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

2 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.

3 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

4 Thermal conductivity of various materials Kovacs

5 Thermal properties of more materials Kovacs

6 Consequences and utilization of the thermal expansion differences

7 Mechanical properties added as useful in MEMS Peterson

8 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

9 Basic Properties of Silicon Silicon in microelecronics Single Crystal PolycrystallineAmorphous and in MEMS periodicsmall crystalsno long range arrangements order between of atomsatoms 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

10 Silicon Crystal Structure Diamond lattice (Si, Ge, GaAs) Two interpenetrating FCC structures 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

11 Intrinsic=Undoped Semiconductor Electron and hole generation occur at elevated temperature (above 0K). n=p Energy Band Gap determines the intrinsic carrier concentration. n i E gGe < E gSi < E gGaAs Plummer

12 Electrical Properties of Semicondutors Explained by a Band Model and Bond Model n=p Intrinsic (Undoped) Silicon Energy Gap T>0K Plummer

13 Band structure of crystalline Si E g [eV] is Bandgap Indirect semiconductor EcEc EvEv EgEg

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15 N- and p-type semiconductor N-typep-type Plummer

16 Electrical Properties of Semicondutors Explained by a Band Model and Bond Model n-type Silicon doped with As Very small ionization energies E D and E A n=N As Plummer

17 Distribution of Free Carries (electrons and holes) Obeys Pauli Exclusion Principle Intrinsic Semiconductorn-type Semiconductorp=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 E i above E i p=N a n=N d Fermi Dirac probability function: Plummer

18 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 E G (eV)= x10 -4 T 2 /(T+636) ≈ (3x10 -4 )T Plummer

19 Dopant Ionization n n >>p n n i ≈p i n-type semiconductor intrinsic semiconductor n i =1.45x10 10 cm -3 at RT (300K) Selected Thermo-resistors will rely on this effect Plummer

20 Measurements of semiconductor properties Conductivity Type Plummer

21 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

22 Resistivity as a Function of Dopant Concentration  =1/(qµ n n+qµ p p) µ carrier mobility depends on scattering e.i. dopants, lattice imperfections (defects) andvibration (temperature) Plummer

23 W t L Concept of Sheet Resistance of doped layers.  s [  /sq.]  4 point probe or van der Pauw ResistivitySheet resistance Sheet resistance in an important parameter both in electron devices ex: in MOSFETs R contact + R source + R ext < 10% R chen  s  but keep x j small to avoid DIBL (conflicting requirements and in MEMS Plummer

24 Measurements of sheet resistance Resistivity Plummer

25 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

26 Spreading resistance temperature sensors n- Si Single probe used to induce current flow in n-type Si r0r0 Resistance measurements is at r 0 where a second probe (contact is located). A(r) Such sensors are widely used (flow sensors etc) cheap but not very accurate.

27 Thermo-resistors (thermistors) Semiconductors (n&p ) and some oxides (“electron- hopping ) show decrease in R T Metals (more carrier scattering) and other oxides (phase transformation, potential barrier at grain boundaries changes also related to polarization changes) show increase in R T with T R(T) T  R <0  R >0 Temperature affects resistance in: Both types have wide applications in MEMS Kovacs

28 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

29 Hall Effect Measurement Plummer

30 Optical Sensors and Actuators Crystalline semiconductors are used for these applications Kovacs

31 Devices for Optical Actuation Kovacs

32 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 E F ) is always filled with electron=majority carrier and waits for a minority hole.  R =1/  v th N t lifetime capture cross section thermal velocity, and traps Plummer

33 Semiconductor Devices Diodes Bipolar Junction Transistors (BJT) Metal Oxide Semiconductor Field Effect Transistors (MOS FET)

34 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

35 Semiconductor Devices Reverse biased diodeForward 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 V f decreases with T but in reverse bias conditions V R may decrease or increase with T depending on a mechanism of breakdown

36 MOS Capacitors and Transistors Electrical Measurements MOS Capacitors are widely used in MEMS Capacitance-voltage method Charge Density accumulator depletion Inversion Equilibrium conditions. ac signal Plummer

37 CV Measurements Low frequency (~1Hz), high frequency (100Khz – 11) AC signals used for C-V Measurements.) Q I follows Q G  C =C OX X D = X Dmax  Q D fixed X D > X Dmax Holes generated in the D.L and attracted by the gate source the DL when |V G | increases To avoid deep depletion*: High frequency AC signal changes faster, then Q I can respond (generation is slow) * Plummer

38 Bipolar Transistors E-B junction is forward biased=injects minority carriers to the base Base (electrically neutral) is responsible for electron transport via diffusion (or drift also if the build in electric field exist) to collector C-B diode is reverse biased and collects transported carries V BE >0 V BC <0 I E =I En +I Ep IC=IEIC=IE  <1 I B =I Ep +I rec IEIE ICIC IBIB

39 Bipolar Junction Transistors n-p-n Integrated circuit BJT p-n-p Individual device

40 Bipolar Junction Transistors minority carriers Injected electrons Extracted electrons holes Forwards biasReverse bias

41 Bipolar Junction Transistors Currents’ Components small

42 Bipolar Junction Transistors Forward Operation Mode Early Effect Early Voltage

43 Bipolar Junction Transistors Breakdown Voltages Common Base Common Emitter Collector-Base junction

44 Bipolar Junction Transistors Current Gain  =  Gummel Plot Kirk Effect Recombination in the E-B SCR  I C /I B

45 Bipolar Junction Transistors and a Switch Schottky Diode used in n-p-n BJTs for faster speed

46 MOS Field Effect Transistors (MOSFET) NMOS and PMOS (used in CMOS circuits) V G >V T to create strong inversion depletion Oxide

47 Operation of NMOS-FET Linear Region, Low V D Saturation Region, Channel Starts to Pinch-Off Saturation Region, channel shortens beyond pinch-off, L’<L

48 Operation of MOS-FET I D (V D ) Channel-Length-Modulation (Shorten by  L) I D =k p [(V G -V T )V D -V D 2 /2 Device transconductance k p =µ n C ox W/L larger for NMOS than PMOS In CMOS for compensation use W p >W n

49 Scaled Down NMOS DIBL Proximity of the drain depletion layer charge sharing DIBL

50 Modern MOS Transistors Gate LDD LDD used to reduce the electric field in the drain depletion region and hot carrier effects Self aligned contacts decrease the resistance isolation DrainSource