Suppose after graduating from a PhD program, you don't do a post-doc. Are the chances of getting a tenure-track position severely reduced? Also is it possible to do a post-doc after a completion of a masters program (probably should be called a "post-masters")?
The purpose of a postdoctoral fellowship is simply to gain the skills detailed in this answer to a similar question, notably:
- Get involved with obtaining funding
- Build an international reputation
- Start collaborating with external parties
- Learn how to manage projects and a lab
- Start to devise a strategic research plan
- Improve your publication record
If you have all those things from your work as a graduate student, then you should have no problem finding employment and furthering your academic career immediately after you earn your PhD. Most students don't, which is why they try to find a postdoc position to help them gain these skills before attempting to run their own lab.
What people expect from a candidate for a tenure-track faculty position is the ability to guide research and to set up an independent research group. The candidate will have to prove extensive (almost) independent research experience and a research vision to last for many years. A post-doc candidate will be stronger in these requirements than someone just graduating with a PhD. It is not impossible to get a tenure-track position directly after the PhD, but I think chances are better with a post-doc.
Nevertheless, if you just graduated and there is a position announced which fits your profile, by all means apply for it. Even if you're not successful, it may give you valuable experience.
All types of faculty positions I know of have a formal PhD requirement, so usually it is not useful to skip that.
Currently, I believe this is a very field-dependent issue. In physics, for instance, it would not be possible to get a faculty position without a postdoc (or even two postdocs) unless you're an Einstein-level talent. In some fields, such as engineering, it may still be possible to get a position directly after a PhD—but in such cases that candidate is usually told to take a year or two, do a postdoc, and then start the faculty position.
However, I think that it is in general a very bad idea to just "take some time off" if one is planning to pursue a faculty position. Working in industry or doing something that keeps one active in research is probably OK, but a "sabbatical" that doesn't contribute toward a CV in any way will likely set off some hackles on the part of the search committee.
Let us start from a different perspective. What is required to get a tenure-track position?
I would say that two things are primarily used as criteria in the selection process: number of publications and ability to secure funding. Related to the publication list is of course aspects of publications, publication rate number of citations and the impact factor of the journals in which you publish. Exactly how these aspects are weighted is varying. Note that rates are important so it is not exclusively a matter of pure numbers.
In both cases time is an aspect and obviously you will standa a better chance the more merits you can accumulate which takes time. I do not know what other possibilities might exist to get some time to improve your merits. In some cases you might be temporarily hired to do teaching. Teaching will of course also be a merit but not on the expense of research. and under such circumstances contnued research output may be a challenge. So obviously a Post-Doc should give you a head start but I would not see it as an exclusive prerequisite.
"Post-Master": Since this concept does not formally exist, I could see there being opportunities to partake in research by being a lab-assistant or something similar. Any opportunity to widen your experience and possibly getting you into the research activities, especially publishing would be beneficial fo r the future.