Lecture6 PN junction and diode

• If VD < 0 reverse bias, the potential barrier to carrier diffusion is increased by the applied voltage.. • If VD > 0 forward bias, the potential barrier to carrier diffusion is reduced

LECTURE 6: PN JUNCTION AND DIODE

The density gradient as producing a "diffusion force" that acts on the majority carriers, called as diffusion forces.

• The net positive and negative charges in the n and p regions induce an electric field in the region near the junction, in the direction from the positive to the negative charge, or from the n to the p region

• The electric field in the space charge region produces another force on the electrons and holes which is in the opposite direction to the diffusion force for each type of particle In thermal equilibrium, the diffusion force and the E-field force exactly balance each other

Charge density

More on the Built-In Potential (V0)

Q: Why can’t we harness V0 and use the PN junction as a battery?

A: A built-in potential also exists at a junction between a metal and a semiconductor (e.g at a

Vbn+V0+Vbp=0

V(x)

x a

Space charge width

Effect of Applied Voltage

• The quasi-neutral N-type and P-type regions have low resistivity, whereas the depletion region has high resistivity.

– Thus, when an external voltage VD is applied across the diode, almost all of this voltage is

dropped across the depletion region (Think of a voltage divider circuit.)

• If VD < 0 (reverse bias), the potential barrier to carrier diffusion is increased by the applied voltage.

• If VD > 0 (forward bias), the potential barrier to carrier diffusion is reduced by the applied voltage.

+ – VD

ID

• A forward bias decreases the potential drop across the junction As a result, the magnitude of the electric field decreases and the width of the depletion region narrows.

PN Junction under Forward Bias

V(x)

x a

-b

V0

ID

0

Minority Carrier Injection under Forward Bias

• The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.

– The carriers which diffuse across the junction become minority carriers in the quasi-neutral regions; they recombine with majority carriers, “dying out” with distance.

np(x)

np0

A

i p

N

n n

2

0 =

Equilbrium concentration of electrons on the P side:

edge of depletion region

x'

0

x'

Minority Carrier Concentrations

at the Edges of the Depletion Region

• The minority-carrier concentrations at the edges of the depletion region are changed by the factor

– There is an excess concentration (∆pn, ∆np) of minority carriers in the quasi-neutral regions,

under forward bias.

• Within the quasi-neutral regions, the excess minority-carrier concentrations decay exponentially

with distance from the depletion region, to zero:

T D

L x A

V V i p

p p

p

e N

e n x

n

x n n

x n

/ /

2

0

1 )

(

) ( )

i n

p n

diff

L N

n

qD x

d

dn qD

Diode Current under Forward Bias

• The current flowing across the junction is comprised of hole diffusion and electron diffusion components:

• Assuming that the diffusion current components are constant within the depletion region (i.e no

recombination occurs in the depletion region):

p n

A

n i

S

V

V S tot

L N

D L

N

D qn

J e

J

0 ,

0 ,

0 ,

n A

i n x

diff

L N

n

qD

2 0

p D

i p x

diff

L N

n qD J

I-V Characteristic of a PN Junction

• Current increases exponentially with applied forward bias voltage, and

“saturates” at a relatively small negative current level for reverse bias voltages

p

n A

n i

S S

V

V S D

L N

D L

N

D Aqn

AJ I

e I

2 / 1

“Ideal diode” equation:

Parallel PN Junctions

• Since the current flowing across a PN junction is proportional to its

cross-sectional area, two identical PN junctions connected in parallel act effectively as

a single PN junction with twice the cross-sectional area, hence twice the current

Diode Saturation Current IS

• IS can vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant

concentrations.

– typical range of values for Si PN diodes: 10-14 to 10-17 A/ µ m2

• In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:

– If the P side is much more heavily doped,

– If the N side is much more heavily doped,

p A

n

n i

S

N L

D N

L

D Aqn

p i

S

N L

D Aqn

n i

S

N L

D Aqn

Reverse Breakdown

• As the reverse bias voltage increases, the electric field in the depletion region increases

Eventually, it can become large enough to cause the junction to break down so that a large reverse current flows:

breakdown voltage

Reverse Breakdown Mechanisms

a) Zener breakdown occurs when the electric field is sufficiently high to pull an electron out of a covalent

bond (to generate an electron-hole pair)

b) Avalanche breakdown occurs when electrons and holes gain sufficient kinetic energy (due to

acceleration by the E-field) in-between scattering events to cause electron-hole pair generation upon colliding with the lattice.

Constant-Voltage Diode Model

• If VD < VD,on: The diode operates as an open circuit.

• If VD ≥ VD,on: The diode operates as a constant voltage

source with value VD,on.

Example: Diode DC Bias Calculations

• This example shows the simplicity provided by a constant-voltage model over an exponential model

• Using an exponential model, iteration is needed to solve for current Using a constant-voltage model, only linear equations need to be solved

S

X T

X D

X X

I

I V

R I V

R I

V 1 for

mA 2

0

V 3 for

mA 2

X X

V I

V I

Summary: PN-Junction Diode I-V

• Under forward bias, the potential barrier is reduced, so that carriers flow (by diffusion) across the junction

– Current increases exponentially with increasing forward bias

– The carriers become minority carriers once they cross the junction; as they diffuse in the quasi-neutral regions, they recombine with majority carriers (supplied by the metal contacts)

“injection” of minority carriers

• Under reverse bias, the potential barrier is increased, so that negligible carriers flow across the junction

– If a minority carrier enters the depletion region (by thermal generation or diffusion from the quasi-neutral regions), it will

be swept across the junction by the built-in electric field

“collection” of minority carriers = ( V D/V T − 1 )

S

D I e I

DIODE APPLICATION

Half Wave Rectifier

• We initially consider the diode to be ideal, such that VC =0 and Rf =0

Half Wave Rectifier

• The (ideal) diode conducts for vi >0 and since Rf =0

v0 ≈ vi

• For vi < 0 the (ideal) diode is an open circuit (it doesn’t conduct) and

v0 ≈ 0

Half Wave Rectifier

• In this simplified (ideal diode) case the input and output waveforms are as shown

The diode must withstand a peak inverse voltage of V M

Half Wave Rectifier

• The average d.c value of this half-wave-rectified sine wave is

Half Wave Rectifier

• So far this rectifier is not very useful

• Even though the output does not change polarity it has a lot of ripple , i.e

variations in output voltage about a steady value

• To generate an output voltage that more closely resembles a true d.c voltage we can use a reservoir or smoothing capacitor in parallel with the output (load)

resistance

Smoothed Half Wave Rectifier

Circuit with reservoir capacitor

Output voltage

The capacitor charges over the period t1 to t2 when the diode is on and discharges from t2 to t3 when the diode is off

Smoothed Half Wave Rectifier

• When the supply voltage exceeds the output voltage the (ideal) diode conducts During the charging period (t1 < t< t2)

vo = VM sin (ωt)(The resistance in the charging circuit is strictly Rf which we have assumed to be zero Even for a practical diode RfC will be very small)

Smoothed Half Wave Rectifier

• When the supply voltage falls below the output voltage the diode switches off and the capacitor discharges through the load.

• During the discharge period (t2 < t< t3 ) and

Smoothed Half Wave Rectifier

• The resistance in the discharge phase is the load resistance R

• RC can be made large compared to the wave period

• The change in output voltage (or ripple) can then be estimated using a linear approximation to the exponential discharge

Smoothed Half Wave Rectifier

• vo = VM exp {- t’ /RC} ≈ VM [ 1- (t’ /RC)]

• The change in voltage ∆V is therefore approximately given by VM t’ /RC

• For a the half wave rectifier this discharge occurs for a time (t3 - t2 ) close to the

period T = 1/f, with f= frequency

• Giving the required result:

RC

T V

Smoothed Half Wave Rectifier

• We can define a ripple factor as

Half Wave Rectifier

• If we don’t consider the diode to be ideal then from the equivalent circuit

−

−

=

c i

c

i f

R R

R iR

Non-Ideal Half Wave Rectifier

VM

Non-Ideal Half Wave Rectifier

• A plot of v0 against vi is known as the transfer characteristic

R/(R + Rf)

Non-Ideal Half Wave Rectifier

• We usually have R>> Rf so that Rf can be neglected in comparison to R

• Often VM >> Vc so Vc can also be neglected

The transfer characteristic then reduces to

v0 ≈ vi

Full-Wave (Bridge) Rectifier

• We initially consider the diodes to be ideal, such that VC =0 and Rf =0

• The four-diode bridge can be bought as a package

vi

Full-Wave (Bridge) Rectifier

• During positive half cycles vi is positive.

• Current is conducted through diodes D1, resistor R and diode D2

• Meanwhile diodes D3 and D4 are reverse biased.

vi

Full-Wave (Bridge) Rectifier

• During negative half cycles vi is negative.

• Current is conducted through diodes D3, resistor R and diode D4

• Meanwhile diodes D1 and D2 are reverse biased.

vi

Full-Wave (Bridge) Rectifier

• Current always flows the same way through the load R.

• Show for yourself that the average d.c value of this full-wave-rectified sine wave is

VAV = 2VM/ π (i.e twice the half-wave value)

Full-Wave (Bridge) Rectifier

• Two diodes are in the conduction path

• Thus in the case of non-ideal diodes vo will be lower than vi by 2VC.

• As for the half-wave rectifier a reservoir capacitor can be used In the full wave case the discharge time is T/2 and

2RC

T V

Diode Clipper Circuits

• These circuits clip off portions of signal voltages above or below certain limits, i.e the circuits limit the range of the output signal

• Such a circuit may be used to protect the input of a CMOS logic gate against static

Diode Clipper Circuits

• When the diode is off the output of these circuits resembles a voltage divider

i S

L

L

R R

R v

Diode Clipper Circuits

• If RS << RL

• The level at which the signal is clipped can be adjusted by adding a d.c bias voltage in series with the diode

v0 ≈ vi

For instance see example sheet 1, Q11

Diode Clipper Circuits

• Let’s look at a few other examples of clipper circuits

Diode Clamper Circuits

• The following circuit acts as a d.c restorer

• see Q9, example sheet1

Diode Clamper Circuits

• A bias voltage can be added to pin the output to a level other than zero

For the following diode circuit, use the ideal diode model to analysis the circuit Sketch

the voltage VO across the resistor 1.5 kΩ for an input voltage of:

For the following diode circuit, use the ideal diode model to analysis the circuit Sketch

the voltage VO across the resistor 1.5 kΩ for an input voltage of:

Light-emitting diodes

•When pn junction is forward biased, large

number of carriers are injected across the

junctions These carriers recombine and emit light

if the semiconductor has a direct bandgap

•For visible light output, the bandgap should be

between 1.8 and 3.1 eV

Solar cells

•Solar cells are large area pn-junction diodes designed

specifically to avoid energy losses

•Voc= the open circuit voltage

•Isc = current when device is

–Isc

–Im

Photodiodes

•Specifically designed for detector application and light penetration

•IL = – q A (LN + W + LP) GL assuming uniform photo-generation rate, GL

Increasing light intensity

Photodiodes

•If the depletion width is negligible compared to Ln + Lp, then IL is proportional to

light intensity

•Spectral response - an important characteristic of any photo-detector Measures

how the photocurrent, IL varies with the wavelength of incident light

varying optical signal The generated minority carriers have to diffuse to the

depletion region before an electrical current can be observed externally Since

diffusion is a slow process, the maximum frequency response is a few tens of MHz for pn junctions Higher frequency response (a few GHz) can be achieved using p-i-

n diodes