This is a great question! Sometimes pockets are too short and sometimes phones are just too dang big!
A few brands come to mind, but I am also interested in other features you may be looking for. For instance, shorts come in a range of different lengths, were you looking for a certain inseam/outseam? Are cargo pockets a must for you? Then we can also talk about fabrics, materials & colors... I could go on and on...
Here are some of our customer favorites with deeper pockets.
I'd check these out at your local REI, or place an order with REI.com to see if they suit your needs.