An elaborate description of the SHE method can be found in the doctoral theses of Markus Bina and Karl Rupp:

• M. Bina: Charge Transport Models for Reliability Engineering of Semiconductor Devices. Institute for Microelectronics, TU Wien, (2014).
• K. Rupp: Deterministic Numerical Solution of the Boltzmann Transport Equation. Institute for Microelectronics, TU Wien, (2011).

where also a list of existing literature on the SHE method can be found. The cell-centered finite volume discretization currently used in ViennaSHE was originally proposed as a vertex-centered method in

• S.-M. Hong, C. Jungemann: A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion. J Comput Electron, vol. 8, p. 225-241 (2009).

A textbook summarizing recent developments is also available:

• S.-M Hong, A.-T Pham, C. Jungemann: Deterministic Solvers for the Boltzmann Transport Equation, Springer-Verlag, ISBN: 978-3-7091-0777-5, 227 pages (2011).

A discussion of the maximum entropy discretization for numerical stabilization as well as the need for good preconditioners is given in

• C. Jungemann et al.: Stable Discretization of the Boltzmann Equation based on Spherical Harmonics, Box Integration, and a Maximum Entropy Dissipation Principle. J Appl Phys, vol. 100, no. 2, p.024502 (2006).