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PN Junction& Schottky

Diode

Cathode Anode

2

Reverse-Bias PN Junction Charge Density

Electric Field

Potential2lni

DATbi n

NNV=φ

mVqkTVT 26≅=

26≅=qkTVT mV at 300oK

ni is the intrinsic carrier concentration approximates 1.5e-10 cm-3 at 300oKK is Boltzsmann Constant

Reverse-biasis similaras 0 biascondition

Built-In Potential (0 Bias)

3

* Built-In Potential oppose the diffusion of mobile holes and electrons across the junction.

Demand overall charge neutrality.*

ερ

−=∂∂

2

2

xV* Apply Poisson’s equation to solve for V

4

* Maximum field increase as the doping density increase.

* Increase reverse bias voltage will increase maximum field.* Junction breakdowns when bias exceeds VBREAKDOWN voltage

I

VBREAKDOWN

V

$ Higher doing will causehigher or lowerVBREAKDOWN?

5

21

1

)0()(

Φ

−

==

∂∂

=

bi

j

V

VCVQVC

31

1

)0()(

Φ

−

==

∂∂

=

bi

j

V

VCVQVC

Graded doping

Junction Capacitance

for uniform doping in bothp,n region

* Apply

for graded doping in bothp,n region

*

V is the reverse bias voltage

$ Higher doping will causehigher or lowercapacitance?

** C-V for forward bias?C-V curve for uniform doping

6

I-V CharacteristicsForwardBias

Impedance of diode vary with bias point and RF swing level

(Curve of exponential)

7

Forward Bias (used to approximate reverse bias too)

)1( −= nkTqV

S eIIideality factor

reverse saturation current

Boltzmann constant

absolute temperature

bias voltage::::

:

VTkIn

S

CMOS

PN junction is everywhere

8

Review:

•Junction capacitance resulted from reverse bias and vary withvoltage

•Breakdown voltage inversely proportional with doping•Diffusion capacitance resulted from forward bias (hard tomeasure C-V curve, more later)

•One thing not mentioned is the leakage current through the the surrounding edge of diode structure for both forwardand reverse bias. It’s a OMIC phenomena.•Breakdown phenomena is not modeled in:

)1( −= nkTqV

S eII

9

10

VII

KTqN

∂∂

≈

11N

12

Straight linein logarithm scalefor large V

=

SII

qkTV log

For large V

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Series Resistance(parasitic component)

• Accounts forOhmic drop, neglected so far

Current (I) appearsin both side of equations

+=

Ss I

IqkTIRV log

For large V

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SIIlogUse here

+=

Ss I

IqkTIRV log

For large V

SIIlogIf =6, IS=1.6e-6 A, and V=0.71V

then what is the value of Rs at 300oK? 0.346 OHM

15

Fabricate PN junction diode in CMOS

Substrate usually is groundedThis P layer substrate provides isolation

16

CMOS

NPN structure is vertical instead of horizontal(meaning of plug)

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* pn junction is one kind of diode

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In Practical!

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Vj can not change abruptly, need to get rid of minoritycarrier

Current Spike

trr is the time requiredto neutralize minoritycarrier

The mass ofP is more heavierthan N

No trr forschottky diode

Cd(V) then Cj(V)?

Cj(V) then Cd(V)

! Initial large or small Cd(V)?

$ Initial large orsmall Cd(V)?

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---+ ++Forward-bias

P

+

- ----

++

++

P

Reverse-bias

- --

+++

Cd(V)Cj(V)

It takes time

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Majority electron

+

- ----

++

++

+

-Vf Vr

P+

- ----

++

++

P Instant switchedto reverse biasForward bias

Act like voltage source, sothe resultant voltage sorce is Vf+Vr-(If*Rs)Majority electron

Generate current spike

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Switch offTransient

Vr >> VfandRs is very small

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Schottky Diode

• Metal-Semiconductor junction.• Lower forward turn-on voltage.

• Steeper I-V curve• Majority-carrier (Electron) device. Not like p-n diode usingminority-carrier charge-storage effects.

• Higher cutoff frequency, reproducibility and ease of fabrication.• Exitaxial and ion-implantation.• Rectifying or non-rectifying (ohmic-contact)

No minoritycarrier storage!ID

VD

Schottky

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Gx : Gx1 // Gx2

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I-V characteristics

• Based on •

)1( −= nkTqV

S eII

::

::::

:

S

x

S

IRVG

VTkIn ideality factor

reverse saturation current

Boltzmann constant

absolute temperature

bias voltage

edge leakage current

voltage drop due to ohmic contact and bulk resistance of semiconductor channel. (ohmic contact is a metal-semiconductor contact that has a linear I-V and non-rectifying characteristics. )

VGeII xnkT

RIVq

SD

sD

+−=

−

)1()(

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C-V characteristics

• Semi-empirical equation•

• approximated by•

:

:

::

0

C

j

j

F

C

Vm

C

n

j

jD

VVC

VC)1(

)( 0

−=

VIG D

D ∂∂

=

grating coefficient

built-in potential of the barrier height of junction

zero-bias junction capacitance.

depletion capacitance coefficient.

m

j

j

VVC

)1(0

−=)(VCD

))1(1()1( 1

0

jCm

j

j

VmvmF

VVC

++−− +

for

for

jCVFV <

jCVFV >

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Diode modeling

• DC I-V measurement

• When IDRs << Bias voltage and ignore Is and GxV as compared with

Total diode current ID approximated by

nkTSeIqV

nkTqV

SD eII =

)log()log()log( nkTqV

SD eII += )log()log( SIenkTqV

+=

VIkTeqn∆∆

=/)log(/)log(

By taking the derivation with respect to V

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• Is can be calculated from the curve.• knowing n and Is. Gx can be found by curve fitting at low current region• At high current region, ignore GxV and Is as compared with

−

nkTRIVq

S

SD

eI)(

−

= nkTRIVq

SD

SD

eII)(

)log()()log()log( enkTRIVqII SD

SD−+=

)log()()log( enkTVVqIS

∆−+=

SDRIV =∆

For Rs is a weak function of bias voltage V and increase with it

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Small signal model

or simplified as

• measure S-parameter at particular bias voltage and curve fitting.• measure S-parameter at various bias V and curve fitting to findC-V relation data. One can use the C-V data and curve fitting to find C-V semi-empirical equation.

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Large Signal Model

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• : cutoff frequency

(bias and RF power dependent)

• Noise: shot noise and thermal noise are two major source

Shot noise (mean square value)

Thermal noise (mean square value)

: bandwidth q : charge of electronn : ideality factorT : absolute temperatureK : Boltzmann constant

• these two noise sources are statistically uncorrelated.

Tf

DsT CRf

π21

=

fIInqi sDs ∆+=>< )2(22

2>< si

2>< Tif

RkTis

T ∆=><42

f∆

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In addition Flicker noise

• A random fashion of generation-recombination effect in the depletion layer.

• Energy concentrated at low frequency.

• ID : the diode current.f : center frequency

: bandwidth, a, b : constant

(device dependent, a in the range of 0.5-2, and b is close to 1)

• flicker noise is in the shunt with shot noise, and is uncorrelated to thermal noise.

2>< fi

ffIki b

aD

ff ∆=>< 2

f∆fk

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Noise model

• model parameters can be estimated from the measurementof the diode noise.

cathode anode

Cp2

Lp2

Rs

CD

ID

2>< fi

2>< siCp1

2>< Ti

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Schottky diode as level shift

ID

V

ID

SffDropD

S

Df

fSD

RIVVII

qKTV

KTqV

II

+=

=

−≅

,

)ln(

)1(exp

• Both Vf and Rs are function of temperature but temperature coefficientof Vf dominates.

• Temperature coefficient of VD drop typically ranges from -1 to –2 mV/oC• Low diode forward current have temperature coefficient close to –2 mV/oC• High diode forward current have temperature coefficient close to –1 mV/oC

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Diode• multiplier• Detector• Mixer• Varactor• Switch• Limiter• Level-Shifting Device

Cathode Anode

Small signal model