A semiconductor's resistance falls as it gets hotter, so its temperature coefficient is negative — option 3.

The mechanism is carrier generation. Conductivity is

\(\sigma=q\left(n\mu_{n}+p\mu_{p}\right)\)

and two of those quantities change with temperature in opposite directions:

The carrier term dominates completely, because

\(n_{i}\propto T^{3/2}\exp\left(-\dfrac{E_{g}}{2kT}\right)\)

— an exponential against the mobility's mere power law. More thermal energy means more electrons excited across the gap, each leaving a hole behind, so conductivity rises and resistance falls.

The contrast with a metal is exactly the opposite and for exactly this reason. A metal has no gap: its carrier concentration is already enormous and fixed. Heating it only increases lattice vibration, which scatters those carriers more, so mobility falls and resistance rises — a positive coefficient, roughly linear, which is what makes platinum a practical thermometer.

Where the property is exploited : the thermistor is a semiconductor deliberately made with a large negative coefficient, used for temperature measurement, for compensating the positive drift of other components, and as an inrush-current limiter — cold and resistive at switch-on, hot and conducting thereafter.

Where it is a hazard : in a power device, rising temperature lowers resistance, which raises current, which raises temperature further — thermal runaway. It is also why parallel bipolar transistors need emitter ballast resistors, whereas power MOSFETs, whose channel resistance has a positive coefficient above about 25 °C, share current naturally.

Hence, semiconductors have a negative temperature coefficient of resistance.