---
title: "Intrinsic conductivity and resistivity of GaAs"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:gaas-intrinsic-conductivity"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/gaas-intrinsic-conductivity
site: BCT Engineering
---

# Intrinsic conductivity and resistivity of GaAs

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2071 Shrawan, 4 marks
- Video: [Intrinsic semiconductors](https://www.youtube.com/watch?v=wcKOMSvdfk0) — Taylor Sparks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/gaas-intrinsic-conductivity
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

Calculate the intrinsic conductivity and resistivity of GaAs at room temperature. The intrinsic concentration, electron mobility and hole mobility of GaAs are 1.8×10⁶ per cm⁻³, 8500 cm² v⁻¹s⁻¹ and 400 cm² v⁻¹s⁻¹ respectively at 300K.

## Short answer

σ_i = e n_i(μe+μh) = 1.6×10⁻¹⁹ × 1.8×10⁶ × 8900 = 2.56×10⁻⁹ S/cm; ρ_i = 1/σ_i ≈ 3.9×10⁸ Ω·cm.

## Answer

For an intrinsic semiconductor $n = p = n_i$, so

$$
\sigma_i = en_i(\mu_e+\mu_h),\qquad \rho_i = \frac{1}{\sigma_i}
$$

**Given (GaAs, 300 K):** $n_i = 1.8\times10^{6}\ \text{cm}^{-3}$, $\mu_e = 8500$, $\mu_h = 400\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}$, $e = 1.6\times10^{-19}$ C.

#### Conductivity

$$
\begin{aligned}
\sigma_i &= 1.6\times10^{-19}\times1.8\times10^{6}\times(8500+400)\\
&= 1.6\times10^{-19}\times1.8\times10^{6}\times8900\\
&= 2.56\times10^{-9}\ \text{S cm}^{-1}\ (= 2.56\times10^{-7}\ \text{S m}^{-1})
\end{aligned}
$$

#### Resistivity

$$
\rho_i = \frac{1}{2.563\times10^{-9}} = 3.90\times10^{8}\ \Omega\,\text{cm}\ (= 3.90\times10^{6}\ \Omega\,\text{m})
$$

**Answer: $\sigma_i \approx 2.56\times10^{-9}$ S cm⁻¹ and $\rho_i \approx 3.9\times10^{8}\ \Omega$ cm.**

Although electrons in GaAs are about six times more mobile than in Si, the much larger band gap (1.42 eV) makes $n_i$ about $10^4$ times smaller, so intrinsic GaAs is nearly an insulator ("semi-insulating" GaAs is used as a substrate).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In intrinsic GaAs, what is the relation between n, p and ni?
   A. n = 2p = ni
   B. n = ni^2, p = 0
   C. n >> p
   D. n = p = ni
   Answer: D. Each broken bond gives an electron-hole pair, so n = p = ni. (Key point: Intrinsic carriers)

2. Which expression gives sigma_i?
   A. e ni (mu_e + mu_h)
   B. e ni (mu_e - mu_h)
   C. e ni mu_e only
   D. ni/(e (mu_e + mu_h))
   Answer: A. Electrons and holes both conduct, so their contributions add. (Key point: Conductivity formula)

3. With ni = 1.8e6 cm^-3, mu_e = 8500, mu_h = 400, sigma_i is about:
   A. 2.56 x 10^-3 S/cm
   B. 2.56 x 10^-9 S/cm
   C. 1.4 x 10^-3 S/cm
   D. 3.9 x 10^8 S/cm
   Answer: B. 1.6e-19 x 1.8e6 x 8900 = 2.56e-9 S/cm, so rho = 3.9e8 ohm cm. (Key point: Magnitude of result)

4. Why is intrinsic GaAs nearly an insulator despite high electron mobility?
   A. Its holes are immobile
   B. It has no conduction band
   C. Its large band gap (1.42 eV) makes ni very small
   D. Its mobility drops at 300 K
   Answer: C. The large gap gives very small ni, which outweighs the higher mobility. (Key point: Why GaAs is nearly insulating)

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