---
title: "Doping to raise Fermi level by 0.7 eV"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:raise-fermi-0-7ev"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/raise-fermi-0-7ev
site: BCT Engineering
---

# Doping to raise Fermi level by 0.7 eV

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2076 Asoj, 4 marks
- Video: [Fermi Energy Level in Extrinsic Semiconductor | Electronics Devices and Circuits - EDC](https://www.youtube.com/watch?v=0H9qIQ2n3kM) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/raise-fermi-0-7ev
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

If it is desired to raise Fermi level to 0.7 eV above the intrinsic Fermi level at room temperature, what type of dopant is to be used? Also determine its doping level if the used intrinsic semiconductor is silicon.

## Short answer

n-type (donor) dopant. Using E_F − E_i = 0.7 eV and non-degenerate formula, N_d = n_i exp(0.7/0.02585) ≈ 8.3×10^21 cm⁻³. This exceeds N_c, so degenerate doping is required; the semiconductor becomes heavily n⁺.

## Answer

To raise the Fermi level **above** $E_{Fi}$, electrons must be made majority carriers, so a **donor (n-type, group V) dopant** such as phosphorus, arsenic or antimony must be used.

#### Doping level

For a non-degenerate n-type semiconductor

$$
n = N_d = n_i\exp\left(\frac{E_{Fn}-E_{Fi}}{kT}\right)
$$

**Data used (Si, 300 K):** $n_i = 1.45\times10^{10}\ \text{cm}^{-3}$, $kT = 8.617\times10^{-5}\times300 = 0.02585\ \text{eV}$, $\mu_e = 1350$, $\mu_h = 450\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}$, $e = 1.6\times10^{-19}\ \text{C}$.

$$
\begin{aligned}
\frac{E_{Fn}-E_{Fi}}{kT} &= \frac{0.7}{0.02585} = 27.08\\
N_d &= 1.45\times10^{10}\times e^{27.08}\\
&= 1.45\times10^{10}\times5.75\times10^{11}\\
&= 8.34\times10^{21}\ \text{cm}^{-3}
\end{aligned}
$$

**Answer: donor doping, $N_d \approx 8.3\times10^{21}\ \text{cm}^{-3}$ (by the formula).**

#### Important remark

For silicon $E_g \approx 1.1$ eV, so $E_c - E_{Fi} \approx 0.55$ eV. Raising $E_F$ by 0.7 eV puts it about **0.15 eV inside the conduction band**. The semiconductor is then **degenerate**:

- $N_d$ would exceed $N_c \approx 2.8\times10^{19}\ \text{cm}^{-3}$, and would be about 17% of the Si atomic density ($5\times10^{22}$), far beyond normal doping (and beyond the solubility of most donors).
- The Boltzmann formula is no longer exact, so the number above is only an estimate; the true requirement is "very heavy doping, $N_d > N_c$".

In practice this degenerate n⁺ doping behaves like a metal and is used for ohmic contacts and tunnel diodes.

## Check yourself

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

1. To raise E_F above E_Fi, which dopant is used?
   A. A group V donor (P, As, Sb)
   B. A group III acceptor
   C. Any isoelectronic atom
   D. No doping can do this
   Answer: A. Donors increase n above ni. (Key point: Dopant type)

2. Which gives the doping level?
   A. Nd = ni exp((E_F - E_Fi)/kT) = 8.3x10^21 cm^-3
   B. Nd = ni ln(0.7/kT)
   C. Nd = ni exp(-0.7/kT) = 1.8x10^-2
   D. Nd = 0.7 ni
   Answer: A. exp(27.08) = 5.75x10^11 times 1.45x10^10. (Key point: Formula)

3. Why is the result only an estimate?
   A. E_F is inside the gap
   B. E_F ends up about 0.15 eV inside the CB, so material is degenerate and Boltzmann fails
   C. ni is unknown
   D. T is too high
   Answer: B. Nd would exceed Nc about 2.8x10^19 and be about 17% of Si atoms. (Key point: Degenerate)

## Close variants set in other exams

- [Doping to raise Fermi level by 0.1 eV](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Araise-fermi-0-1ev) — Electrical Engineering Material, chapter 6, asked 2×

## Related in Electrical Engineering Material

- [Intrinsic Fermi level of pure semiconductor](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aintrinsic-fermi-level) — Electrical Engineering Material, chapter 6
- [Fermi level with 10¹⁷ Sb then further doping](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aantimony-1e17-fermi-shift) — Electrical Engineering Material, chapter 6, asked 6×
- [Temperature for 30% occupation 0.75 eV above](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-temperature-30-percent) — Electrical Engineering Material, chapter 1
- [Occupation probability 3kT above Fermi level](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-probability-3kt-above) — Electrical Engineering Material, chapter 1, asked 2×
- [Non-occupation probability 5kT above Fermi level](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-probability-5kt-not-occupied) — Electrical Engineering Material, chapter 1, asked 2×