<Page> Exhibit 4.1 AMENDMENT TO RIGHTS AGREEMENT This AMENDMENT (the "Amendment") is being entered into as of September 6, 2001, between Veeco Instruments Inc., a Delaware corporation (the "Company"), and American Stock Transfer and Trust Company, a New York banking corporation, as rights agent (the "Rights Agent"). WHEREAS, the Company and the Rights Agent are parties to a Rights Agreement, dated as of March 13, 2001, between the Company and the Rights Agent (the "Rights Agreement"); WHEREAS, it is proposed that the Company enter into an Agreement and Plan of Merger (the "AE Merger Agreement") by and among the Company, Veeco Acquisition Corp., a Minnesota corporation and a wholly owned subsidiary of the Company ("Veeco Acquisition"), Applied Epi, Inc., a Minnesota corporation ("Applied Epi"), and certain Applied Epi security holders pursuant to which Veeco Acquisition will merge with and into Applied Epi with the result that Applied Epi will be the surviving corporation and shall become a wholly owned subsidiary of the Company (the "AE Merger"); WHEREAS, pursuant to the AE Merger, Paul E. Colombo, Founder and Chairman of Applied Epi, will receive 3,646,969 shares of common stock and other securities of the Company, representing approximately 14.7% of the outstanding shares of common stock of the Company as of September 6, 2001; and WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company and the Rights Agent may supplement or amend the Rights Agreement in accordance with the provisions of Section 27 thereof. The Company now desires to amend the Rights Agreement as set forth in this Amendment and deems such amendments to be necessary and desirable. Capitalized terms used but not defined herein shall have the meanings ascribed to such terms in the Rights Agreement. NOW THEREFORE, in consideration of the premises and the mutual agreement herein set forth, the parties hereby agree as follows: 1. AMENDMENT OF SECTION 1(a). Section 1(a) of the Rights Agreement is hereby amended to add the following sentence at the end thereof: "Notwithstanding anything in this Agreement to the contrary, for so long as Paul E. Colombo and/or any of his existing or future Affiliates or Associates that have reported or are required to report ownership on Schedule 13G or Schedule 13D under the Exchange Act (or any comparable or successor report) and do not state any intention to, or reserve the right to, control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of Schedule 13D (other than the disposition of the Common Stock), none of Paul E. Colombo or any of his existing or future Affiliates or Associates shall be deemed to be an Acquiring Person solely by virtue of: (i) the execution of the AE Merger Agreement; (ii) the acquisition of Common Stock or other securities of the Company by Paul E. Colombo or his existing or future Affiliates or Associates <Page> pursuant to the AE Merger; (iii) the grant by the Company of options to purchase Common Stock to Paul E. Colombo or his existing or future Affiliates or Associates in their capacity as consultants, employees or directors of the Company, or the exercise of such options; (iv) the acquisition by Paul E. Colombo or his existing or future Affiliates or Associates of up to one percent (1%) of the shares of Common Stock then outstanding in excess of the percentage of shares of Common Stock beneficially owned by Paul E. Colombo or his existing or future Affiliates or Associates under clauses (i), (ii) and (iii) above; and/or (v) the transfer of shares of Common Stock received pursuant to (ii), (iii) or (iv) above by and among Paul E. Colombo and/or any of his existing or future Affiliates or Associates." 2. AMENDMENT OF SECTION 1(kk). Section 1(kk) of the Rights Agreement is hereby amended to add the following proviso at the end thereof: "; PROVIDED, HOWEVER, that for so long as Paul E. Colombo and/or any of his existing or future Affiliates or Associates that have reported or are required to report ownership on Schedule 13G or Schedule 13D under the Exchange Act (or any comparable or successor report) and do not state any intention to, or reserve the right to, control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of Schedule 13D (other than the disposition of the Common Stock), no Triggering Event shall result solely by virtue of: (i) the execution of the AE Merger Agreement; (ii) the acquisition of Common Stock or other securities of the Company by Paul E. Colombo or his existing or future Affiliates or Associates pursuant to the AE Merger; (iii) the grant by the Company of options to purchase Common Stock to Paul E. Colombo or his existing or future Affiliates or Associates in their capacity as consultants, employees or directors of the Company, or the exercise of such options; (iv) the acquisition by Paul E. Colombo or his existing or future Affiliates or Associates of up to one percent (1%) of the shares of Common Stock then outstanding in excess of the percentage of shares of Common Stock beneficially owned by Paul E. Colombo or his existing or future Affiliates or Associates under clauses (i), (ii) and (iii) above; and/or (v) the transfer of shares of Common Stock received pursuant to (ii), (iii) or (iv) above by and among Paul E. Colombo and/or any of his existing or future Affiliates or Associates." 3. AMENDMENT OF SECTION 1. Section 1 of the Rights Agreement is hereby amended to add the following subparagraphs at the end thereof: (ll) "Applied Epi" shall mean Applied Epi, Inc., a Minnesota corporation. (mm) "AE Merger" shall mean the merger of Veeco Acquisition with and into Applied Epi pursuant to the AE Merger Agreement with the result that Applied Epi will be the surviving corporation and shall become a wholly owned subsidiary of the Company. 2 <Page> (nn) "AE Merger Agreement" shall have the meaning set forth in Section 35 hereof. (oo) "Veeco Acquisition" shall mean Veeco Acquisition Corp., a Minnesota corporation and a wholly owned subsidiary of the Company. 4. AMENDMENT OF SECTION 3(a). Section 3(a) of the Rights Agreement is hereby amended to add the following sentence at the end thereof: "Notwithstanding anything in this Agreement to the contrary, for so long as Paul E. Colombo and/or any of his existing or future Affiliates or Associates that have reported or are required to report ownership on Schedule 13G or Schedule 13D under the Exchange Act (or any comparable or successor report) and do not state any intention to, or reserve the right to, control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of Schedule 13D (other than the disposition of the Common Stock), a Distribution Date shall not be deemed to have occurred solely by virtue of: (i) the execution of the AE Merger Agreement; (ii) the acquisition of Common Stock or other securities of the Company by Paul E. Colombo or his existing or future Affiliates or Associates pursuant to the AE Merger; (iii) the grant by the Company of options to purchase Common Stock to Paul E. Colombo or his existing or future Affiliates or Associates in their capacity as consultants, employees or directors of the Company, or the exercise of such options; (iv) the acquisition by Paul E. Colombo or his existing or future Affiliates or Associates of up to one percent (1%) of the shares of Common Stock then outstanding in excess of the percentage of shares of Common Stock beneficially owned by Paul E. Colombo or his existing or future Affiliates or Associates under clauses (i), (ii) and (iii) above; and/or (v) the transfer of shares of Common Stock received pursuant to (ii), (iii) or (iv) above by and among Paul E. Colombo and/or any of his existing or future Affiliates or Associates." 5. AMENDMENT OF SECTION 7(a). Section 7(a) of the Rights Agreement is hereby amended to add the following sentence at the end thereof: "Notwithstanding anything in this Agreement to the contrary, for so long as Paul E. Colombo and/or any of his existing or future Affiliates or Associates that have reported or are required to report ownership on Schedule 13G or Schedule 13D under the Exchange Act (or any comparable or successor report) and do not state any intention to, or reserve the right to, control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of Schedule 13D (other than the disposition of the Common Stock), none of: (i) the execution of the AE Merger Agreement; (ii) the acquisition of Common Stock or other securities of the Company by Paul E. Colombo or his existing or future Affiliates or Associates pursuant to the AE Merger; (iii) the grant by the Company of options to purchase Common Stock to Paul E. Colombo or his existing or future Affiliates or Associates in their capacity as consultants, employees or directors of the Company, or the exercise of such options; (iv) the acquisition by Paul E. Colombo or his existing or future Affiliates or Associates 3 <Page> of up to one percent (1%) of the shares of Common Stock then outstanding in excess of the percentage of shares of Common Stock beneficially owned by Paul E. Colombo or his existing or future Affiliates or Associates under clauses (i), (ii) and (iii) above; and/or (v) the transfer of shares of Common Stock received pursuant to (ii), (iii) or (iv) above by and among Paul E. Colombo and/or any of his existing or future Affiliates or Associates shall be deemed to be events that cause the Rights to become exercisable pursuant to the provisions of this Section 7 or otherwise." 6. AMENDMENT OF SECTION 11. Section 11 of the Rights Agreement is hereby amended to add the following sentence after the first sentence of said Section: "Notwithstanding anything in this Agreement to the contrary, for so long as Paul E. Colombo and/or any of his existing or future Affiliates or Associates that have reported or are required to report ownership on Schedule 13G or Schedule 13D under the Exchange Act (or any comparable or successor report) and do not state any intention to, or reserve the right to, control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of Schedule 13D (other than the disposition of the Common Stock), none of: (i) the execution of the AE Merger Agreement; (ii) the acquisition of Common Stock or other securities of the Company by Paul E. Colombo or his existing or future Affiliates or Associates pursuant to the AE Merger; (iii) the grant by the Company of options to purchase Common Stock to Paul E. Colombo or his existing or future Affiliates or Associates in their capacity as consultants, employees or directors of the Company, or the exercise of such options; (iv) the acquisition by Paul E. Colombo or his existing or future Affiliates or Associates of up to one percent (1%) of the shares of Common Stock then outstanding in excess of the percentage of shares of Common Stock beneficially owned by Paul E. Colombo or his existing or future Affiliates or Associates under clauses (i), (ii) and (iii) above; and/or (v) the transfer of shares of Common Stock received pursuant to (ii), (iii) or (iv) above by and among Paul E. Colombo and/or any of his existing or future Affiliates or Associates shall be deemed to be events of the type described in this Section 11 or to cause the Rights to be adjusted or to become exercisable in accordance with this Section 11." 7. ADDITION OF SECTION 35. The Rights Agreement is hereby amended to add the following new Section 35: "Section 35. MERGER WITH APPLIED EPI The Company, Veeco Acquisition and Applied Epi have entered into an Agreement and Plan of Merger, dated as of September 6, 2001, as it may be amended from time to time (the "AE Merger Agreement"). Notwithstanding anything in this Agreement to the contrary, if the AE Merger Agreement shall be terminated for any reason, then, effective as of the time of such termination, the following provisions which were added to this Agreement by the Amendment to Rights Agreement, dated as of September 6, 2001, shall be deemed repealed and deleted without any further action on the part of the Company or the Rights 4 <Page> Agent: (1) the last sentence of Section 1(a) hereof, (2) the proviso at the end of Section 1(kk) hereof, (3) subsections (ll), (mm), (nn) and (oo) of Section 1 hereof, (4) the last sentence of Section 3(a) hereof, (5) the last sentence of Section 7(a) hereof and (6) the second sentence of Section 11 hereof." 8. EFFECTIVENESS. This Amendment shall be deemed effective as of the date first written above. Except as amended hereby, the Rights Agreement shall remain in full force and effect and shall be otherwise unaffected hereby. 9. MISCELLANEOUS. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such state applicable to contracts to be made and performed entirely within such state without giving effect to the principles of conflict of laws thereof. This Amendment may be executed in any number of counterparts, 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. If any term or other provision of this Amendment is determined to be invalid, illegal or incapable of being enforced by any rule of law, or public policy, all other terms and provisions of this Amendment shall nevertheless remain in full force and effect and upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, this Amendment and such term or other provision shall be deemed to have been amended so as to effect the original intent of the parties as closely as possible in an acceptable manner to the board of directors of the Company. 5 <Page> IN WITNESS WHEREOF, this Amendment to the Rights Agreement is executed under seal as of the date first set forth above. VEECO INSTRUMENTS INC. By: /s/ Edward H. Braun -------------------------------- Name: Edward H. Braun Title: Chief Executive Officer and President AMERICAN STOCK TRANSFER AND TRUST COMPANY By: /s/ Herbert J. Lemmer -------------------------------- Name: Herbert J. Lemmer Title: Vice President and General Counsel 6