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Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 3
INTRODUCTION
Resistors are used as heaters, temperature sensors, piezoreistorsensors and photoconductors. Heaters are used in many MEMS applications including ink jet print heads, actuators, bio-mems, chemical detectors and gas flow sensors. Diodes, Capacitors, electrostatic comb drives, magnetic devices, and many other devices are used in many applications. This module will discuss these devices as they apply to MEMS.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 11
OHMS 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.
Electron and hole mobilitiesin silicon at 300 K as functions of the total dopantconcentration (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:
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 15
EXCELL WORKSHEET TO CALCULATE MOBILITY
MICROELECTRONIC ENGINEERING 3/13/2005
CALCULATION OF MOBILITY Dr. Lynn Fuller
To use this spreadsheed change the values in the white boxes. The rest of the sheet isprotected and should not be changed unless you are sure of the consequences. Thecalculated results are shown in the purple boxes.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 16
EXCELL WORKSHEET TO CALCULATE RESISTANCE
MICROELECTRONIC ENGINEERING 7/23/2007Rochester Institute of Technology Dr. Lynn Fuller
CALCULATION OF RESISTANCE FROM LENGTH, WIDTH, THICKNESS AND IMPLANT DOSE
To use this spreadsheed change the values in the white boxes. The rest of the sheet isprotected and should not be changed unless you are sure of the consequences. Thecalculated results are shown in the purple boxes.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 17
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
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 18
RESISTANCE AS A FUNCTION OF TEMPERATURE
R(T,N) = 1
qµn(T,N) n + q µp (T,N) pL
Wt
L, W, t, are physical length width and thickness and do not change with TConstant q = 1.6E-19 coulµn (T,N) = see expression on previous pageµp (T,N) = see expression on previous pagen = Nd and p = 0 if doped n-typen=0 and p = Na if doped p-typen = p = ni(T) if undoped, see exact calculation on next page
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 20
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
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 24
DIFFUSION FROM A LIMITED SOURCE
for erfc predepositQ’A (tp) = QA(tp)/Area = 2 No (Dptp) / π = Dose
N(x,t) = Q’A(tp) Exp (- x2/4Dt)π 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
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 27
THIN FILM RESISTOR
Aluminum contacts
n-wafer Thin Layer of Poly SiliconOr Metal
Silicon dioxide
For polysilicon thin films the Dose = film thickness ,t, x Solid Solubility No if doped by diffusion, or Dose = ion implanter dose setting if implanted
The Sheet Resistance Rhos = ~ 1/( qµ Dose) ohms/square
For metal the Sheet Resistance is ~ the given (table value) of bulk resistivity, Rho, divided by the film thickness ,t.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 32
TEMPERATURE SENSOR EXAMPLE
Example: A diffused heater is used to heat a sample. The temperature is measured with a poly silicon resistor. For the dimensions given what will the resistance be at 90°C and 65°C
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 34
GAS FLOW SENSORS
Constant heat (power in watts) input and two temperature measurement devices, one upstream, one downstream. At zero flow both sensors will be at the same temperature. Flow will cause the upstream sensor to be at a lower temperature than the down stream sensor.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 36
SINGLE WIRE ANEMOMETER
A single heater/sensor element is placed in the flow. The amount of power supplied to keep the temperature constant is proportional to flow. At zero flow a given amount of power Po will heat the resistor to temperature To. With non zero flow more power Pf is needed to keep the resistor at To.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 38
PHYSICAL FUNDAMENTALS - PIEZORESISTANCE
Piezoresistance is defined as the change in electrical resistance of a solid when subjected to stress. The piezorestivity coefficient is Π and a typical value may be 1e−10 cm2/dyne.
The fractional change in resistance ∆R/R is given by:
∆R/R = Π σ
where σ is the stress. Other references use the gage factor GF to describe the piezoresistive effect where
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 42
CALCULATION OF EXPECTED OUTPUT VOLTAGE
The sheet resistance (Rhos) from 4 point probe is 61 ohms/sqThe resistance is R = Rhos L/WFor a resistor R3 of L=350 µm and W=50 µm we find:
R3 = 61 (350/50) = 427.0 ohms
R3 and R2 decrease as W increases due to the strainassume L is does not change, W’ becomes 50+50x0.131%W’ = 50.0655 µmR3’ = Rhos L/W’ = 61 (350/50.0655) = 426.4 ohms
R1 and R4 increase as L increases due to the strainassume W does not change, L’ becomes 350 + 350x0.131%R1’ = Rhos L’/W = 61 (350.459/50) = 427.6 ohms
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 48
MEMS CANTILEVER WITH ELECTROSTATIC ACTUATOR
Poly 2
Poly 1
Metal
y
V0 10 20 30
1
2
3um
3µm gap
As the voltage is increased the electrostatic force starts to pull down the cantilever. The spring constant opposes the force but at the same time the gap is increased and the force increases. The electrostatic force increases with 1/d2 so eventually a point is reached where it is larger than the spring and the cantilever snaps down all the way. The voltage has to be reduced almost to zero to release the cantilever.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 49
MEMS CANTILEVER WITH ELECTROSTATIC ACTUATOR
Example: Plot the displacement versus current assuming poly sheet resistance of 200 ohms/sq, a piezoresistance coefficient of 1e-10 cm/dyne, d=1.5 µm, h=2µm and other appropriate assumptions.
The magnetic pole strength is m (webers) = B A where A is the pole area
Magnetic flux density of a permanent magnet B is given by the manufacturer in units of weber/sq.meter or Tesla. (some of the magnets we use in MEMS are 2mm in diameter and have B=0.5 Tesla)
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 59
MAGNETIC SOLENOID
Example: Given a nickel core solenoid of length 200 µm with 25 turns and 0.1 amp of current. The cross-sectional area is 40 µm by 2µm. Calculate the force needed to move the core.
F = (µo/2)(µr-1) (NI/L)2A
F = (4π e-7/2)(600-1)[(25)(0.1)/200e-6)]2(40e-6)(2e-6)
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 63
PIEZOELECTRIC DRIVES
A piezoelectric material will exhibit a change in length in response to an applied voltage. The reverse is also possible where an applied force causes the generation of a voltage. Single crystal quartz has been used for piezeoelectric devices such as gas grill igniters and piezoelectric linear motors. Thin films of various materials (organic and inorganic) exhibit piezoelectric properties. ZnO films 0.2 µm thick are sputtered and annealed 25 min, 950C giving piezoelectric properties. Many piezoelectric materials also exhibit pyroelectricproperties (voltage - heat).
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 64
SEEBECK EFFECT
When two dissimilar conductors are connected together a voltage may be generated if the junction is at a temperature different from the temperature at the other end of the conductors (cold junction) This is the principal behind the thermocouple and is called the Seebeck effect.
∆V
Material 2Material 1
Hot
Cold
Nadim Maluf, Kirt Williams, An Introduction to Microelectromechanical Systems Engineering, 2nd Ed. 2004
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 65
PELTIER EFFECT
Heat pump device that works on the gain in electron energy for materials with low work function and the loss in energy for materials with higher work function. Electrons are at higher energy (lower work function) in n-type silicon.
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 75
LIGHT EMITTING DIODES (LEDs)
P-side N-side
SpacechargeLayer
LightLight
Hole concentration vs distnace
xx
Electron concentration vs distance
In the forward biased diode current flows and as holes recombine on the n-side or electrons recombine on the p-side, energy is given off as light, with wavelength appropriate for the energy gap for that material. λ = h c / E
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 76
REFERENCES
1. Mechanics of Materials, by Ferdinand P. Beer, E. Russell Johnston, Jr., McGraw-Hill Book Co.1981, ISBN 0-07-004284-5
2. Electromagnetics, by John D Kraus, Keith R. Carver, McGraw-Hill Book Co.1981, ISBN 0-07-035396-4
3. “Etch Rates for Micromachining Processing”, Journal of Microelectromechanical Systems, Vol.5, No.4, December 1996.
4. “Design, Fabrication, and Operation of Submicron Gap Comb-Drive Microactuators”, Hirano, et.al. , Journal of Microelectromechanical Systems, Vol.1, No.1, March 1992, p52.
5. “Piezoelectric Cantilever Microphone and Microspeaker”, Lee, Ried, White, Journal of Microelectromechanical Systems, Vol.5, No.4, December 1996.
6. “Crystalline Semiconductor Micromachine”, Seidel, Proceedings of the 4th Int. Conf. on Solid State Sensors and Actuators 1987, p 104
7. Fundamentals of Microfabrication, M. Madou, CRC Press, New York, 19978. Element properties: http://web.mit.edu/3.091/www/pt/
Rochester Institute of TechnologyMicroelectronic Engineering
MEMS Electrical Fundamentals
Page 77
HOMEWORK – MEMS ELECTRICAL
1. Calculate the voltage needed to pull down a polysilicon cantiliverby electrostatic force. Make appropriate assumptions for dimensions.
2. Calculate the number of fingers needed in an electrostatic comb drive to create a force of 10 micro newtons. Make appropriate assumptions for dimensions.
3. What coil current is needed to create a force of 10 micro newtonsin a magnetic field of 0.5 Tesla. Make appropriate assumptions for dimensions.
4. In a thermocouple made of aluminum on n+ poly what voltage will be generated for a temperature difference of 70 °C?
5. A diode is used as a temperature sensor and is forward biased with a 1.5 Volt battery in series with a 10Kohm resistor. If the device is used to measure body temperature (nominal 98.6 °F) how much change in voltage across the diode if someone had a temperature of 102.6°F.