These moments are very much part of the writing. You are creating a script that includes both verbal and nonverbal elements, and it's how the two interplay with each other that determines the shape and rhythm of each scene. All nonverbal physical actions influence how your characters relate to each other and what they say and think. And this is especially true for silences.
Playwright Harold Pinter is the all-time master at this, and I urge you to look at his plays to see how artfully he orchestrates and weaves pauses and silences into his work.
One cautionary note is to not overuse the words "pause" or "silence" and the like when indicating a desired break in your dialogue, because you may be missing the opportunity to bring your script more fully to life by describing the action taking place during such moments. You may determine that the use of a simple "pause" best suits your needs at a particular moment, but always consider if it wouldn't be better to describe the action during the pause. If done carefully, it can often heighten the impact of a moment visually and guide readers to a deeper engagement with the scene.
Always remember that your script is being written to play out "in time" and in that sense you are like a composer, using a form of notation when writing your play or screenplay. This is especially true when capturing a sense of time duration either during a line or between lines. And at times there's a need to be quite accurate in describing specific pauses and silences--it's one of the significant ways you can control how your script moves from moment to moment through a scene. One of my favorite examples this is the way Edward Albee expertly orchestrates the closing scene between George and Martha in Who's Afraid of Virginia Woolf? His notation of silences and pauses is truly masterful.
* * * *
I'm the Program Director of the low-residency MFA in Writing for Stage and Screen being offered by the New Hampshire Institute of Art. Our next residency runs January 3-11, 2016 and we are now considering applications for starting the program with our July 2016 residency that runs July 18-28. I'm also a playwright and screenwriter, producing partner in my production company Either/Or Films (The Sensation of Sight and Only Daughter), and a professional script consultant.