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A conductor is just that - something that conducts electric current. A semiconductor, however, is a material that can be and is used because by doing some things to it, we can cause its resistance to vary dramatically over a fairly wide range of values. We can cause it to conduct with little resistance, and we can cause it to resist current flow completely and prevent current from flowing. The material is a semiconductor, and it "sort of" conducts - either well or poorly or something in between, depending on how the device is made and on what we tell it to do. Conductor will pass electrons by the laws of electrical conductivity. Semiconductor will pass electrons basically only one way.
Conductors, like copper, are materials that simply conduct electricity from point A, such as the negative terminal of a battery, to point B.

Semiconductors are materials that conduct electricity from point A to point B, but have high high resistance. Many conductors can be modified to have unique properties when electricity is applied, such as in transistors. Put simply, semiconductors have an electrical conductivity somewhere between that of conductors (gold, copper) and insulators (wood, rubber).
A conductor allows an electric current to flow through it equally well in either direction. The amount of current which flows depends only on the amount of resistance of the conductor and on the amount of voltage applied across it. The direction of flow can always be considered as being from the positive to the negative pole of the source of the voltage applied, so the direction of flow through a conductor is always determined by which end of the conductor is connected to the positive pole of the source. A semiconductor allows an electric current to flow very strongly in one direction (this is known as the forward current) and very weakly in the opposite direction (which is known as the reverse current). The amounts of current which flow in each direction depend partly on the amount of the voltage applied but mainly on the forward resistance (which is relatively low) and the reverse resistance (which is always very high). So, unlike a conductor, the flow of current through a semiconductor is not the same amount of current whichever way the voltage is applied. The direction in which a semiconductor allows the forward current to flow depends on whether it is a p-type semiconductor or an n-type semiconductor. How are semiconductors made? Certain elements, such as Germanium or Silicon, are not naturally semiconductors but can be made into semiconductors by melting them and adding very small amounts of other chemicals. This process is called doping. Whether a p-type semiconductor or an n-type semiconductor is produced depends on the type of doping chemical used.

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