The Density of States (contd..)

[@shuangyangzou8631]

Came for The Density of States, sat for the full lecture. Thank you sir!

[@MuhammadAli-px1ob]

Dear Prof M R Shenoy! You are simply Awesome!

[@PoojaGupta-mn8qe]

Really appreciate ur efforts to mk evrything clear in simple way.. Thanks alot

[@bharatheshbadadamath5394]

Nice explanation! enjoying your series of lectures.

[@aryansudan2239]

proud to be taught by this legendary prof

[@deeptisharma9817]

The Best explanation

[@akashgugnani546]

Very simple and beautiful derivation for density of states.

[@VimalPandey-yu1gl]

Amazing Lecture Sir.

[@anitamekap6584]

Awesome explanation Sir

[@adijopp1z12gorama]

Sir plz clear one the whose effective mass is greater of electrons in C.B and V.B or of holes in valance band and whats the reason

[@priyamsaha]

sir i am having a minus sign in the derivatrion of density of states in the valance band due to dE/dK

[@leehw7499]

Great lecture

[@madhumitabanerjee7731]

Sir you are really great.

[@amanladdu9664]

sir yeh 3d me h koi or se dimension me

[@asriedagnaw9958]

i have got some information about the density of state.tank you

[@debabratadey923]

absolutely brilliant

[@PushparajPathak]

Why is the k-space considered spherical?

[@prajneshkumar6447]

I was wondering the same..

[@vjencislavbarac1499]

if you draw one milion dots in each direction, one after another, which would look like line and then if you take large number of these lines. Each line would be equally long, the whole picture would look like a sphere, simple as that. If you consider other geometrical shape, you know that these lines cant be equally long.

[@mursalayub5167]

@@vjencislavbarac1499 very straightforward

[@himvar007]

we are figuring out number of states at value k. what all points in k space have same magnitude of k? kx^2+ky^2+kz^2=constant. it will lie in a sphere.

[@laks318]

Thanks a ton Sir!!!!!!!!!❤

[@sandeepchhangani939]

how to calculate volume between k & k+dk radius octant ,? if some one know then please explain

@sharma this should be divided by 8 as you want the first octant. Recall that the unit volume in spherical coordinates is dV=r^2sin(theta)dr dtheta dphi. In the first octant, theta and phi runs from zero to pi/2. Integrate over the angles you get the volume between r and r+dr giving: pi*r^2 dr/2.

[@108109093]

Because k_x, k_y and k_z can take large number of values which are m(pi/L_x), p(pi/L_x) and q(pi/L_x) respectively where m, p and q are integers. But my doubt is, why does he consider only the 1st octant to calculate the number of states and not the whole spherical region? Also, he says that m, n and p cannot be 0. Is that is the case, how can k=0 (gamma point) ever be realized because for gamma point all three k_x, k_y and k_z must be zero, i.e. essentially m, p and q must be zero?

[@mohammedsahal7]

Only first octant is valid since the n can take only positive integer values in the relationship between energy and k

[@himvar007]

kx can take both negative and positive values but we have considered standing waves which is superposition of positive and negative waves i.e. e^(jkx)+e^(-jkx). so we are just taking magnitude of k which is always positive.

[@Oindrih]

why is Ec taken as zero.. for the dE/dk value... are we following the boundary condition here.

[@himvar007]

total energy of electron = PE + KE. KE = p^2/2m. in derivation KE is taken. in conduction band, EC is the minimum energy and is the PE of electron. if electron is in any state above EC the difference in energy is because of KE.

[@amanladdu9664]

at 24.35 why ec become o

[@sunil5330]

One question, if K is discrete, then how can we take the integration/derivation or delta-k?

[@himvar007]

K has very large number values from 0 to pi/a in step of pi/L. L is sample width and a is atomic distance. so pi/L is ~billion times smaller than pi/a. Truly it is discrete but going in very very small step makes it looks continuous and results are accurate from practical considerations.

[@shaikhnoman2879]

@@himvar007 hello friend. What is step & what is L ,please say in briefly. & How we say that, the pi/L is billions time smaller than pi/a......thanks

[@108109093]

My doubt is, why does he consider only the 1st octant to calculate the number of states and not the whole spherical region?

[@mursalayub5167]

@@dasgoood2811 nice

[@maneeshpant5554]

well each sate in k space is eigen value solution of the Schrodinger equation and represented by a tiny cube of length pi/L since length cant be taken negative that's why we need to consider only the first octant.

[@marcos1289]

00:20

[@irtizahasan6107]

marcos1289 wads Ur pblm dude

[@mursalayub5167]

@@irtizahasan6107 hahha

[@mursalayub5167]

42:04

[@new-jj5il]

❤

[@gauravsemwal1912]

Thanx.....

[@mishuk2008]

why k space needs to be a sphere?

[@himvar007]

we are figuring out number of states at value k. what all points in k space have same magnitude of k? kx^2+ky^2+kz^2=constant. it will lie in a sphere.

[@ashokans913]

First of to find the one octant value, and then to integrated to 8 times