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

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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)

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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

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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( )

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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

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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

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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

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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

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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

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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= =

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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

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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

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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+

+ = = +

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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

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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.

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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

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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

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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

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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

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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