1 ECE7397 MEMS, NEMS, and NanoDevices Review of Essential Electrical, Thermal, and Mechanical Concepts.

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ECE7397MEMS, NEMS, and

NanoDevices

Review of Essential Electrical, Thermal, and Mechanical Concepts

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Versatility of MEMS MEMS, because they rely on various material properties, facilitate measurements of parameters describing many phenomena/processes in science and engineering. • Physical dimensions: Length, depth, and roughness• Temperature • Pressure• Mass • Force• Friction• Electrical Resistance• Thermal conductivity• Stress and Strain

and many others.

Selection of appropriate materials for specific actuator mechanism is critically important in MEMS designs and fabrication.

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Phenomena provided by various materials to ensure the best actuation

• Thermal Expansion Themoresistance

Thermal conductivity

• Electrical Electrostatic Piezoelectric Piezoresistance

• Optical Photovoltaic Radiation/absorption

• Mechanical Strain/stress Hardness and stiffness

• Magnetic Hall effect, magneroresistance Magneto-optics

• Biological Electrical and biochemical effects

• Chemical

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Thermal conductivity of various materials

Kovacs

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Thermal properties of more materials

Kovacs

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Kovacs

Consequences and utilization of the thermal expansion differences

L LL

1

T[oC 1]

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Mechanical properties added as useful in MEMS

Peterson

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Semiconductor Si as a MEMS material

Four valence electrons

Covalent bonding: no free electrons at 0K

P-type dopants

N-type dopants

similarly: Ge and Compound (III-V, II-VI) semiconductors

Plummer

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Basic Properties of Silicon

Silicon in microelecronics Single Crystal Polycrystalline Amorphous and in MEMS periodic small crystals no long range

arrangements order between of atoms atoms

Crystal lattice is described by a unit cell with a base vector (distance between atoms)

Types of unit cells

Face Centered CubeBody Centered Cube

Plummer

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Silicon Crystal Structure

Diamond lattice (Si, Ge, GaAs)

Two interpenetrating FCCstructures shifted by a/4 in all three directions

All atoms in both FCCs

Atoms inside one FCC come from the second lattice

Diamond covalent bonding

(100) Si for devices(111) Si not used - oxide charges

Plummer

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Intrinsic=Undoped Semiconductor

Electron and hole generation occur at elevated temperature (above 0K). n=p

Energy Band Gap determines the intrinsic carrier concentration. ni EgGe< EgSi< EgGaAs

Plummer

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Electrical Properties of Semicondutors Explained by a Band Model and Bond Model

n=pn=p

Intrinsic (Undoped) Silicon

Energy Gap T>0K

Plummer

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Band structure of crystalline Si

Eg [eV] is Bandgap

Indirect semiconductor

Ec

Ev

Eg

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N- and p-type semiconductor

N-type p-type

Plummer

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Electrical Properties of Semicondutors Explained by a Band Model and Bond Model

n-type Silicon doped with As

Very small ionization energies ED and EA

n=NAs

Plummer

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F(E) 1

1 exp(E EF

kT)

Distribution of Free Carries (electrons and holes) Obeys Pauli Exclusion Principle

Intrinsic Semiconductor n-type Semiconductor p=type Semiconductor

Conduction Band

Valence Band

Fermi level is the energy at which the probability of finding an electron F(E) is 0.5

below Ei

above Ei

p=Na

n=Nd

Fermi Dirac probability function:

Plummer

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Energy Band Dependence on Temperature

Larger temperature weakens the bonding between atoms causing the band gap energy (energy needed to free e-h pairs) to decrease

EG(eV)=1.17-4 -4. 73x10-4T2/(T+636)≈1.16 - (3x10-4)T

Plummer

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Dopant Ionization

nn>>pn ni≈pi

n-type semiconductor

intrinsic semiconductorni=1.45x1010cm-3 at RT (300K)

Selected Thermo-resistors will rely on this effect

Plummer

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Measurements of semiconductor properties

Conductivity Type

Plummer

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n J

EnVq

EnnEq

Ennq

Conductivity determined by carrier concentrations and mobility

Conductivity and Resistivity

Mobility depends on carrier scattering: lattice vibration (µ with T)defects (µ with density)doping (µ with

concentrations) Resistivity

1

1

n p

1

q(nn pp)

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Resistivity as a Function of Dopant Concentration

=1/(qµnn+qµpp)

µ carrier mobility depends on scattering e.i. dopants, lattice imperfections (defects) andvibration (temperature)

Plummer

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W

t

L

Wt

LR

W

L

Wt

LR s

Concept of Sheet Resistance of doped layers.

s[/sq.] 4 point probe or van der Pauw

s 1

_

x i

1

q n x NB n x dx

Resistivity Sheet resistance

Sheet resistance in an important parameter both in •electron devices ex: in MOSFETs

•Rcontact + Rsource + Rext < 10% Rchen

s but keep xj small to avoid DIBL (conflicting requirements and in

• MEMS

Plummer

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Measurements of sheet resistance

Resistivity

Plummer

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Spreading Resistance

R(x) (x) n(x)

Compare with C(x) from SIMS to get dopant activation.

(information on defects, clusters etc.)

8’- 34’

From Wolf, VLSi Era

Plummer

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Spreading resistance temperature sensors

n- Si

Single probe used to induce current flow in n-type Si

r0

Resistance measurements is at r0 where a second probe (contact is located).

Rs dr

A(r)0

ro

A(r)

Such sensors are widely used (flow sensors etc) cheap but not very accurate.

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R LA

RT R0[1R (T T0)]

Thermo-resistors (thermistors)

Semiconductors (n&p ) and some oxides (“electron-hopping ) show decrease in RT

Metals (more carrier scattering) and other oxides (phase transformation, potential barrier at grain boundaries changes also related to polarization changes) show increase in RT with T

R(T)

T

R<0R>0

Temperature affects resistance in:

Both types have wide applications in MEMS

Kovacs

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Thermoelectric effect in semiconductors or Peltier effect

Electric current generates a heat flux i.e. cools or warms-up selected regions.

Thermal conductivity will counteract i.e. will decrease the Peltier effect. So use materials with high electrical conductivity and low thermal conductivity.

Current

Bismuth

R.B. Darling

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Hall Effect Measurement

Plummer

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Optical Sensors and Actuators

Crystalline semiconductors are used for these applications

Kovacs

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Devices for Optical Actuation

Kovacs

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Recombination of Carriers in Silicon

Si is an indirect semiconductor so indirect recombination (Shockley-Read-Hall) occurs through traps located in the mid-gap

intrinsic Si n-type Si; a trap (below EF) is always filled with electron=majority carrier and waits for a minority hole.

R=1/vthNt

lifetime capture cross sectionthermal velocity, and traps

Plummer

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Semiconductor Devices

• Diodes• Bipolar Junction Transistors (BJT)• Metal Oxide Semiconductor Field Effect Transistors (MOS

FET)

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Semiconductor Technology Families

First circuits were based on BJT as a switch because MOS circuits limitations related to large oxide charges

isolation

BL

n-p-n

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Semiconductor Devices

Reverse biased diode Forward biased diode

p-n Diodes

after Kano, Sem. Dev.

Thermal behavior of a diode (or transistor operating as a diode) used to measure very temperature accurately.

in forward bias conditions Vf

decreases with T

butin reverse bias conditionsVR may decrease or increase with T depending on a mechanism of breakdown

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MOS Capacitors and TransistorsElectrical Measurements

MOS Capacitors are widely used in MEMS

Capacitance-voltage method

Charge Density

DDDG XNQQ

TDDDG QXNQQ

accumulator

dV

dQC

X

AC

OX

OXOX

depletion

D

SD X

AC

Inversion Equilibrium conditions.

ac signal

Plummer

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CV MeasurementsLow frequency (~1Hz), high frequency (100Khz – 11) AC signals used for C-V Measurements.)

QI follows QG C =COX

XD= XDmaxQD fixed

XD> XDmax

Holes generated in the D.L and attracted by the gate source the DL when |VG| increases

To avoid deep depletion*:

U ni

G

,Jgen qniWG

dVdt

Jgen

C

Jgen

COX

qniWACOX

0.1V /sec

High frequency AC signal changes faster, then QI can respond (generation is slow)

QG QD

xD xD max CD CD max

*

Plummer

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Bipolar Transistors

E-B junction is forward biased=injects minority carriers to the baseBase (electrically neutral) is responsible for electron transport via diffusion (or drift also if the build in electric field exist) to collectorC-B diode is reverse biased and collects transported carries

VBE>0 VBC<0

IE=IEn+IEp IC=IE<1

IB=IEp+Irec

IE IC

IB

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Bipolar Junction Transistors

n-p-nIntegrated circuit BJT

p-n-p Individual device

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Bipolar Junction Transistors

minority carriers

Injectedelectrons

Extracted electronsholes

Forwards bias Reverse bias

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Bipolar Junction Transistors

Currents’ Components

small

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Bipolar Junction Transistors

Forward Operation Mode

Early Effect

Early Voltage

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Bipolar Junction Transistors

Breakdown Voltages

Common BaseCommon Emitter

Collector-Base junction

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Bipolar Junction Transistors

Current Gain =

Gummel Plot

Kirk Effect

Recombination in the E-B SCR

IC/IB

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Bipolar Junction Transistors and a Switch

SchottkyDiode used in n-p-n BJTs forfaster speed

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MOS Field Effect Transistors (MOSFET)

NMOS and PMOS (used in CMOS circuits)

VG>VT to create strong inversion

depletion

Oxide

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Operation of NMOS-FET

Linear Region, Low VD

Saturation Region, Channel Starts to Pinch-Off

Saturation Region, channel shortens beyond pinch-off, L’<L

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Operation of MOS-FET

ID(VD)

Channel-Length-Modulation(Shorten by L)

ID=kp[(VG-VT)VD-VD2/2

Device transconductancekp=µnCoxW/L larger for NMOS than PMOSIn CMOS for compensation use Wp>Wn

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Scaled Down NMOS

DIBL

Proximity of the drain depletion layer charge sharing DIBL

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Modern MOS Transistors Gate

LDDLDD used to reduce the electric field in the drain depletion region and hot carrier effects

Self aligned contacts decrease the resistance

isolation

DrainSource