Semiconductor fuses are fast acting fuses used to protect semiconductors e.g diodes and thyristors from being destroyed by an large overcurrent or a short circuit or to remove single defective device from a parallel connection.
Sometimes, e.g. in IGBT-circuits, they are employed just to avoid explosion of the case of a failed component (There are better ways to protect an IGBT as long as it is working !, so its not useful to use a fuse to protect an IGBT from short circuit)
In case of a short circuit a semiconductor fuse is able to clear the fault within the halfwave where the short circuit occured.
Semiconductor fuses are sized using the Integral of I²t (which has to be sized according to the semiconductors I²t-raing) and, of course, the voltage.
Compared to standard fuses they are much faster, but losses are significantly higher. Usually a semiconductor fuse is not able to protect against overload only slightly above nominal current. So sometimes standard fuses and semicondcutor fuses are connected in series.
Sizing a semiconductor fuse correctly is a quite difficult task. Search for information from one of the major suppliers e.g. Ferraz or Bussman for further information.