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445.664 445.664

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Light - - Emitting Diodes Emitting Diodes

Chapter 4.

LED Basics : Electrical Properties LED Basics : Electrical Properties

Euijoon Yoon Euijoon Yoon

p- p -n junction band diagram n junction band diagram

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445.664 (Intro. LED) / Euijoon Yoon 3

Schockley Equation Schockley Equation

•

V

_D

(diffusion voltage)

N_A, N_D: acceptor and donor concentration n_i: intrinsic carrier concentration

The diffusion voltage represents the barrier that free carriers must overcome in order to reach the neutral region of opposite conductivity type.

•

Schockley equation (the I-V characteristic of a p-n junction)

i2 D A D

n N ln N e V = kT

} / 1 )

{ ( − −

⎟⎟ ⎠

⎞

⎜⎜ ⎝

= ⎛

⁺

e V V kT

e D N

D N eA

I

^D ^D

n n A p

p

τ τ

D_{n, p}: electron and hole diffusion constants p

,

τ

n : electron and hole minority carrier lifetimes A : cross-sectional area, V : diode bias voltage

•Threshold voltage (V_th) -the voltage at which the current strongly increase -V_th~ V_D

Diode current

Diode current- -voltage characteristics voltage characteristics

•

Forward voltage is approximately equal to E

_g

/e.

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Diode forward voltage Diode forward voltage

•

Most semiconductor LEDs follow the solid line, except for LEDs based on III-V nitrides.

1. Large bandgap discontinuities -> additional voltage drop 2. Poor contact technology in the nitrides

3. Low p-type conductivity in bulk GaN

4. Parastic voltage drop in the n-type buffer layer

Deviations from the ideal I

Deviations from the ideal I- -V characteristic V characteristic

•

eV /( n kT )

e I

I =

^s ^ideal

( ) e ( V IR ) /( n kT )

e R I

IR

I V

^s ^s ^ideal

p

s

= −

− −

•

n

_ideal

: ideality factor

R

_s

: parasitic series resistance

R

_p

: parasitic parallel resistance

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Non- Non -ideal I ideal I- -V characteristics V characteristics

•

Problems area of diodes can be identified from I-V characteristic.

- A series resistance can be caused by contact resistance or by the resistance of the neutral region.

- A parallel resistance can be caused by any channel that bypasses the p-n junction. The bypass can be caused by damaged regions of the p-n junction or by surface imperfections.

Parallel resistance R_p=dV/dI

Methods to determine series resistance Methods to determine series resistance

•

Method shown above suitable for series resistance measurement.

•

At high currents, diode I-V becomes linear due to dominance of

series resistance. Diode series resistance can be extracted in

linear regime.

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Carrier distribution in p

Carrier distribution in p- -n homo n homo- - and heterojunctions and heterojunctions

Double heterostructure (DH) Double heterostructure (DH)

• Einstein relation - D_n= kTμ_n/ e - D_p= kTμp/ e

•

In typical semiconductors, the diffusion length is of the order of a several micrometers.

ex) in p-type GaAs, L

_n

= (220 cm

²

/s x 10

^-8

s)

^1/2

= 15μm

•

Minority carriers are distributed over quite a large distance. The

large recombination region in homojunctions is not beneficial for

efficient recombination.

•

Introduction of double heterostructure (DH) makes it possible to confine the carriers in active region. The thickness of the region in which carriers recombine is given by the thickness of the active

region rather than the diffusion length.

•Diffusion length (L) - L_n= (D_nτ_n)^1/2 - L_p= (D_pτ_p)^1/2

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The effect of heterojunctions on device resistance The effect of heterojunctions on device resistance

•One of the problem introduced by heterostructures is the resistance caused by the heterointerface and it can have a strong deleterious effect on device performance, especially in high-power devices.

•The resistance introduced by abrupt heterostructures can be

completely

eliminated by parabolic grading.

Grading of heterostructures Grading of heterostructures

•In order to compensate for the

parabolic shape of the depletion potential, the composition of the semiconductor is varied parabolically as well, so that an overall flat potential results.

•If the potential created in the depletion region is equal to E_g/e, then electrons will no longer transfer to the small- bandgap material. The thickness of the depletion region is,,,

•The “spikes” are a result of the linear grading assumed, and would not result for parabolic grading.

D 2

2 x eN

= ε φ

Δ

2 D D C

N e

E

W

₌

2 ε Δ

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Carrier loss in double heterostructures Carrier loss in double heterostructures

•The concentration of electrons with energy higher than the barrier

∫ ∞ρ

=

B FD DOS

B E

f ( E ) dE

n E E ) / kT

e N

n

^B ^C ⁽ ^Fn

−

^B

=

(Fermi-Dirac distribution) (Boltzmann distribution)

•The diffusion current density of electrons leaking over the barrier

n n n

n

L ) 0 ( eD n dx

) x ( eD dn

J

^x=⁰

= −

^B ^x=⁰

= −

^B

Fn n

n

N e ( E E ) / kT e x / L L

/ e x ) 0 ( n ) x (

n

^B

=

^B

− =

^C

−

^B

− −

Carrier overflow in double heterostructures Carrier overflow in double heterostructures

•The current density at which the active region overflows,,,

DH C 3

2 C

overflow eBW

kT E 3

N

J 4 ⎟

⎠

⎜ ⎞

⎝

⎟ ⎛ Δ

⎠

⎜ ⎞

⎝

⎛

= π (for DH structure LED)

QW 2 o 2 C

overflow

W ) eB E E ) ( 2 / h (

*

J m ⎥

⎦

⎢ ⎤

⎣

⎡ Δ −

π

= π (for QW structure LED)

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Carrier overflow

Carrier overflow - - For DH structure LED For DH structure LED

eW Bnp J dt dn

DH

−

=

•The rate equation of carrier supply to (by injection) and removal from the active region (by recombination) is given by

(B: the bimolecular recombination coefficient)

•At high injection levels, the Fermi energy rises and will eventually reach the top of the barrier. At that point, . Using this value, the current density at which the active region overflows is given by

C C

F E E

E − =Δ

•For high injection densities: n=p

•Under steady-state conditions (dn/dt=0), eBW_DH n= J

DH C 3

2 C

overflow eBW

kT E 3

N

J 4 ⎟

⎠

⎜ ⎞

⎝

⎟ ⎛ Δ

⎠

⎜ ⎞

⎝

⎛

= π

3 / 2

C C

F

N n 4 3 kT

E

E ⎟⎟

⎠

⎞

⎜⎜ ⎝

⎛ π

− =

•In the high-density approximation, the Fermi level is given by (Nc: effective density of states)

Carrier overflow

Carrier overflow - - For QW structure LED For QW structure LED

•For QW structures, we must employ the 2D density of states, rather than the 3D density of states. The Fermi level in a QW with one quantized state with energy E₀is given by

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ ⎟⎟−

⎠

⎜⎜ ⎞

⎝

= ⎛

− 1

N exp n kT ln

E E

D c2

D 0 2

F ( n^2D: the 2D carrier density per cm²,

N_c^2D: the effective 2D density of states)

) kT 2 / h (

* N^C²^D m ₂

π

=π

•Nc^2Dis given by

•The high-degeneracy approximation (at high carrier densities) is employed and one obtains

D 2 2 0

F n

* m

) 2 / h E (

E − =π π

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Carrier overflow

Carrier overflow - - For QW structure LED For QW structure LED

•The rate equation for the QW of carrier supply to (by injection) and removal from the active region (by recombination) is given by

D 2 D 2 D 2 D

2

p n e B J dt dn = −

(B^2D

≈

B/W_QW: the bimolecular recombination coefficient for a 2D structure)

•For high injection densities: n^2D=p^2D

•Under steady-state conditions (dn^2D/dt=0), eB JW eB

n²^D= J₂_D = ^QW

•At high injection levels, the Fermi energy will reach the top of the barrier.

At that point, . Using this value, the current density at which the active region overflows is given by

0 C 0

F E E E

E − =Δ −

QW 2 o 2 C

overflow

W ) eB E E ( ) 2 / h (

*

J m ⎥

⎦

⎢ ⎤

⎣

⎡ Δ −

π

= π

Saturation of output power due to leakage Saturation of output power due to leakage

•

In order to avoid the carrier overflow, high current LEDs must

employ thick DH active regions, or many QWs of multiple QW

(MQW) active regions, or a large injection (contact) area.

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Electron blocking layers Electron blocking layers

•

The barrier in the valence band is screened by free carriers so that there is no barrier to the flow of holes in the p-type confinement layer.

Diode forward voltage Diode forward voltage

•The total voltage drop across a forward-biased LED is given by

•One finds experimentally that the diode voltage can be slightly lower than the minimum value predicted by above Eq’n, i.e. ~ E_g/e

e E E e

E IR E

e

V = E

g

+

S

+ Δ

^C

−

^o

+ Δ

^V

−

^o

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Temperature dependence of diode voltage Temperature dependence of diode voltage

•

Diode voltage decreases with increasing temperature due to decrease in energy gap and increase in saturation current density.

•The temperature dependence of the diode voltage

•first term : due to the changes of the Fermi level with temperature

•The contribution of the first term is generally smaller than the contribution of the second term.

e ) T ( E I* ln I e ) kT T (

V ^g

S

+

=

Temperature dependence of diode voltage Temperature dependence of diode voltage

•

Diode forward voltage can be used to assess junction temperature

with high accuracy.

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Drive circuits Drive circuits

•

Constant current-drive circuit

•

Constant voltage-drive circuit

•

What are the advantages and disadvantages?