Large Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 0.8
Situational Awareness; Human-Machine Interface
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Separated Traffic; Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory
Human Factors; Procedure; Airspace Structure
I issued Aircraft X a clearance for the ILS approach. As Aircraft X was descending on the EMZOH3 Arrival I observed an unidentified VFR aircraft 12 miles west level at 4000 feet in the flight path of Aircraft X.  I cancelled Aircraft X approach clearances and assigned 5500 feet to pass above the VFR traffic.  The unidentified VFR aircraft proceeded to climb at a quick rate which then caused Aircraft X to respond to an RA to descend.On this sector we are not protected by the Class B which causes numerous VFR aircraft to transition through the finals of the airport.  We can assume at times the path and altitude the unidentified VFR aircraft take; but usually it's difficult to plan on what action to take to avoid these aircraft. An extended Class C or a lower Class B may prove beneficial.
NCT Controller reported assigning an air carrier an altitude to stay above unidentified VFR traffic. The VFR traffic climbed toward the air carrier which responded to a TCAS RA alert.