# Temparature dependence of intrinsic silicon

• Mechdude
In summary, the question asks for the temperature at which a silicon sample with a donor concentration of 10^22 cm^-3 will stop exhibiting intrinsic behavior. The equation used for intrinsic semiconductors is n_{i}^{2} = 4 \left[ \frac{k_B T} {2 \pi \hbar^2 } \right]^{3/2} (m_e m_h)^{3/4} e^{ \beta E_g /2}, where n_i is the intrinsic carrier concentration, k_B is Boltzmann's constant, T is temperature, \hbar is Planck's constant, m_e and m_h are the effective masses of the electrons and holes, and E_g
Mechdude

## Homework Statement

A sample of silicon is purified until it contains only $10^22$ donors per $cm^3$ . Below what temparature will it cease to show intrinsic behaviour? ( take $E_g = 1eV$ ; $E_d = 0.05eV$ ; $m_e =m_h = 0.2$

## Homework Equations

for intrinsic semiconductors:
$$n_{i}^{2} = 4 \left[ \frac{k_B T} {2 \pi \hbar^2 } \right]^{3/2} (m_e m_h)^{3/4} e^{ \beta E_g /2}$$
this is from his notes.

## The Attempt at a Solution

im i looking for the point at which $n_i$ is zero? or something else? and where does the $E_d$which is $=$ donor ionization, fit in the equation?

Last edited:
n_{i}^{2} = 4 \left[ \frac{k_B T} {2 \pi \hbar^2 } \right]^{3/2} (m_e m_h)^{3/4} e^{ \beta E_g /2} I tried to rewrite the equation to solve for T: T = 2 \pi \hbar^2 \left[\frac{n_i^2}{4(m_e m_h)^{3/4}} \right]^{2/3} e^{\beta E_g /2}and then plug in the given values, but I dont know what to do from here.Also, I'm not sure how to interpret the question. What does it mean by intrinsic behaviour? Is that the same as intrinsic semiconductor?

## 1. What is the temperature dependence of intrinsic silicon?

The temperature dependence of intrinsic silicon refers to the relationship between the temperature and the electrical properties of pure silicon material. It is a measure of how the conductivity, resistivity, and other characteristics of silicon change as the temperature changes.

## 2. Why is it important to study the temperature dependence of intrinsic silicon?

Studying the temperature dependence of intrinsic silicon is important because it helps us understand how silicon behaves in different environments. It is also crucial for designing and optimizing electronic devices that use silicon as a semiconductor material.

## 3. How does the temperature affect the electrical conductivity of intrinsic silicon?

The electrical conductivity of intrinsic silicon increases as the temperature increases. This is because at higher temperatures, more electrons are excited from the valence band to the conduction band, resulting in a higher number of free charge carriers and thus higher conductivity.

## 4. What is the temperature coefficient of intrinsic silicon?

The temperature coefficient of intrinsic silicon is a measure of how the electrical properties of silicon change with temperature. It is typically represented as the change in electrical conductivity or resistivity per degree Celsius (or Kelvin) of temperature change.

## 5. How does the temperature dependence of intrinsic silicon differ from that of doped silicon?

The temperature dependence of intrinsic silicon is mainly influenced by the number of free charge carriers, while the temperature dependence of doped silicon is also affected by the type and concentration of dopants present. Intrinsic silicon has a higher temperature coefficient compared to doped silicon, which makes it more sensitive to temperature changes.

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