Is there any rule for when to use ‘semi’ and when to use ‘half’?
The Latin prefix semi- means “half.”
The earliest “semi-” words documented in English are semicircular (1432-1450 and semi-mature (c.1440). Both William Langland (c.1332-c.1386) and Chaucer (c.1343-1400) use “semi-” constructions. According the OED,
In the 16th-18th c., the number of permanent compounds was increased mainly by the accession of terms more or less technical [such as semicircle and semivowel].”Although there’s no rule, sometimes half would be the better choice, as in this example from Fowler:
This would be an immense gain over the existing fashion of a multitude of churches ill-manned & semi-filled.
Some common semi- words:
semiabstract
semiannual
semiautomatic
semicolon
semiconscious
Two other prefixes that mean “half” are hemi,-, from the Greek, and demi-, from Old French.
In some English words, the French prefix is attached to an English word, as in demigod. Sometimes, as with demitasse and demimonde, the entire word is French.
demimonde: n. The class of women of doubtful reputation and social standing, upon the outskirts of ‘society.’[Fr.; lit. ‘half-world’, ‘half-and-half society’, a phrase invented by Dumas the younger.]The prefix hemi- is not as common as the other two. The most familiar word is hemisphere. Less common are words like hemicycle, hemistich, and hemitrope.
demitasse: n. a small coffee cup. [Fr., lit. ‘half-cup’]
In some contexts, the prefixes are used as nouns.
Men in U.S. truck commercials rapturize over “Hemi” trucks. This use of hemi refers to a type of internal combustion engine that has a “bowl-shaped or ‘hemispherical’ combustion chamber.”
In England, a semi [sĕm'ē] is a semi-detached house. In the U. S., a semi [sĕm'ī] is a big truck of the tractor-trailer variety.
*http://www.dailywritingtips.com/semi-demi-and-hemi/