Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 2
Distraction; Workload
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Human Factors
What led to the event happening: I had just gotten back from leave.  I worked the mid the night before after returning from that leave; and then had an OT shift to work an early morning.  Traffic was fairly light; but complexity was fairly high due to multiple things happening all over the sector.  The sector is fairly complex in that it requires changing transmitters and receivers constantly to talk to and hear aircraft in the sector.   This sector often has a D side.  My D side had just gone on break and the sector seemed to be fine; but then I was overcome with some additional challenges; and my D side returned from break right about as this situation was happening. Terrain in this sector is the highest in the center and it requires a lot of monitoring of aircraft to make sure they are meeting MIA's.  We have been on 6 day work weeks for a long time due to the staffing issues FAA wide; but it definitely has impacted the moral and has exhausted myself.  I was slightly blind-sided by the call from the aircraft due to no weather reports south of ZZZ1.As the complexity was rising in the sector due to multiple different situations; I had a departure aircraft of type I am not familiar; depart one of the busiest departure airports in our center.  The aircraft was a slow climber and requested to deviate below the terrain.  The call caught me off guard and I approved his request to deviate noticing the terrain close to him but not the MIA he was currently in.  I approved a slight deviation to avoid the higher terrain to his right; and shortly after noticing my mistake; I corrected myself and asked the pilot to tell me the conditions (IFR/VFR) to see if that could save me; but then ultimately told him that I cannot approve his request to deviate below the terrain until he was above unless he was declaring an emergency.  He said that he was not declaring an emergency and was correcting back on course.  I then issued a proper clearance to deviate out of the MIA.  The pilot had already turned off of the SID a few degrees before I caught the mistake and corrected it.-Hiring needs to improve in the FAA so that we are not working 6 day works weeks constantly and getting exhausted-Staffing needs to improve from hiring more people so that we can not be overcome with sick leave requests and the constant COVID happenstances that we are finding ourselves in today.  There is a constant out flux of people due to sickness or the FAA medical office taking peoples medical clearances away even when they are not sick and are testing negative for COVID.  -People are abusing the system most likely due to the two reasons above and are finding every way they can to get out of work because of the poor mental health and low staffing numbers that we are in every day.  My recommendation is that the FAA fixes their hiring issues immediately so that more problems don't continue to arise from the extreme apparent staffing issues we are currently seeing.
Center Controller reported an aircraft that was climbing below the MIA and wanted permission to do so.