MEMS Electrical Fundamentals - RIT - People · MEMS Electrical Fundamentals Page 3 INTRODUCTION Resistor heaters are used in many MEMS applications including ... This module will

© May 4, 2015 Dr. Lynn Fuller

MEMS Electrical Fundamentals

Page 1

ROCHESTER INSTITUTE OF TECHNOLOGY MICROELECTRONIC ENGINEERING


Dr. Lynn Fuller webpage: http://people.rit.edu/lffeee

Electrical and Microelectronic Engineering Rochester Institute of Technology

82 Lomb Memorial Drive Rochester, NY 14623-5604

email: [email protected] microE program webpage: http://www.microe.rit.edu

5-4-2015 MEMSOutline.ppt

http://people.rit.edu/lffeee

mailto:[email protected]

http://www.microe.rit.edu/



Page 2

OUTLINE

Introduction Resistors for temperature and light Resistor as Heaters Uniform Doped pn Junction Photodiodes and LEDs Diode Temperature Sensors Capacitors Capacitors as Sensors Chemicapacitor Diaphragm Pressure Sensor Condenser Microphone Capacitors as Electrostatic Actuators Signal Conditioning



Page 3

INTRODUCTION

Resistor heaters are used in many MEMS applications including

ink jet print heads, actuators, bio-mems, chemical detectors and

gas flow sensors. Resistors are used as temperature sensors,

strain sensors and light sensors. Diodes are used for sensing

temperature and light. Capacitors are used for sensing

displacement in accelerometers and gyroscopes. Capacitors are

also used in chemical sensors, liquid level sensing and

microphones. This module will discuss the electrical

fundamentals for these applications.



Page 4

OHM’S LAW

I

V

Resistor a two terminal device that exhibits a

linear I-V characteristic that goes through the

origin. The inverse slope is the value of the

resistance.

R = V/I = 1/slope

I

V

-

+

R



Page 5

THE SEMICONDUCTOR RESISTOR

Resistance = R = L/Area = s L/w ohms

Resistivity = Rho = 1/( qµnn + qµpp) ohm-cm

Sheet Resistance = Rhos s = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square

L Area

R

w t

s = / t

Note: sheet resistance is convenient to

use when the resistors are made of thin

sheet of material, like in integrated

circuits.

R = Rho L / Area

= Rhos L/W

Rho is the bulk resistivity of the material (ohm-cm)

Rhos is the sheet resistance (ohm/sq) = Rho / t



Page 6

MOBILITY

Total Impurity Concentration (cm-3)

0

200

400

600

800

1000

1200

1400

1600

10^13

10^14

10^15

10^16

10^17

10^18

10^19

10^20

ArsenicBoronPhosphorus

Mo

bil

ity (

cm2/

V s

ec)

electrons

holes

Parameter Arsenic Phosphorous Boron

µmin 52.2 68.5 44.9

µmax 1417 1414 470.5

Nref 9.68X10^16 9.20X10^16 2.23X10^17

0.680 0.711 0.719

µ(N) = µ mi+ (µmax-µmin)

{1 + (N/Nref)}

Electron and hole mobilities in silicon at 300 K as functions of the total dopant concentration (N). The values plotted are the results of the curve fitting measurements from several sources. The mobility curves can be generated using the equation below with the parameters shown:

From Muller and Kamins, 3rd Ed., pg 33



Page 7

TEMPERATURE EFFECTS ON MOBILITY

Derived empirically for silicon for T in K between 250 and 500 °K and for

N (total dopant concentration) up to 1 E20 cm-3

µn (T,N) =

µp (T,N) =

88 Tn-0.57

54.3 Tn-0.57

Where Tn = T/300

From Muller and Kamins, 3rd Ed., pg 33

1250 Tn-2.33

407 Tn-2.33

1 + [ N / (1.26E17 Tn 2.4)] ^0.88 Tn -0.146

1 + [ N / (2.35E17 Tn 2.4)]^ 0.88 Tn -0.146

+

+



Page 8

MOBILITY CALCULATIONS

This spreadsheet calculates the mobility from the equations given

by Kamins, Muller and Chan, shown on the previous two pages.



Page 9

TEMPERATURE COEFFICIENT OF RESISTANCE

R/T for semiconductor resistors R = Rhos L/W = Rho/t L/W assume W, L, t do not change with T Rho = 1/(qµn + qµp) where µ is the mobility which is a function of temperature, n and p are the carrier concentrations which can be a function of temperature (in lightly doped semiconductors) as T increases, µ decreases, n or p may increase and the result is that R usually increases unless the decrease in µ is cancelled by the increase in n or p



Page 10

DIFFUSED RESISTOR

Aluminum contacts

The n-type wafer is always biased positive with respect to the p-type diffused region. This ensures that the pn junction that is formed is in reverse bias, and there is no current leaking to the substrate. Current will flow through the diffused resistor from one contact to the other. The I-V characteristic follows Ohm’s Law: I = V/R

n-wafer Diffused p-type region

Silicon dioxide

Sheet Resistance s ~ 1/( qµ Dose) ohms/square Ro = s L/W ohms



Page 11

RESISTOR NETWORK

500 W 400 250 W

Desired resistor network

Layout if Rhos = 100 ohms/square

L

W



Page 12

R AND C IN AN INTEGRATED CIRCUIT

Estimate the sheet resistance of the 4000 ohm resistor shown.

R

C

741 OpAmp



Page 13

DIFFUSION FROM A CONSTANT SOURCE

N(x,t) = No erfc (x/2 Dptp)

Solid Solubility Limit, No

x

into wafer

Wafer Background Concentration, NBC

N(x,t)

Xj

p-type

n-type

erfc function

for erfc predeposit

Q’A (tp) = QA(tp)/Area = 2 No (Dptp) / Dose

Where Dp is the diffusion constant at the predeposit temperature and tp is the predeposit time



Page 14

DIFFUSION FROM A LIMITED SOURCE

for erfc predeposit

Q’A (tp) = QA(tp)/Area = 2 No (Dptp) / Dose

N(x,t) = Q’A(tp) Exp (- x2/4Dt)

Dt

Where D is the diffusion constant at the drive in temperature and t is the drive in diffusion time, Dp is the diffusion constant at the predeposit temperature and tp is the predeposit time

Gaussian function



Page 15

DIFFUSION CONSTANTS AND SOLID SOLUBILITY

DIFFUSION CONSTANTS

BORON PHOSPHOROUS BORON PHOSPHOROUS

TEMP PRE or DRIVE-IN PRE DRIVE-IN SOLID SOLID

SOLUBILITY SOLUBILITY

NOB NOP

900 °C 1.07E-15 cm2/s 2.09e-14 cm2/s 7.49E-16 cm2/s 4.75E20 cm-3 6.75E20 cm-3

950 4.32E-15 6.11E-14 3.29E-15 4.65E20 7.97E20

1000 1.57E-14 1.65E-13 1.28E-14 4.825E20 9.200E20

1050 5.15E-14 4.11E-13 4.52E-14 5.000E20 1.043E21

1100 1.55E-13 9.61E-13 1.46E-13 5.175E20 1.165E21

1150 4.34E-13 2.12E-12 4.31E-13 5.350E20 1.288E21

1200 1.13E-12 4.42E-12 1.19E-12 5.525E20 1.410E21

1250 2.76E-12 8.78E-12 3.65E-12 5.700E20 1.533E21

Dp Dp or D D



Page 16

ION IMPLANTED RESISTOR

Like the diffused resistor but more accurate control over the sheet resistance. The dose is a machine parameter that is set by the user. Sheet Resistance s ~ 1/( qµ Dose) ohms/square Also the dose can be lower than in a diffused resistor resulting in higher sheet resistance than possible with the diffused resistor.

Aluminum contacts

n-wafer Ion Implanted p-type region

Silicon dioxide



Page 17

THIN FILM RESISTOR

Aluminum contacts

n-wafer Thin Layer of Poly Silicon

Or Metal

Silicon dioxide

For polysilicon thin films the Dose = film thickness ,t, x Solid Solubility No if doped by diffusion, or Dose ~ 1/2 ion implanter dose setting if implanted The Sheet Resistance Rhos ~ 1/( qµ Dose) + Rgrain boundaries ohms/square For metal the Sheet Resistance is ~ the given (table value) of bulk resistivity, Rho, divided by the film thickness ,t. Rhos = Rho / t ohms/square



Page 18

POLY SILICON

Grain boundary take up some of the implanted dose. They also add resistance to the resistor that is less sensitive to temperature and doping concentration. We assume grain size ~ equal to ½ the film thickness (t) and the number of grains equals the path length (L) divided by grain size (t/2). Each grain boundary adds a fixed resistance which is found empirically. (example 0.9 ohms)



Page 19

CALCULATION OF RESISTANCE

Dose/t = Concentration



Page 20

POLY RESISTOR

Poly

R = 1/SLOPE

= 1/0.681m

= 1468 ohm

Rhos = 1468/39

=37.6 ohm/sq

Use t=0.6, L=390u, W=10u Dose =1e16cm-2, N-type poly, and 0.9 ohms per boundary



Page 21

RESISTOR I-V CHARACTERISTICS

R= 1/1.44e-3

= 694 ohms

Use t=1.5u, L=500u, W=100u Dose =0.5e15cm-2 p-type single crystal silicon

Gives R=683 ohms



Page 22

CLOSE UP OF RESISTORS AND THERMOCOUPLE

Red N+ Polysilicon Resistor 60 um x 20 um + 30 to contact so L/W ~ 6

Green P+ Diffused Resistor 200 um wide x 180 um long

Aluminum – N+ Poly Thermocouple

Use t=0.5, L=120, w=20 dose =1e16, n-type poly, and 0.9 ohms per boundary Rmeas = 448

Use t=1.5, L=180, w=200 dose =2e14, p-type crystalline, Rmeas = 207



Page 23

RESISTOR TEMPERATURE RESPONSE

I

V 1 2 3 4

-4 -3 -2 -1

-0.002

-0.003

-0.004

0.004

0.003

0.002

Cold

Hot

L,W,xj do not change with light, µn and µp does not change with light but can change with temperature, n and p does not change much in heavy doped semiconductors (that is, n and p is determined by doping)

R = L/(W xj) ohms

1/( qµnn + qµpp)



Page 24

RESISTOR LIGHT RESPONSE

No light

Full light

R = L/(W xj) ohms

1/( qµnn + qµpp)

L,W,xj do not change with light, µn and µp does not change with light but can change with temperature, n and p does not change much in heavy doped semiconductors (that is, n and p is determined by doping)



Page 25

HEATERS

P= IV = I2R watts

Final steady state temperature

depends on power density in

watts/cm2

and

the thermal resistance

from heater to ambient

I

V

-

+

R = s L/W



Page 26

THERMAL CONDUCTIVITY

Temp ambient

Thermal Resistance, Rth

to ambient

Temp above ambient

Power input

Rth = 1/C L/Area where C=thermal conductivity L= thickness of layer between heater and ambient Area = cross sectional area of the path to ambient



Page 27

THERMAL PROPERTIES OF SOME MATERIALS

MP Coefficient Thermal Specific °C of Thermal Conductivity Heat Expansion ppm/°C w/cmK cal/gm°C Diamond 1.0 20 Single Crystal Silicon 1412 2.33 1.5 Poly Silicon 1412 2.33 1.5 Silicon Dioxide 1700 0.55 0.014 Silicon Nitride 1900 0.8 0.185 Aluminum 660 22 2.36 0.215 Nickel 1453 13.5 0.90 0.107 Chrome 1890 5.1 0.90 0.03 Copper 1357 16.1 3.98 0.092 Gold 1062 14.2 0.032 Tungsten 3370 4.5 1.78 Titanium 1660 8.9 0.17 Tantalum 2996 6.5 0.54 Air 0.00026 0.24 Water 0 0.0061 1.00

1 watt = 0.239 cal/sec



Page 28

HEATER EXAMPLE

Example: Poly heater 100x100µm has sheet resistance of 25 ohms/sq and 9 volts is applied. What temperature will it reach if built on 1 µm thick oxide?

Power = V2/R = 81/25 = 3.24 watt

Rthermal = 1/C L/Area = (1/0.014 watt/cm °C)(1e-4cm/(100e-4cm x100e-4cm))

= 71.4 °C/watt

Temperature = Tambient + (3.24) (71.4) = Tambient + 231 °C



Page 29

TEMPERATURE SENSOR EXAMPLE

Example: A poly heater is used to heat a sample. The temperature is measured with a diffused silicon resistor. For the dimensions given what will the resistance be at 90°C and 65°C

R(T,N) = 1

q µn (T,N) n

L

Wt

50µm 10µm

xj=t=1µm

Nd= n =1E18cm-3

(n-type)

q µn (T=273+65=338,N=1e18) n = 1.6e-19 (196) 1e18 = 31.4

q µn (T=273+90=363,N=1e18) n = 1.6e-19 (165) 1e18 = 26.4

50,000

R=1894 ohms

R=1592 ohms



Page 30

TEMPERATURE SENSOR EXAMPLE

Dose/t = Concentration



Page 31

DIODES AND HEATERS

Poly Heater on top of Diodes

Integrated n-well series resistor.

VDD

Vo ~ 0.6

-2.2mV/°C

I

V

T1 T2

T2>T1

I ~ (VDD-0.6)/R

R



Page 32

UNIFORMLY DOPED PN JUNCTION

n-type

p-type

Space Charge Layer

Potential,

Electric Field,

charge density,

n = ND p = NA

+qND

-W1

W2

+VR

x

+VR

-qNA

Ionized Immobile Phosphrous donor atom

Ionized Immobile Boron acceptor atom

Phosphrous donor atom and electron P+ -

B- +

Boron acceptor atom and hole

qNA W1 =qND W2

P+

B- B- +

B- +

P+ -

P+ B-

B- B-

P+

P+ P+ P+ -

P+ -

P+ -

P+ -



Page 33

UNIFORMLY DOPED pn JUNCTION

From Physical Fundamentals:

Relationship between electric flux D and electric field : D =

Gauss’s Law, Maxwells 1st eqn: = D

Poisson’s Equation: 2 = - /

Definition of Electric Field: = - V

Potential Barrier - Carrier Concentration: = KT/q ln (NA ND /ni2)

From Electric and Magnetic Fields :



Page 34

EXAMPLE CALCULATIONS

Width of space

charge layer depends

on the doping on

both sides and the

applied reverse bias

voltage and

temperature.



Page 35

CURRENTS IN PN JUNCTIONS

Vbi = turn on voltage

~ 0.7 volts for Si

VD

Id

VRB = reverse

breakdown voltage

p n

Id

+ VD -

Forward Bias

Reverse Bias

Id = Is [EXP (q VD/KT) -1]

Is

Ideal diode equation



Page 36

INTEGRATED DIODES

p-wafer

n+ p+ n-well

p+ means heavily doped p-type n+ means heavily doped n-type n-well is an n-region at slightly higher doping than the p-wafer

Note: there are actually two pn junctions, the well-wafer pn

junction should always be reverse biased



Page 37

REAL DIODES

Series Resistance =1/4.82m=207

Junction Capacitance ~ 2 pF

Is = 3.02E-9 amps

BV = > 100 volts

Size 80µ x 160µ

N

P



Page 38

DIODE SPICE MODEL

MEMS Diode

Model Parameter Default Value Extracted Value

Is reverse saturation current 1e-14 A 3.02E-9 A

N emission coefficient 1 1

RS series resistance 0 207 ohms

VJ built-in voltage 1 V 0.6

CJ0 zero bias junction capacitance 0 2pF

M grading coefficient 0.5 0.5

BV Breakdown voltage infinite 400

IBV Reverse current at breakdown 1E-10 A -

DXXX N(anode) N(cathode) Modelname

.model Modelname D Is=1e-14 Cjo=.1pF Rs=.1

.model RITMEMS D IS=3.02E-9 N=1 RS=207

+VJ=0.6 CJ0=2e-12 M-0.5 BV=400

DIODE Parameters



Page 39

DIODE TEMPERATURE DEPENDENCE

Id = IS [EXP (q VD/KT) -1]

Neglect the –1 in forward bias, Solve for VD

VD = (KT/q) ln (Id/IS) = (KT/q) (ln(Id) – ln(Is))

Take dVD/dT: note Id is not a function of T but Is is

dVD/dT = (KT/q) (dln(Id)/dT – dln(Is)/dT) + K/q (ln(Id) – ln(Is))

zero VD/T from eq 1 Rewritten

dVD/dT = VD/T - (KT/q) ((1/Is) dIs/dT )

Now evaluate the second term, recall

Is = qA (Dp/(LpNd) +Dn/(LnNa))ni2

eq 1

eq 2

Note: Dn and Dp are proportional to 1/T



Page 40

DIODE TEMPERATURE DEPENDENCE

and ni2(T) = A T 3 e - qEg/KT

This gives the temperature dependence of Is

Is = C T 2 e - qEg/KT

Now take the natural log

ln Is = ln (C T 2 e - qEg/KT)

Take derivative with respect to T

(1/Is) d (Is)/dT = d [ln (C T 2 e -qEg/KT)]/dT = (1/Is) d (CT2e-qEg/KT)dT

eq 3

= (1/Is) [CT2 e-qEg/KT(qEg/KT2) + (Ce-qEg/KT)2T]

= (1/Is) [Is(qEg/KT2) + (2Is/T)] Back to eq 2

dVD/dT = VD/T - (KT/q) [(qEg/KT2) + (2/T)])

dVD/dT = VD/T - Eg/T - 2K/q)



Page 41

EXAMPLE: DIODE TEMPERATURE DEPENDENCE

dVD/dT = VD/T - Eg/T - 2K/q

Silicon with Eg ~ 1.2 eV, VD = 0.6 volts, T=300 °K

dVD/dT = .6/300 – 1.2/300) - (2(1.38E-23)/1.6E-19

= -2.2 mV/°

I

V

T1 T2

T1<T2



Page 42

DIODE AS A TEMPERATURE SENSOR

Compare with theoretical -2.2mV/°C

Poly Heater Buried pn Diode,

N+ Poly to Aluminum Thermocouple

P+

N+



Page 43

SPICE FOR DIODE TEMPERATURE SENSOR



Page 44

PHOTODIODE

B -

P+ Ionized Immobile Phosphrous donor atom

Ionized Immobile Boron acceptor atom

Phosphrous donor atom and electron P+

-

B-

+ Boron acceptor atom and hole

n-type

p-type

B - P+

B - B -

B - B -

P+ P+ P+ P+

P+

P+

P+

-

B-

+

B - B -

P+

- P+

- P+

-

B-

+

- +

- +

I

electron

and hole

pair

- +

- +

space charge layer



Page 45

CHARGE GENERATION IN SEMICONDUCTORS

E = h = hc /

What wavelengths will not

generate e-h pairs in silicon.

Thus silicon is transparent or

light of this wavelength or

longer is not adsorbed?

From: Micromachined Transducers,

Gregory T.A. Kovacs

Material Bandgap

eV @ 300°K

max

(um)

GaN 3.360 0.369

ZnO 3.350 0.370

SiC 2.996 0.414

CdS 2.420 0.512

GaP 2.260 0.549

CdSe 1.700 0.729

GaAs 1.420 0.873

InP 1.350 0.919

Si 1.120 1.107

Ge 0.660 1.879

PbS 0.410 3.024

PbTe 0.310 4.000

InSb 0.170 7.294



Page 46

CHARGE GENERATION vs WAVELENGTH

I I

n-type

p-type

1 3 4 2

E = h = hc /

h = 6.625 e-34 j/s

= (6.625 e-34/1.6e-19) eV/s

E = 1.55 eV (red)

E = 2.50 eV (green)

E = 4.14 eV (blue) B - P+

B - B -

B - B -

P+ P+ P+ P+

P+

P+

P+

-

B-

+

B - B -

P+

- P+

- P+

-

B-

+

- + -

+ -

+



Page 47

ADSORPTION VERSUS DISTANCE

I

V

n

p

I V

I

+

V

-

More Light

No Light

Most Light

f(x) = f(0) exp- x

Find % adsorbed for Green light

at x=5 µm and Red light at 5 µm

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

250 450 650 850 1050 1250 1450

Adsorption Coefficient vs Wavelength

Wavelength (nm)

Adso

rpti

on C

oef

fici

ent,

(

1/c

m) For Silicon



Page 48

PN JUNCTION DESIGN FOR PHOTO DIODE

0µm 1µm 2µm 3µm 4µm

67%

100%

@850nm

@550nm

1017

1015

Space Charge Layer

60%



Page 49

SINGLE AND DUAL PHOTO CELL

Isc = 0.585 uA

Isc = 1.088 uA

Pmax=0.32V 0.909uA

=0.29uW



Page 50

CAPACITORS

Capacitor - a two terminal device whose current is proportional to the time rate of change of the applied voltage; I = C dV/dt a capacitor C is constructed of any two conductors separated by an insulator. The capacitance of such a structure is: C = o r Area/d where o is the permitivitty of free space r is the relative permitivitty Area is the overlap area of the two conductor separated by distance d

o = 8.85E-14 F/cm

I

C V

+

-

Area

d r air = 1 r SiO2 = 3.9



Page 51

OTHER CAPACITOR CONFIGURATIONS

C2

C1

C Total = C1C2/(C1+C2)

Two Dielectric Materials between Parallel Plates

Example: A condenser microphone is made from a polysilicon plate 100 µm

square with 1000Å silicon nitride on it and a second plate of aluminum with a

1µm air gap. Calculate C and C’ if the aluminum plate moves 0.1 µm.



Page 52

DIELECTRIC CONSTANT OF SELECTED MATERIALS

Vacuum 1

Air 1.00059

Acetone 20

Barium strontium titanate

500

Benzene 2.284

Conjugated Polymers

6 to 100,000

Ethanol 24.3

Glycerin 42.5

Glass 5-10

Methanol 30

Photoresist 3

Plexiglass 3.4

Polyimide 2.8

Rubber 3

Silicon 11.7

Silicon dioxide 3.9

Silicon Nitride 7.5

Teflon 2.1

Water 80-88

http://www.asiinstruments.com/technical/Dielectric%20Constants.htm

http://www.asiinstruments.com/technical/Dielectric Constants.htm



Page 53

CALCULATIONS



Page 54


Interdigitated Fingers with Thickness > Space between Fingers

h = height of fingers s = space between fingers N = number of fingers L = length of finger overlap

C = (N-1) or L h /s

Example:



Page 55


Interdigitated Fingers with Thickness << Space between Fingers

C = LN 4 or

n=1

0 0 1

2n-1 Jo2 (2n-1)s

2(s+w)

Jo = zero order Bessel function w = width of fingers s = space between fingers N = number of fingers L = length of finger overlap

Reference:

Lvovich, Liu and Smiechowski,



Page 56


Two Long Parallel Wires Surrounded by Dielectric Material

C/L = 12.1 r / (log [(h/r) + ((h/r)2-1)1/2]

h = half center to center space r = conductor radius (same units as h)

Capacitance per unit length C/L

Reference: Kraus and Carver

Example: Calculate the capacitance of a meter long connection of parallel wires.

Solution: let, h = 1 mm, r = 0.5mm, plastic er = 3 the equation above gives

C/L = 63.5 pF/m

C = 63.5 pF



Page 57


Coaxial Cable

C/L = 2 r / ln(b/a)

b = inside radius of outside conductor a = radius of inside conductor

Capacitance per unit length C/L

Reference: Kraus and Carver

Example: Calculate the capacitance of a meter long coaxial cable.

Solution: let b = 5 mm, a = 0.2mm, plastic er = 3 the equation above gives

C/L = 51.8 pF/m

C = 51.8 pF



Page 58

CAPACITORS AS SENSORS

C d

C1

C2

C

d

C1

d

C2

One plate moves relative to other changing gap (d)

One plate moves relative to other

changing overlap area (A)

Center plate moves relative to the two

fixed plates



Page 59

CAPACITORS AS SENSORS

Change in Space Between Plates (d) Change in Area (A)

Change in Dielectric Constant (er)

microphone gyroscope

position sensor



Page 60

CHEMICAL SENSOR

Two conductors separated by a material that changes its dielectric constant as it selectively absorbs one or more chemicals. Some humidity sensors are made using a polymer layer as a dielectric material.

Change in Dielectric Constant (er)

chemical sensor



Page 61

REFERENCES

1. Device Electronics for Integrated Circuits, Richard S. Muller, Theodore I. Kamins, John Wiley & Sons., 3rd edition, 2003.

2. Micromachined Transducers, Gregory T.A. Kovacs, McGraw-Hill, 1998.

3. Microsystem Design, Stephen D. Senturia, Kluwer Academic Press, 2001.

4. “Optimization and fabrication of planar interdigitated impedance sensors for highly resistive non-aqueous industrial fluids”, Lvovich, liu and Smiechowski, Sensors and Actuators B:Chemical, Volume 119, Issue 2, 7 Dec. 2006, pgs 490-496.

5. Solar Cells, Martin A. Green, Prentice-Hall

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MEMS Electrical Fundamentals - RIT - People · MEMS Electrical Fundamentals Page 3 INTRODUCTION Resistor heaters are used in many MEMS applications including ... This module will