How Do You Sketch Energy Bands and Determine Effective Mass in a Semiconductor?

[me_master]

Hi,

I have a question regarding Energy band.

The energy band of a simple cubic semiconductor crystal with a lattice constant b can be represented as in the following function:

E(k) = E₀ + E₁[cos(k_xb) + cos(k_yb) +cos(k_zb)]

where E₀ and E₁ are independent of the wave vector k.

i) Sketch the dependence of E and k from k=0 to the edge of the Brillouin zone in the [100] direction.

For this question, please help to explain whether I need to partial differentiate in the x direction only since the question is for [100] direction?

ii) Determine the effective mass of electron at k=0 in the [100] direction.

 

[kanato]

Yeah, you only need to do the x direction.

 

[asheg]

1- Set ky=0 kz=0 plot the function (Constant+Cos(kx.b))
2- mx = Constant*1/(d^2E/dkx^2)

 

[me_master]

Thanks asheg and kanato