ECE606: Solid State Devices Lecture 17 Schottky Diode

ECE606: Solid State Devices Lecture 17

Schottky Diode

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 1

Presentation Outline

1) Importance of metal-semiconductor junctions 2) Equilibrium band-diagrams 3) DC Thermionic current (simple derivation) 4) Intermediate Summary 5) DC Thermionic current (detailed derivation) 6) AC small signal and large-signal response 7) Additional information 8) Conclusions

Reference : Semiconductor Device Fundamentals, Chapter 14, p. 477

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 2 Metal-semiconductor Diode

Symbols

M N

Metal Wire N

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 3

Applications of M-S Diode …. STM (scanning tunneling microscope) Detectors on semiconductor

CNT (carbon nanotube) www.fz-juelich.de/ibn/index.php?index=674 Original Bipolar Transistors

Originally, Gelena (PbS), Si as semiconductor and Phospor Bronze for metal (cat ’s whisker) Klimeck – ECE606 Fall 2012 – notes adopted from Alam 4 Presentation Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 5

Topic Map

Equilibrium DC Small Large Circuits signal Signal Diode

Schottky

BJT/HBT

MOS

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 6 Drawing Band Diagram in Equilibrium…

∇•= −++ − − D qpnN( D N A ) Equilibrium ∂n 1 = ∇•J −r + g ∂t q N N N =µ E + ∇ J Nqn N qD N n DC dn/dt=0 Small signal dn/dt ~ jωtn ∂p 1 =− ∇•J −r + g Transient --- full sol. ∂t q P P P =µ E − ∇ J Pqp P qD P p

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 7

Band-Diagram

1. E F flat in equilibrium

2. E C/E V in Metal 3. Vacuum level in Metal N D 4. Ec/Ev in semiconductor 5. Vacuum level in semiconductor 6. Connect vacuum levels Vacuum level Φ 7. duplicate the connections M χ down to Ec/Ev

EC EF Since N A is large, xp is negligible .. EV = NxAp Nx Dn Charge(metal) = charge(semiconductor)

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 8 Built-in Potential: bc @Infinity

neglect

qV bi Φ M χ Φ B ∆

∆ + χ + = Φ =(Φ−χ ) − ∆ ≡ Φ − ∆ qV bi M qV bi M B

N non- =Φ − k T ln D B B degenerate NC

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 9

Analytical Solution (Simple Approach )

Depletion Approximation E ρ

qN D integrate Actual Xn x x Xn Q qN x E =D = − D n max ε ε QD = Area negligible Ks0 K s 0 QM =-QD NDXn integrate φ

φB q Φ =qV E max bi C x Xn

EV E x φ = − max n x max Xn 2 Notice how we neglect xp here, is Klimeck – ECE606 Fall 2012 – notes adopted from Alam there a proof? 10 Complete Analytical Solution

+ qN x E ()0 = D n ε Charg ks 0 e − qN M xp + x E ()0 = ? n ε - ks 0 Position x = p ⇒ ND xn NM xp E-field

− + Position E(0) x E ( 0 ) x qV =n + p bi 2 2 Potentia 2 l qN x 2 qN x =D n + M p ε ε 2ks0 2 k s 0 Position

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 11

Depletion Regions

xp xn

ε ε = 2ks 0 NM 2 k s 0 1 NDxn N M xp x =V → V n ()+ bi bi qNNNDMD qN D ∞ 2 2 NM qN x qN M xp qV =D n + 2k ε N bi 2k ε 2 k ε x =s0 D V → 0 s 0s 0 p ()+ bi q NMN M N D

This is why we can neglect xp

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 12 Presentation Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 13

Topic Map

Equilibrium DC Small Large Circuits signal Signal Diode

Schottky

BJT/HBT

MOS

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 14 Band Diagram with Applied Bias…

∇•= −++ − − D qpnN( D N A ) Band diagram … ∂n 1 = ∇•J −r + g This works for doping-modulated ∂t q N N N Semiconductors. J =qnµ E + qD ∇ n N N N Does not work for heterostructures ∂p 1 (when the conduction band is not =− ∇•J −r + g ∂t q P P P continuous) =µ E − ∇ J Pqp P qD P p Metal-Semiconductor is a HS

Need theory of thermionic

Klimeck – ECE606 Fall 2012 – notes adopted from Alam emission 15

Depletion Regions with Bias

xp xn

2kε N 2 k ε 1 x=s0 M V → s 0 () VV − n ()+ bi bi A qNNNDMD qN D

Forward bias: x decrease 2kε N n x=s0 D V → 0 Reverse bias: x increase p ()+ bi n q NM N M N D

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 16 Band-diagram with Bias

Forward Bias

qV bi -V EC-EF VA

qV bi

EC-EF

Reverse Bias

EC-EF

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 17

I-V Characteristics

N-type Forward Bias VA Metal Ec I Semi. EF EF M ESF 1,2,3 EV 4 – generation current I 5 – impact ionization

Reverse Bias 6,7 EF M 4 1 – diffusion control 5 Ec 2 – ambipolar EF 3 – resistance drop ESF 6 – defects – trap assist 7 – Esaki EV

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 18 Current Flow Concept

Barrier Barrier smaller Partition problem in The same! M<=S increased M=>S current qV -V 2 currents bi A E -E Φ C F unchanged! B M=>S S<=M VA Forward Bias

qV Φ bi B Barrier EC-EF The same! Barrier bigger M=>S current M<=S decreased Φ unchanged! B q(V bi +V A)

In Equilibrium: M=>S current EC-EF and Independent Reverse Bias are equal of bias!

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 19

Left Boundary Condition

We use thermionic emission q(V bi -VA) because: EC 1. EC is not continuous here V 2. There’s no minority carriers! A

J( V ===0) 0 J (0) − J (0) T A m→s s→ m (detailed balance) = ⇒ Jm→ s (0) J s→ m (0) J (V ) =J( V ) − J( V ) T A m→ s A s→ m A M=>S current = − independent of bias Jm→s (0) J s→ m(V A ) = − JVTA() J sm→ (0) JV smA → ()

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 20 Semiconductor to Metal Flux

V n −q bi = −s kT υ = J s→ m (0) q e th Jm→ s (0) J → (0) = m s 2 V− V Φ −q bi A q B n n − s kT m kT J→ ( V ) = − q e υ J → (V ) = − q e υ s m A th m s A 2 th M 2 n υ − qV bi qV A Only the ones = −s th kT × kT Only half of above the q e e them goes to 2 barrier goes to qVA the right the right = kT J s→ m (0) e qVA q(Vbi -VA) = kT Jm→ s (0) e VA EC-EF Φ n υ − qB qV A = − qm th M ekT e kT 2 −q Φ Φ qV qn υ mB A  =− =m th M kT kT − JT J s→m(0)J s → m ( V A ) e e 1  Klimeck – ECE606 Fall 2012 – notes adopted from Alam 2   21

Diffusion vs. Thermionic Emission

∆n

Fn Fp Check that both gives the same result for a diode…

Thermionic Emission theory is a more general approach, can be used for device so small that no scattering F n occur (can’t use diffusion!). Fp

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 22 Intermediate Summary

Schottky barrier diode is a majority carrier device of great historical importance.

There are similarities and differences with p-n junction diode: for electrostatics, it behaves like a one-sided diode, but current, the drift-diffusion approach requires modification.

The trap-assisted current, avalanche breakdown, Zener tunneling all could be calculated in a manner very similar to junction diode.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 23

Presentation Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 24 Energy Resolved Thermionic Flux 1 Energy < m*υ 2 Occupation 2 min ~ DOS (non-denegerate) will be bounced back −υ ∞ ∞ min Ω −() − β J= − qdk dkedk E E F υ s→m ∫ ∫ ∫ π 3 xy z x −∞ −∞ −∞ 4

Only movement in the υ x direction will contribute min to the current flux

q(Vbi -VA)

EC-EF x

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 25

Thermionic Flux from Semi to Metal .. E ∞ ∞ −υ min E Ω −()− β C E E F E J= − q dk dk dk e υ F sm→ ∫ ∫ ∫ π 3 xyz x −∞ −∞ −∞ 4

1 1 1 E− E =()EE− + ()EE−= mmm*2υ + *2 υ+ *2 υ + () EE − F CCF 2 xyz 2 2 C F

∞ ∞ −υ ** * (mυ 2+ mυ 2+ m υ 2 ) min υ υ υ − x y z β −()− β Ω dm( x) dm( y) dm( z ) = qe Ec E F e 2 υ ∫ ∫ ∫ π 3 x −∞ −∞ −∞ 4 ℏ ℏ ℏ

3m *υ 2   υ 2  υ 2  * ∞−y  β   ∞ − m* z β  −υ − m* x β  qΩ() m    min    −()E − E β 2  2 2 J= ec F ededυ υ   de υ υ  s→ m π 3ℏ 3 ∫y  ∫ z ∫ x x 4 −∞ −∞   −∞       

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 26 Thermionic Current … 2q υ =()V − V min m* bi A

3m *υ 2  υ2  υ2  * ∞−y  β   ∞ − m* z β  −υ − m* x β  qΩ() m    min    −()E− E β 2  2 2 J= ec F ededυ υ   de υυ  s→ m π 3 3 ∫y  ∫ z ∫ x x 4 ℏ −∞− ∞   −∞       

1 − − β π π e q(Vbi V A ) 2

* 2 π ()− − β β β 4 qm k 2 EF E C qV bi qVAq V A J→ = Te eAe = s m h3 0

β =−=qVA − JJT sm→ J ms → Ae0 ( 1)

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 27

Some insight of the Thermionic Current …

Compare to the current of p-n diodes… β =−=qVA − JJT sm→ J ms → Ae0 ( 1) Schottky diode

2 2  D n Dp n β =−n i +i qV A − JT q  () e 1 p-n diode Wp N A Wn N D 

Both of them depends exponentially on V A, however current of p-n diodes depends more on temperature (since ni depends strongly on Eg), where the Schottky diode doesn’t have that dependence.

However, Eg hides in… * 2 π ()− − β β β 4 qm k 2 EF E C qV bi qVAq V A J→ = Te eAe = s m h3 0 The information of material hides in m*

The information of doping concentration hides in E F-EC

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 28 Recombination/Generation/Impact-ionization

EF M Ec EF EF M ESF EV

SAME technique as in p-n junction except integrate to xp only Klimeck – ECE606 Fall 2012 – notes adopted from Alam 29

Presentation Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 30 Topic Map

Equilibrium DC Small Large Circuits signal Signal Diode

Schottky

BJT/HBT

MOS

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 31

AC response

Conductance Junction Capacitance

Series Resistanc Diffusion e Capacitance

We will not have Diffusion Capacitance here…

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 32 Forward Bias Conductance

m depends on which operation regime you are gFB ()− β =qVA RI S / m − I Io ( e 1) RS

I+ I o = − β lnqV (A RI S ) / m I0

m dV =A − R 1 = + m β ()+ S RS q I Io dI β + gFB qII(0 )

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 33

Junction Capacitance (Majority Carriers)

Junction Capacitance

κ ε A C = s 0 J W κ ε A C = s 0 J 2κ ε s 0 (V− V ) qN bi A Response time – dielectric D Very fast propagation Klimeck – ECE606 Fall 2012 – notes adopted from Alam 34 No Diffusion Capacitance in Schottky Diode

p-n Diode Schottky diode

When electrons reach the metal side, they n quickly scatter and join the majority carriers there. Nothing is diffusing…

No minority carrier transport and therefore no diffusion capacitance ..

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 35

Reducing diffusion capacitance in p-n diode

p-n Diode Schottky diode n

Provide lots of VA traps

Short minority carrier lifetime in p-n junction diode equivalent to rapid energy relaxation in SB diode. Klimeck – ECE606 Fall 2012 – notes adopted from Alam 36 Presentation Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 37

Ohmic Contact vs. Schottky contacts ..

What if we just want the p-n junction? How to Metal Oxide reduce the barrier of For majority carriers: Metal-Semiconductor? there’s not barrier For minority carriers: n+ high doping allows them to tunnel through n-Si Metal will just act like Ohmic Contact

Low Doping Moderate High Doping Doping

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 38 Lowering of Schottky Barrier

E The fields on the metal must be qφB qφ1 qφB qφ1 perpendicular (otherwise there will be tangential current flow which is impossible) Metal Semi Metal Semi as if there’s an image charge - - (positive) in the - Image metal, results in - Electron - Charge Surface- lowering the - Charge - barrier height x x

Klimeck – ECE606 Fall 2012 – notes adopted from Alam Ref. Sze/Ng., p. 143 39

Fermi-level Pinning

Density of States Why sometimes we don’t get conductance at all? E surface states bends E /E so Ec C V Full f that the Fermi level is at the Ev Full center of the bandgap, they exchange carriers with metals, MetalSemiconduct Metal blocking the bulk or semiconductor inside no modulation in potential Shift in the barrier even you connected to Band different metals. E edge c E Regardless the workfunction , no f Full Full modulation in potential. Ev (e.g. Modern high-k dielectrics) Metal Metal AB

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 40 Conclusion

1) Schottky diodes have wide range of applications in practical devices. 2) The key distinguishing feature of Schottky diode is that it is a majority carrier device. 3) We use a different technique to calculate the current in a majority carrier device. => thermionic emission. 4) Elimination of diffusion capacitance make the response of the diodes very fast.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 41