METAL SEMI-CONDUCTOR CONTACT

Schottky diodes Ohmic contacts

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Philippe LORENZINIPolytech-Nice Sophia

Plan:

• Two types of contact:• Contact between Metal and heavily doped semiconductors:

• Interconnections• Ohmic Contacts

• Contact between Metal and ligthly doped semiconductors:• Schottky diode

• Comparison between Schottky and PN junction

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interconnections

• Nowadays , in ULSI IC, 6 to 8 metal levels (=> 10)

• Problems / Issues :• delays• heating• Compatibility/ diffusion

with devices

• Copper technology used for interconnections

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Interconnections / Insulating layers

• Low dielectric materials« low k »

• Low resistivity materials: « Copper » solution

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dSC

SlR

RC

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Stack of metal layers

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inte

l

Schottky Diode• Two definitions (only 2!)

• Work Function (Travail de sortie) : this is the energy we have to give to an electron to extract it of metal without kinetic energy. It reaches the "vacuum level". Work function is the energy difference between the vacuum level and the highest occupied energy level, ie the Fermi level.

• Electron Affinity (Affinité électronique ) : it’s the difference between the vacuum level and the bottom of the conduction band. It’s only defined for SC and not for Metal.

• Unity : eV (electron volt)

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Me

SCe

Schottky Diode

• Contact Formation :• We assume• Onset of an energy barrier for

electrons in the metal :

• Onset of an energy barrier for electrons in the SC :

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SCM ee

SCMb eee

bi bi d M SC MSeV e eV e e e

No bias !!Fermi level is flat, aligned !!

Ohmic contact or diode ?

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N type Semi‐conductor

sm ee sm ee

« ohmic » « rectifier »

10sm ee sm ee

Ohmic contact or diode ?

« ohmic » « rectifier »P type Semi‐conductor

• At the real metal - SC interface, large numberof interface states in the bandgap region the previous simplist model has to beimproved

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Ohmic contact or diode ?

Non ideal Schottky Diode: interface states

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SCMb eee

MSSCMdbi eeeeVeV

cteeEe gb 0

Ohmic Contacts

• The end of interconnections on the devices.• Ohmic contact:

• No drop voltage (short circuit?)• No resistance to current flow

• how ?• 1st method : chose the metal with appropriate work function

(see above), but not always possible ( and problem withinterface states)

• 2nd method : use heavily doped semiconductors

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• Ohmic contact • Very high doping to the

interface region• Depletion layer will be

extremely narrow, thin• Electrons tunneling

allowed

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Ohmic Contacts

*4   exp ( ) / ( )c b sc eR m eNdh

Voltage - Capacitance characteristic C(V).

• We get the same results as with the PN Junction:

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SC

xdx

xVd )()(

2

2

)()( WxeN

xESC

d

)2

()(2

WxxeNxVSC

d

d

biSC

eNVV

W)(2

WA

VVNe

AdVdQAC SC

bi

dSC

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)(2

Current in the Schottky diode :I(V)

• Several mechanisms are responsible of current:• Thermionic emission• Tunnel flowing

• The main difference withPN junction:• Current only due to majoritary

carriers !!

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Thermionic current: the electrons which can overcome the barrier e(Vbi‐V) will contribute to the current:

kTVVe

nn bib)(

exp0 avec

kTEENn FCC exp0

or:

kTVe

NkT

VVEENn bC

biFCCb

)(expexp

Current in the Schottky diode :I(V)

• We can show (Singh) that the average flux of electronsimpinging the Metal/SC barrier is where isthe average speed of the electrons.

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4bnv v

The corresponding current is then given by (A is thedevice area) :

kTVe

NAveVI bCSM)(

exp4

)(

kTeNAveII bCSMMS

)(exp4

)0(

When the applied voltage is zero, the current is null. Infact the current IMS flowing from metal to SC is balancedby the current ISM from SC to Metal.

Current in the Schottky diode :I(V)

• When a potential V is applied, IMS = cte = IS and the current is given by:

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1expkTeVIIII SMSSM

The above expression can be rewritten (MB statistics):

1expexp

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32

2*

kTeV

kTe

TekmAI b

constant  of Richardson

Current in the Schottky diode :I(V)

Small signal equivalent circuit

• Equivalent circuit components:• Differential resistance

• Differential capacitance of depletion layer

• Serie resistance

• Parasitic Inductance

• Device geometric capacitance (L: device length)

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dIdVRd

21

)(2

VV

eNAC

bi

SCdd

RNcontactsS RRR

SL

LA

C SCgéom

Cs

C - V Data

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2( )sc d SC

ddep bi

A eNC AW V V

2

1 2( )²

bi

d D SC

V VC eN A

Vbi-V

By determining Vbi and Nd (slope), we can get b (if SC is unknown)

Wdep

Comparison PN vs Schottky (from Singh)22

PN Diode Schottky Diode

Reverse current due to minoritycarriers diffusion => strongtemperature dependance

Forward current due to Minoritary carriers from n andp regions

Forward bias ( the « on voltage ») needed to make the device on isquite large

Switching controlled by eliminationof minority injected carriers

Forward current due to majoritary carriers from the SC

The « on voltage » is small

Switching speed controlled by thermalisationof electrons across the barrier : few ps

Reverse current due to minority carriers diffusion => strong temperaturedependance

Ideality factor between 1 and 2 due to recombination process in depletion layer

Essentially no recombination in depletionregion => Ideality factor ~ 1

heterojunction• Contact between two different semiconductor materials

different gaps energy bands discontinuity at interface.

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)( pnC eE

gVC EEE

Junction formation SC(n)/SC(P)24

Mise à l’équilibre SC(n)/Sc(N)

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Junction formation SC(n)/SC(N)

Occurrence of a two-dimensional electron gas

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