EE331 13 Pn Junction Diode 2

7/30/2019 EE331 13 Pn Junction Diode 2

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µ P-N Junction Diodes ¸How do they work?

(A little math)

Movement of Electrons and Holeswhen Forming the Junction

Circles are charges free to move (Electrons and Holes)Squares are charges NOT free to move (Ionized Donor or Acceptor Atoms)

Space Charge or Depletion Region

Electron diffusion

Hole diffusionHigh hole

Concentration

High electron

Concentration

Local region of

positive charge

due to

imbalance inelectron-donor

concentrations

Local region of

negative charge

due to

imbalance inhole-acceptor

concentrations

High hole

Concentration

High electron

Concentration

E



Uniformly doped p-type and n-type

semiconductors before the junction

is formed.

The electric field in the depletion region

and the energy band diagram of a p-n

junction in thermal equilibrium.

E

(a) A p-n junction with abrupt dopingchanges at the metallurgical junction.

(b) Energy band diagram of an abrupt junction at thermal equilibrium.

(c) Space charge distribution.

(d) Rectangular approximation of the spacecharge distribution.





Space charge distribution in the

depletion region at thermal

equilibrium.

Electric-field distribution.

The shaded area corresponds to the

built-in potential.

N D

- N A


No net current flow

in equilibrium

Einstein Relationq

kT D

n

n=

µ

Built-in-Potential


¾ For N A=N D=1015 /cm-3 in Silicon at room temperature,

V bi ~ 0.6 V

¾ For a non-degenerate semiconductor, |-qV bi |<|E g |

Note: This is not the diode turn-on voltage!

This is the voltage required to reach a flat band diagram and sets an upper limit

(typically an overestimate) for the voltage that can be applied to a diode before it

burns itself up.

Built-in-Potential

function of

impurity concentration


Built-in potentials on the p-side and n-side of abrupt junctions

in Si and GaAs as a function of impurity concentration.




Depletion Region Approximation

Depletion Region Approximation states that approximately no free

carriers exist in the space charge region and no net charge exists

outside of the depletion region ( known as the quasi-neutral region).

within the quasi-neutral region

within the space charge region

K s: dielectric constant

ε

0: permittivity of free space

Poisson’s Equation

E C

E V

E F

E i E C

E V

E F

E i

p-Type Material n-Type Material

- qxV BI

+ +++++ +++ ++ ++ ++++++

Thus,


Depletion Region Approximation: Step Junction Solution

0

ρ

s K dx

dE = Poisson’s Equation











Diode under Forward Bias.mov Diode under no Bias.mov Diode under Reverse Bias.mov

Schematic representation of

depletion layer width and

energy band diagrams of a p-n junction under various

biasing conditions.

Reverse-bias condition

Forward-bias condition

Thermal-equilibrium


Depletion Region

Forward bias Reverse bias


Depletion Region

Carrier distribution

Energy band diagram



Fig. 4-8: Double-het

erostructure configur

ation

Thus, only the boundary conditions change resulting in

direct replacement of V bi with (V bi -V A) with V A ≠ 0.




Depletion Region Approximation:

Step Junction Solution with V A ≠ 0

Consider a p+n junction (heavily doped p-side, lightly doped n side)





Electron diffusion across a pn junction


Forward bias condition


Reverse bias condition



µ P-N Junction Diodes ¸

Current Flowing through a DiodeI-V Characteristics

Quantitative Analysis

(Math, math and more math)

p-n Junction I-V Characteristics

In Equilibrium (no bias)Total current balances due to the sum of the individual components

Electron Drift

Current

Electron Diffusion

Current

Hole Drift

CurrentHole Diffusion

Current

Diode under no Bias.mov

no net current!

E C

E V

E F

E i

p-Type Material n-Type Material- qxV BI

+ +++++ +++ ++ ++ ++++++

0n DqnE q J J J nn Diffusionn Drift nn µ

no net current!


E C

E V

E F

E i

n vs. E

p vs. E

In Equilibrium (no bias)Total current balances due to the sum of the individual components

0 p Dq pE q J J J p p Diffusion

p Drift

p p µ


Forward Bias (V A > 0)

I

Hole Drift

Current

Electron Drift

Current

Electron Diffusion

Current

Hole Diffusion

Current I P

I N

Diode under Forward Bias.mov

Current flow is dominatedby majority carriers flowing

across the junction and

becoming minority carriers

V A

Current flow is

proportional to

e(Va/Vref) due tothe exponential

decay of carriers

into the majority

carrier bands

Lowering of

potential hill

by V A

surmount potential barrier

P N I I I +



Hole Diffusion Current negligible

due to large energy barrier

Hole Drift

Current

Electron Drift

Current

Electron Diffusion Current negligible

due to large energy barrier

Reverse Bias (V A < 0)

Diode under Reverse Bias.mov


Current flow is constant

due to thermally generated

carriers swept out by E

fields in the depletion

region

Current flow is dominated by

minority carriers flowing

across the junction and

becoming majority carriers

Increase of

potential hill

by V A

Where does the Reverse Bias Current come from?

¾ Generation near the depletion region edges “replenishes” the

current source.


Putting it all together


for Ideal diode

V ref = kT/q

-I 0

−

= 1

0

kT

qV exp I I

η

η : Diode Ideality Factor


Diode Equation



Quantitative p-n Diode Solution

Assumptions:

1) Steady state conditions

2) Non- degenerate doping

3) One- dimensional analysis

4) Low- level injection

5) No light (G L = 0)

Current equations:

) x ( J ) x ( J J n p p +

−

dx

dpqD pE q J p p p µ

−dx

dnqDnE q J nnn µ

Application of the Minority Carrier Diffusion Equation

Since electric fields

exist in the

depletion region,

the minority carrier

diffusion equation

does not apply

here.

Quisineutral Region Quisineutral Region

00 0 0


minority carrier diffusion eq. minority carrier diffusion eq.



kT )F F (

i P N ennp

−=2

quasi-Fermi levels formalism

kT E E i

kT E E

i

f i

i f

en p

enn

)(0

)(

0

−

−

=

=

Equilibrium

kT F E i

kT E F

i

P i

i N

en p

enn

)(

)(

−

−

=

=

Non-Equilibrium

¾ The Fermi level is meaningful only when the system is in thermal equilibrium.

¾ The non-equilibrium carrier concentration can be expressed by defining

Quasi-Fermi levels F n and F p .

Equilibrium Non-Equilibrium

Quasi - Fermi Levels





kT )F F (

i P N ennp

−=2

quasi-Fermi levels formalism

?



+

dx

dn DnE q J nnn µ

( )

dx

nnd qD

p

n

∆=

0

dx

nd qD

p

n

∆=

+

dx

dp D pE q J

p p p µ

( )

dx

p pd qD

n

p

∆= 0

dx

pd qD

n

p

∆=

0 0

Approach:

¾ Solve minority carrier diffusion equation in quasineutral regions.

¾ Determine minority carrier currents from continuity equation.

¾ Evaluate currents at the depletion region edges.

¾ Add these together and multiply by area to determine the total

current through the device.¾ Use translated axes, x t x’ and -x t x’’ in our solution.


x”=0 x’=0



x”=0 x’=0


Holes on the n-side





x”=0 x’=0 Holes on the n-side


Similarly for electrons on the p-side…


x”=0 x’=0


Depletion Region

Negligible thermal R-G implies

J n and J p are constant throughout

the depletion region. Thus, the

total current can be define in

terms of only the current at the

depletion region edges.


0 0

0 0 ( ) ( )

( ) ( ) N P p p P

p N p p N

x J x x x J

x J x x x J

−

−

) x ( J ) x ( J J p P p N +

Continuity equation

...light assuch processesother All

G RThermal

P

...light assuch processesother All

G RThermal

N

t

p

t

p J

qt

p

t

n

t

n J

qt

n

∂

∂+

∂

∂+

∂

∂

∂

∂+∂

∂+∂

∂

−

−

1

1

Continuity Equations





x”=0 x’=0


Total on current is constant throughout the device.

Thus, we can characterize the current flow components as…

-x p x n

J

pn-junction diode structure used in the discussion of currents. The sketch

shows the dimensions and the bias convention. The cross-sectional area

A is assumed to be uniform.

Hole current (solid line) and recombining electron current (dashed line) in the quasi-neutr

al n-region of the long-base diode of Figure 5.5. The sum of the two currents J (dot-dash l

ine) is constant.

Hole density in the quasi-neutral n-region of an ideal short-basediode under forward bias of Va volts.



The ratio of generation-region width xi to space-charge-region width xd as a

function of reverse voltage for several donor concentrations in a one-sided step junction.

The current components in the quasi-neutral regions of a long-base diode

under moderate forward bias: J (1) injected minority-carrier current, J (2)

majority-carrier current recombining with J (1), J (3) majority-carrier currentinjected across the junction. J (4) space-charge-region recombination current.

(d ) Adapted from [8]. Current-voltage characteristic for a diode near the

boundary between (a) and (c ), showing diffusion current at lower voltages and

a transition to thermionic-emission current at higher biases.Current in a Heterojunction



(a) Transient increase of excess stored holes in a long-base ideal diode for a

constant current drive applied at time zero with the diode initially unbiased. Note

the constant gradient at x = xn as time increases from (1) through (5), which

indicates a constant injected hole current. (Circuit shown in inset.) (b) Diode

voltage VD versus time.

(a) Transient decay of excess stored holes in a long-base ideal diode. In the case

shown, the initial forward bias applied through the series resistor is abruptly

changed to a negative bias at time t = 0. (Circuit shown in inset.) (b) Diode current

ID versus time.

Junction and Free-Carrier Storage

J elec

x

n-region

J = J elec + J hole

SCL

Minoritycarrierdiffusion

current

Majority carrier diffusion

and drift current

Totalcurrent

J hole

W n –W

p

p-region

J

¾ The total current anywhere in the device is constant.

¾ Just outside the depletion region it is due to the diffusion of

minority carriers.





Thus, evaluating the current components at the depletion region edges,

we have…

Note: V ref from our previous qualitative analysis equation is the thermal voltage, kT/q

J = J n ( x”=0) + J p ( x’=0) = J n ( x’=0) + J n ( x”=0) = J n ( x’=0) + J p ( x’=0)

ÆÆÆ

Ideal Diode Equation Shockley Equation

Current-Voltage Characteristics

of a Typical Silicon p-n Junction


ExamplesDiode in a circuit

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EE331 13 Pn Junction Diode 2

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