3110018 Lecture 4: Intrinsic_Hole density at VB_VAA_Student copy
27 May 2023
Department
Course
Professor
Page 1 of 3 V. A. Adhwaryu @Physics class
Calculation of Hole density (p) in
‘Intrinsic Semi conducting material’
Prerequisites:
(a) Density of states 𝑍(𝐸) V.B.
(b) Fermi energy level (𝐸)
(c) F-D Distribution Function 𝑓(𝐸) But Here in this case [1-f(E)]
(d) Standard Gamma function Γ
𝑑𝑝- No. of holes whose energy lies
between 𝐸 & (𝐸+ 𝑑𝐸) in valence band.
𝑍(𝐸)- Density of states in an energy
interval 𝐸 & (𝐸+ 𝑑𝐸) in valence band .
𝑓(𝐸)-Probability that a state of energy is
occupied by an electron.
[1−𝑓(𝐸)]
–
Probability that state of
energy occupied by holes.
A) The total hole density:
…………. (i)
………… (ii)
(B) The density of states 𝑍(𝐸) for 𝑬<𝑬𝒗 in a valence band.
𝑍(𝐸) 𝑑𝐸=
(2𝑚
∗)
𝑬𝟏
𝟐 dE…........ (iii)
Here, (𝐸−𝐸) is true for valence holes (∵𝐸<𝐸), where 𝐸 shows the
potential energy of holes at rest. So, from equation (iii)
𝟒𝝅
𝒉𝟑𝒉
∗𝟑
𝟐𝒗𝟏
𝟐 dE…......(iv)
