Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 3
Communication Breakdown; Confusion; Situational Awareness; Time Pressure
Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance
Aircraft; Human Factors
Aircraft X was a departure off of SDL; he was given an altitude of 070 and direct to the first fix in our airspace.  I climbed him to FL210. He read it back but wasn't climbing well he was headed for higher terrain so I issued a vector to clear.  Once I saw he was descending and I verified he was on the appropriate altimeter setting as this has happened quite a few times to pilots in the last week.  I asked if he had the terrain in sight; he said he was looking for traffic.  I had given him two vectors to clear terrain he read back both but never turned to the first heading I gave but took the second vector.  I asked if he had the terrain in sight and needed assistance; he replied he was looking for traffic and needed no assistance.
A Phoenix TRACON (P50) Controller reports of a pilot issue with communications. The Controller climbed the aircraft to a higher altitude; but it wasn't climbing well. The Controller asked the pilot if he had the terrain insight and issued two vectors away from the higher terrain. The pilot reported he was looking for traffic. The Controller continued to vector the aircraft; and the pilot took the second heading.