How can a master thesis in STEM approach the level of a doctoral thesis? Can someone shed some light on the subtle difference between a master thesis and a doctoral thesis so that a master student can arrange his or her research strategy geared to produce work at near the level doctoral thesis assuming that time is not a factor.

Note: I come from an engineering background so research encompasses both theoretical work (derivation of equations, modeling) and experiments (software analysis, characterization of physical devices)

Please also feel free to comment on the feasibility of actually producing PhD level dissertation at the master level
Requirements vary widely from program to program and from institution to institution. 

Some programs require a doctoral candidate to publish in a peer-reviewed journal (probably most programs would take issue if you didn't publish or present anything). Most programs (or committees) wouldn't let you graduate with a PhD unless you published at least once, and would expect at least twice. 

My general hunch is that a doctoral dissertation (rarely called a "doctoral thesis") is generally several times longer. While a masters thesis might be 20-50 pages, dissertations are routinely 80-150 pages...and sometimes way more (this varies widely by discipline, by the academic culture of your institution, and by your committee). Some programs allow the doctoral candidate to use three publications, combined into a single manuscript, as his or her dissertation. 

Lastly, the doctoral degree is intended to show that the recipient can perform original research. Masters degrees have a wide variety of understandings or intents, from "the recipient passed our comprehensive exams", to "the recipient performed an original research project and published it". 

Whatever you've done for your masters thesis, focus on research for your PhD. Learn what interesting questions are in your field and choose one to focus on. Read the background literature to learn how others have approached the problem. Work with your advisor and committee to figure out how you can contribute something new and useful to the field, and then do it. Publish your findings in a journal; present your results and network with peers at conferences. Finally, write it all up in your dissertation, defend it, and graduate. That sums up getting a PhD. The rest are details.

You may find this page useful.