Q.13 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 13 Solution

Topic: Semiconductor Electronics: Materials, Devices and Simple Circuits · Official NTA Booklet Code M1

Question

The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.

✓

Verified Against NTA Final Answer Key

Option (3) : current in n-type > current in p-type.

📚 Semiconductor Electronics: Materials, Devices and Simple Circuits Easy

📋 Given Parameters & Problem Setup

Electron concentration in n-type (n_e) Equal to hole concentration in p-type (n_h)

External Electric Field (E) Same for both

⚡

The 30-Second Exam Hall Shortcut: ⚡ Electron Mobility Rule: μ_e > μ_h $\implies$ I_n > I_p

⏱️ Save ~20 seconds

Electrons move freely in the conduction band, whereas holes move through valence bond step-by-step jumping. Hence, electron mobility is always strictly greater than hole mobility ( $\mu_e > \mu_h$ ). With identical carrier densities and electric fields, $I_n > I_p$ ! Match Option (3)!

1 Current in semiconductor:

I = n q A v_d = n q A \mu E

2 For n-type:

I_n = n_e e A \mu_e E

. For p-type:

I_p = n_h e A \mu_h E

3 Given

n_e = n_h

and

E

is identical.

4 Since electrons in conduction band have higher mobility than valence band holes (

\mu_e > \mu_h

), we have

I_n > I_p

5 Match Option (3) current in n-type > current in p-type.

🛡️

Why You Can 100% Trust This Shortcut: Canonical solid state physics energy band theory of carrier mobility.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating Current in Terms of Carrier Mobility

The drift velocity of a charge carrier under an electric field $E$ is $v_d = \mu E$ , where $\mu$ is mobility. Current through a semiconductor of cross-sectional area $A$ with carrier concentration $n$ is:

I = n e A v_d = n e A \mu E

Step 2

Comparing n-type and p-type Currents

For n-type with electron density $n_e$ and p-type with hole density $n_h$ :

I_n = n_e e A \mu_e E, \quad I_p = n_h e A \mu_h E

Step 3

Physical Reason for Mobility Difference

Electrons in n-type occupy the conduction band, where they behave almost as free electrons with small effective mass. Holes in p-type move via the sequential vacancy-hopping of bound valence electrons. Consequently, in all semiconductors (Silicon, Germanium, GaAs):

\mu_e > \mu_h \implies I_n > I_p

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Fails to consider that electrons and holes have different mobilities ($mu_e eq mu_h$).

⚠️

Student Fallacy (Why candidates pick this trap): Assuming equal carrier concentrations guarantee equal currents.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Inverts the mobility relationship (holes never have higher mobility than electrons).

⚠️

Student Fallacy (Why candidates pick this trap): Falsely assuming holes move faster.

3 3

✓ 100% Correct

Verdict & Scientific Reason:

Exact physical conclusion: because $mu_e > mu_h$ , the drift current in n-type exceeds that in p-type.

💡

Why this is airtight: None; rigorous semiconductor physics.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Holes are mobile positive charge carriers that conduct macroscopic current readily.

⚠️

Student Fallacy (Why candidates pick this trap): Thinking holes cannot conduct electrical current.

⚠️

NTA Trap Alert: Carrier Density vs. Current Equality Trap

Students frequently equate current solely with carrier density ( $I \propto n$ ), forgetting that current also depends on drift velocity ( $v_d = \mu E$ ). Since $\mu_e > \mu_h$ , current in n-type is always greater.

🛡️ How to avoid the -1 mark: Remember:

I = n e A \mu E

. Even if

n_e = n_h

, electron mobility is ALWAYS higher (

\mu_e > \mu_h

📖

Core NEET Syllabus Standard

NCERT Physics · Semiconductor Electronics: Materials, Devices and Simple Circuits Standard Benchmark

Core Scientific Principle Tested:

"Electron mobility in conduction band is significantly higher than hole mobility in valence band ( $\mu_e > \mu_h$ )."

Syllabus Focus: Extrinsic Semiconductors

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 13 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Electron Mobility Rule: μ_e > μ_h ⟹ \implies⟹ I_n > I_p

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating Current in Terms of Carrier Mobility

Comparing n-type and p-type Currents

Physical Reason for Mobility Difference

360° Option Elimination Engine Key Feature

NTA Trap Alert: Carrier Density vs. Current Equality Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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The 30-Second Exam Hall Shortcut: ⚡ Electron Mobility Rule: μ_e > μ_h $\implies$ I_n > I_p