Q.38 Which of the following statement(s) is/are true?
(A) In intrinsic semiconductors, the number of electrons is equal to the number of holes at any
temperature
(B) An intrinsic semiconductor changes to an n-type semiconductor upon addition of a trivalent
element
(C) The shape of the I-V characteristics of a p-n diode is a straight line
(D) In the reverse bias condition, the current in a p-n diode is due to the minority carriers
Options (A) and (D) are true.
In intrinsic semiconductors, electrons and holes are generated in equal numbers through thermal excitation, making their concentrations equal at any temperature. The reverse bias current in a p-n diode arises from minority carriers crossing the junction.
Option Analysis
(A) Intrinsic Semiconductors
Pure semiconductors lack impurities, so thermal energy excites electrons from the valence band to the conduction band, creating equal numbers of electrons (n) and holes (p), expressed as n=p=ni where ni is the intrinsic carrier concentration. This equality holds at all temperatures as each excitation produces one electron-hole pair. Thus, statement (A) is true.
(B) Trivalent Doping Effect
Trivalent elements like boron (group 13) have three valence electrons and create acceptor levels, producing holes as majority carriers and forming p-type semiconductors, not n-type. N-type requires pentavalent dopants like phosphorus for excess electrons. Thus, statement (B) is false.
(C) I-V Characteristics Shape
The p-n diode I-V curve shows exponential current rise in forward bias after ~0.7 V (silicon) and near-constant small reverse saturation current, forming a non-linear curve, not a straight line. A straight line indicates ohmic behavior like resistors, absent in diodes. Thus, statement (C) is false.
(D) Reverse Bias Current
Reverse bias widens the depletion region, blocking majority carriers while minority carriers (electrons in p-side, holes in n-side) diffuse across due to concentration gradients, causing the small reverse saturation current. This current remains nearly constant with voltage until breakdown. Thus, statement (D) is true.
In intrinsic semiconductors electrons holes balance perfectly due to thermal generation, while PN diode reverse bias current flows via minority carriers—key concepts for CSIR NET exams.
Core Concepts
Intrinsic semiconductors feature pure materials like silicon where charge carriers arise solely from thermal excitation across the band gap.
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Electron-hole pairs form equally: n=p at any temperature.
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No dopants alter this neutrality.
Doping and Types
Adding trivalent impurities (e.g., boron) accepts electrons, creating p-type with hole majority.
Pentavalent doping yields n-type with electron majority.
Option (B) misstates this by claiming n-type from trivalent.
PN Diode I-V Curve
Forward bias reduces barrier, enabling exponential current; reverse shows saturation.
Non-linear shape rules out straight line for (C).
Reverse Bias Mechanism
Minority carriers dominate reverse current as majority are repelled.
This explains the microampere leakage in diodes.
