No... eliminate R1 it will limit the current flow through the Mosfet as it is in series with the source lead, Ground the source and all should work fine except the analogwrite() function will be reversed, I believe, where 255 would be off and 0 would be fully on and you might well SLOWLY reduce the 150 ohm resistor value (NO Pot will work well here) if needed start with a 4700 ohm in parallel with the 150 ohm, the resultant resistance will be about 110 ohms (113.7 ohms) but only if the brightness of the back-light isn't workable in normal room lighting. Most LCD's aren't of the daylight viewing types. IMO
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