Generally speaking, it is the speed of the air that determines the range. (This is inversely related to the volume of the air.) So it's getting control of this faster airspeed that will increase your upper register.
For brass players, lip slurs are very good for improving range. In the following example, each two-measure group uses the same fingering for all five of its pitches; this fingering is shown above the first pitch of the group.
As you play, really conceptualize the syllables that I've placed below each pitch. "Oh" is the bottom syllable because it's the most open and allows for the greatest volume of air. "Ah" (as in "hot") is in connecting link to the "ee" (as in "heed"), which allows for the fastest air on account of the condensed oral shape.
You can continue this pattern down by semitone using the following valve patterns:
And then back up by semitone if you wish. Consistent practice with this exercise (and others like it) will improve your range considerably over time.