DVT Tower Controller reported a departing aircraft climbed slower then anticipated and into the path of a helicopter resulting in a NMAC report from the helicopter pilot.

Narrative

I issued a left downwind departure to the aircraft as they wanted to go eastbound. Meanwhile; the helicopter was in bound on a Helo south arrival (LOA (Letter of Agreement) with DVT). I continued my scan for runway separation with other aircraft and made sure everything was as it should be. Then I went to look at the STARS and noticed aircraft pilot had turned but was not climbing or climbing very slow. I wasn't expecting him to be that low in the turn to the east. I immediately gave a traffic call to the aircraft informing them of the helicopter inbound from the south. He replied with looking or something to that extent. I then issued a traffic call to helicopter but at this time they were very close to one another; and I told the helicopter to hold south trying to get them to turn around to avoid the aircraft. The aircraft never reported the helicopter in sight. The helicopter took evasive action and turned south and descended 200ft to avoid the aircraft. They avoided one another and continued on their path. The helicopter never reported a NMAC on frequency but did say on the recorded line when he called the Tower to talk about what happened.The only recommendation I have is to wait a bit longer to issue the turn to the aircraft. Or recognize the conflict earlier and have the aircraft fly southbound to avoid flying so close to the helicopter. These operations happen daily and are usually never an issue; had I anticipated the aircraft's slow climb it would have never been an issue. The only other recommendation I have is what I did; turn the helicopter to avoid a potential collision.