Energy band gap of semiconductors

[quietrain]

ok let's say i have a semiconductor like germanium with band gap of around 0.67eV at rtp.

so this means that i need around 0.67 x 10^-19 J of energy to cause valence electrons to jump to conduction band right?

do i use the formula E = 1/2 kT to relate this energy to temperature?

so i calculated the temperature required which is 9000 K ! is this right? generally what temp does intrinsic conductivity occur for germanium?

thanks!

 

[kanato]

Yes, that's about right. Intrinsic semiconductors have very few charge carriers until rather high temperatures.

 

[quietrain]

so i need roughly 9000 K temp for electricity to flow? wow.

this flow of intrinsic charge carriers is the same as breakdown voltage charge carriers in the semiconductor right?

 

[nasu]

so i need roughly 9000 K temp for electricity to flow? wow.

this flow of intrinsic charge carriers is the same as breakdown voltage charge carriers in the semiconductor right?

Remember than 1/2kT is the average thermal energy (per degree of freedom). There are particles (phonons) with energies larger than average and they may excite electrons into the conduction band. So you'll have some conduction at temperatures well below the estimate. You can estimate how many if you find the conductivity of intrinsic germanium (at room temperature, for example).

 

[quietrain]

Remember than 1/2kT is the average thermal energy (per degree of freedom). There are particles (phonons) with energies larger than average and they may excite electrons into the conduction band. So you'll have some conduction at temperatures well below the estimate. You can estimate how many if you find the conductivity of intrinsic germanium (at room temperature, for example).

wiki says its resistivity p is (20 °C) 1 Ω·m,

so conductivity = 1/p = 1/1 = 1 Ω^-1·m^-1 ?

so how should i intepret this conductivity value?

 

[nasu]

You cannot calculate the number just from resistivity alone because this depends on other factors like relaxation time or (related to it) mobility.
But we can compare for example copper with a resitivity of the order of 10^(-8) and germanium with 1 (both in Ohm-m).
As the resistivity is proportional with carrier concentration, we can estimate that the concentration in Ge will be maybe smaller than in copper by a factor of 10^8 or even more.
However the electron concentration in copper is 10^22 per cubic cm.
So even a decrease by a factor of 10^10 still leaves some carriers in.

 

[quietrain]

oh isee thanks

just a last question, about how much carriers is required so that current flows reasonably?