Gulfstream IV Captain reported a CFTT event during departure. The Captain prompted the First Officer to climb and the flight crew continued to destination.

Narrative

Departing out of ZZZ; no passengers on Day 0 to ZZZ1 on the ZZZZZ Departure. Copilot was flying. After speaking with another pilot earlier at the hotel; copilot was fixated on the below 1;750 ft. restriction off of the departure end of Runway XX. It was his leg to fly so I asked him how he wanted to depart. He set 1;800 ft. in the altitude alert. I asked him what he was going to do after that; and he replied; climb to 4;000 ft.; which was correct. We tookoff; reached 1;800 ft.; leveled off; (and stayed level even after resetting alt alert to 4;000 ft.); the throttles came back and a configuration alarm started going off. I told him to climb while I searched for the reason for the configuration alarm. Meanwhile we headed towards rising terrain. After determining that we were in the correct configuration; but low in altitude; I looked at the instruments and saw we were still level and told copilot to climb. He was like a deer in the headlights...frozen; so this time I yelled; CLIMB!"; and I was getting ready to take the controls while looking out the window to make sure we were not going to hit something. That seemed to unfreeze copilot and he started climbing.About then; Tower asked our altitude and I replied 1;800 ft. and climbing; and then handed us off to Departure. We climbed back on to profile and continued uneventful. Being fixated on an altitude restriction and not flying the airplane.Flying the proper departure procedure. A few days later at the hotel after dinner; copilot mentioned to me that after all of his years of being an instructor and in the military; he has never had anyone yell at him like I did and he didn't appreciate it. I asked him if he would have appreciated hitting the hillside; to which he replied; "no; what you should have done is calmly take the controls from me. I did that as an instructor with students all the time." I replied; "Let me get this straight. You; who has been stating that you are ready to be a Captain on the Gulfstream for months now; want me to take the controls from you should there be a problem like that again?" He said yes. I responded; "Good to know; and who will take the controls from you when you are Captain and you have a problem; your co-pilot?" He didn't respond.Because of this incident; plus a previous incident (again on take-off out of ZZZ2 with report filed); and direct observations and concerns with this person; I feel compelled to also file [another] report. My corrective recommendations will be on that report."