3.1551/6.152 Home work set 3. fall 2003 3.155J/6,152J Microelectronic Processing Fall Term. 2003 Bob HAndley Martin schmidt Problem set 3 Out Sept. 29, 2003 Due Oct 8. 2003 Diffusion: Read Plummer Chap. 7, sections 7.1-7.4,, 7.53, 7.5.8 Show that c(zt) Wroexpfzla)I,with a=2VDf, is a solution to Fick's second law of diffusion. ac(z, t) dc(zt) 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections)for As impurities in Si at 1100 C for two cases: 1)CAs=10 cm and ii) CA= 10 9cm 3.(Use Table 7.5 in Plummer.) c) What is the diffusion length in each case for t= I hr 3. You start with a uniformly doped (NA =10cm). p-type silicon wafer. Then a predeposition of phosphorus is made at 1000C to a concentration equal to it solubility limit(see class notes, Diff I figure). This process takes 2 min a)What is the surface dose, 2, of phosphorus? After the deposition, the surface of the Si was sealed and a"drive-in"anneal was made at 1100°C b)For how long must the"drive-in"anneal be carried out to put the n-p junction 0.4 microns beneath the surface?(Here you have to make a sensible approximation about the role of t) a) What is the surface concentration, C (0, 0), after"drive-in"? lon implantation: Read Plummer Chap. 8, sections 8.1-8.4, and 8.5.1-8.5.6 Or Campbell 5.1-5.6 4. Calculate and plot the concentration of boron atoms as a function of x(one dimension into the Si wafer) following ion implantation. The boron atoms are incident to the surface with energy 40Kev and the dose was 5 x 10 5 cm. The sample is then ubjected to an anneal for 37 minutes at 950 C; plot the dopant concentration after the anneal. if the silicon substrate has a back ground concentration of 2x 10>.at what depth is the pn junction?3.155J/6.152J Homework set 3, fall 2003 1 3.155J/6.152J Microelectronic Processing Fall Term, 2003 Bob O'Handley Martin Schmidt Problem set 3 Out Sept. 29, 2003 Due Oct. 8, 2003 Diffusion: Read Plummer Chap. 7, sections 7.1-7.4, 7.5.2, 7.5.3, 7.5.8 1. Show that c(z,t) = Q pDt exp -(z/ a) 2 [ ], with a = 2 Dt , is a solution to Fick's second law of diffusion, dc(z,t) dt = D d2 c(z,t) dz2 . 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections) for As impurities in Si at 1100 C for two cases: i) CAs = 1015 cm-3 and ii) CAs = 1019 cm-3. (Use Table 7.5 in Plummer.) c) What is the diffusion length in each case for t = 1 hr. 3. You start with a uniformly doped (NA = 1017 cm-3), p-type silicon wafer. Then a predeposition of phosphorus is made at 1000o C to a concentration equal to its solubility limit (see class notes, Diff I figure). This process takes 2 min. a) What is the surface dose, Q, of phosphorus? After the deposition, the surface of the Si was sealed and a "drive-in" anneal was made at 1100o C. b) For how long must the "drive-in" anneal be carried out to put the n-p junction 0.4 microns beneath the surface? (Here you have to make a sensible approximation about the role of t). a) What is the surface concentration, Cs(0, t), after "drive-in"? Ion implantation: Read Plummer Chap. 8, sections 8.1-8.4, and 8.5.1-8.5.6 Or Campbell 5.1-5.6 4. Calculate and plot the concentration of boron atoms as a function of x (one dimension into the Si wafer) following ion implantation. The boron atoms are incident to the surface with energy 40KeV and the dose was 5 x 1015 cm-2. The sample is then subjected to an anneal for 37 minutes at 950 C; plot the dopant concentration after the anneal. If the silicon substrate has a background concentration of 2 x 1015 cm-3, at what depth is the pn junction?