Temparature dependence of intrinsic silicon

[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?

 

[NateD]

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?