What is Density of States (DOS). Derivation of Density of States and important in Hindi

Notes
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Classical Free electron Theory Assumptions Success,Drawbacks, Drude
• Classical Free electro...
Kronig Penney Model Bands in Solids K P Model
• Kronig Penney Model Ba...
E-k Diagram, Difference Between Direct Indirect band gap (DBS IBS)
• E-k Diagram, Differenc...
What is Density of States (DOS)
• What is Density of Sta...
Effective mass in semiconductor
• Effective mass in semi...
Probability of Occupation, Fermi Energy, Fermi Level, Fermi Dirac Distribution Function
• Probability of Occupat...
What is Phonon
• What is Phonon in Soli...
Density: Per unit volume.
State: Allowed solution which satisfy the boundary condition.
Definition 1: The density of states gives the number of allowed electron (or hole) states per volume at a given energy.
Definition 2: The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy.
DOS calculations allow one to determine the general distribution of states as a function of energy and can also determine the spacing between energy bands in semi-conductors . Derivation of density of states can be derived from basic quantum mechanics.
Applications:
The density of states plays an important role in the kinetic theory of solids.
The product of the density of states and the probability distribution function is the number of occupied states per unit volume at a given energy.
Bulk properties such as specific heat, paramagnetic susceptibility, and other transport phenomena of conductive solids depend on this function.

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If density increases then what happen to the stress and displacement????

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Volume of sphare to 4/3πr^3 hoti h fir apne 4πr^3 q liya 1/8 th part of volume jha apne liya hai sir

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Sir volume of sphere ...4πr^2 nii hota h ......lateral surface area hota h ....vo ....🤦🤦🤦🤦

[@nishu0826]

sir volume of sphere is 4 pi r^3 but during derivation of DOS you were taking it 4 pi r^2 is this really correct sir i'm unable to understand the derivation bcz of this small doubt can u plzz clear it to me?

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it's 4πr^2*dr , it's for small portion,

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sir yeh apne 2*k.r = n*2*pie kaise likha

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[@vijithvisweswaran5262]

Sir isnt volume of sphere 4/3πr³?

[@VishnuAwasthi]

Yes you are right.but Here we take positive quadrant only, so it's 1/8th of the same as per the condition of standing wave.

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@@VishnuAwasthi sir for +ve qt you multiply 1/8. But for volume if sphere we have to multiply 4/3

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Ye density of states for electron in 3-D k leye b applicable h ??

[@VishnuAwasthi]

Yes

[@englishgrammarquiz4709]

@@VishnuAwasthi thanku sir for replying.. kya ap muje clear kr den gye? Q:Derive an expression for density of state when an electron is busy to make oscillations in 3-Dimension Sir ye question h exactly.. ap clearify kr skty hain k is k answer mai ye video wali derivation e aye gi ?? Please sir reply.. I shall be very grateful to you for this:) Waiting for your consideration

[@VishnuAwasthi]

@@englishgrammarquiz4709 ha DOS ke liye yahi derivation hai. Or density Hamesha 3D me hi li jati hai. density is always per unit volume(means 3D).

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Sir g , can we say it variation of density of states with energy?

[@VishnuAwasthi]

Yes DOS is proportional to Square root of energy

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