Unbounded growth in cellular traffic is continuing to increase network power consumption meaning that the need for energy efficient cellular network design is more critical than ever. To find the trade-off between the spectral and energy efficiency, stochastic geometry has been widely employed where the cellular nodes are considered as being distributed according to a Poisson point process (PPP). Most of the prior works using stochastic geometry commonly assumed Rayleigh fading as the de facto fading model due to its tractability and simplicity. However, the propagation environments in which emerging cellular networks will operate, are diverse in nature, constituted by many different propagation phenomena which can not be fully captured by the Rayleigh distribution. To incorporate these physical attributes into the calculation of the network performance metrics, we consider kappa-mu shadowed fading, which contains the majority of the well-known fading models as special cases. Using stochastic geometry, we evaluate the spectral efficiency and energy efficiency of a K- tier HetNet with K classes of BSs, differing in terms of the transmit power, BS density, shadowing and fading. Through numerical evaluation, we observe a trade-off relationship between the shadowing and fading parameters, spectral efficiency and energy efficiency, which provides important new insights into energy efficient network design.