NDA (II) 2017 General Ability Test · Question 78 of 150

Correct — D, holes. A p-type semiconductor is made by adding a trivalent impurity such as boron, aluminium, gallium or indium to a tetravalent crystal of silicon or germanium. The impurity atom takes a lattice site that needs four bonding electrons but brings only three, so one covalent bond is left short of an electron. That vacancy is a hole. It behaves like a mobile positive charge, because a neighbouring bonding electron can slip into it and leave a fresh vacancy behind, so the hole appears to travel through the crystal. Since one hole is created for every impurity atom added, holes vastly outnumber the few electrons that thermal energy frees, and the holes are therefore the majority carriers. The letter p in p-type comes from this positive-carrier picture.

• (a)free electrons — Free electrons are the majority carriers in an n-type semiconductor, which is doped with a pentavalent impurity such as phosphorus, arsenic or antimony. Those atoms bring five valence electrons where four suffice, so the fifth is left loose. In p-type material electrons exist only as thermally generated minority carriers, in very small numbers.
• (b)conduction electrons — This is the same claim as option (a) worded differently — an electron in the conduction band is a free electron. Conduction electrons are again the majority carriers of n-type material, not of p-type.
• (c)ions — Ions carry the current in electrolytes, not in a solid semiconductor. The dopant atoms in the crystal do become charged cores once they accept or give up an electron, but they are locked into the lattice and cannot move, so they carry no current.

A pure semiconductor has few free carriers at room temperature. Doping fixes that. Adding a trivalent impurity to silicon leaves one covalent bond incomplete for every impurity atom, producing a hole and giving p-type material; adding a pentavalent impurity leaves one electron unbonded for every impurity atom, producing an extra free electron and giving n-type material. The doped crystal as a whole stays electrically neutral — it is the balance of mobile carriers that changes, not the total charge.

The safe way to read this question is to translate the label. In p-type the p stands for positive carriers, and among the four options only a hole behaves as a mobile positive charge. It also helps to remember that both types of doped semiconductor contain both kinds of carrier; the word 'majority' is doing real work in the question, and in p-type material electrons still exist as minority carriers. Putting a p-type and an n-type region together in one crystal gives the p-n junction, the basis of the diode, the transistor, the solar cell and the light-emitting diode.

• Trivalent dopants — boron, aluminium, gallium, indium — give p-type material in which holes are the majority carriers.
• Pentavalent dopants — phosphorus, arsenic, antimony — give n-type material in which electrons are the majority carriers.
• A doped semiconductor stays electrically neutral overall; doping changes which carrier is plentiful, not the net charge.
• In p-type material electrons are still present as thermally generated minority carriers, and in n-type material holes play that role.
• The conductivity of a semiconductor rises with temperature, unlike that of a metal, because heat frees more carriers.

• Reading p-type as 'plenty of electrons'; the p is for positive carriers, which are holes.
• Assuming p-type material carries a net positive charge — it is neutral overall.
• Forgetting that minority carriers exist in both types, which is what makes the word 'majority' the key word in the question.

NDA asks this as a one-line recall item, and also indirectly through questions on diodes, doping and the temperature behaviour of semiconductors.

• practice — not a real PYQ

  Silicon doped with phosphorus gives a semiconductor in which the majority carriers are

  • (a)holes
  • (b)free electrons
  • (c)positive ions
  • (d)protons

  Answer(b) free electrons — phosphorus is pentavalent, so each atom leaves one electron unbonded, giving n-type material.

• practice — not a real PYQ

  Which of the following elements, when added to silicon, produces a p-type semiconductor?

  • (a)Arsenic
  • (b)Antimony
  • (c)Boron
  • (d)Phosphorus

  Answer(c) Boron — it is trivalent, so it leaves one covalent bond short of an electron and creates a hole.