  We show theoretically that finite two-dimensional (2D) photonic crystals in
thin semiconductor membranes strongly modify the spontaneous emission rate of
embedded dipole emitters. Three-dimensional Finite-Difference Time-Domain
calculations show over 7 times inhibition and 15 times enhancement of the
emission rate compared to the vacuum emission rate for judiciously oriented and
positioned dipoles. The vertical index confinement in membranes strongly
enhances modifications of the emission rate as compared to vertically
unconfined 2D photonic crystals. The emission rate modifications inside the
membrane mimic the local electric field mode density in a simple 2D model. The
inhibition of emission saturates exponentially as the crystal size around the
source is increased, with a $1/e$ length that is inversely proportional to the
bandwidth of the emission gap. We obtain inhibition of emission only close to
the slab center. However, enhancement of emission persists even outside the
membrane, with a distance dependence which dependence can be understood by
analyzing the contributions to the spontaneous emission rate of the different
vertically guided modes of the membrane. Finally we show that the emission
changes can even be observed in experiments with ensembles of randomly oriented
dipoles, despite the contribution of dipoles for which no gap exists.
