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Diode Operation

ELEC 3908, Physical Electronics, Lecture 8

ELEC 3908, Physical Electronics: Diode Operation Page 8-2

Lecture Outline

• Have looked at basic diode processing and structures• Goal is now to understand and model the behavior of the

device under bias– First consider the carrier exchange and interaction between p and n

materials in equilibrium, and discuss concept of the depletion region

– Then examine carrier profiles under forward and reverse bias, and derive a model for the diode current flow in terms of applied potential and physical parameters

• Concepts of 1D area and doping profiles from lecture 6 as well as GR and diffusion from lecture 7 are required for current model


Junction Materials Just Before Connection• To understand carrier flow in biased diode, first examine behaviour of

carriers during establishment of equilibrium between p and n materials• Start with situation below, where p+ and n materials are separated, and

hence cannot exchange carriers (would be a p+ implant diffusion into nsubstrate structure)

• Electrons are majority in n-type (ND) and minority in p-type (ni2/NA),

holes are majority in p-type (NA) and minority in n-type (ni2/ND)


Junction Materials Immediately After Connection• After materials are connected, they can exchange carriers• Large concentration gradients exist across the metallurgical junction• Following slides show enlargement of boxed region


Charge Distributions at t = 0+

• Just after connection, the hole and electron distributions are flat in each material (uniform doping) and discontinuous across the metallurgical junction

• Large concentration gradients exist, so there will be a large component of carrier flux due to diffusion, recall

Θ = −Ddc x

dx( )


Charge Distributions at Later t• At some later time, charge

redistribution has taken place• Holes move to n-type, creating

+ve charge, electrons move to p-type, creating -ve charge

• Concentration gradients, and hence diffusion flux, decrease as carriers redistribute

• Charge redistribution causes electric field which also tends to oppose further diffusion of carriers


Charge Distributions for t →∞, Equilibrium• After a long time, charge will

have redistributed so that the forces due to the concentration gradient and the electric field balance

• Forces due to diffusion and electric field are still present, but exactly balance

• If electrons and holes were not charged, this would not occur (no charge separation, no E)

• Note that areas away from metallurgical junction are unaffected

ELEC 3908, Physical Electronics: Diode Operation -8

Diode Regions• Identify two distinct regions in

the pn-junction structure:– The neutral regions are those

which are essentially unaffected by the charge redistribution

– The depletion region is the transition region where charge redistribution has taken place


Forward Bias Injection Components• Forward bias raises potential of

p with respect to n, causes current flow from p to n

• Two current components:– Injection of holes from p to n,

in the direction of current– Injection of electrons from n to

p, in the opposite direction to current

• Note that electrons injected into p, holes injected into n, hence the term minority carrier injection for forward bias


Forward Bias Carrier Density Profiles• In forward bias, injection of carriers raises the value of the carrier

density throughout the device - note linear behaviour in thin p+ region• In the neutral regions, the increase is negligible compared to the

doping level for moderate bias levels• This is therefore a low level injection situation


Current Components in Forward Bias

• Boundary conditions on electron and hole densities are

n x n e p x p ep poqV kT

n noqV kTD D( ) ( )/ /

p-depl edge n-depl edge= =


Components of Ideal Diode Equation

• Develop expressions for minority densities, then use diffusion relationship to derive current components due to electron injection Jn and hole injection Jp as

• Total current is sum of individual components, this is the ideal diode equation (for current density) but illustrating the physical components of the saturation term

( ) ( )JqD n

we J

qD pL

enn po

p

qV kTp

p no

p

qV kTD D= − = −/ /1 1

( )JqD n

wqD p

LeD

n po

p

p no

p

qV kTD= +⎛

⎝⎜⎜

⎞

⎠⎟⎟ −/ 1


Ideal Diode Equation

• Total current is sum of individual components, this is the ideal diode equation (for current density) but illustrating the physical components of the saturation term

( )JqD n

wqD p

LeD

n po

p

p no

p

qV kTD= +⎛

⎝⎜⎜

⎞

⎠⎟⎟ −/ 1


Saturation Current Density

• The physical expression for the saturation current density can be extracted from the previous expression

• This is only valid for a p+n junction, since it contains the width of the p-type material, wp. For an n+p junction with a thin n+-type region (e.g. an n+p implanted junction)

S p n n po p noS p n

D p p

I qD n qD pJ

A w L+

+ = = +

S n p n po p noS n p

D n n

I qD n qD pJ

A L w+

+ = = +


Example 8.1: Saturation Current Density Calculation• Find the saturation current

density for a p+n junction with the 1D doping profile shown to the right. Assume the minority lifetime is 0.5 μsec, use a uniform doping approximation and assume the width of the neutral p+ region is equal to the material width


Example 8.1: Solution• The uniform approximation to

the 1D profile is shown to the right.

• Using the uniform approximation, the doping in the p+ region is 1018 /cm3, and the doping in the n-type region is 8x1015 /cm3.

• The width of the p+ region, from the location of the metallurgical junction on the plot, is 1 μm or 10-4 cm.


Example 8.1: Solution (con’t)

• Using the values extracted from the uniform doping approximation

• This gives a saturation current density of (Lp was calculated last lecture)

JqD n

wqD p

LS p n

n po

p

p no

p+ = +

= ×⋅ ×

+⋅ ××

⎛⎝⎜

⎞⎠⎟

= ×

−− −

−

16 1034 9 21 10

1012 4 2 6 10

2 49 10

327 10

192

4

4

3

11

.. . . .

.

. A / cm2

( ) ( )n ppo no=

×= × =

××

= ×145 10

1021 10

145 108 10

2 6 1010 2

182

10 2

154.

. /.

. /cm cm3 3


Reverse Bias Injection Components• Reverse bias raises potential of

n with respect to p, causes current flow from n to p

• Two current components:– Injection of holes from n to p,

in the direction of current– Injection of electrons from p to

n, in the opposite direction to current

• Note that electrons injected into n, holes injected into p, hence the term majority carrier injection for forward bias


Reverse Bias Carrier Density Profiles• In reverse bias, injection of majority carriers lowers the value of the

minority densities - again note linear behavior in thin p+ region• In the neutral regions, the increase is negligible compared to the

doping level for moderate bias levels• This is therefore again a low level injection situation

pno

npo

NA

ND

n Ni2/ A

n Ni D2/

p(x)n(x)

p+ implant n-type substrate

p (x)n

n (x)p

depletion region carrier densities: equilibrium forward bias

e injectionh injection


Current Components in Reverse Bias

• Because the boundary conditions used in the forward bias case still apply in reverse bias, the previous current expression also still holds

• Note that in reverse bias for VD < -3kT/q the exponential term is negligible compared to 1, and JD ≈ -JS

( )JqD n

wqD p

LeD

n po

p

p no

p

qV kTD= +⎛

⎝⎜⎜

⎞

⎠⎟⎟ −/ 1


Lecture Summary

• pn junction examined in equilibrium, balance between carrier diffusion and opposing electric field

• Neutral region basically unaffected by carrier exchange, depletion region approximated as empty of free carriers

• Injection under bias– Minority injection in forward bias– Majority injection in reverse bias

• Saturation current density JS derived as basic structure dependent parameter in ideal diode equation

• Computation of JS may require extraction of doping using uniform approximation

physical electronics lecture 1, diode operationsmcgarry/elec3908/slides/elec3908...elec 3908,...

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