jremington:
Yes, reverse bias it. Also note that the quoted 7 us is with a 1K resistor load, so it would be 0.7 us with a 100 Ohm load. You probably don't need a 1 cm x 1 cm area, either.But even 7 us rise time should be more than fast enough for your application, especially if you are using a 16 MHz Arduino.
Perhaps you all are looking at the wrong end of the problem. If the code is using an interrupt, that interrupt is triggered the instant the pulse rises above a minimum threshold, not when it reaches a 5 volt peak. So, any rise-time above that threshold is not used.
Does the same apply to "reading" a regular digital input?
Paul