Electronics The fifth and Sixth Lectures

Seventh weekهـ 1436/ 12/ 24 - 21

السلمي / سمر أ

Outline for today Chapter Two: Junction Diode Physical Electronics

Definition. Its symbol. Types

pn Junction structure and fabrication

What happing inside pn Junction

The Contact Potential and Energy Level in pn Junction at Equilibrium

Conditions

Diffusion and Drift in pn Junction at Equilibrium Conditions

Derive Contact Potential at Equilibrium Conditions from Current Density in pn

Junction

Mathematical description at Equilibrium Conditions in pn Junction to Contact

Potential and Carrier Concentrations

Derive Contact Potential and depletion region width at Equilibrium Conditions

in pn Junction from Poisson’s equation

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Junction Diode Physical Electronics

We studied in previous lectures about semiconductor properties and mentioned

in the last slide about the subject (the existence of two different types of

semiconductor next to each other) or (the existence of two different materials

next to each other)

In the second chapter, we will examine the two cases

the first case is diode or pn Junction

If a piece of intrinsic semiconductor is doped so one part is n-type and the other

part is p-type, and pn junction forms at the boundary between the two regions.

pn Junction’s Symbol

Symbol of diode as in the first figure, triangle

base is p-type and triangle head is n-type.

pn Junctions’ types

Light Emitting Diode LED

Photodiode

Zener Diode.

Avalanche Diode

Tunnel Diode

Scottky Diode

Varactor Diode

Laser Diode

PIN Diode…etc

=

pn Junction structure and fabrication

The pn junction do not made up simply by surface adhesion of two types n-type &

p-type as in the figure of previous slide (slid 4) Due to the irregular surfaces and

Failure harmonization of covalent bonds at surfaces etc. However, manufacturing

will be by putting one of extrinsic semiconductor type in the top center of other

type as in the next figure. This happened by long steps of oxidize, expose,

implant , diffusion and etc. to reach the final figure (some of manufacturing steps

of diode)

pn Junction structure and fabrication

the pn junction do not made up simply by surface adhesion of two types n-type &

p-type as in the figure of previous slide (slid 4) Due to the irregular surfaces and

Failure harmonization of covalent bonds at surfaces etc. However, manufacturing

will be by putting one of extrinsic semiconductor type in the top center of other

type as in the next figure. This happened by long steps of oxidize, expose,

implant , etch, diffusion and etc. to reach the final figure.

What happing inside pn Junction

when the n-type and p-type join next to each other in the diode, we obtain one

side of semiconductor has plenty electron and few holes (n-type) next to other

side that has plenty holes and few electron (p-type) . Therefore, there will be

diffusion between two sides. Electron diffuse from n-type to p-type leaving

behind positive ions ND

+ in region called (depletion region). The opposite, holes

diffuse from p-type to n-type leaving behind negative ions NA

_

in depletion

region.

What happing inside pn Junction

Diffusion will not continue to infinity. Due to the two types of ions trying to pull

charge carriers which trying to diffusing far away. donors seek of keeping

electrons and acceptors seek of keeping holes; therefore, electric field is created

from ions and works to slow of diffusion process and reaches out to the state of

stability; therefore, far from depletion region, the semiconductor will be intrinsic

neutral

What happing inside pn Junction

Depletion region : It is the contact area between n-type and p-type and contains

of positive space charge of n – side and negative space charge of p – side , also it

not contains charge carriers. The symbol for it is W . In some book it called space

charge region or transition region .

The Contact Potential and Energy Level in pn Junction at Equilibrium Conditions

Before the n-type and p-type join next to each other in the diode, we know that Fermi level

is near conduction band in n -type and Fermi level is near valence band in p-type as in

figure (a)

but how will be Fermi level in the case of n-type and p-type join next to each other in

the diode??

Will Fermi level be in the same place to two types or will be separated at adhesion

point?

will conduction and valence bands in the diode at the same place?

The Contact Potential and Energy Level in pn Junction at Equilibrium Conditions

In fact at energy bands in pn junction, Fermi level must be at the same energy

level in the two types at equilibrium condition. Therefore, conduction or valence

bands must be at the different energy level in the two types as in the figure below.

So, we notice that bending the levels of conduction or valence bands; therefore,

bending intrinsic level in

the region between xn

and –xp which is depletion

region. This bending and

difference of energy levels,

therefore potential difference

between n-type and p-type is

called contact potential

The Contact Potential and Energy Level in pn Junction at Equilibrium Conditions

Contact potential; the potential difference between n-type region and p-type region in

diode which prevents more electrons flow from n-type to p-type, and more holes flow from

p-type to n-type. The symbol for it is V0

=

The Contact Potential and Energy Level in pn Junction at Equilibrium Conditions

from the figure,

we can calculate

contact voltage

by a number of

equations

=

Diffusion and Drift in pn Junction at Equilibrium Conditions

As we discussed earlier, we expect diffusion in junction due to the large carrier

concentration gradients . Thus , as we notice, electrons diffuse from n side into p

side and holes diffuse from p to n. Also, we mentioned an opposing electric field

is created at junction due to pulling of positive and negative ions to charge

carriers. Their directions are opposite to directions of carrier diffusion. Therefore,

electrons drift from p- type to n- type and holes drift from n- type to p- type as in

the figure below at equilibrium conditions.

Diffusion and Drift in pn Junction at Equilibrium Conditions

notice to electron and hole diffusion direction, also to electron and hole drift direction. Therefore, the sum of total current density to electron and hole are zero at equilibrium conditions

=

Derive Contact Potential at Equilibrium Conditions from Current Density in pn Junction

We start from the total current density of holes in diode

By assuming to deal in one dimension (x) and the use of Einstein relationand by substitute with relation voltage and electric field

therefore

=== >>

Derive Contact Potential at Equilibrium Conditions from Current Density in pn Junction following

=== >>

Integration the two sides

Therefore

Finally, we get the relation connecting contact potential and concentrations

=

Derive Contact Potential at Equilibrium Conditions from Current Density in pn Junction

Similar if we start from the total current density of electron in diode

By assuming to deal in one dimension (x) and the use of Einstein relationAnd by substitute with relation potential and electric field

therefore

=== >>

=

Derive Contact Potential at Equilibrium Conditions in pn Junction

following

Integration the two sides

Therefore

Finally, we get the relation connecting contact potential and concentrations

=

Mathematical description at Equilibrium Conditions in pn Junction to Contact Potential and Carrier Concentrations

From last equation, we can write the equation as following We represent the equation as ratio of majority carrier concentration to minority carrier concentration

because we deal with equilibrium conditions, the best to write it as

Therefore, electrons and holes concentrations are

=

Derive Contact Potential and depletion region width at Equilibrium Conditions in pn Junction from Poisson’s equation =

Derive Contact Potential and depletion region width at Equilibrium Conditions in pn Junction from Poisson’s equation

In the beginning, we know from Maxwell equation

Where ρ charge density and ϵ0 permittivity in a vacuum

Since the electric field connects with Potential by relation

We get Poisson's equation

=

Derive Contact Potential and depletion region width from the figure, we notice that

When focusing at one dimension (x),

Also we study material not vacuum

is relative permittivity

=

ϵr

Derive Contact Potential and depletion region width

charge density in the regain is

and is

With substitute charge density in Poisson's equation to obtain , than integrate

=

Derive Contact Potential and depletion region width The maxim value of electric field is

To calculate contact potential from equation

Integrate the electric filed along depletion region, therefore

We can easily find the integration from triangle area in the previous figure of the relation between electric field and X-axis

With substitute of electric field value, we obtain

Derive Contact Potential and depletion region width From previous equations

We find xn

with substitute xn value in to contact potential equation, we obtain

Derive Contact Potential and depletion region width From contact potential last relation, we can find depletion region width W

or

Also, xn & xp

xn is depletion region width From n-type sidexp is depletion region width From p-type side

=

Solving first Homework