Problem_Set_4_soln

Problem_Set_4_soln - Problem Set 4 Soln 1 The structure...

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Problem Set 4 Soln 1. The structure shown below is implanted with oxygen using a 1 x 10 18 cm -2 implant at 200 keV (R P = 0.35 µm) . The left hand side is masked from the implant. Following the implant, a high temperature anneal is performed which forms stoichiometric SiO 2 in a buried layer on the right side. Calculate the structural dimensions on the right side following this anneal (oxide thickness, distance from the surface and all other important dimensions). You can assume the silicon atomic density is 5 x 10 22 atoms cm -3 , and the Si lattice planes are 0.25 nm apart. State any other assumptions you make. Answer: Given the Si lattice density and the lattice plane spacing, we have: # of Si atoms per lattice plane = 5x10 22 ( ) 2.8x10 8 cm ( ) = 1.25x10 15 cm 2 Thus a 1 x 10 18 cm -2 oxygen implant will consume (1 x 10 18 )/(2)(1.25 x 10 15 ) = 400 planes of Si atoms in making SiO 2 . This corresponds to 100 nm (0.1 µ m) of Si being consumed. Mask O implant
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Because of the volume expansion in forming SiO 2 , 100 nm of Si will form 220 nm of SiO 2 . Thus the buried SiO 2 layer will be centered 0.35 µm below the surface (at R P ), and extend 110 nm up and down from that point. The final issue to be considered is how the volume expansion is accommodated. The Si above the buried SiO 2 will be pushed up and the Si below the SiO 2 will be pushed down. Since the buried SiO 2 is closest to the top surface, the biggest effect will be there, resulting in the structure shown below. The 120 nm distance should be regarded as approximate and would require a detailed mechanical calculation to compute accurately.
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