended by inserting each of the following definitions in its appropriate alphabetical order in Section 1:

“Effective Time” shall have the meaning ascribed to such term in the Merger Agreement.

“Merger” shall have the meaning ascribed to such term in the Merger Agreement.

“Merger Agreement” shall mean that certain Agreement and Plan of Merger by and among Parent, Purchaser and the Company, dated as of September 18, 2012 (as such agreement may be amended from time to time).

“Offer” shall have the meaning ascribed to such term in the Merger Agreement.

“Parent” means Cypress Semiconductor Corporation, a Delaware corporation.

“Purchaser” means Rain Acquisition Corp., a Delaware corporation and wholly-owned subsidiary of Parent.

“Top-Up Option” shall have the meaning ascribed to such term in the Merger Agreement.”

SECTION 2. Amendment to Section 3(a). The definition of “Distribution Date” in Section 3(a) of the Rights Agreement is hereby amended by adding the following sentence to the end of said definition:

“notwithstanding anything in this Agreement to the contrary, no Distribution Date shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the public announcement, commencement or consummation of the Offer, Merger or Top-Up Option, (iii) the public announcement, commencement or consummation of any of the other transactions contemplated by the Merger Agreement, or (iv) the acceptance for payment and purchase or exchange of the Rights pursuant to the Merger Agreement, including, without limitation, in connection with the Offer, the Merger or the exercise of the Top-Up Option.”

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SECTION 3. Amendment to Section 7(a). Section 7(a) of the Rights Agreement is hereby deleted in its entirety and replaced with the following:

“Subject to Section 7(e) hereof, at any time after the Distribution Date the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein including, without limitation, the restrictions on exercisability set forth in Section 9(c), Section 11(a)(iii) and Section 23(a) hereof) in whole or in part upon surrender of the Rights Certificate, with the form of election to purchase and the certificate on the reverse side thereof duly executed, to the Rights Agent at the principal office or offices of the Rights Agent designated for such purpose, together with payment of the aggregate Purchase Price with respect to the total number of one one-hundredths of a share (or other securities, cash or other assets, as the case may be) as to which such surrendered Rights are then exercisable, at or prior to the earlier of (i) 5:00 p.m., New York City time, on April 19, 2016 or such later date as may be established by the Board of Directors prior to the expiration of the Rights (such date, as it may be extended by the Board, the “Final Expiration Date”), (ii) the time at which the Rights are redeemed or exchanged as provided in Section 23 and Section 24 hereof, or (iii) immediately prior to the Effective Time (the earlier of (i), (ii) or (iii) being herein referred to as the “Expiration Date”).”

SECTION 4. Amendment to Section 13. Section 13 of the Rights Agreement is hereby amended by adding the following Section 13(e) to the end of Section 13:

“Notwithstanding anything in this Agreement to the contrary, the provisions of Section 13 shall not be applicable to the Offer, Merger or Top-Up Option.”

SECTION 5. Full force and Effect. Except as expressly amended hereby, the Agreement shall continue in full force and effect in accordance with the provisions thereof and is ratified and confirmed in all respects.

SECTION 6. Governing Law. This Amendment shall be deemed to be a contract made under the law of the State of Delaware and for all purposes shall be governed by and construed in accordance with the law of that State applicable to contracts made and to be performed entirely within that State.

SECTION 7. Counterparts; Effectiveness. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. This Amendment shall be effective as of the date hereof. A signature to this Amendment transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

SECTION 8. Descriptive Headings. Descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

SECTION 9. Rights Agreement as Amended. From and after the date hereof, any reference to the Agreement shall mean the Agreement as amended hereby.

SECTION 10. Severability. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties have caused this Amendment to be duly executed as of the day and year first above written.