The Electromagnetic Properties of Materials •  Electrical conduction –  –  –  – 

Metals Semiconductors Insulators (dielectrics) Superconductors

•  Magnetic materials

–  Ferromagnetic materials –  Others

•  Photonic Materials (optical) –  Transmission of light –  Photoactive materials

•  Photodetectors and photoconductors •  Light emitters: LED, lasers

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Current Density

•  Electron current is by diffusion j = - ne

–  n = conduction electrons/unit vol –  µ = mobility

•  Quality of metallic conductor

–  n = bonding and crystal structure –  µ = microstructure sensitive



j = −ne δv = neµE 2 ne 2τ ne l σ= = m mv

€ ρ= € MSE 200A Fall, 2008

€

σ = neµ

mv ne 2 l

J.W. Morris, Jr.

€

University of California, Berkeley

Resistivity

•  Resistivity

®

increasing purity

–  Impurities and phonons add –  Phonon linear in T –  Impurity independent of T

T

phonon

ρ = ρ 0 + AT

•  Use “residual resistivity” to measure purity

impurity

€

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Semiconductors: The Bottom Line •  Semiconductors are poor conductors of electricity •  Semiconductors are useful because they are controllable –  Can adjust conductivity –  Can choose type of conductor: electrons or positive “holes”

•  Most microelectronic devices use semiconductor junctions –  Diodes (n|p) –  Transistors (n|p|n or p|n|p)

•  Other devices are based on controlling band gap –  Especially photonic materials (optical properties) –  We shall cover these later

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Semiconductors •  Semiconductor type and conductivity

–  Conductivity dominated by carrier density –  Intrinsic semiconductors (excitation across band gap) –  Extrinsic semiconductors •  n-type (donors) or p-type (acceptors) •  Permit precise control over σ and type of carrier

•  Semiconductor junctions

–  n|p diode –  n|p|n bipolar transistor –  Field effect transistor (mosfet)

•  Manufacturing semiconductor devices –  Lithography –  Doping –  Packaging

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Intrinsic Semiconductor

conduction band

e-

E

EF

EG valence band

• 

Filled bands separated by a gap

• 

Excitation creates two carriers:

• 

Conductivity controlled by carrier density

–  EF approximately in center of the gap –  Free electron in conduction band –  Hole in valence band

x

σ = n e eµe + n p eµ p

MSE 200A Fall, 2008

€

J.W. Morris, Jr. University of California, Berkeley

Carrier Density in an Intrinsic Semiconductor •  Electrons (n)

conduction band

 EG  n ≈ N 0 exp  −  2kT 

E

EG

EF

valence band €

x

•  Holes (p)

∞

 EG  p ≈ N 0 exp−  2kT  MSE 200A Fall, 2008

€

n=

∫ P(E)N(E)dE

Ec

(= n) €

Ev

p= €

∫ p(E)N(E)dE −∞

J.W. Morris, Jr. University of California, Berkeley

€ €

Conductivity of an Intrinsic Semiconductor •  σ sums electrons and holes: σ = neµe + peµ p

 EG  ≅ N 0e(µe + µ p )exp−  2kT  €

 E  σ ≈ N 0eµe exp− G   2kT 

(µe >> µ p )

€

•  Plot ln(σ) vs. 1/kT: € MSE 200A Fall, 2008

–  Straight line € –  Slope is (EG/2)

J.W. Morris, Jr. University of California, Berkeley

Semiconductors •  Semiconductor type and conductivity

–  Conductivity dominated by carrier density –  Intrinsic semiconductors (excitation across band gap) –  Extrinsic semiconductors •  n-type (donors) or p-type (acceptors) •  Permit precise control over σ and type of carrier

•  Semiconductor junctions

–  n|p diode –  n|p|n bipolar transistor –  Field effect transistor (mosfet)

•  Manufacturing semiconductor devices –  Lithography –  Doping –  Packaging

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Extrinsic Semiconductors: n-Type e

Conduction band

Si

Si

E

P

} ÎED

ÎEG

donor levels

Si Si

Valence band

x

•  n-type semiconductors are doped with donors –  –  –  –  – 

MSE 200A Fall, 2008

Common donor has 1 extra valence electron (e.g., P in Si) Donor electron in excited state weakly bound to extra + on donor Corresponds to localized “donor levels” just below conduction band Electrons are excited from donor levels to produce carriers Conduction is by electrons

J.W. Morris, Jr. University of California, Berkeley

Extrinsic Semiconductors: p-Type

Si

Conduction band

Si E

B

acceptor levels

ÎEG

} ÎEA

Si Si

Valence band

x

•  p-type semiconductors are doped with acceptors –  –  –  –  – 

MSE 200A Fall, 2008

Common acceptor has 1 less valence electron (e.g., B in Si) “Hole” in valence state weakly bound to effective - on acceptor Corresponds to localized “acceptor levels” just above valence band Electrons are excited to acceptor levels to produce free holes Conduction is by holes

J.W. Morris, Jr. University of California, Berkeley

Extrinsic Semiconductors: Conductivity of an n-type Semiconductor •  Carrier density determines σ

intrinsic

σ = neµe saturation ln(n)

 E − EF  n ≈ N 0 exp− c  kT 

extrinsic EG/2kT

€

higher N ∆ED/2kT

€

 E − EV  p ≈ N 0 exp− F  2kT 

n = N D+ + p

1/kT

€  N N   ΔE D  0 D exp   − 2kT €  2     n= ND   E  N 0 exp− G    2kT   

MSE 200A Fall, 2008

(low T) (saturation) (high T)

J.W. Morris, Jr.

University of California, Berkeley

€

Extrinsic Semiconductors: Degeneracy Conduction band

donor band

E

acceptor levels Valence band

•  At a critical concentration, donor states overlap –  “Donor band” = continuous band of donor states –  Degenerate semiconductor is a metallic conductor

•  Overpopulation of acceptors also creates degeneracy MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Extrinsic Semiconductors: Titration Conduction band

donor levels

E

acceptor levels Valence band

x

• 

Donor electrons fill acceptor levels –  n-type behavior is not achieved until acceptors filled –  Acceptors must be titrated before donor states overlap ⇒  Semiconductors must have high purity prior to doping

• 

Converse applies: acceptors titrate donors –  Can convert n-type to p-type if donor concentration is small

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Semiconductor Junctions

•  Join n- and p-type regions to create a junction –  Junctions have asymmetric electrical properties

•  Can be done by doping adjacent regions –  Write junction devices onto a single crystal (chip) –  This is the basis of all microelectronics

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

The Band Structure at an n|p Junction ++ + ++ ++

n e

e

e

e

e

- ---

p

e e

E EF

e

e

e

e

e

e EF

E

x x

• 

Join n and p regions –  –  –  – 

• 

Just prior to join, EF high on n-side Electrons flow from n to p (holes flow p to n) Charges at interface create potential, Δφ, across interface Potential raises E on p-side (ΔE = -eΔφ )

Equilibrium (current stops) when EF(n)=EF(p)

–  The electron and hole occupancies are constant across the interface at every E

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Current-Voltage Characteristic: n|p Junction •  Electron current density   eV   j e = j + j = j exp  −1  kT    + e

− e

0 e

•  Hole current density j p = − je

€

V

•  Total current €  eV   0 j = j p − j e = −2 j e  exp  −1  kT   

Ie= - I

J.W. Morris, Jr.

MSE 200A Fall, 2008

University of California, Berkeley

€

Mechanism of Conduction under Bias

-

e

e

-++ + ++ - ++ --

n

e

e

e

p

} eV

Forward bias:

• 

Reverse bias:

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p

-

e e EF

e

e

e

e

e

EF

eV{

E

x

• 

++ + - -++ ++ - -

n

+

+

e

e

E

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x

–  Electrons and holes diffuse across interface from majority side –  Recombine with majority carriers –  Electrons and holes diffuse from minority side –  Carrier density replenished by excitation

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

The Bipolar Transistor emitter

base

n

E

e

e e

e

collector

p

e

n

e

e

e e

e

e

e EF

x

• 

The transistor is an n|p|n (or p|n|p) device

• 

Characteristics

–  Two n|p junctions joined in opposite orientation –  Voltages controlled independently (Ve, Vb, Vc) –  Base is thin compared to emitter and collector

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

The Bipolar Transistor under Bias

n

-

p

n

+

e E

e e e

e

e

e e e e

e

e

e

EF

x

•  Transistor acts like a closed switch when Vb=0 –  p|n junction is in reverse bias ⇒ Only leakage current transmitted

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

The Bipolar Transistor as a Switch Controlled by Vb +

n

-

e e e

p

e

e

e

e e

n

e

E

e e e

e

The image cannot be displayed. Your computer may not have enough memory

• 

MSE 200A Fall, 2008

e

e EF

Vb > 0 opens switch

–  So long as Vb > Ve, electrons flow into the base –  To achieve equilibrium, electrons recombine with holes in base –  Given small size of base, holes are exhausted by recombination –  Holes cannot be replenished •  • 

• 

+

Collector in reverse bias Emitter voltage attracts holes

Base becomes transparent to electrons –  Current controlled by Vb-Ve

J.W. Morris, Jr. University of California, Berkeley

The Bipolar Transistor as an Amplifier Controlled by Vc + -

n

e e e

e

p

e

e

+

n e

e

E

e e e

e

e EF

x

• 

• 

MSE 200A Fall, 2008

Current is controlled by ΔVeb –  After saturation,

 eΔVeb   j e = 2 j e0  exp −1   kT   

Potential drop into collector imparts energy ΔE = -e ΔVbc

–  Transistor functions as a power amplifier with amplification set by ΔVbc

€

J.W. Morris, Jr. University of California, Berkeley

The Field Effect Transistor: Metal-Oxide-Semiconductor Junctions (MOS) V+

metal oxide

p

+ + + +metal+ + + + oxide n p-

inversion

E

• 

MOS can invert semiconductor type

• 

Potential creates “field effect” -

EF

normal

o conduction band x e e i e e d e

metal

p

depletion

+ + +

EF valence band

–  Positive potential lowers EC, attracts electrons –  When EC-EF < EG/2, semiconductor “inverts” (p→n)

MSE 200A Fall, 2008

–  n-region near surface –  p-region in depth –  p- (depleted zone) acts as insulator

J.W. Morris, Jr. University of California, Berkeley

MOSFET: Metal-Oxide-Semiconductor Field Effect Transistor V+ gate V-

source

+ + +

n+

+metal+ oxide n p-

+ + +

p

Vg >VI

drain V+ n+

I Vg = 0

channel

V

MSE 200A Fall, 2008

• 

Construct n|p|n junction at MOS as shown

• 

When Vg = 0, gate|drain in reverse bias

• 

When Vg > VI, gate is n-type and current flows

–  In this case n|p|n called source|gate|drain (Vd > Vs) –  Switch is off –  Switch is on

J.W. Morris, Jr. University of California, Berkeley

Semiconductors •  Semiconductor type and conductivity

–  Conductivity dominated by carrier density –  Intrinsic semiconductors (excitation across band gap) –  Extrinsic semiconductors •  n-type (donors) or p-type (acceptors) •  Permit precise control over σ and type of carrier

•  Semiconductor junctions

–  n|p diode –  n|p|n bipolar transistor –  Field effect transistor (mosfet)

•  Manufacturing semiconductor devices –  Lithography –  Doping –  Packaging

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley

Semiconductor Device Processing oxide passivation metallic conductors active devices (transistors, etc.) silicon chip

MSE 200A Fall, 2008

• 

Manufacture millions of devices simultaneously on a “chip”

• 

Steps in manufacture (simplified) –  –  –  –  –  –  – 

Crystal growth and dicing to “chip” Photolithography to locate regions for doping Doping to create n-type regions Overlay to create junctions Metallization to interconnect devices Passivation to insulate and isolate devices Higher level “packaging” to interconnect chips

J.W. Morris, Jr. University of California, Berkeley

Photolithography light mask

coating oxide silicon

coating oxide silicon

•  Minimum feature size depends on wavelength of “light” –  –  –  – 

Visible light: ~ 1 µm Ultraviolet light: ~ 0.1 µm Electrons, x-rays 0.1-1 nm New and exotic methods

•  Must have photoresist suitable to the “light” MSE 200A Fall, 2008

–  Or use “light” to cut through oxide directly

J.W. Morris, Jr.

University of California, Berkeley

Doping dopant ions

MSE 200A Fall, 2008

• 

Add electrically active species

• 

Simple method: Coat surface and diffuse

• 

More precise:Ion implantation:

dopant distribution

–  Diffusion field is electrically active

–  Accelerate ions of the electrically active species toward surface –  Ions embed to produce doped region

J.W. Morris, Jr. University of California, Berkeley

Doping: The Chemical Distribution ion implantation laser anneal c

laser light

dopant distribution

diffusion

x

MSE 200A Fall, 2008

• 

Initial distribution is inhomogeneous

• 

Can homogenize by “laser annealing”

–  Diffusion produces gradient from surface –  Ion implantation produces concentration at depth beneath surface –  Use a laser to melt rapidly, locally –  Rapid homogenization n melted region –  Rapid re-solidification since rest of body is heat sink

J.W. Morris, Jr. University of California, Berkeley

Overlay to Create Junctions n n

p

n

n p

•  Once primary doping is complete –  –  –  – 

MSE 200A Fall, 2008

Re-coat Re-mask Re-pattern Dope second specie to create desired distribution of junctions

J.W. Morris, Jr. University of California, Berkeley

Metallization diffusion barrier conductor diffusion barrier

conductor oxide

Si

MSE 200A Fall, 2008

diffusion barrier conductor

Si

oxide

Si

oxide

devices

• 

After devices are made

• 

Coat and etch (Al)

• 

Damascene process (Cu, which is difficult to pattern-etch)

–  Coat with oxide for insulation –  Etch for conductor pattern –  Coat surface with Al(Cu) –  Pattern and etch to create desired pattern of conductors –  Pattern oxide with trenches for Cu lines –  Coat with Cu, polish off to leave filled trenches

J.W. Morris, Jr. University of California, Berkeley

Passivation and Packaging = oxide = metal = devices = semiconductor

•  Coat with insulator to isolate device

–  Oxide to isolate metallic conductors –  “Hermetic seal”, usually polymer, to insulate form environment –  Sealing is difficult since electrical contacts must penetrate

•  Interconnect devices

–  Wire and solder chips to “boards” –  Boards to one another to make electronic device

MSE 200A Fall, 2008

J.W. Morris, Jr. University of California, Berkeley