Small Aircraft
Air Traffic Control Time Certified In Pos 1 (yrs) 20
Situational Awareness; Time Pressure; Human-Machine Interface; Distraction; Confusion; Workload
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Airspace Structure; Human Factors
Aircraft X entered a terrain area at 7;200 ft. with a Minimum IFR Altitude (MIA) of 7;400 ft. Aircraft X was cleared for the RNAV [Runway] XX approach. Aircraft X executed the missed approach. Aircraft X requested vectors for the RNAV [Runway] XX Approach. I issued a turn 30 degrees left when able direct to the Initial Approach Fix (IAF) and notify me when he was direct. Aircraft X reported they were ready for the approach clearance. I issued '[Aircraft X] maintain seven thousand until established. Cleared RNAV approach Runway XX at ZZZ.' Aircraft X read back the correct clearance.Aircraft X continued on their heading past the IAF without beginning a procedure turn for the approach. I was busy with multiple requests from other aircraft and fighters departing a military base for active Warning Areas. And didn't notice Aircraft X missed the fix. I was giving a relief briefing and noticed Aircraft X was not on his cleared route. I asked him where he was heading. Aircraft X stated he was waiting for vectors to the approach. I pulled up the MIA's and noticed he was about to enter a 7;400 ft. MIA block. I issued a safety alert for the terrain and climbed Aircraft X to 8;000 ft.In my scan I knew that Aircraft X was out of position but assumed he was unfamiliar with how to execute the procedure turn at the IAF and was going to get back on a correct course soon. Every time I checked back in my scan he was a bit further off course. The workload was high. Frequency congestion was causing a lot of missed and stepped on clearances further increasing workload. I had requested help from the Controller-in-Charge twice prior to this happening. I needed assistance with a flight break up flight plan and to notify the surrounding facilities the Special Use Airspace went cold. A dedicated D-side (Radar Assist) would have helped notice the aircraft off course.
Center Controller reported frequency congestion and a high workload caused them to not detect an erroneous altitude read back and an aircraft flew below the Minimum IFR Altitude.