Assuming dopant atoms are uniformly distributed in a silicon crystal, how far apart are these atoms when the doping concentrations are 5.0x1015 cm-3 and 5.0x1020 cm-3?

d = ~ 5.8μm

d = ~ 0.13 μm

Explanation:

when the doping concentrations are 5 * 10^15 cm^-3

d = v^-1/3; where d represent the distance between the atoms, and v represent the volume

d = 1 / ∛v

d = 1 / ∛5 * 10^15

d = 1 / 170997.5

d = 5.85 * 10 ^ - 6

d = ~ 5.8μm

when the doping concentrations are 5 * 10^20 cm^-3

d = v^-1/3; where d represent the distance between the atoms, and v represent the volume

d = 1 / ∛v

d = 1 / ∛5 * 10^20

using the principle of surds and standard forms, we have

d = 1 / ∛0.5 * 10^21

d = 1/7937005.26

d = 1.26 * 10 ^ - 7

d = 0.126 * 10 ^ - 6

d = ~ 0.13 μm