Worksheet: Doped Semiconductors

In this worksheet, we will practice describing the effect that doping a semiconductor has on its electrical properties.

Q1:

A doped semiconductor that contains donor ions and is at thermal equilibrium is modeled using three variables. The density of free electrons in the semiconductor is represented by 𝑛. The density of donor ions in the semiconductor is represented by 𝑁. The density of vacancies in the semiconductor is represented by 𝑝. Which of the following formulas correctly represents the relationship between these variables in the semiconductor?

  • A𝑛=𝑁𝑝
  • B𝑛=𝑝+𝑁
  • C𝑛=𝑝𝑁
  • D𝑛=𝑝𝑁
  • E𝑛=𝑁𝑝

Q2:

A doped semiconductor that contains acceptor ions and is at thermal equilibrium is modeled using three variables. The density of free electrons in the semiconductor is represented by 𝑛. The density of acceptor ions in the semiconductor is represented by 𝑁. The density of vacancies in the semiconductor is represented by 𝑝. Which of the following formulas correctly represents the relationship between these variables in the semiconductor?

  • A𝑝=𝑁𝑛
  • B𝑝=𝑛𝑁
  • C𝑝=𝑛𝑁
  • D𝑝=𝑁𝑛
  • E𝑝=𝑁+𝑛

Q3:

The diagram shows a lattice of silicon atoms that contains one atom of phosphorus. One of the electrons from the outermost shell of the phosphorus atom moves freely in the lattice. What is the net relative electronic charge of the phosphorus?

  • A0
  • B4
  • C+4
  • D+1
  • E1

Q4:

In a semiconductor that contains acceptor ions and is at thermal equilibrium, the number of vacancies can be modeled as being equal to the number of acceptor ions. Using this model, which of the following formulas correctly represents the semiconductor? The density of free electrons in the semiconductor if it was undoped is represented by 𝑛, the density of free electrons in the semiconductor is represented by 𝑛, and the density of acceptor ions is represented by 𝑁.

  • A𝑛=𝑁𝑛
  • B𝑛=𝑛𝑁
  • C𝑛=𝑁𝑛
  • D𝑛=𝑁+𝑛
  • E𝑛=𝑛𝑁

Q5:

In a semiconductor that contains donor ions and is at thermal equilibrium, the number of free electrons can be modeled as being equal to the number of donor ions. Using this model, which of the following formulas correctly represents the semiconductor? The density of free electrons in the semiconductor if it was undoped is represented by 𝑛, the density of vacancies in the semiconductor is represented by 𝑝, and the density of donor ions is represented by 𝑁.

  • A𝑝=𝑁𝑛
  • B𝑝=𝑁𝑛
  • C𝑝=𝑛𝑁
  • D𝑝=𝑁+𝑛
  • E𝑝=𝑛𝑁

Q6:

In a doped semiconductor that is at thermal equilibrium, the density of free electrons in the semiconductor is represented by 𝑛, and the density of vacancies in the semiconductor is represented by 𝑝. The density of either free electrons or vacancies in pure silicon is represented by 𝑛. Which of the following formulas correctly models the semiconductor?

  • A𝑝𝑛=𝑛2
  • B𝑝𝑛=2𝑛
  • C𝑝𝑛=𝑛
  • D𝑝𝑛=𝑛
  • E𝑝𝑛=(𝑛)

Q7:

The diagram shows a lattice of silicon atoms that contains one atom of boron.

What is the number of electrons that covalently bond the boron atom with the silicon atoms that surround it?

What is the number of electrons that would covalently bond with a silicon atom that occupies the position of the boron atom?

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