One of the first films of this kind was The House on 92nd Street (1945): Time used the term "semidocumentary" to describe this film in 1952
The producer of the film had previously worked on newsreels which inspired the film making style.
In the late-1940s, semidocumentary films were often associated with film noir thrillers, sharing a commitment to on-location shooting, gritty realism, and understated performances. Several of Richard Fleischer's films had semidocumentary qualities; see external links below.
Some examples of movies that at least have some elements of a semidocumentary in their style: