It is very difficult to write a biography of Muhammad, since to do so the writer would have to master at least Arabic, Syriac and Armenian in order to access all the primary sources, and have training in several different fields in order to critically analyse all the sources. Too often historians are tempted by the volume of later Muslim sources and use them exclusively to construct a detailed narrative, when we wouldn't do the same for any other periods of history. Luckily there has been a growing awareness of this problem from the 60s/70s onwards, to the extent that our view of early Islam now is much less clear than before, but also much more exciting. No-one now would dream of writing about Muhammad without at least commenting on the contradictory evidence found in fragmentary seventh-century Syriac sources or the detailed account found in Pseudo-Sebeo's Armenian History from the 660s, which is a huge change from even a few decades before.

Unfortunately, there hasn't been a comprehensive biography of Muhammad approaching the problem from this perspective in recent years, so Michael Cook's Muhammad from 1983 is probably your best bet - it's very short but includes a concise summary of the traditional narrative of Muhammad's life along with some very relevant criticisms. It doesn't really provide a suitable alternative, but it's still the best we got right now.

The topic is also discussed in Fred Donner's Muhammad and the Believers (2010) and Robert Hoyland's In God's Path (2014), but it does not dominate these books as they aim to cover early Islam as a whole, but they do of course provide excellent summaries of what modern Western historians think Muhammad's life was like, especially as both historians are very respected for their research. Both books are very easy to read (as both were written for a popular audience) and I highly recommend them as introductions to the exciting world of early Islamic history!

I'm sure that there are others here much more knowledgable on this topic than I am, but one of the most critically acclaimed recent English-language biographies of Muhammad was written by Abu Bakr Siraj ad-Din (formerly Martin Lings), titled Muhammad: His Life Based on the Earliest Sources. Ad-Din has received praise from throughout the Muslim world for this book and used several Arabic sources from the 8th and 9th century that had never been translated into English. Published in 1983 and still in print.

I will obviously defer to people who study this part of history full time, but as a person interested in studying the historical foundations of Islam more casually, I found Karen Armstrong's Muhammad:A Prophet For Our Time to be compelling, unbiased, and well researched.