Extreme ultraviolet (EUV) lithography devices that use laser-produced plasma (LPP), discharge-produced plasma (DPP), and hybrid devices need to be optimized to achieve sufficient brightness with minimum debris generation to support the throughput requirements of high-volume manufacturing lithography exposure tools with a long lifetime. Source performance, debris mitigation, and reflector system are all critical to efficient EUV collection and component lifetime. Enhanced integrated models continue to be developed using the High Energy Interaction with General Heterogeneous Target Systems (HEIGHTS) computer package to simulate EUV photon emission, debris generation, and transport in both single and multiple laser beam interaction systems with various targets. A new Center for Materials under Extreme Environments (CMUXE) was recently established to benchmark HEIGHTS models for various EUV-related issues. The models being developed and enhanced were used to study the effect of plasma hydrodynamics evolution on the EUV radiation emission for planar and spherical geometry of a tin target and explain the higher conversion efficiency of a planar target in comparison to a spherical target. HEIGHTS can study multiple laser beams, various target geometries, and pre-pulses to optimize EUV photon production. Recent CMUXE and other experimental results are in good agreement with HEIGHTS simulation.