p-n junctionscombine p- and n-type semiconductor region

most important characteristics: rectification(current flows easily only in one direction)

important as rectifier but also: Basic building block in bipolar transistors, field-effect transistors, LEDs, solar cells .

forward bias

reversebias region

S. M. Sze, Semiconductor Devices Physics and Technology

Formation of a p-n junction:

Conceptionally:

Take a p-type SC and combine it with an n-type SC

The actual process isof course different

S. M. Sze, Physics of Semiconductor Devices

Static conditions thermodynamic equilibrium

We start with:

S. M. Sze, Semiconductor Devices Physics and Technology

D. A. B. Miller, lecture notes, Stanford University, 1999

Establish contact: e- and h+ concentration gradient !

electrons diffuse from the n-side into the p-side and holes diffuse from the p-side into the n-side DIFFUSION CURRENT !

Acceptor and donor ions are fixed !

negative space charge on the p-side of the junction

positive space charge on the n-side of the junctionD. A. B. Miller, lecture notes, Stanford University, 1999

depletion region

(virtually no freecarriers charged dopands !)

electric field

DRIFT CURRENT !

(In the oppositedirection of thediffusion current)

electrons holes

Diffusion current density

xdndDej ndiff,n = xd

pdDej pdiff,p =

Dn, Dp diffusion coefficients given by the Einstein relations

nn ekTD = pp e

kTD =

n and p mobilities of electrons and holes, respectively

Drift current densitypFej pdrift,p =nFej ndrift,n =

F driving electric field

What happens, if we apply an electric field to the semiconductor ?

dxdE

edxdUF 1==

S. M. Sze, Semiconductor Devices Physics and Technology

U electrostatic potential

E EC, EV, Evac, Ei (intrinsic Fermi level)

Junction in thermodynamic equilibrium

Lets look at the hole current density

xdpdDepFej ppp =

=

=

=

dxdE

xdEd

Tkp

xdpd

dxdE

xdEd

TkTkEEexpn

xdpd

TkEEexpnp

Fi

b

Fi

bB

Fii

B

Fii

1

and

dxdE

eF i1=

D. A. B. Miller, lecture notes, Stanford University, 1999

dxdEpj

dxdE

xdEd

Tkp

eTke

dxdE

epej

Fpp

Fi

bp

Bipp

=

=

1

Thermodynamic equilibrium: The current flow across thejunction has to be zero !

0=dx

dEF

In the thermodynamic equilibrium (i.e., if no charge carriersare injected), the Fermi energy in the device is CONSTANT !

What is the electrostatic potential difference between the p-side and the n-side ?

D. A. B. Miller, lecture notes, Stanford University, 1999

Vbi built in potentialeVbi= minus

But: How do the bands inside the depletion region reallylook like ?

D. A. B. Miller, lecture notes, Stanford University, 1999

Assume abrupt junction:

S. M. Sze, Physics of Semiconductor Devicesjunction

Red: assumed abrupt junction (abrupt changes of the net chargesbetween the depletion region and the p and n regions)

Potential from Poisson equation

=22

dxVd

charge density; dielectric constant

0

Solving these differential equations allows usto calculate:

The field-distribution in the depletion region

The maximum field in the depletion region

The width of the depletion region

The shape of the band bending The capacitance of the diode

..

Biasing a diode:

Forward bias of VF: total electrostatic potential across junction decreases by VF depletion layer width decreases

Reverse bias of VR: total electrostatic potential across junction increases by VF

depletion layer width increases

The system is no longer in thermodynamic equilibrium !

current will flow !

S. M. Sze, Semiconductor Devices Physics and Technology

Current through diode

Applying a voltage: disturb balance between diffusioncurrent and drift current

Forward bias: drift current reduced in comparison to diffusion current

enhanced diffusion of holes from p-side to n-side

enhanced diffusion of electrons from n-side to p-side

minority-carrier injection current

Reverse bias: increase of electrostatic potential acrossdepletion region

reduce minority carrier concentrations

reduce also diffusion current

S. M. Sze, Semiconductor Devices Physics and Technology

Ideal current-voltage characteristicsSeveral approximations including no generation or recombinationof carriers in the depletion region

Using the semiconductor statistiscs and current equations wediscussed before (after a somewhat lengthy derivation):

( )1= Tk/eVS BejjjS sturation current (contains diffusion coefficients, diffusionlengths and equilibrium concentrations of the minority carriersin the p and n regions)

Current grows exponentially with the applied voltage in forward direction Current density saturates at jS in reverse direction

S. M. Sze, Semiconductor Devices Physics and Technology

Deviations from the ideal characteristics

Most relevant for our purposes:

Recombination currente- from n-type region and h+ from p-type region recombine in thedepletion region

added current in forward direction

can happen through traps (heating of the device)

or through the emission of a photon (LED)

PhotocurrentOptical absorption extra pair of e- and h+ in depletion region

extra reverse current

Heterostructure diodesBand bending of course also happens in heterostructures withdifferent doping levels

But then in addition to the band bending also band offsets

D. A. B. Miller, lecture notes, Stanford University, 1999

D. A. B. Miller, lecture notes, Stanford University, 1999

Metal-semiconductor contacts (Schottky-contacts)

(here we again assume that there are no interface dipoles and weneglect effects like mirror charges and Fermi level pinning )

S. M. Sze, Semiconductor Devices Physics and Technology

Some similarities to a p-njunction (metal plays the role of the p or n type semiconductor)

But also certain differences

D. A. B. Miller, lecture notes, Stanford University, 1999n-type semiconductor:

p-type semiconductor:

EF constant !

e- or h+ flow from semiconductor into metal

built-in voltage Vbi and band bending in the SC

depletion region

potential barrier bn (lowered by Schottky effect)DN

width 1

Charging, fields and shape og band bending

S. M. Sze, Semiconductor Devices Physics and Technology

Charge transport through Schottky-junctionsdifferent from p-n junction:

charge transported by the majority carriers

thermionic emission of majority carriers from the semiconductorover the potential barrier into the metal

equilibrium: balanced by flow of electrons from metal intosemiconductor

rectification ! with current density given by: ( )1= Tk/eVS Bejj

Ohmic contact:

Definition: metal-semiconductor contact with negligiblecontact resistance

How can this be realized ?

very high doping of the semiconductor

depletion region extremely short

e- and h+ can easily tunnel through resulting very thin barrier

Ohmic contacts

no rectification !

D. A. B. Miller, lecture notes, Stanford University, 1999