Oxidation diffusion 3. a) Explain why Sio, grows on Si not at the outer surface(gas/SiO, interface), but at the si/ sio. interface Say why this is beneficial. [41 A: Diffusion of O in SiO2> diffusion of Si in SiO, This leads to a clean si/sio interface b)Briefly describe 3 other beneficial physical or chemical qualities of Sio2.[3x21 A: (any three) Diffusion barrier for p.b. as therefore. can be used as a mask Etched by hf which does not attack Si: allows creation of a mask from Sio High electrical resistivity; useful as insulator Epitaxial, clean interface; reproducible electrical properties High dielectric breakdown; stable under high voltage Stable to 900 C or 10 Torr; unaffected by subsequent processing c)There are two general types of solutions to the diffusion equation that are relevant to processing, one Gaussian and the other a complementary error function iList the two boundary conditions and one initial condition for the Gaussian solution and sketch the form of this solution for small time and a later time 51 11)List the two boundary conditions and one initial condition for the complementary error function solution and sketch the form of this solution for small time and a later time.51 A: 1) Gaussian: BC: dc(o, /dx=0, C(oo, t )=0: C(r, t) IC:C(x>0,0)=0 Some gave C(0,0)governed by Q. I took off points because this is a normalization condition that sets the vertical scale of the gaussen it does not affect the shape of the solution 11)Comp erf: BC: C(O 1)= C0, C(oo, t)=0 C(r,t) time IC:C(x>0,0)=0 There was some confusion with the initial slope of the erfc solution; it is not zero3 Oxidation, diffusion 3. a) Explain why SiO2 grows on Si not at the outer surface (gas/SiO2 interface), but at the Si / SiOx interface. Say why this is beneficial. [4] A: Diffusion of O in SiO2 > diffusion of Si in SiO2. This leads to a clean Si / SiOx interface. b) Briefly describe 3 other beneficial physical or chemical qualities of SiO2. . [3x2] A: (any three) Diffusion barrier for P, B, As; therefore, can be used as a mask. Etched by HF which does not attack Si; allows creation of a mask from SiO2. High electrical resistivity; useful as insulator. Epitaxial, clean interface; reproducible electrical properties. High dielectric breakdown; stable under high voltage. Stable to 900 C or 10-9 Torr; unaffected by subsequent processing. c) There are two general types of solutions to the diffusion equation that are relevant to processing, one Gaussian and the other a complementary error function. i)List the two boundary conditions and one initial condition for the Gaussian solution and sketch the form of this solution for small time and a later time. [5] ii) List the two boundary conditions and one initial condition for the complementary error function solution and sketch the form of this solution for small time and a later time. [5] A: i) Gaussian: BC: dC(0,t)/dx = 0, C(∞,t) = 0; C(x,t) time IC: C(x> 0, 0) = 0 Some gave C(0,0) governed by Q. I took off points because this is a normalization condition that sets the vertical scale of the Gaussean; it does not affect the shape of the solution. t ii) Comp erf: BC: C(0,t) = C0, C(∞,t) = 0; C(x,t) time IC: C(x> 0, 0) = 0 t There was some confusion with the initial slope of the erfc solution; it is not zero