GATE Electrical Engineering (EE) Test: Semiconductor Physics Free Online

The intrinsic conductivity for germanium is

The intrinsic conductivity for silicon is

The assertion is true: n-type semiconductors have electrons as majority carriers because donor impurities (e.g., phosphorus) add extra electrons. The reason is also true: donors create energy levels just below the conduction band, allowing easy electron excitation to the conduction band, increasing electron concentration. The reason correctly explains why electrons dominate in n-type semiconductors.

• Option A: Correct, as both statements are true and R explains A.

When an electron is accelerated by the potential applied to a semiconductor, the energy gained from the field may then be transferred to an atom when the electron collides with the atom.

• Drift: Carriers (e.g., electrons) move due to an electric field, producing a net current (matches 2).

• Diffusion: Carriers move from high to low concentration areas, driven by a concentration gradient (matches 1).

• Recombination: Electrons and holes combine, reducing carrier density (matches 3).
  Option A: Correct, as A-2, B-1, C-3 aligns with definitions.

The bandgap determines how easily carriers (electrons or holes) can be excited to the conduction band. A small bandgap, as in semiconductors like gallium arsenide, allows easier carrier excitation, enabling faster carrier movement and higher switching speeds, which are critical for high-frequency devices. Large bandgaps (e.g., insulators) hinder carrier excitation, while metals (no bandgap) have different limitations.

To arrange the elements in column IV of the periodic table by their atomic number:

• Carbon (C) has the lowest atomic number.
• Silicon (Si) follows Carbon.
• Germanium (Ge) comes next.
• Tin (Sn) has the highest atomic number in this group.

The correct increasing order of atomic numbers is:

• C, Si, Ge, Sn

Both assertion and reason are individually correct statements. However, the reason for assertion is that due to the applied electric field, and electrostatic force is developed on the electron and the electrons would be accelerated in a direction opposite to the applied electric field and this motion is called directed motion of electron.

The current density is given by 

Given, N_A = 0
Using “charge neutrality equation”, we have:
N_D + P = N_A + n
or, N_D + p = ....(i) 
Using'“Mass-action law”, we have:

Substituting value of p from equation (ii) in equation (i), we have:



Neglecting negative sign, we get:

= free electron density or concentration

• Option A: Incorrect. Adding donor impurities (n-type doping) increases electron concentration, enhancing conductivity.

• Option B: Incorrect. Acceptor impurities (p-type doping) increase hole concentration in the valence band, not electrons in the conduction band.

• Option C: Incorrect. Simultaneous doping (compensation) reduces net carrier concentration, but the material remains extrinsic unless perfectly balanced.

• Option D: Correct. Heavy donor doping significantly increases electron concentration, reducing the bandgap effect and causing the semiconductor to behave like a metal with high conductivity.