Chapter 2 1

Three MITs of the Day

• Band diagrams for ohmic and rectifying Schottky contacts• Similarity to and difference from bipolar junctions on

electrostatic and IV characteristics.• Surface Fermi level pinning

Reading assignment: Sections 2.4 of Taur & Ning

Schottky Diodes (M-S Contacts)

Chapter 2 2

• Ideal MS contacts:– Intimate contacts (no hole or bubble)– No intermixing/diffusion– No surface charge/traps

• If we keep on increasing the p doping of a p+-n diode, the p side will go through Mott transition around 1021cm-3 and can be regarded as a M-S contact

• Work function of metal: energy necessary for electrons to be free electrons in vacuum.

• Metals can be viewed with negative or negligible bandgap(many silicides are metals electrically)

qVbi

EV

E0

EFM

x=Wx=0

EFn

ΦM

ΦB

ΦSχ

EV

E0

EFM

x=0

EFn

ΦM ΦSχ

(1) n-type Si, ΦM >ΦS , Rectifying

(2) n-type Si, ΦM <ΦS, Ohmic

E0

E0

Band Diagrams

Chapter 2 3

Steady-state IV of a Schottky diode• N-type semiconductors

– ΦM > ΦS: retifying– qVbi= ΦM - ΦS= ΦB - (EC-EF)FB

– ΦM < ΦS: Ohmic

• P-type semiconductors– ΦM < ΦS: retifying– ΦM > ΦS: Ohmic

q(Vbi-VA)

EV

E0

EFM

x=Wx=0

EFn

ΦM

ΦB

ΦSχ

(1) n-type Si, ΦM >ΦS , Rectifying

E0IM→SIS→M

• What is different from the bipolar diodes?

• IV are dominated by carriers having enough kinetic energy to ballistically pass the potential barrier (thermionic emission)

• IM→S remains almost constant for changing VA, since the metal electrons look at the same barrier

• Is→M will change exponentially with VA (with η=1) since the semiconductor electrons look at a barrier height lowered by VA

Chapter 2 4

constant IM→Svanishing IS→M

Retifying Schottky contactI=IM→S+IS→M

constant IM→Sexponential IS→M

VA large IM→S

I=IM→S+IS→M

large IS→M

VA

Ohmic Schottky contact

Electrostatic analysis is expected to be identical to bipolar diodes: the charge in the depletion region will support (Vbi-VA) by Poisson Eq.

( )

( )2/1

0

0

2

0

elsewhere00

⎥⎦

⎤⎢⎣

⎡−=

≤≤−−=

≤≤=

AbiD

si

si

D

D

VVqN

W

WxxWqNF

WxqN

εε

εε

ρ

Electrostatics in Schottky Contacts

• The currents are dominated by carriers having enough kinetic energy to overcome the potential barrier (thermionic emission, with correction later)

• The minority diffusion/recombination exists, but usually not important due to the lower barrier height.

Chapter 2 5

Thermionic Emission Over the Potential Barrier( )

( )

220

**

//2

2//)(3

2*

2/1

*min

2*

120

)(

)(surefor

4)(

2

21..

min

2*

KcmA

mm

eeTA

dvvvnqAI

ndvvn

eeh

kTmvn

VVm

qvvor

VVqvmEK

n

kTqVkT

v

xxxMS

xx

kTvmkTEEnx

Abin

x

Abixn

AB

xnCF

≅ℜℜ=ℜ

ℜ=

−=

=

=

⎥⎦

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⎡−=≥

−≥≅

−

−

∞−→

∞

∞−

−−

∫∫

φ

π

*

Richarson’s constant in vacuum tube theory!!

( )kT

S

kTqVSMSSM

kTAMSSM

B

A

B

eTAI

eIIIIeTA

VII

/2

/

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→→

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ℜ−=

==

*

*

• No ND dependence except from ΦB

• Have different temperature dependence from bipolar diodes

• No recombination, high-level injection, ideality factor close to 1 for all forward-bias regions

• Generally called thermionic emission current through this derivation

Chapter 2 6

• The reverse current never saturates to IM→S though as predicted in the ideal IV, since ΦB needs to be corrected in the reverse bias due to tunneling and image charge in the metal.– barrier lowering due to tunneling: also called

thermionic field emission– barrier lowering due to image charge: also called

image lowering• The tunneling current through the thin Schottky

barrier is actually VERY important, since many M-S contacts contain A LOT of surface traps that pin the Fermi level at the mid-gap, which results in retifyingcontacts regardless (we need Ohmic contacts for transistors though).

• The key is to dope the semiconductor heavily so that the barrier is thin, thin enough that tunneling can dominate to give Ohmic contacts.

EFMΦB

Effective ΦB due to barrier lowering

VA

I

EF

EC

EV

ET

surface fermi-level pinning

0/ 4 siqFϕ πε εΔ =

3/2Fαφ =Δ

Barrier Lowering in Schottky Contacts

Chapter 2 7

Image Force Lowering

0

0

/ 4B si

B B B

qFφ πε εφ φ φΔ =

= − Δ

2

016q

xπε−

∝

Chapter 2 8

• From the Poisson equation, a discontinuous potential requires a 2D charge dipole, which is the case here. The 2D charge dipole is formed by the interface trap charge and the image charge in the metal..

Band Diagram in Surface Fermi Level Pinning

EC

EV

EF

Ei

E0Independent of ΦM and ΦS, whenever Fermi level is pinned at the midgap, then there is always a half-bandgap barrier for the majority carrier.

Chapter 2 9

Surface Fermi Level Pinning

Chapter 2 10

• The small-signal behavior of Schottky diodes is similar to the bipolar diode case (required by electrostatics)

• The transient response of the Schottky diodes is much faster than the bipolar diode case, since the minority carrier does not “participate in” (they surely exist, but usually very small) and there is no hold time for diode to go from ON to OFF.

• The bipolar current (diffusion) and the Schottky current (thermionic emission with correction) can actually be unified in one expression, but the algebra is too complex, and the interested reader should visit S. M. Sze’s Physics of Semiconductor Devices (Wiley 1981), presented under the thermionic diffusion theory.

Schottky Diodes vs. Bipolar Diodes

Chapter 2 11

Schottky Barrier Heights for Electrons and HolesMetal Mg Ti Cr Ni W Mo Pd Au PtφBn (V) 0.4 0.5 0.61 0.61 0.67 0.68 0.77 0.8 0.9φBp (V) 0.6 0.5 0.51 0.42 0.3ΨM (V) 3.7 4.3 4.5 4.7 4.6 4.6 5.1 5.1 5.7

Silicide HfSi MoSi2 ZrSi2 TiSi2 CoSi2 WSi2 NiSi Pd2Si PtSiφBn (V) 0.45 0.55 0.55 0.61 0.65 0.67 0.67 0.75 0.87φBp (V) 0.65 0.55 0.55 0.49 0.45 0.45 0.43 0.35 0.23

• Silicide is often more stable than metal on Si due to the gradual transition layer (in terms of adhesion and interface states).

• Silicidation together with maintaining a high surface doping concentration is still a critical CMOS technology.

• Typical value of contact resistance in deep submicron CMOS technology is around 10-7 Ωcm2. For a (0.1μm)2 contact, this is already too large, and innovation is necessary in the next ten years.

Chapter 2 12

Semiconductor Heterojunction Classification• According to the values of χ and Egap, there are three types of

semiconductor heterojunctions: Type I, II and III.

Narrow/wide bandgap, popular in electronic devices

Discontinous bandgap, popular in photovoltaic

Broken bandgap, special use in superlattices

Chapter 2 13

Semiconductor Heterojunction Diodes

For abrupt interface, ΔEC=|(χ1 − χ2)| and ΔEV=|(χ1 − χ2) + Egap1 − Egap2| are material constant

Chapter 2 14

Common Pseudomorphic Heterojunctions• Assume the lattice mismatch and residual stress are negligible,

and the lattice interface at the heterojunction is ideal. • This is not a good approximation for the SiGe/Si system, but

acceptable for AlGaAs/GaAs system when the Al alloy composition is less than 25%.

• Both SiGe/Si and AlGaAs/GaAs systems are Type I • For the Al1-xGaxAs/GaAs system, χGaAs=4.2eV, EgapGaAs =

1.44eV, AlGaAs has a larger bandgap with ΔEC = 0.15x eV and ΔEV = 0.58x eV.

• For the Si/Si1-xGex system, χSi=4.1eV, EgapSi = 1.1eV, ΔEC = 0.05x eV and ΔEV = 0.47x eV.

• Remember that bandgap can be measured accurately, while affinity cannot. Therefore, the bandgap difference in the heterojunction can usually be accurately given, while the ΔECand ΔEV is less accurate.

Chapter 2 15

Quantum Well Heterojunctions

Al0.2Ga0.8AsNA = 1018cm-3

2μm

GaAsundoped0.5μm

Al0.2Ga0.8Asundoped0.5μm

Al0.2Ga0.8Asundoped0.5μm

Al0.2Ga0.8AsND = 1018cm-3

2μm

EF

E0

EC

Ei

ΔEC

ΔEV

EV

ΔEC and ΔEV are material constant

E0 is continuous unless there are charge dipole at the interface

Chapter 2 16

Three MITs of the Day

• Relations of semiconductor bandgap and optical properties• Photosensitive regions of diodes: optical generation that

can produce currents• Avalanche operations for photo-amplification

Diode Applications

Chapter 2 17

Main applications of diodes• Electrical:

– Current rectifier: using the asymmetrical forward and reverse biases for ac-to-dc conversion or charge pumps

– Voltage clamp: in forward bias, regulate voltage drop across the diode to be Vth; in reverse bias (either high avalanche VBRor low Zener VBR), regulate voltage drop to be VBR.

– Varactor (variable capacitor): using the reverse-bias nonlinear junction capacitance

• Optoelectronic:– LED (spontaneous emission) and laser (stimulated emission)– Photodiode and (photovoltaic) solar cell

Chapter 2 18

Optoelectronic Diodes

λ = 1.3μm for minimal dispersionλ = 1.55μm for minimal lossfor Egap between 0.95 and 0.8eV

optical fiber (glass fiber with cylindrical index gradients)

LED or laserheavily forward bias to create population inversion

Photodiode often in avalanche breakdown to improve the signal-to-noise ratio

λ (μm)

human sensitivity to visible light

GaN GaP AlAs

ultraviolet

GaAs Si

0.4 0.7 0.85 1.1

infrared

)(24.1)(

eVEm

photon

=μλ

light light

AlGaAsGaAsP

Chapter 2 19

Electrical Properties of Photovoltaic Diodes

light

EC

EV

Crude approximation: if the e-h pair is generated within Ln, W and Lp close to the junction (long-base case, of course), then they can be separated by the junction field to cause net current.

WLnLp

p i n

( ) Lpn GWLLqAIIII ++−=+= darkillumidark

What can cause net current?• Net charge has to arrive at

contact with some velocity• The electron-hole pair has to

be generated in places where there is a separation F.

• Or they can diffuse into places where there is separation Fbefore a recombination event.

Chapter 2 20

zero-bias current

I

zero-current bias

VA

p

n

light absorbing coefficient α (cm-1)

~1/α for ideal absorption

log(α)

λ

IL/Imax

λ

sample becomes transparent

surface absorption

• To enlarge W, an intrinsic layer can be added, but this lowers Fmax.• To maximize Ln and Lp, the lifetime has to be large.• When Ln+Lp >> W, IL will be less sensitive to the applied bias.

operating point for photovoltatic cells

Design Considerations of Photovoltaic (PV) Cells

Chapter 2 21

• Photodetectors:– Preferably operating in the avalanche region (sometime called avalanche

diodes) to improve sensitivity, since one photon can generate multiple electron/hole pairs from multiplication.

• Solar cells:– Most sunlight is visible to infrared (before the ozone layer is gone)– Si and GaAs can be used, but how to grow on a large area?? (thin-film)– Satellite applications (cost and integration not a problem): GaAs or other

direct bandgap materials (about 25-35% efficiency)– Commercial applications: a-Si and c-Si (about 10-15% efficiency)

• LEDs (light-emitting diodes):– Large direct bandgap material is needed for visible light (1.77eV < Egap <

3.10eV) for (0.4μm < λ < 0.7μm).– Need to have both electrons and holes at the same location with small τ.– New directions: GaN and organic LED.

Three Basic Types of “Photo” Diodes