Should I Apologize for Yelling At an Employee?
We all know that we are supposed to "praise in public and reprimand in private," but we are also human beings. And there are times ... ah, there are times ... when doing that can be extremely difficult. However, it sounds to me from what you have said that you may have embarrassed a good employee in front of his co-workers, maybe even his staff.
If you are thinking about this situation and brooding about how you behaved, the chances are that you should apologize. We all raise our voices from time to time; sometimes we say things that we later regret. The key ingredient that differentiates a leader and which takes him to a higher level -- deserving of more respect -- is his willingness to admit when something that he said or did was not exactly at the level of professionalism or courtesy that he expects of himself and from others on the team. It goes a long way when someone says that she recognizes her own less-than-perfect behavior and says that she will genuinely strive not to repeat it in the future.
You set the tone for this workplace. If you make it seem okay to yell at one another, it may become the norm more often than the exception. And, for a myriad of excellent reasons, I doubt that you want that to be the case. People want to work where they are appreciated and respected. That is just the way it is. The most talented people will not tolerate less; and I am sure that the most talented people are the ones you want on your team.