{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

C02 Equilibrium Concentration Anoted 0929

# C02 Equilibrium Concentration Anoted 0929 - Equilibrium...

This preview shows pages 1–5. Sign up to view the full content.

- - 24 Equilibrium Carrier Concentrations in Semiconductors To predict quantitatively electrical behavior of a semiconductor, we need to know (a) Density of states function D ( E ). (b) Probability of occupancy of those states in order to evaluate carrier concentrations. Water Analogy A very good analogy exists between water in a container and electrons in a semiconductor. Water cannot occupied the same space. (i.e. Water cannot be compressed.) Versus Electrons cannot occupied the same state (Pauli’s exclusio n principle) To predict quantitatively the total amount of water in the container, we need to know (a) Crossectional area of container at various height and (b) Probability of water occupancy at various height.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
- - 25 Probability of Occupancy Fermi-Dirac Distribution Function The probability that an allowed state is occupied is described by the Fermi-Dirac distribution function: f E e E E kT f ( ) 1 1 (1) Where E f Fermi Level Energy at which probability of occupancy is ½ . 1 1 1 f E e E E kT f ( ) (2) Probability of a state not being occupied Probability of a state to have a hole
- - 26 For T = 0 K All states < E f are occupied All states > E f are empty. For T > 0 K Some electrons have E > E f Some holes have E < E f . Note that: ) ( ) ( 1 E E f E E f f f i.e. Fermi-Dirac distribution is complementary and independent of temperature for a symmetric pair of energy about Fermi level. Boltzmann Approximation The FD distribution f ( E ) can be approximated by the Maxwell-Boltzmann distribution as: f E e E E kT f ( ) kT E E f 3 (3a) kT E E f e E f ) ( 1 kT E E f 3 (3b) This is a good approximation for many device applications, as we will see later. (3 kT 78 meV @ room temperature)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
- - 27 Density of State function When an electron in the conduction band gains energy, it moves up to an E > E c . Similarly when a hole in the valence band gains energy, it moves down to an E < E v . From quantum mechanical considerations, it may be shown that: D E h m E E n e c ( ) ( ) ( ) 4 2 3 3 (4) = Density of state in the conduction band D E h m E E p h v ( ) ( ) ( ) 4 2 3 3 (5) = Density of state in the valence band where h = Plank‘s constant = 6.63
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 18

C02 Equilibrium Concentration Anoted 0929 - Equilibrium...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online