The term semicolon is misleading; it is not half a colon rather half a full stop GB or period US. As the symbol perhaps suggests, a semicolon is stronger than a comma and weaker than a full stop or period.
A number of examples are given below:
I’ve run out of funding; I don’t know what to do.
Up to a point this may be true; however, …
The first chapter discusses the problem; the second chapter examines previous research; finally, the third chapter draws a number of conclusions.
Dividing a complex list
A semicolon is sometimes used to divide a complex list that could be confusing with a comma, particularly if the list already contains commas, for example:
Lee (1999:218); Anderson (2014), see especially pp. 296–300; Shimizu (1971:7–12); Zhang (2011:57; 2012:133)
However, as a semicolon is stronger than a comma, it interrupts the flow of the text for the reader and should therefore be used sparingly.