Today’s semi-conductor innovations allow chip makers to design

KEY NOTES:
- Comparison: "than any other" is always preferable to "than any". Why?
For example:
Wrong: Henry is taller than any people in his class --> you're comparing Henry with a group of people including himself.
Correct: Henry is taller than any other people in his class.

Today’s semi-conductor innovations allow chip makers to design silicon wafer chips more space efficient now than at any time since their inception.

(A) silicon wafer chips more space efficient now than at any time since their
Wrong.
"than any" is wrong. See explanation above.
"their" is wrong. "their" refers to current silicon wafer chips.

(B) silicon wafer chips that are more space efficient than they were at any time since their
Wrong.
"they" refers to current silicon wafer chips. That's a wrong comparison. You're comparing those chips with themselves? You need a new copy of "chips" --> "those" is correct.
"their" is wrong. See option A.

(C) silicon wafer chips that are more space efficient than those at any other time since
Correct. Good comparison.

(D) more space efficient silicon wafer chips than those at any other time since their
Wrong.
"their" refers to what? "silicon wafer chips" or "those".

(E) more space efficient silicon wafer chips now than at any time since
Wrong.
"now" is redundant. See the non-underlined "Today......"
"than any time" is wrong. See explanation above.

Hope it helps.