Lect05 Diode

8/10/2019 Lect05 Diode

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Advanced VLSI Design CMPE 640Diode Details

Physical Representation

Abrupt junction betweenpand nmaterials creates a concentration gradient among the car-

riers.

Electrons diffusefrom ntopwhile holes diffuse frompto n.

The diffusion leaves behind bound chargein the lattice.

The bound charge sets up an electric field that counteracts the diffusion.

Electrons driftfrompto nwhile holes drift from ntop.

p

n

SiO2acceptor (boron) holes

donor (phosphorus) electrons


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Charge Distribution, Electric Field and Electrostatic Potential

- --

- -

+ ++

+ +

Hole diffusionElectron diffusion

Electron drift

Hole drift

p n

NA>ND

pregion more heavily

doped,

Charge Density

-

+

Electric Field

Potential0

neutral regionneutral regionplateplate

Distance

Distance

Distance


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Built-In Potential and I-V Characteristics

Build-in potential:

For example:

Forward bias

Raising potential of thep w.r.t ncauses current to flow frompto n.

Lowers potential barrier and diffusiondominates drift.

Minority carriers injected into neutral region and diffuse toward plates.

Recombine with majority carrier causing a net flow of current.

0

T

lnN

AN

D

n

i

2-----------------= where T

kT

q-------= = 26mV at 300K (Thermal V)

ni 1.5

10

10 carriers/cm3

=

N

A10

15carriers/cm

3=

0 2610

1510

16

2.2520

10--------------------------ln 638mV= =

ND

1016

carriers/cm3

=


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I-V Characteristics

Reverse bias

Raising potential of the nw.r.tpcauses current to flow from ntop.

Driftdominates diffusion.

However, current is small since the number of minority carriers (e.g., electrons inp

neutral region) is small.

For forward bias, the current is exponentiallyrelated to applied bias.

Current increases by a factor of 10 for every 60mV (2.3fT) of forward bias.

10

-15

10-10

10-510

0

0.0

ID(A)

0.2 0.4 0.6 0.8

2.3TV/decade

VD

0.5

1.0

1.5

0.5 1.0

VD

ID(mA)

Log scaleLinear scale

Small deviation

due to recombinationin depletion region.


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Static Behavior

Reverse BiasIdeal diode equation predicts diode current approaches the saturation current as VD

gets much smallerthan the thermal voltage.

Concentration of minority carriers at depletion-region approaches 0 under sufficient

reverse bias.

VD

T

>forID IS

Metalcontacttopregio

n

Metalcontacttonregion

-Wp p-region -W1 0 W2 n-region Wn x

np(x)

pn(x)

pn0

np0

Minority carrier concentration


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Static Behavior

Simple models of the diode.Left model based on ideal diode but is strongly non-linear and approximated by a sim-

ple model on the right.

Example: Assume VS= 3V and RS= 10kW and IS= 0.5X10-16.

+

-

VD

ID IS e

VD

T

1

=+

-

ID

VDonVD

+

-

Ideal diode model For a fully conducting diode, voltage drop

First order approx.

across diode is ~0.7V

+

-

VSRS VD

ID

Assuming VD=0.7V yields ID=0.23mA

Using non-linear model yields:

VD=0.757V and ID=0.224mA


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Dynamic Behavior

Dynamic behavior determines the maximum operational frequency.

It is dependent on how fast charge can be moved around.

Two capacitances

Depletionand diffusion.

Depletionregion andJunctioncapacitance:

Under the ideal model, the depletion region is void of mobile carriers.

Its charge is determined by the immobile donor and acceptor ions.

Intuitively:

Forward bias: Potential barrier is reduced which means that lessspace chargeis

needed to produce the potential difference.

This corresponds to a reduceddepletion-region width.

Reverse bias: Potential barrier increased, increase in space charge, widerdepletion

width.


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Dynamic Behavior

Expressions that convey this fact.Depletion region charge(VDis positive for forward bias):

Depletion-region width:

Maximum electric field:

The ratio of the n-side versus p-side depletion region width is determined by the dopinglevel ratios:

Qj

AD

2si

qN

AN

D

NA

ND

+-----------------------

0

VD

( )= (1)

Wj

W2

W1

2si

q----------

NA

ND

+

NA

ND

-----------------------

0

V D( )= =(2)

Ej

2q

si

-------

NA

ND

NA

ND

+-----------------------

0

VD

( )=where

si 11.7 1.05312

10 F/cm=

W2

W 1

-----------------

NA

ND

--------=


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Dynamic Behavior

The model (for an abrupt junction):

Imagine the depletion region as the dielectricof a capacitor with dielectric constant of

silicon.

And the n- and p-neutral regions act as the capacitor plates:

A small change in the voltage applied to the junction (dVD) causes a change in the spacecharge (dQj).

- --

- -

+ ++

+ +

p n

neutral regionneutral regionplateplate

Forward bias, cap increases

Reverse bias, cap decreases

insulator


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Dynamic Behavior

Depletionlayer capacitance:

Junction capacitance is easily computed by taking the derivative of equation (1) with

respect to VD. For an abrupt junction:

Cj0is the capacitance underzero-biasconditions and is only a function of the physical

parametersof the device:

The same result can be obtained using the standard parallel-plate capacitor equation:

Cj

dQj

dVD

----------- AD

si

q

2----------

NA

ND

NA

ND

+----------------------- 0 V D( ) 1

Cj0

1 VD

0

--------------------------------= = =

Cj0

AD

si

q

2----------

NA

ND

NA

ND

+-----------------------

01

=

Cj

si

AD

Wj

--------

= where Wjis given by equation (2).


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Dynamic Behavior

Junctioncapacitance plotted as a function of applied voltage bias:

Capacitance decreases with an increasingreverse bias.

For -5V, the cap. is reduced by more than a factor of 2 over the zero bias case.:

0.0

0.5

1.0

1.5

2.0

Cj(fF)/um

2

-4.0 -2.0 0.0VD

Strongly non-linearAbrupt junctionm = 0.5

Linear junctionm = 0.33

Cj0

Cj0

23

10 F/m2=

0

0.64V=

AD

0.5um2

= then a reverse bias of -2.5V yields

0.9fF um2

0.5um

2 0.45fF=


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Dynamic Behavior

For the general case:

Where mis the grading coefficient.

For an abrupt junction, m = 1/2.

For a linearly graded junction, m = 1/3 (see previous figure).

For digital circuits, operating voltages tend to move rapidly over wide ranges.

In these cases, we can replace the voltage-dependent, nonlinear capacitance Cj with anequivalent, linear capacitanceCeq.

Cj

Cj0

1 VD

0

( )m

-------------------------------------=

Ceq

Qj

VD

------------

Qj

Vhigh

( ) Qj

Vlow

( )

V

high

V

low

---------------------------------------------------------- Keq

Cj0

= = =

Keq

0m

Vhigh

V low( ) 1 m( )---------------------------------------------------------------

0V high( )

1 m

0V low( )

1 m=


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Dynamic Behavior

For example:

Cj0

0.5fF um2

=

0 0.64V=

AD

12um2

=

Compute the average junction capacitance if

this diode is switched between 0 and -5V.

Keq

0.64 0.5

0 5 V( ) 1 0.5( )---------------------------------------------------- 0.64 0( )

1 0.50.64 5( )( )

1 0.50.502= =

m 0.5=

AverageCj

0.502 0.5fF/ um2

0.25fF

um2-----------= =


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Secondary Effects

Actual diode current is less than what is predicted by the ideal eq.

Not all of the applied bias voltage falls across the junction, some falls across the neu-

tral regions.

However, the resistivity of the neutral regions is generally small (1 to 100 Ohms).This is usually modeled with a series resistance at the contacts.

Avalanche breakdown(MOS and bipolar processes):

ID(A)

0.1

-0.1-25 -15 -5 0 5

VD(V)

Breakdownvoltage

Increased reverse bias increases electric field across

the junction to Ecrit.

Electron-hole pairs are created on collision with

immobile silicon atoms.

Non-destructive but increases power consumption


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Secondary Effects

Operating temperature effects

The thermal voltageis linearly dependent upon temperature (increasing fTcauses the

current to drop).

The thermal equilibrium carrier concentrations increasewith increasing temperaturecausing ISto increase.

Experimentally, the reverse current doubles every 8 degrees C.

These have a dramatic effect on the operation of the circuit.Current levels can increase substantially (~2X every 12 degrees C).

The increase in leakage current through reverse-biased diodes decreases isolation qual-

ity.

ID

IS

eVD

T

1

=TkT

q-------=


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SPICE Models

The preceding discussion presented a model for manual analysis.

If second-order effects or more accuracy (better model) is desired, simulation is required.

The standard SPICE model:

RSmodels the series resistanceof the neutral regions (reducing current).

RS

CDVD

+

-

ID

IS

eVD

nT

1

=

ID

Extra parameter n is called the emission coefficient

It is equal to 1 for most diodes.


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SPICE Models

The dynamic behavior is modeled by thenonlinear

capacitance CD.Two different charge storage effects are combined in the diode:

excess minority carrier charge(not discussed, forward bias only)

depletion-region charge

Table 1: First-order SPICE diode model parameters

Parameter name Symbol SPICE Name Units Default Value

Saturation Current IS IS A 1.0E-14

Emission Coefficient n N - 1

Series Resistance RS RS 0

Transit Time T TT s 0Zero-bias Junction Cap Cj0 CJ0 F 0

Grading Coefficient m M - 0.5

Junction Potential 0 VJ V 1

CD

T

I

sT

-----------e

VD n

T

Cj0

1 VD

0

( )m---------------------------------------+= T transit time=where:

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Lect05 Diode