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3325.32

# 3325.32 - 5.32 P hosphorus atoms are to be diffused into a...

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5.32 Phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of P in this silicon material is known to be 5 10 19 atoms/ m 3 . The predeposition treatment is to be conducted at 950°C for 45 minutes; the surface concentration of P is to be maintained at a constant level of 1.5 10 26 atoms/m 3 . Drive-in diffusion will be carried out at 1200°C for a period of 2.5 h. For the diffusion of P in Si, values of Q d and D 0 are 3.40 eV and 1.1 10 -4 m 2 /s, respectively. (a) Calculate the value of Q 0 . (b) Determine the value of x j for the drive-in diffusion treatment. (c) Also for the drive-in treatment, compute the position x at which the concentration of P atoms is 10 24 m -3 . Solution (a) For this portion of the problem we are asked to determine the value of Q 0 . This is possible using Equation 5.12. However, it is first necessary to determine the value of D for the predeposition treatment [ D p at T p = 950°C (1223 K)] using Equation 5.8. Thus D p = D 0 exp ! Q d kT p

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3325.32 - 5.32 P hosphorus atoms are to be diffused into a...

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