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3. Carrier action

(a) Under normal operating conditions the three primary types of carrier action occurring inside

semiconductors are drift, diffusion, and recombination-generation.

(b) In this chapter we first describe each primary type of carrier action qualitatively and then

quantitatively relate the action to the current flowing within the semiconductor.

(1) Drift

(1-1) Definition

(a) Drift is charged-particle motion in response to an applied electric field: When an electric field

(𝜀) is applied across a semiconductor, the resulting force on the carriers tends to accelerate the

+q charged holes in the direction of the electric field and the –q charged electrons in the

direction opposite to the electric field.

(b) Because of collisions with ionized impurity atoms and thermally agitated lattice atoms,

however, the carrier acceleration is frequently interrupted (the carriers are said to be

scattered). Averaging over all electrons or holes at any given time, we find that the resultant

motion of each carrier type can be described in terms of a constant drift velocity vd.

1

3. Carrier action

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Photonics Laboratory

(1-2) Drift current

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dp/drift

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for

2

(1-2) Drift current

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(1-3) Mobility

Standard units: cm2/V-sec.

*d

d

2

p

2

n

315

AD

2

p

2

n

314

A

314

D

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sec-/Vcm 400 sec,-/Vcm 0008

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3

Mobility calculation: http://www.el-cat.com/silicon-properties.htm

(1-3) Mobility

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Photonics Laboratory

electrons. GaAs theofmobility higher theexplainingthereby

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decreases collisions impeding-motion ofnumber theincreasing Since (a)

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4

(1-4) Scattering

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Photonics Laboratory

(1-5) Doping dependence:

(a) At low doping concentrations, below approximately 1015/cm3 in Si, the carrier mobilities are

essentially independent of the doping concentration.

(b) For dopings in excess of 1015/cm3, the mobilities monotonically decrease with increasing NA

or ND.

(c) At sufficiently low doping levels, ionized impurity scattering can be neglected:

Rtotol=RL+Ri≅RL.

(d) When lattice scattering, which is not a function of NA or ND, becomes the dominant scattering

mechanism, it automatically follows that the carrier mobilities will be likewise independent of

NA or ND.

(e) Increasing the number of scattering centers by adding more and more acceptors or donors

progressively increases the amount of ionized impurity scattering and systematically

decreases the carrier mobilities.

(1-5) Doping dependence

5

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(1-5) Doping dependence

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(1-6) Temperature dependence:

(a) For dopings of NA or ND ≤ 1014/cm3, the data of the temperature dependence of the electron

and hole mobilities in Si merge into a single curve: 𝜇𝑛 ∝ 𝑇−2.3±0.1and 𝜇𝑝 ∝ 𝑇−2.2±0.1.

(b) For progressively higher dopings, the carrier mobilities still increase with decreasing

temperature, but at a systematically decreasing rate.

7

(1-6) Temperature dependence

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(1-7) Resistivity

(a) Resistivity is an important material parameter that is closely related to carrier drift.

(b) Qualitatively, resistivity is a measure of a material’s inherent resistance to current flow – a

“normalized” resistance that does not depend on the physical dimensions of the material.

(c) Quantitatively, resistivity (ρ) is defined as the proportionality constant between the electric

field impressed across a homogeneous material and the total particle current per unit area

flowing in the material.

8

(1-7) Resistivity

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Photonics Laboratory

(3.8B) 1

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for

9

(1-7) Resistivity

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Photonics Laboratory

(1-8) Band bending

(a) When an electric field (ε) exists inside a material, the band energies become a function of

position.

(b) The resulting variation of Ec and Ev with position on the energy band diagram is popularly

referred to as “band bending.”

(c) If an energy of precisely EG is added to break an atom-atom bond, the created electron and

hole energies would be Ec and Ev, respectively, and the created carriers would be effectively

motionless.

(d) Absorbing an energy in excess of EG, on the other hand, would in all probability give rises to

an electron energy greater than Ec and a hole energy less than Ev, with both carriers moving

around rapidly within the lattice.

(e) Therefore, E – Ec is interpreted to be the kinetic energy (KE) of the electrons and Ev – E to be

the kinetic energy of the holes. Moreover, Ec minus the energy reference level (Eref) must

equal the electron potential energy.

10

(1-8) Band bending

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Photonics Laboratory 11

(1-8) Band bending

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Photonics Laboratory

(3.15) 1)2/(1

1)(1

1 )E-(E

1

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d-

(3.14) dx

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12

(1-8) Band bending

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Photonics Laboratory

2. Diffusion

(2-1) definition

Diffusion is a process whereby particles tend to spread out or redistribute as a result of their

random thermal motion, migrating on a macroscopic scale from regions of high particle

concentration into regions of low particle concentration.

(2-2) Diffusion currents

: The diffusion current density due to electrons and holes is obtained by simply multiplying the

carrier flux by the carrier charges:

ly.respective ts,coefficiendiffusion electron and hole the

as toreferred are and /seccm of units have ,D and D ality,proportion of constants The

(3.17a)

(3.17a)

2

np

/

/

nqDJ

pqDJ

ndiffn

pdiffp

13

2. Diffusion

KOREA UNIVERSITY

Photonics Laboratory

The total or net carrier currents in a semiconductor arise as the combined result of drift and

diffusion. From Eqs. (3.4) and (3.5),

ly.respective ,tscoefficiendiffusion electron and hole the

as toreferred are and /seccm of units have ,D and D ality,proportion of constants The

(3.19)

(3.18b)

(3.18a)

2

np

////

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nqDnqJJJ

pqDpqJJJ

nnppdiffndriftndiffpdriftpnp

nndiffndriftnn

ppdiffpdriftpp

14

(2-2) Diffusion currents

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Photonics Laboratory

(2-3) Relating diffusion coefficients/mobilities

Consider a nondegenerate, nonuniformly doped n-type semiconductor sample, a sample where the

doping concentration varies as a function of position:

(a) Under equilibrium conditions, dEF/dx=dEF/dy=dEF/dz=0.

(b) The Fermi level inside a material or a group of materials in intimate contact is invariant as a

function of position.

15

(2-3) Diffusion coefficients

KOREA UNIVERSITY

Photonics Laboratory

(3.25) holes and electronsfor iprelationshEinstein :D

,D

.0 ,0

(3.24) 0

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(3.20) Eq. From

p ,n ,q

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i

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ii

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iF

Fi

FiiF

(c) Einstein relationship : Under equilibrium conditions,

16

(2-3) Diffusion coefficients

KOREA UNIVERSITY

Photonics Laboratory

/seccm 35.2/Vscm 1358 eV 0.026D

Sifor /Vs))cm 1358( /cm10N and re temperaturoomAt Example)

22

n

2

n

314

D

17

(3.25) holes and electronsfor iprelationshEinstein :D

,D

p

p

n

n

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kT

q

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(2-3) Diffusion coefficients