It is the responsibility of the project manager to ensure that the team's output meets the performance requirements stated in the project definition and delivers the goals of the project.
Why a team member would be a non productive? Either he is not up to that level of his work means his skill set is weak. So the answer is coaching/mentoring. Ask Tech Lead to communicate with him frequently & face to face. Don’t wait for the task to complete go to his seat, talk friendly, ask indirectly what he is doing and give your suggestions. Don’t point him forward some good article to whole team. Give your feedback early to the member. Indirectly share your experience about the problems he is facing. Realize him that he the important valuable member of the project team and you have lot of expectations from him.
Second thing is , some team members are careless or your environment is not productive. The solution is, explain clearly what is expected from the team. Don’t wait for status report, communicate frequently with team and remind their goals step by step goals.
Appreciate the members who are doing good work. Involvement is the key to handle non productive members. Don’t assign them work through mail. First meet with team, explain the goals, divide the goals into parts & Let the team members pick tasks of their own choice. That will make them more responsible for their task. I think in this way you can change their professional attitude.