sd 07 excess carriers_transient

8/10/2019 Sd 07 Excess Carriers_transient

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Physical Electronics

Excess Carriers: Transient


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Today

Excess carriers

Electrons and holes can be generated by external excitation but thermal

one. ( electron hole generation)

This is not thermal equilibrium condition any more. (Thermal equilibrium

.)

But steady-state condition can be reached with constant excitation. (

steady state)

In this topic, we will study;

Generation

Life time

Steady state carrier concentration

Quasi Fermi level


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At thermal equilibrium,

Electron and hole concentrations are constant as n0

and p0

But, electrons are dynamically excited to conduction band from valence

band by random nature of the thermal process (carrier generation).

At the same rate, free electrons in crystal solid (generated electrons) drop

to vacant states (hole) in valence band (carrier recombination).

The constant concentration of electrons and holes can be maintained by

the balancing of generation and recombination process.

Semiconductor in Thermal Equilibrium


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Excess carriers generation

For example, the electron in valence band can be excited to conduction

band by photon () not by thermal energy. electron-hole

pare generation (excess electrons and excess holes).

Figure shows the generation of excess carriers in n-type by light energy.

With the Excess carrier generated, this is not thermal equilibrium any

more, and equation, np=ni2 is not available.

Excess Carrier Generation and Recombination


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Excess carriers recombination

When the external excitation is turned off, all the excess carriers

recombine to zero. ( excess carrier

recombination.)

thermal equilibrium condition.

What is the recombination time for excess carriers? (,

excess carrier?) carrier life time

Excess Carrier Generation and Recombination


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, p-type excess electron. (Excess carrier recombination process)

Assume that excess carrier concentration is much lower than majority carrier

concentration Majority carrier: hole, Minority carrier: electron

Carrier life time in Direct recombination

)()()( 2

tptnndt

tdnrir =

Net rate of change in conduction band electron concentration:

)()(

)()(

0

0

tpptp

tnntn

+=

+=

Thermal

generation rateRecombination rate ( concentration of electron and hole)

( )

{ }

{ }2000000

2

2

0

)()()(

)()()()(

)()(

)()()(

tntnpn

tptnpntnptpnn

tptnndt

tdn

dt

ntnd

dt

tnd

r

rir

rir

++=

+++=

=

=

=


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For P-type: Ignore n0 Assume Low level injection: Ignore n(t)2

excess carrier concentration is lower than the majority carrier concentration (n, p


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Life time of Minority carrier is inversely proportional to the

majority carrier concentration

Excess carrier life time is shorter at high doping condition. ( doping

excess carrier.)

How about majority excess carrier

Majority carrier life time:

Majority excess carrier life time is also inversely proportional to majority

carrier concentration

For N-type

Minority carrier life time:

In general, recombination life time:

Minority carrier life time

0

1

pr

p

=

0

1

nr

p

=

)(

1

00 pnrn

+=

Valid for both n- and p-type for low level injection


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Example 4.2


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Large percentage change in minority carrierconcentration

Small percentage change in majority carrier

concentration

The conductivity during the decay

])()([)(pn

tptnqt +=


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In a real semiconductor

Defects occur within the crystal create discrete energy states within the

bandgap

Defect energy states may be a dominant effect in determining the mean

carrier life time

Indirect recombination: Trapping

Recombination level Er

(a) hole capture at Er(b) Electron capture at Er

sd 07 excess carriers_transient

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