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Metal-Semiconductor Interfaces
• Metal-Semiconductor contact
• Schottky Barrier/Diode
• Ohmic Contacts
• MESFET
UMass Lowell 10.523 - Sanjeev Manohar
Device Building Blocks
UMass Lowell 10.523 - Sanjeev Manohar
UMass Lowell 10.523 - Sanjeev Manohar
Energy band diagram of an isolated metal adjacent to an isolated n-type semiconductorsemiconductor
UMass Lowell 10.523 - Sanjeev Manohar
Energy band diagram of a metal-semiconductor contact in thermal equilibriumequilibrium.
UMass Lowell 10.523 - Sanjeev Manohar
Measured barrier height for metal-silicon and metal-gallium arsenide contacts
UMass Lowell 10.523 - Sanjeev Manohar
Energy band diagrams of metal n-type and p-type semiconductors under thermal equilibrium
UMass Lowell 10.523 - Sanjeev Manohar
Energy band diagrams of metal n-type and p-type semiconductors under forward bias
UMass Lowell 10.523 - Sanjeev Manohar
Energy band diagrams of metal n-type and p-type semiconductors under reverse bias.
UMass Lowell 10.523 - Sanjeev Manohar
Charge distribution
electric-field distribution
UMass Lowell 10.523 - Sanjeev Manohar
Depletion Layer
DqN−=ρ Wx <<0
qNs
D
s
qNVε
−=ερ
=∇2
qNdEs
DqNdxdEE
ε−==∇
)()( xWqNxEs
D −ε
=
UMass Lowell 10.523 - Sanjeev Manohar
W W
s
Dbi dxxWqNdxxEVV ∫ ∫ −
ε==− )()(
0 0
s
D
Ws
D WqNxWdxWqNε∫ =−−
ε=
2)()(
20
Dbis qNVVW /)(2 −ε=Depletion width
Dbis q)(
)(2 VVNqWQNQ ε
Charge per unit area
)(2 VVNqWQNQ biDsD −ε==
UMass Lowell 10.523 - Sanjeev Manohar
Capacitance
NqQC sDs εε∂Per unit area:( ) WVVq
VC s
bi
Ds =−
=∂
=2
Per unit area:
( )Ds
bi
NqVV
C ε−
=21
2
Rearranging:
Dsq
Or: ⎤⎡ 12( ) ⎥
⎥
⎦
⎤
⎢⎢
⎣
⎡ −ε
=dVCdq
Ns
D /112
2
UMass Lowell 10.523 - Sanjeev Manohar
1/C2 versus applied voltage for W-Si and W-GaAs diodes
UMass Lowell 10.523 - Sanjeev Manohar
1/C2 vs V
•If straight line – constant doping profile –
slope = doping concentrationslope doping concentration
•If not straight line, can be used to find profile
Intercept V can be used to find φ•Intercept = Vbi can be used to find φBn
+=φ VV
⎟⎞
⎜⎛
+=φ binBn
NkT
VV
⎟⎠
⎞⎜⎝
⎛=
i
Dn n
Nq
kTV ln
UMass Lowell 10.523 - Sanjeev Manohar
Current transport by the thermionic emission process
Thermal equilibrium forward biasreverse bias
UMass Lowell 10.523 - Sanjeev Manohar
Thermionic emission
Number of electrons with enough thermal energy to overcome barrier:
⎟⎠⎞
⎜⎝⎛ φ−
= kTq
Cth
Bn
eNn
At thermal equilibrium, current going both ways is the same:
⎟⎠⎞
⎜⎝⎛ φ−
kTq Bn
eNCjj ⎠⎝→→ == kT
Cmssm eNCjj 1
UMass Lowell 10.523 - Sanjeev Manohar
Forward Bias
Barrier for electrons in semiconductor is reduced by VF
⎟⎠⎞
⎜⎝⎛ −φ−
= kTVq
Cth
FBn
eNn)(
Barrier for electrons from metal to semiconductor is the same
Net current:
1
)(
1 eNCeNCjjj kTq
CkT
Vq
Csmms
BnFBn
−=−=⎟⎠⎞
⎜⎝⎛ φ−
⎟⎠⎞
⎜⎝⎛ −φ−
→→
1
11
1eeNCj kTqV
kTq
C
CCsmms
FBn
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
⎟⎠⎞
⎜⎝⎛ φ−
→→
UMass Lowell 10.523 - Sanjeev Manohar
21 *TANC C =
⎠⎝
Forward Bias
kTqV
s ejj ⎟⎟⎠
⎞⎜⎜⎝
⎛−= 1
kTq Bn
TAjφ−
⎠⎝
2* kTs eTAj = 2*
2*4 kqmπ3
4*h
kqmA eπ=Effective Richardson Constant
Derive by determining current with integral of velocity and density of states
∫ ∫== dEEfEgEvEdNEvj )()()()()(
UMass Lowell 10.523 - Sanjeev Manohar
∫ ∫== dEEfEgEvEdNEvj )()()()()(
Forward current density vs applied voltage of W-Si and W-GaAs diodes
UMass Lowell 10.523 - Sanjeev Manohar
Thermionic Emission over the barrier – low doping
UMass Lowell 10.523 - Sanjeev Manohar
Tunneling through the barrier – high doping
UMass Lowell 10.523 - Sanjeev Manohar
Tunneling through the barrier
Narrow depletion width for high doping – tunneling
F QM 101From QM 101:Wavefunction is exponential depending on barrier width and heightprobability of making it to the other side ~ ψ2
xti eetx α−ω−=Ψ ),( ( )2
2h
EUm −=α
[ ]2/)(22exp~ hqVqmWI Bn −φ−
Dbis qNVVW /)(2 −ε=
( )⎤⎡ −φ− B VCI 2 h/4 mCUMass Lowell 10.523 - Sanjeev
Manohar
( )⎥⎦
⎤⎢⎣
⎡ φ
D
Bn
NVCI 2exp~ h/42 smC ε=
Contact resistance
Specific Contact Resistance(based on current density)
1−⎞⎛ ∂J
0=⎟⎠⎞
⎜⎝⎛∂∂≡
VC V
JR
( )⎥⎤
⎢⎡ −φ− Bn VCI 2exp~
For tunneling current through barrier (high doping):
⎥⎦
⎢⎣ DN
I exp
⎞⎛ φC⎟⎟⎠
⎞⎜⎜⎝
⎛ φhD
BnC N
CR 2exp~Ohmic Contact:
UMass Lowell 10.523 - Sanjeev Manohar
Calculated and measured values of specific contact resistance
UMass Lowell 10.523 - Sanjeev Manohar
MESFET
UMass Lowell 10.523 - Sanjeev Manohar
MESFET – Qualitative Operation
•No gate voltage – depletion from built-in voltage•Positive drain voltage causes reverse bias •Increased depletion width with increased V
)( WaZNqL
ALR
Dn −μ=ρ=
UMass Lowell 10.523 - Sanjeev Manohar
MESFET – Qualitative Operation
At higher drain voltages, W=a – pinch off at VDsat
s
Dbi
WqNVVε
=−2
2
bis
DDsat VaqNV −
ε=
2
2
⇒
UMass Lowell 10.523 - Sanjeev Manohar
s
MESFET – Qualitative Operation
Above pinchoff voltage, drain current does not increaseVoltage at pinch-off point is still Vdsat
UMass Lowell 10.523 - Sanjeev Manohar
MESFET – Qualitative Operation
Addition of gate voltage (negative) increases baseline depletion widthPinch-off occurs soonerSaturation voltage and current are reduced (narrower channel)
GbiD
Dsat VVaqNV −−ε
=2
2
UMass Lowell 10.523 - Sanjeev Manohar
sε2
I-V Characteristics – Linear Region
[ ])(yWaZNqdyIdRIdV D
D μ== [ ])(yWaZNq Dn −μ
( )biGs VVyVW ++ε )(2)( ( )D
biGs
qNyyW =
)()(
qND
UMass Lowell 10.523 - Sanjeev Manohar
WdWqNdVs
D
ε=
I-V Characteristics – Linear Region
[ ]
[ ] WdWqNWaZNq
dVyWaZNqdyI
DDn
DnD
−μ=
−μ= )(
[ ]qs
Dn εμ
∫ −μ
=22
)(2
WdWWaNqIW
Dn ∫ε= )(
1
WdWWaL
IWs
D
( ) ( )⎥⎦⎤
⎢⎣⎡ −−−
εμ
= 31
32
21
22
22
32
2WWWWa
LNqIs
DnD
UMass Lowell 10.523 - Sanjeev Manohar
I-V Characteristics – Linear Region
D
biGs
qNVVW )(2
1+ε
=
D
biGDs
qNVVVW )(2
2++ε
=
biGbiGDDPD V
VVV
VVVVVII
⎥⎥⎤
⎢⎢⎡
⎟⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ ++−=
32
32 2
32
3
DnP
PPP
aNqZI
VVV
μ≡
⎥⎦⎢⎣ ⎠⎝⎠⎝ 33322
DP
sP
aqNV
L
≡
ε
2
22
UMass Lowell 10.523 - Sanjeev Manohar
sP ε2
Normalized ideal current-voltage characteristics of a MESFET
UMass Lowell 10.523 - Sanjeev Manohar
with VP = 3.2 V.
UMass Lowell 10.523 - Sanjeev Manohar
Transconductance
⎤⎡ 33
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ ++−=
23
23
32
32
P
biG
P
biGD
P
DPD V
VVV
VVVVVII
⎦⎣
In Saturation:biGDP VVVV ++= biGPDsat VVVV −−=⇒
⎤⎡
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ ++−−−
−−=
23
23
32
32
P
biG
P
biGbiGP
P
biGPPDsat V
VVV
VVVVVV
VVVII
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ++−
+−=
23
32
321
P
biG
P
biGPDsat V
VVV
VVII
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ++
+−=
⎥⎦⎢⎣ ⎠⎝
23
32
31 biGbiG
PDsat VVV
VVVII
UMass Lowell 10.523 - Sanjeev Manohar
⎥⎦⎢⎣ ⎠⎝33 PP VV
Transconductance
( ) ⎤⎡ ⎞⎛ 23
21 VVVV( )⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ++
+−=
2
32
31
P
biG
P
biGPDsat V
VVV
VVII
∂∂
=VG
Dm V
IgD
( ) ( ) ⎥⎦
⎤⎢⎣
⎡++−= −
biGPP
Pm VVVV
Ig
D
23*
3210 2
12
3
⎟⎟⎠
⎞⎜⎜⎝
⎛ +−=
P
biG
P
Pm V
VVVIg 1
⎟⎟⎠
⎞⎜⎜⎝
⎛ +−
μ=
P
biGDnm V
VVL
aqNZg 12
UMass Lowell 10.523 - Sanjeev Manohar
Equivalent Circuit - High Frequency AC
• Input stage looks like capacitances gate-to-channelO t t it i d d i t it• Output capacitances ignored -drain-to-source capacitance small
UMass Lowell 10.523 - Sanjeev Manohar
Maximum Frequency (not in saturation)
• Ci is capacitance per unit area and Cgate is total capacitance of the gate
ZLCC =
• F=fmax when gain=1 (iout/iin=1)
ZLCC igate =
max g ( out in )
gate
m
Cgfπ
=max 2
Sgate
g
WZLC ⎟
⎠⎞
⎜⎝⎛ ε=
Dn
Dn
LaqNL
aqNZ
fεπ
μ=
⎞⎛ ε
μ
≈ 2
2
max 2
2
UMass Lowell 10.523 - Sanjeev Manohar
sS LW
ZL επ⎟⎠⎞
⎜⎝⎛ επ 22
Velocity Saturation
sDsD qNWaZqnAI υ−=υ= )(*
Drain current:
Transconductance
WZ
VW
WI
VIg ss
G
D
G
Dm
ευ=
∂∂
∂∂
=∂∂
=GG
Cutoff Frequency:
Cgf m=
2max
WZ
Cgateπ
/
2max
UMass Lowell 10.523 - Sanjeev Manohar
( ) LWZLWZf S
s
ss
πε
=επευ
=2/2
/max
Figure 7.15. The drift velocity versus the electric field for electrons in various semiconductor materials.
UMass Lowell 10.523 - Sanjeev Manohar
III-V MESFETs – GaAs and InP
+Semi-insulating material – high speed devices (like built-in SOI)
+High Electron Mobility/Saturation Velocity – high speed
+Direct Bandgap – photonic devices
+Heterostructures bandgap engineering+Heterostructures – bandgap engineering
-No Simple Oxides – MOSFETS not viable – no equivalent to SiO2
UMass Lowell 10.523 - Sanjeev Manohar
III-V Transistors: GaAs
No simple oxides for GOX – MOSFETS not widely used
MESFET structure more common – mesa structuredepletion mode transistor
Source DrainGate
Semi-insulating Substrate
UMass Lowell 10.523 - Sanjeev Manohar
Depletion Mode GaAs MESFETDepletion Mode GaAs MESFET
•N-type material – high electron mobility
•Mesa etch for isolation on SI substrate
•Ohmic contacts for Source and Drain – alloyed
•Shottky contact for Gate Ti•Shottky contact for Gate – Ti
•Recessed gate – depth determines threshold
UMass Lowell 10.523 - Sanjeev Manohar
GaAs MESFET Fabrication
Si Implant
Si3N4
Semi-insulating GaAs Substrate
Deposit Si3N4 layer implant Si and anneal for form n-type material
UMass Lowell 10.523 - Sanjeev Manohar
Deposit Si3N4 layer, implant Si and anneal for form n type material Can also grow n-type epi layer by MBE or MOCVD
N-type GaAs
Semi-insulating GaAs Substrate
Ohmic contact formation for source and drain – NiAuGeOhmic contact formation for source and drain – NiAuGe
evaporate Au(88wt%)Ge(12wt%) then Ni (+Au)l 30 i t 450°C i H /Nanneal 30 min at 450°C in H2/N2
Au reacts with Ga from substrate – Ga vacanciesGe fills Ga vacancies – heavy n-type doping
UMass Lowell 10.523 - Sanjeev Manohar
y y glow contact resistance ohmic Ge doping not uniform – spreading resistance effect
Semi-insulating GaAs Substrate
Gate Recess Etch
Wet etchingWet etchingChannel depth determines pinch-off voltageChannel resistance can be monitored in-situ
UMass Lowell 10.523 - Sanjeev Manohar
Semi-insulating GaAs Substrate
Mesa Recess Etch
Wet etchingWet etchingSemi-insulating substrate for device isolation
UMass Lowell 10.523 - Sanjeev Manohar
Semi-insulating GaAs SubstrateSemi-insulating GaAs Substrate
Shottky Gate Electrode deposition – Ti/Pt/Au or Ti/Pd/Au
Almost any metal will form barrieryGa diffuses in many metalsTi –contact Pt or Pd barrier layer
UMass Lowell 10.523 - Sanjeev Manohar
Pt or Pd barrier layerAu added for low resistivity
GaAs Digital Circuits:
Direct Coupled FET Logic (DCFL) – lowest power and highest level of integration
Uses enhancement and depletion mode transistors
Enhancement mode transistors madeusing thinner gate recess ordifferent doping to changedifferent doping to changethreshold
UMass Lowell 10.523 - Sanjeev Manohar
DCFL Fabrication Sequence
UMass Lowell 10.523 - Sanjeev Manohar
DCFL Fabrication Sequence(cont.)
UMass Lowell 10.523 - Sanjeev Manohar