Intrinsic Semiconductors

Introduction

An intrinsic semiconductor is a pure semiconductor material without any significant impurity atoms. In an intrinsic semiconductor, the number of free electrons equals the number of holes, and all charge carriers are generated solely by thermal excitation of electrons from the valence band to the conduction band.

Crystal Structure of Pure Silicon

Electron-Hole Pair Generation

When thermal energy breaks a covalent bond, an electron becomes free and leaves behind a hole:

Key Properties

Equal Carrier Concentrations

In intrinsic semiconductors:

Intrinsic Carrier Concentration

Mass Action Law

The product of electron and hole concentrations is constant at a given temperature:

Fermi Level in Intrinsic Semiconductors

The Fermi level (Eᶠ) lies approximately at the middle of the band gap:

Conductivity of Intrinsic Semiconductors

Temperature Dependence

The conductivity approximately doubles for every 8-11°C rise in temperature.

Drift and Diffusion

Drift Current

Current due to applied electric field:

Diffusion Current

Current due to concentration gradient:

Numerical Examples

Example 1: Carrier Concentration

Problem: Calculate the intrinsic carrier concentration of silicon at 400K. Given: nᵢ(300K) = 1.5 × 10¹⁰/cm³, Eg = 1.12 eV.

Solution:

Example 2: Conductivity Calculation

Problem: Find the resistivity of intrinsic germanium at 300K. Given: nᵢ = 2.5 × 10¹³/cm³, µn = 3900 cm²/V·s, µp = 1900 cm²/V·s.

Solution:

Limitations of Intrinsic Semiconductors

1. Too few carriers: At room temperature, Si has only 1.5×10¹⁰/cm³ vs 5×10²² atoms/cm³
2. Temperature sensitive: Properties change dramatically with temperature
3. Cannot be controlled: No way to independently adjust n or p
4. High resistivity: Not useful for practical devices

These limitations are overcome by doping — intentionally adding impurities to create extrinsic semiconductors.

Interview Questions

1. What is the significance of nᵢ in semiconductor physics?

nᵢ is the intrinsic carrier concentration — the equilibrium concentration of electrons and holes in pure semiconductor at a given temperature. It sets the minimum carrier density and appears in the mass action law (np = nᵢ²) that governs all semiconductor devices.

1. Why does germanium have higher leakage current than silicon in devices?

Germanium has a smaller band gap (0.67 vs 1.12 eV), so its nᵢ is ~1000× higher than silicon at room temperature. This means more thermally generated carriers, leading to higher reverse-bias leakage currents in junctions.

1. Explain why the Fermi level is at mid-gap in intrinsic semiconductors.

For n = p, the Fermi function must give equal probability of finding an electron at the conduction band edge and a hole at the valence band edge. This symmetry places Eᶠ midway between Ec and Ev (with slight deviation due to effective mass differences).

1. What happens to an intrinsic semiconductor at absolute zero?

At 0K, all electrons remain in covalent bonds (valence band), with no thermal energy to excite them to the conduction band. The material behaves as a perfect insulator with zero free carriers.

1. How does the mass action law apply when a semiconductor is doped?

Even in doped (extrinsic) semiconductors, np = nᵢ² at thermal equilibrium. If doping increases electrons (n >> nᵢ), holes must decrease proportionally (p = nᵢ²/n << nᵢ). The product remains constant at a given temperature.

Summary

Intrinsic semiconductors are pure materials where all charge carriers originate from thermal generation of electron-hole pairs. While their properties (nᵢ, σ, Eᶠ) establish fundamental physical relationships used throughout semiconductor device theory, practical devices require extrinsic (doped) semiconductors for controllable and useful electrical behavior.