You want to be sure, hire an attorney. Here is the NC law:
Grounds for Termination of Parental Rights North Carolina -
The key here is that the law states the court MAY terminate rights. That leaves it up to the discretion of the court. Traditional courts have declined to terminate rights except in extreme circumstances. You said that he hasn't tried to be a part of his child's life. Well the court is then going to ask what you gain by a TPR. Since you appear to gain nothing, it is unlikely you will get one.
Now if you were applying for sole legal custody with no visitation, you might get that. Or, if you have remarried and want your husband to adopt, the court is more likely to grant the TPR to clear the way for an adoption. But based on what you have posted, I think your chances are slim.
A local attorney will know the mode of the local
Family Court. So would be in a better position to advise you of the mood of the court in these matters.
P.S. If you have a follow-up question or info, please use the ANSWER options near the bottom of the page, not COMMENTS.