chapter 3 diodes - maranatharudy-wawolumaja.lecturer.maranatha.edu/wp-content/... · chapter 3 –...

Chapter 3 – Diodes

Introduction

http://jas2.eng.buffalo.edu/applets/education/pn/biasedPN/index.html

Textbook CD

http://jas2.eng.buffalo.edu/applets/education/pn/cv/index.html

http://jas2.eng.buffalo.edu/applets/education/pn/biasedPN/index.html

http://jas2.eng.buffalo.edu/applets/education/pn/cv/index.html

Introduction

The ideal diode: (a) diode circuit symbol; (b) i-v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in

the forward direction.

The Ideal Diode

Rectifier circuit

Rectifier Circuit

Output waveform.

Input waveform.

Equivalent circuit when v1 0 Equivalent circuit when v1 > 0

Rectifier Circuit

Example 3.1

Rectifier Circuit

Example 3.2

Terminal Characteristics of Junction Diodes – Forward Region

Example 3.3

Terminal Characteristics of Junction Diodes – Reverse-Bias Region

Exercise 3.9

Rectifier Circuit

Exercises 3.4 and 3.5

The i-v characteristic of a silicon

junction diode.

Diode – i-v Characteristic

The diode i-v relationship with some scales expanded and others compressed in order to reveal details.


i IS e

v

n VT1

VTk T

q

for i>> Is

i IS e

v

n VT

v n VT lni

IS

e is the base for the natural log

Thermal Voltage

25mV at room temp.

ln = 2.3 log


Exercise 3.6

Consider a silicon diode with n=1.5. Find the change in voltage if current changes

from 0.1 mA to 10 mA.

i IS e

v

n VT n 1.5 VT 0.025

I1 0.0001 I2 0.01

I1 IS e

v1

n VT

I1

I2e

v1 v2( )

n VT

I2 IS e

v2

n VT v1_v2 n VT ln

I1

I2

v1_v2 0.173 V


A diode for which the forward voltage drop is 0.7 V at 1 mA and for which n=1 is

operated at 0.5 V. What is the value of the current?

i IS e

v

n VT

0.001 IS e

0.7

1 0.025

I IS e

0.5

1 0.025

I 0.001e

0.2

0.025 10

6

I 0.335 uA

Simplified physical structure of the junction diode.

(Actual geometries are given on Appendix A.)

Diode – Simplified Physical Structure

Diode – Semiconductor Physics

The semiconductor diode is what is called a pn junction and is shown in the figure on the right

Both the p and the n sections are part of the same crystal of silicon. At room temp., some

of the covalent bonds in silicon break and electrons are attracted to other atoms. These moving

electrons leave a hole behind that is filled by another electron, thus continuing the cycle. In

thermal equilibrium the concentration of holes (p) and the concentration of free electrons (n) are

equal to each other and to ni which is the number of holes or free electrons in silicon at a given

temp. Study of semiconductor physics yields the following equation for the free electrons.

In this eqaution, B is a material dependant parameter (5.4x10^31) for sil icon, Eg

is a parameter known as the bandgap energy (1.12electron volts (eV) for sil icon),

and k is the Boltsmann's constant (8.62x10^-5 eV/K). T hus, at room temp

(300K), the number of holes or free electrons is 1.5x10^22.

The two methods by which holes and electrons move are called diffusion and drift. In diffusion, the flow

moves from areas of higher concentration of p or n to areas of lower concentration. This flow gives rise to

a flow of charge or diffusion current. This is given by the following

J p q D pxP

d

d

Here, Jp is the current density (in Amps/cm^2), q is the magnitude of electron

charge (1.6x10^-19C) and Dp is called the diffusivity of the holes. the differential

dP is the rate of change for hole concentration.

J n q D nxn

d

d

Here, Jn is also the current density. The only difference is the differential dn.

Here, it stands for the rate of change of free electron concentration.


v drift p E

The other method is called drift. Free holes and e- are moved by an electric field (E) and have a velocity

p is the mobility of holes and has the units of (cm^2)/V*s.

This method also gives rise to diffusion currents.

Jp_drift q p p E Jn_drift q n n E

The total drift current is written as fol lows.

Jdrift q pp nn E


A relationship, known as the Einstein relationship can be noted below.

Dn

n

Dp

p

VT The Vt term is what is called the thermal voltage. At room temperature, the

thermal voltage is approximately equal to 25mV

Silicon is often doped to give it better conductivity. Doping is the process by which impurity atoms are

added to the sil icon to provide more holes (p-type) or more free electrons (n-type). One thing to note is

the way the various terms are defined. For n-type sil icon, the hole concentration is np and the electron

concentration is nn. The concentration of donor (n-type) atoms or accpetor (p-type) atoms is denoted Nd

and NA respectively. Study of doped sil icon revealed the following.

Pn

ni2

ND

nn Nd

np

ni2

NA

pp NA



The pn junction under open-circuit conditions

When a diode (l ike the one shown above) is existing in a open circuit form two currents wil l naturally

occur.

Because the concentration of holes is high in the p-region and low in the n-region, holes wil l diffuse

from the p-region to the n-region. Likewise, free electrons wil l diffuse from the n-region to the p-region.

These two components add together to form the diffusion current Id whose direction is from the p-side

to the n-side. When the free electrons diffuse to the p-side, many are paired up with holes very close

to the border of the two regions thus depleting the number of free electrons. This uncovers a positive

charge at the edge of the n-region. On the other side, due to the same (but exact opposite) situation, a

negative charge is uncovered at the boundary of the p-region. T his results in what is called the

carrier-depletion region (shown in the figure below) because the two extremes create a potential

difference to result. This is in the form of a barrier that holes and electrons must cross in order to

create a current. T hus, it can be seen that the current ID depends on this barrier voltage (which is

denoted V0).


The voltage across this region can be found by the following equation:

In this equation, Na, Nd, and Vt are the same as they are previously

defined above. In open circuit conditions, V0 is 0 because the voltages

existing at the metal contacts of the diode (in the diagram above)

counteract the voltage at the barrier. If this were not so, energy could be

drawn from the isolated diode which is clearly incorrect.

Vo VT

NA ND

ni2

In addition to the diffusion current, there is also a drift current. When some of the thermally generated

holes (holes created by a temp. increase which releases some outer electrons from their bonds) reach

the edge of the depletion region, they are swept accross the area because of the electric field present

in that region. This also happens to the free electrons. The addition of these two currents is the drift

current Is which flows in the opposite direction of ID. Under open circuit conditions, no external current

exists and the two currents are equal to each other. Under these conditions, if one current for some

reason is not equal to the other, they wil l shift and change unti l the equil ibrium is once again attained.


The carrier depletion region has a width and if the doping was equal for both the n and p regions, the

depletion region would be symetrical. However, this is not the case so the widths wil l be different on

either side. Because the depletion region has a balanced amount of charge, i t wil l have to extend

deeper into the l ighter doped region so that the holes and electrons wil l a l l have a match. If the width in

the p side is denoted xp and the width in the n side is xn, the charge-eqaulity condition is this:

q xp A NA q xn A ND Here, A is the cross-sectional area of the junction.

This equation can be rewritten to yield the fol lowing, more clear

equality.

In actual practice, one si de is usually more heavily doped than the

other causing the depletion region to exist almost entirely on one

side (the l ightly doped si de).

xn

xp

NA

ND

The width of the depletion region can be given (based on the above assumption that i t exists

mainly on one side) by the fol lowing equation.

Wdepletion_region xn xp2s

q

1

NA

1

ND

Vo

In this equation, s is the electrical permittivity of si l icon (1.04x10^-12 Farrads/cm). The width of

the region is usually 0.1 to 1 m.

The pn Junction under rev erse-bias conditions

To best describe the pn junction diode under reverse bias conditions, the diode is modelled to

have a current source exciting it. This current is kept lower than Is to keep the diode from

experiencing breakdown. The current (I) wil l be carried by electrons that move (in the opposite

direction of I) from the n-region to the p-region. T his process creates a voltage (denoted Vr) for

which the voltage tries to flow into the n-region of the diode. This voltage is, l ike the current,

less than the breakdown voltage (the voltage at which current wil l flow in the negative direction).

Because the positive end of the voltage is trying to enter the diode through the positive wall of

the barrier, the voltage actually increases the barrier's size. No current, therefore, is allowed to

pass through the diode. From this reasoning, it is relatively easy to see that as the current (and

thus Vr) changes, the charge in the depletion region is going to change. In this way, the diode

has some capacitance. The charge in the depletion region qj can be found by finding the charge

in either of the two regions (because the charge is equal in both). Using the n-side, the following

equation is derived.

For this equation, A is the cross-sectional area of the junction.

Using the above eq. for the width of the depletion region, the

following can be written

qj qn q ND xn A

qj qNA ND

NA ND A Wdepletion_region Here, Wdep is sl ightly different from the above

equation and can be written as follows.

Diode –Physical Structure

This adjustment is made because

it is no longer an open circuit. Wdepletion_region xn xp

2s

q

1

NA

1

ND

Vo VR

There is now an external voltage source acting on the diode so the voltage is the addition of the

open circuit voltage and the reverse voltage. The capacitance can then be written as the

derivative of the charge in the depletion region. WIth a l i ttle bit of algebra and the combining of

previous equations, the value for the capacitance (Cj) can be found to be as fol lows:

Here, Cjo is the value of the capacitance of the open circuit diode

and is defined below. m is a value that depends on the manner in

which the concentration changes from the p to the n side of the

juncion. It is called the grading coefficient (for the case of the

diode we are using, i t is .5 but i t ranges from .5 to about .333)

Cj

Cj0

1VR

Vo

m

This is the value of the open circuit capacitance. This is

readily made apparant by the fact that i t does not depend

on Vr.

Cj0 Aq s

2

NA ND

NA ND

1

Vo


The pn Junction in the Breakdow n Region

As was explained earl ier, the voltage for reverse bias conditions cannot exceed the breakdown voltage.

If i t does, the barrier wil l no longer hinder the flow of current. As the voltage, in reverse, accross the

diode increases, the voltage across the depletion layer also increases. When this voltage is sufficiently

high enough, one of two mechanisms comes into play that allows current to flow through the diode.

The first of these mechanisms is called the zener effect. If the breakdown voltage of the diode is less

than 5V, the zener effect is usually what happens. Zener breakdown occurs when the electric field in

the depletion layer increases to the point where it can break covalent bonds and generate electron-hole

pairs. T hese holes and pairs are then swept to their respective sides causing a reverse current to form

which supports the outside current source. While this happens, the voltage across the diode wil l

remain relatively close to the breakdown voltage while the current wil l be largely determined by the

outside source.

The other mechanism is called the avalanche effect. This usually happens when the breakdown

voltage is greater than 7V. In this effect, the voltage or current basically forces its way through the

barrier. The covalent bonds are broken by the incoming voltage/current and as the first few bonds

break, more carriers are freed up to break more bonds causing an avalanche of current to flow. This

causes large current changes for small voltage changes.

A couple of things to note:

1. In the 5V to 7V range, the breakdown could be either zener or avalanche or a combination fo the

two.

2. pn junction breakdown is not a destructive process. It only causes problems when the maximum

dissapated power is exceeded. This max. value, in turn, implies a max. value for the reverse current.


The pn Junction Under Forw ard-Bias Conditions

When a diode is under forward bias condtions, an external voltage or current source is applied with the

positive side of the voltage entering the p-side of the diode. When this happens, the electrons from the

incoming current (which enter at the n-side) and the holes from the positive voltage (entering from the

p-side) wil l nuetralize and diminish the depletion region barrier. A result of this is that the concentration

of minority carriers at the edge of the depletion region (denoted pn(xn) is related to the forward voltage

V by the following equation.

In this equation, pn0 is the concentration of minority carriers when no external

source is added. VT is the thermal voltage (ususlly 25mV). T his is known as

the law of the junction.pn xn pn0 e

V

VT

The concentration of excess holes in the n-region can be expressed as the following.

Here, Lp is a canstant that determines the steepness of

the exponential decay of excess holes. It is called the

diffusion length of holes in the n-type sil icon. T he smaller

the value of Lp, the faster the injected holes wil l

recombined with the majority electrons.

pn x( ) pn0 pn xn pn0 e

x xn

Lp

The constant Lp is also related to another parameter called the excess-minority-carrier lifetime p.

This is the average time it takes for an injected hole to recombine. Lp is also related to the diffusion

constant Dp.

Lp Dp p Typical values for Lp range from 1 to 100um and p usually ranges from 1 to

10,000ns.


The holes diffusing in the n-region wil l give rise to a holes current. The density (which is greatest at the

edge of the depletion region - x = xn) is given by the following.

Jp qDp

Lp

pn0 e

V

VT

1

In a similar manner, the analysis can extendd to the electrons injected into the p-region

Ln is the diffusion length of the electrons in the p-region.Jn q

Dn

Ln

np0 e

V

VT

1

Because both of the densities are in the same direction, the total current (I) can be found. Substituting

for pn0 = ni^2/ND and similarly for np0, the current can be expressed as follows.

I A q ni2

Dp

Lp ND

Dn

Ln NA

e

V

VT

1


Minority-carrier distribution in a forward-biased pn junction. It

is assumed that the p region is more heavily doped than the n

region; NA ND.

Thus, the diode saturation current is defined to be

IS A q ni2

Dp

Lp ND

Dn

Ln NA

Because of the excess carriers in forward bias, when the voltage is changed, the charge of the diode

wil l have to change to achieve steady state. T his causes a form of charge storing in the depletion

region. This charge can be calculated by adding up the charge in the p and n regions. T his charge

turns out to be as follows.

Q p Ip n In

Q T IBecause it was earl ier defined that Ip + In is equal to I, the equation can be rewritten as

where T is related to n and p and is called the mean tranit time. With this, i t can be shown that

the capacitance is defined as follows.

Cd

T

VT

I As can be seen, the diffusion capacitance is directly proportional to the current.

This means that the capacitance for reverse bias is almost negligably small.

The capacitance over the depletion layer under forward bias is written asCj 2 Cj0

This eqation is actually a fairly poor model so it is used as a rule of thumb rather than a solid fact.


Lessons In Electric Circuits copyright (C) 2000-2002 Tony R. Kuphaldt

Diode – Characteristic

Lessons In Electric Circuits copyright (C) 2000-2002 Tony R. Kuphaldt

Diode – Applications

Diode – Applications

A simple diode circuit.

Analysis of Diode Circuits

Graphical analysis of the circuit above

Graphical Analysis

ID IS e

v1

n VT

IDVDD VD

R

Iterative Analysis

Example 3.4

V2 0.762V2 0.763 0.1 logID2

ID

ID2 4.237 103

ID25 0.763

1000

V2 0.763V2 V1 0.1 logI2

I1

For our case 2.3.n.VT = 0.1 V (This results from the condition of 0.1 V change for every

decade change in current

mAI1 1mAI2 4.3VV1 0.7V2 V1 2.3n VT logI2

I1

We then use the diode equation to obtain a better estimate for VD

ID 4.3 103

IDVDD VD

1000

VD 0.7R1 1000VDD 5

Determine ID and VD for this circuit with VDD = 5 V and R1 = 1 K ohm.

Assume diode current 1 mA at voltage 0.7 V, and that i ts voltage drop changes by 0.1 V for

every decade change in current.

Approximating the diode forward characteristic with two straight lines.

Simplified Diode Models

Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.

Simplified Diode Models

Example 3.5

Development of the constant-voltage-drop model of the diode forward characteristics. A vertical straight line (b) is used to approximate

the fast-rising exponential.

The Constant-Voltage Drop Model

The constant-voltage-drop model of the diode forward characteristic and its equivalent circuit representation.

The Constant-Voltage Drop Model

Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

The Small-Signal Model

Equivalent circuit model for the diode for small changes around bias point Q. The incremental resistance rd is the inverse of the slope

of the tangent at Q, and VD0 is the intercept of the tangent on the vD axis.


Example 3.6

The analysis of the circuit in (a), which contains both dc and signal quantities, can be performed by replacing the diode with the model

of previous figure, as shown in (b). This allows separating the dc analysis [the circuit in (c)] from the signal analysis [the circuit in

(d)].


Circuit symbol for a zener diode.

Zener Diode - Characteristics

The diode i-v characteristic with the breakdown region shown in some detail.

Model for the zener diode.

6.8 –V, 10mA

0.5W, 6.8-V, 70mA

Vz = Vzo + r2Iz

Vz > Vzo

Block diagram of a dc power supply.

Rectifier Circuits

(a) Half-wave rectifier. (b) Equivalent

circuit of the half-wave rectifier with the

diode replaced with its battery-plus-

resistance model. (c) transfer

characteristic of the rectifier circuit. (d)

Input and output waveforms, assuming

that rD R.

Rectifier Circuits

vo 0 vs VDO

voR

R rDvs VDO

R

R rD vs VDO

rD R vo vs VDO

PIV Vs

Full-wave rectifier utilizing a transformer with a center-tapped

secondary winding. (a) Circuit. (b) Transfer characteristic

assuming a constant-voltage-drop model for the diodes. (c) Input

and output waveforms.

Rectifier Circuits

PIV 2 Vs VDO

The bridge rectifier: (a) circuit and (b) input and output

waveforms.

Rectifier Circuits

PIV V s V DO

Voltage and current waveforms in the peak rectifier circuit with CR T. The diode is assumed ideal.

Rectifier Circuits

With A Filter Capacitor

Rectifier Circuits

With A Filter Capacitor iL

vo

R

iD iC IL CtvI

d

d iL IL

Vp

R

CR >> T vo Vp e

t

C R

at the end of the discharge intervall

Vp Vr Vp e

T

C R

SInce CR >> T and e

T

CR1

T

CR

Vr VpT

CR

Vr

Vp

f C RVr << Vp

Rectifier Circuits


Vp cos t Vp Vr

for small angles (t)

cos t 11

2t 2

Vp 11

2t 2

Vp Vr

Vp1

2 t 2 Vr t 2

Vr

Vp

to determine the average diode current during

conduction we equate the charge that the diode

supplies the capacitor

Qsupplied iCav t

to the charge the capacitor losses during the discharge

Qlost C Vr

iDav IL 1 2Vp

Vr

iDmax IL 1 2 2Vp

Vr

Rectifier Circuits


If Vp = 100 V

R = 10 K

Calculate the value of the

capacitance C that will result

in a peak-to-peak ripple

Vr of 5 V, the conduction

angle and the average and

peak values of the diode

current.

Vp 100 R 10000 f 60

Vr 5 IL

Vp

R IL 0.01 mA

CVp

Vr f R C 3.333 10

5

t 2Vr

Vp

t 0.316 rad

iDav IL 1 2Vp

Vr

iDav 0.209

iDmax IL 1 2 2Vp

Vr

iDmax 0.407

The Spice Diode Model and Simulation Examples

The dc characteristics of the diode are determined by the parameters IS and N. An ohmic resistance, RS, is included.

Charge storage effects are modeled by a transit time, TT, and a nonlinear depletion layer capacitance which is

determined by the parameters CJO, VJ, and M. The temperature dependence of the saturation current is defined by the

parameters EG, the energy and XTI, the saturation current temperature exponent. Reverse breakdown is modeled by an

exponential increase in the reverse diode current and is determined by the parameters BV and IBV (both of which are

positive numbers).

name parameter units default example

---- --------- ----- -------

1 IS saturation current A 1.0E-14 1.0E-14 *

2 RS ohmic resistance Ohm 0 10

*

3 N emission coefficient - 1 1.0

4 TT transit-time sec 0 0.1Ns

5 CJO zero-bias junction capacitance F 0 2PF *

6 VJ junction potential V 1 0.6

7 M grading coefficient - 0.5 0.5

8 EG activation energy eV 1.11 1.11 Si

0.69 Sbd

0.67 Ge


The dc characteristics of the diode are determined by the parameters IS and N. An ohmic resistance, RS, is included.

Charge storage effects are modeled by a transit time, TT, and a nonlinear depletion layer capacitance which is

determined by the parameters CJO, VJ, and M. The temperature dependence of the saturation current is defined by the

parameters EG, the energy and XTI, the saturation current temperature exponent. Reverse breakdown is modeled by an

exponential increase in the reverse diode current and is determined by the parameters BV and IBV (both of which are

positive numbers).

name parameter units default example a

---- --------- ----- ------- --

-----

9 XTI saturation-current temp. exp - 3.0 3.0 jn

2.0 Sbd

10 KF flicker noise coefficient - 0

11 AF flicker noise exponent - 1

12 FC coefficient for forward-bias - 0.5

depletion capacitance formula

13 BV reverse breakdown voltage V infinite 40.0

14 IBV current at breakdown voltage A 1.0E-3

PN Junction Diodes

Name Parameter Units Default

IS saturation current A 1.0E-14

N emission coefficient - 1

BV reverse breakdown voltage V infinite

RS diode series resistance 0

CJO zero-bias junction capacitance F 0

VJ junction potential V 1

M grading coefficient - 0.5


A variety of basic limiting circuits.

Limiting and Clamping Circuits

chapter 3 diodes - maranatharudy-wawolumaja.lecturer.maranatha.edu/wp-content/... · chapter 3 –...

Documents