p

metal

n+ orp+p

metal

n+ p+

p+

p

oxiden

p

metaln

PN junction on a wafer• Actual PN junction is 2-D and 3-D

• Integrated diodes usually have top contacts to both terminals

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

Physical View of a PN Junction

• The + after n/p means heavy doping

2-D 3-D

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

When P- and N- Types Meet [1]From your previous notes

P Si Si+

-Si Si B

• when a electron made available from a group V element moves to a location with a hole made available from a group III element, the electron may take it place by recombination

• at the site of the group V element becomes slightly positive and at the location of the group III element becomes slightly negative

• No special effects if it is distributed over the entire system• What happens if the group V elements and group III elements

are separated into different locations?

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

When P- and N- Types Meet [2]

Si Si Si Si Si B Si P P Si Si P

Si B Si Si B Si P Si Si P P Si

B Si Si B Si Si Si P Si P Si P

Si Si B Si Si B Si Si P Si Si Si

Si B Si Si Si Si P P Si Si P Si

Atomic view right after PN junction formation• Right after putting the P and N together, the excess carriers

stay with the parent atoms and the whole system is neutral

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

Formation of depletion region

Si Si Si Si Si B Si P P Si Si P

Si B Si Si B Si P Si Si P P Si

B Si Si B Si Si Si P Si P Si P

Si Si B Si Si B Si Si P Si Si Si

Si B Si Si Si Si P P Si Si P Si

++

+++

++

--

-----

When P- and N- Types Meet [3]

• Carriers near the junction recombines and removed (depleted) forming a region with charges but no (very few) carriers

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

Properties of the PN junction regions

Si Si Si Si Si B Si P P Si Si P

Si B Si Si B Si P Si Si P P Si

B Si Si B Si Si Si P Si P Si P

Si Si B Si Si B Si Si P Si Si Si

Si B Si Si Si Si P P Si Si P

++

+++

++

--

-----

When P- and N- Types Meet [4]

Si

negative charge• neutral region • with carrierpositive charge

depletion region (no carrier)• neutral region • with carrier

P-type N-type

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

Abrupt junction approximationApproximations used

+-

---

--++

+++

xnxp

• There is a clear boundary between the n-type and p-type silicon• In really, there is a transition region where both donors and

acceptors co-exist

Depletion approximation• There is a clear boundary between the depletion region and

the neutral region• All carriers in the depletion region are depleted

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [1]Band diagram representation• PN junction are formed by injecting dopants to different

locations of a piece of silicon• Starts from the band diagram of an intrinsic silicon at thermal

equilibrium• Gradually dope one side to P-type and the other to N-type

Intrinsic silicon N-doping P-doping

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [2]Band Diagram Representation• the Fermi level (represent external

forces or voltages) of the system align at thermal equilibrium (or there will be continuous current flow)

EC

EV

EF

p

n Ei

VBi

Quantity of interest• How high is the energy barrier for electron from the n-region to

the p-region• How wide is the depletion region

Ø Noted that energy is proportional to voltage like mechanical potential energy is proportional to height

Ø We have E = qV where q is the electron charge =1.6x10-19C

• The band diagram defines the static landscape (or voltage) of the system sense by the carriers

VBi the built-in potential of a PN junction

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [3]Determining the built-in potential• As the band bending for the

conduction band is the same as the band bending of Ei, we have

EC

EV

EF

p

n Ei

VBiVP

VN

VBi = VP + VN

• Recall that for P-silicon, we have

qVN = EF −EiN = kT lnND

ni

⎛

⎝⎜

⎞

⎠⎟• For N-silicon, we have

qVP = EiP −EF = kT lnNA

ni

⎛

⎝⎜

⎞

⎠⎟

• Adding together, we have

!"# = !% + !' = ()* ln

'-./

+ ()* ln

'0./

= ()* ln

'0'-./1

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [3]Determining the depletion region width

• For charge neutrality, the charge at p-side depletion region has to be balanced by the charge at the n-side

• We have

• From this point onward, we’ll normalize with respect to the area to simplify the calculations

+-

---

--++

+++

xnxp

• Want to find xp and xn in the given figure

NDxn=NAxp

• Still two unknown and we have to find another relationship to solve for both xp and xn

NDxnA=NAxpA or

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [4]

erf -=Ñ2

er

-=2

2

dxVd

er

=dxEd!

The Poisson’s Equation

• Interpretation of the Poisson’s equation

• A very important equation relating voltage, electric field and charge density

dVdx

= −!E

+--

++

--

+++-

-+-

V = −!Edx∫

!E = 1

ερ dx∫

where

f : the spatial potential (or voltage)r : the charge densitye : dielectric constant of the material

(8.85x10-14F/cm for free space (e0) and 11.9e0 for silicon and 3.9e0 for SiO2 )

• In 1-D, it becomes

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [5]Apply to PN Junction• Solving the Poisson’s

equation graphically

ionized dopant

NA

ND

-+xpxn

Q=qNDxnQ=qNAxp

xp xn

Si

pAxqNe Si

nD xqNe

or

xp xn

VSi

pA

Si

nDbi

xqNxqNV

ee 22

22

+=

E!

integrate

integrate

+-

---

--++

+++

xnxp

Charge distribution

Electric field

Voltage• The voltage at the two end

of the PN junction is known to be Vbi

Solution

21

)(2

÷÷ø

öççè

æ+

=DAD

AbiSin NNN

NqV

xe 2

1

)(2

÷÷ø

öççè

æ+

=DAA

DbiSip NNN

NqV

xe

21

112úû

ùêë

é÷÷ø

öççè

æ+=+=

DA

biSipnd NNq

Vxxx

e

Si

pA

Si

nDbi

xqNxqNV

ee 22

22

+=• solving NDxn=NAxpand

• result

• where ÷÷ø

öççè

æ= 2ln

i

ADbi n

NNqkTV

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [6]

• Now we have two equations to solve for the two unknown

• very often we have N+/P or P+/N junction- note that: ni/pi ~ 1010cm-3

ND+/NA

+ ~1018cm-3

ND/NA ~1015cm-3

• e.g. for P+/N, only xn has to be considered

21

12÷÷ø

öççè

æ=

D

biSin Nq

Vx

e

NA

ND

-

+xn

xp ~ 0

- ND above is only about 0.1% of ND+

- note: depletion region have carriers ~ ni

Asymmetric Junctions

ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering

PN Junction at Thermal Equilibrium [7]

r

ansunMansunMHong Kong University of Science & Technology, Department of Electrical & Electronic Engineering

What have we learned up to this point• the property of the PN junction is mostly controlled by

the lighter doped side

xp xnP+ N0

EC

EV

EFp+ n Ei

VBi

D

biSinnp Nq

Vxxx

12e=»+ ÷÷

ø

öççè

æ= 2ln

i

ADbi n

NNqkTVand

PN Junction at Thermal Equilibrium [8]

ansunMansunMHong Kong University of Science & Technology, Department of Electrical & Electronic Engineering

Contact PotentialCan built-in potential be measured?• For any two materials in contact, there exist a contact potential

p n

V

m1 m2

BA

( ) ( ) ( ) 2121 mmmnnppmAB VVVVVVVVV -=-+-+-=

• Can the voltage be measured by the voltmeter?• The answer is no, because contact potential is also developed

between at the leads voltmeter made up of the same material• No matter how many different materials you connected, it will

end up with a close loop without any measurable voltage• So, even there is a build-in potential in a PN junction, no

voltage can be measured• Metal semiconductor contact will be covered later

m3