ts3201f07 - EMSE 201 Introduction to Ma teria ls Science...

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5 December 2007 Name: Department of Materials Science and Engineering 1 of 5 Case Western Reserve University Test #3 — 75 minutes; 150 points; 6 questions; 5 pages; 15% of course grade Partial credit will be given for correct set-ups and reasoning. Give units on numerical answers where ap- propriate. Please write all answers on these pages; use the backs if needed. Constants : Wiedemann-Franz constant, £ = π 2 k B 2 /(3q e 2 ) = 2.445 × 10 -8 W K -2 Boltzmann’s constant, k B = 1.381 × 10 -23 J K -1 = 8.620 × 10 -5 eV K -1 gas constant, R : 8.314 J mol -1 K -1 Charge on an electron, q e = –1.602 × 10 -19 C Faraday’s constant, F = 96,500 C mol –1 1) One of the steps in the production of integrated circuits is the formation of a thin layer of SiO 2 on the surface of Si wafers. This is accomplished by oxidizing the surface of the wafers in an oxidizing atmos- phere at an elevated temperature. The thickness x of the oxide layer varies with time t according to: x 2 = Bt (1) The parameter B depends on temperature T and the oxidizing atmosphere as indicated in the table on the next page. a) (10 points) Given eq. (1), indicate whether the oxidation of silicon obeys linear, parabolic, or loga- rithmic kinetics. What does the form of eq. (1) indicate about the nature of the SiO 2 layer on silicon? Propose two possible rate-determining steps in the growth of SiO 2 on Si. This problem is based on Callister problem 18.D7. The form of eq. (1) indicates parabolic kinetics ( 2 pts ). This implies that the rate of film growth varies inversely with the film thickness, i.e. dx / dt 1/ x ( 4 pts ). This therefore implies that two possible rate-determining steps are transport of oxy- gen (probably as O 2– ions) across the layer from the atmosphere to the metal-metal oxide interface ( 2 pts ), or silicon (probably as an ionic species) across the layer from the wafer to the layer surface ( 2 pts ). AW or MW (g mol –1 ) density (g cm –3 ) Si 28.09 2.33 b) (10 points) Given the data on atomic weight, molecular weight, and density at right, compute the Pilling-Bedworth ratio for SiO 2 on Si. Discuss whether the result is consistent with eq. (1) and with your answer for part a). SiO 2 60.09 2.20 PBR ! molar volume of oxide formed molar volume of metal consumed = ( density metal )( MW oxide ) n ( AW metal )( density oxide ) = 2.33 " 60.09 1 " 28.09 " 2.20 = 2.26 ( 5 pts ) For most metals that have a protective oxide, 1 < < 2 ( 2 pts ), suggesting that the oxide is in moderate compression ( 2 pts ). Many metals with values of > 2 or < 1 have oxides that are non-protective ( 2 pts ). Si, with a protective oxide and > 2, is an ex- ception ( 2 pts ). (See Callister Table 17.3.) Protective oxides are typically pore- and crack-free and adherent, and yield parabolic oxidation kinetics ( 2 pts ; 5 pts max). continued on next page
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ts3201f07 - EMSE 201 Introduction to Ma teria ls Science...

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