Read Chapter 3, Section 3.1, 3.7 Sedra/Smith’s...

Ching-Yuan Yang

National Chung Hsing UniversityDepartment of Electrical Engineering

Diodes

Read Chapter 3, Section 3.1, 3.7Sedra/Smith’s Microelectronic Circuits

3A-1 Ching-Yuan Yang / EE, NCHUElectronics (I)

Ideal diode


Two modes of operation for an ideal diode

Forward-biased mode Reverse-biased mode


Rectifier

Equivalent circuits

Input waveform

Output waveform


ExampleExample

Diode conducts when vS exceeds 12 V.

Find θ :

The conduction angle is 120° (or 1/3 cycle).

The peak value of the diode current:

The maximum reverse voltage across the diode: 24+12 = 36 V

24cos 12 60θ θ= ⇒ = °

24 120.12 A

100dI−

= =


Diode logic gates

OR gate

AND gate

Y A B C= + +

Y A B C= ⋅ ⋅


ExampleExample

Both diodes (D1&D2) are conducting.

VB = 0, V = 0

Node equation at B:

0 ( 10)1

5I

− −+ =

2

10 01 mA

10D

VI

R

Δ −= = =

1 mAI =


ExampleExample

Assume that D1&D2 are conducting: VB = 0, V = 0 and I > 0, ID2 > 0

Node equation at B:

Incorrect !!

Assume that D1 is off and D2 is on.

D1 is reverse-biased as assumed.

2

10 02 mA

5DI−

= =

0 ( 10)2

10I

− −+ = 1 mAI = −

2

10 ( 10)1.33 mA

510 10 1.33 3.3 V

D

B

I

V

− −= =

= − + × = +

I = 0 and V = 3.3 V


PN junction diode

Symbol

Structure

Junction


I-V characteristic

Three operational regions:

Forward-bias, v > 0

Reverse-bias, v < 0

Breakdown, v < −VZK


Basic semiconductor physics

At 0 K, all bonds are intact and no free electrons are available for current conduction.

At room temperature, some of the covalent are broken by thermal ionization. Each broken bond gives rise to a free electron and a hole, both of which become available for current conduction.


Basic semiconductor physics

A semiconductor (Silicon, Germanium) is neither a perfect conductor (metal) nor an insulator (sand).

Pure semiconductor (Intrinsic semiconductor) has tetrahedron crystal structure. Four valence electrons orbit around the most outer-shell orbit of each atom.

Electron & Holes:

Raising temperature breaks covalent bond and produces electron-hole pair.

In thermal equilibrium, n = p = ni.

ni : intrinsic concentration at a given temperature.

B = 5.4×1031, EG = 1.12 eV (bandgap energy)

k = 8.62×10−5 eV/K (Boltzmann’s constant)

For silicon at T = 300K, ni ≈ 1.5×1010 carriers/cm3.

/2 3 GE kTin BT e−=


Diffusion and Drift

Free electrons or holes will diffuse from the region of high concentration to the region of low concentration. This process gives rise to a net flow of charge, or diffusion current, which is proportional to the concentration gradient:

Drift of carriers occurs when an electric field is applied. Free electrons and holes are accelerated by the field and acquire a velocity component proportional to the field strength E. The result is a current density component of

p p n n

dp dnJ qD J qD

dx dx= − = unit: A/cm2

Dp and Dn are diffusion constants, unit: cm2/s.

( )drift p nJ E q p n Eσ μ μ= = +

μn and μp are mobilities of electron and hole (cm2/Vs).σ: conductivity, (Ω⋅cm)-1


N-type semiconductor

Increasing electron density (n) by introducing pentavalentatoms, which have “5” valence electrons, one extra electron to donate after forming covalent bonds with silicon.

One short of forming 4 covalent bonds with silicon thereby creating a “electron”.

N-type atom ≡ donor

The major carrier is electron (majority).

nn0 ≈ ND (donor concentration)

The minor carrier is hole

In thermal equilibrium, 2

0no n in p n=2i

noD

np

N=(mass - action law)

(minority).


P-type semiconductor

Increasing hole density (p) by doping with P-type atoms. Trivalent atom has only “3”valence electrons.

One short of forming 4 covalent bonds with silicon thereby creating a “hole”.

When the p-type atom captures an electron, it accepts an electron.

P-type atom ≡ acceptor

Hole is majority.

pp0 ≈ NA (acceptor concentration)

Electron is minority.

In thermal equilibrium,

20po p in p n=

2i

poA

nn

N=(mass - action law)


Physical operation of PN junction – under open circuit conditions

Diffusion current

Holes: p side → n side

Electrons: n side → p side

Current: p side → n side

Carrier depletion

Holes diffused to n-side recombine with the majority there (electrons), making the region close to the junction depleted of free electrons and containing uncovered bound positive charges.

Called “depletion region” or “space-charge region”, a carrier-depletion region exists on both sides of the junction.

neutral region neutral region



Carrier depletion (cont’)

A electric field is established across the region.

The resulting electric field opposites the diffusion of holes into the n-region and electrons into the p-region.

The diffusion strongly depends on the voltage drop across the junction.

A barrier has to be overcome for holes to diffuse into the n region and electrons to diffuse into the p region.




Drift current IS & equilibrium

Minorities diffused to the edge of the depletion region will experience the electric field and drift current will be generated.

Direction: n side → p side

Drift current is carried by thermally generated minorities and thus strongly depends on temperature.

It is independent of the barrier voltage.

Under open-circuit condition,

ID = IS.

This equilibrium is maintained by the barrier voltage V0.




Junction built-in voltage

Depend on doping concentrations and temperature

In the range of 0.6 to 0.8 V

Under open circuit, V0 does not appear between the diode terminal because the contact voltages counter and exactly balance the barrier voltage.


0 2ln A DT

i

N NV V

n

⎛ ⎞= ⎜ ⎟

⎝ ⎠



Depletion region width

Charge-equality condition

The depletion region exists almost entirely on the lightly doped side.


p A n Dqx AN qx AN=

A: cross-sectional area of the junction

n A

p D

x N

x N=

0

2 1 1

dep n p

s

A D

W x x

Vq N N

ε

= +

⎛ ⎞= +⎜ ⎟

⎝ ⎠

where 12011.7 1.04 10 F/cm, : 0.1~1 ms depWε ε μ−= = ×


Physical operation of PN junction – under reverse-bias conditions

Apply a reverse constant current source I (I < IS to avoid break-down) across the diode.

Holes leave p material and free electrons leave n material to the external source.

Depletion layer widens.

The barrier voltage increases.

ID decreases.

Equilibrium is reached when

IS − ID = I.

In equilibrium, the increase in barrier voltage above the built-in voltage V0

will appear as an external voltage (VR) that can be measured between the diode terminals.


Physical operation of PN junction – under reverse-bias conditions

Depletion capacitance

As the voltage across the pn junction changes, the charge stored in the depletion layer changes accordingly – the junction behaviors like a capacitor.

The resulting expression is:

R Q

Jj

R V V

dqC

dV =

= or sj

dep

AC

W

ε=

( )0

2 1 1sdep R

A D

W V Vq N N

ε ⎛ ⎞= + +⎜ ⎟

⎝ ⎠

0

0

1

jj

R

CC

VV

=+

00

1

2s A D

jA D

q N NC A

N N V

ε ⎛ ⎞⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠⎝ ⎠⎝ ⎠where


Physical operation of PN junction – in the breakdown region

When a reverse current source I > IS is applied across the diode, the barrier voltage continuous to climb until a breakdown mechanism sets in to support the external current I.

Breakdown

Zener breakdown

Avalanche breakdown



Two possible breakdown mechanisms are the zenereffect (the breakdown voltage < 5 V) and the avalanche effect (the breakdown voltage > 7 V) or the combination of the two.

Breakdown is not a destructive process provided that the maximum specified power dissipation is not exceeded.



Zener breakdown:

The electric field in the depletion layer reach a point that it can break the covalent bonds and generate electron-hole pairs. These electrons and holes constitute a reverse current across the junction that helps support the external current I.

Avalanche breakdown:

The minority carriers that across the depletion layer under the influence of the electric field gain sufficient kinetic energy to be able to break covalent bonds in atoms which they collide. The carriesliberated by this process may have sufficiently high energy to be able to cause other carriers to be liberated in this manner. This process occurs in the fashion of an avalanche, with the result that many carriers are created that are able to support any value of reverse current as determined by external circuits, with a negligible change in the junction voltage drop.


Physical operation of PN junction – under forward-bias conditions

Majority carriers are supplied from the external source:free electrons → n side, holes → p side.Depletion layer narrows and barrier voltage decreases.ID increases, in equilibrium: ID − IS = IThe decrease in barrier voltage appears as an external voltage V.


Physical operation of PN junction – under forward-bias conditions

Minority-carrier distribution


Current-voltage relationship

Law of the junction:

The excess holes decays exponentially with x-axis as they recombine with the majority carriers, i.e., free electrons.

where Lp is diffusion length of holes in the n-type silicon.

Hole current density:

Jp is largest at x = xn , and decays exponentially with distance due to recombination. In steady stage, the electrons will be supplied from external circuits to the n region at a rate that will keep the current constant at the value it has at x = xn . Thus,

Total current: I = A(Jp + Jn)

/0( ) TV V

n n np x p e=

[ ] ( ) /

0 0( ) ( ) n px x L

n n n n np x p p x p e− −= + −

( ) ( ) //0 1 n pT

x x Lp V Vnp p n

p

DdpJ qD q p e e

dx L− −= − = −

( )/0 1Tp V V

p np

DJ q p e

L= − Similarly, ( )/

0 1TV Vnn p

n

DJ q n e

L= −

( ) ( ) ( )0 0 / / /21 1 1T T Tp n n p pV V V V V Vni S

p n p D n A

qD p qD n D DI A e Aqn e I e

L L L N L N

⎛ ⎞ ⎛ ⎞= + − = + − = −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

2 20 0/ /n i D p i Ap n N n n N= =Reminder that : and


Diffusion capacitance

The excess minority-carrier charges is a function of terminal voltage – a capacitive effect referred to as diffusion capacitance.

Total excess minority carrier charge:

τT is called the mean transit time and is related to minority carriers lifetimes.

Small signal diffusion capacitance:

To keep Cd small, the transit time τT must be made small, an important requirement for diodes intended for high-speed or high frequency operation.

T p p n nQ I I Iτ τ τ= = +

Td

T

C IV

τ⎛ ⎞=⎜ ⎟⎝ ⎠


Terminal characteristics

Forward-bias region:

IS is the saturation current:Proportional to the area of the junctionA design parameter in IC to scale the current for the same vOf the order of 10−15 ADoubles in value for every 5°C rise in temperature

n has a value between 1 and 2, depending on the material and physical structure of the diode. Diodes in IC exhibit n = 1. Discrete diodes generally exhibit n = 2.

For v >> nVT ,Diode current is negligibly small for v < 0.5V and increases rapidly for v > 0.7V.

Reverse-bias region: i = −IS

Breakdown region: Diode enters this region when the reverse bias voltage exceeds the breakdown voltage. The reverse current increase rapidly with the associated increase in voltage drop being very small.

( )/ 1Tv nVSi I e= −

/ Tv nVSi I e

Read Chapter 3, Section 3.1, 3.7 Sedra/Smith’s...

Documents

Transcript of Read Chapter 3, Section 3.1, 3.7 Sedra/Smith’s...