ndian nstitute of Technology Jodhpur, Year 08 Analog Electronics (ourse ode: EE34) ecture 8 9: MOSFETs, Biasing ourse nstructor: Shree Prakash Tiwari Email: sptiwari@iitj.ac.in Webpage: http://home.iitj.ac.in/~sptiwari/ / / ourse related documents will be uploaded on http://home.iitj.ac.in/~sptiwari/ee34/ Note: The information provided in the slides are taken form text books for microelectronics (including Sedra & Smith, B. Razavi), and various other resources from internet, for teaching/academic use only MOSFET in ON State ( > ) The channel charge density is equal to the gate capacitance times the gate voltage in excess of the threshold voltage. Areal ersion charge density [/cm ]: Q ( ) Note that the reference voltage is the source voltage. n this case, is defined as the value of at which the channel surface is strongly erted (i.e. n = N A at x=0, for an NMOSFET).
MOSFET as oltage ontrolled Resistor For small, the MOSFET can be viewed as a resistor, with the channel resistance depending on the gate voltage. R ON Note that resistivity t qn t W q n Q R ON n n W t W MOSFET hannel Potential ariation f the drain is biased at a higher potential than the source, the channel potential increases from the source to the drain. The potential difference between the gate and channel decreases from the source to drain.
hannel harge MOS structure looks like parallel plate capacitor while operating in ersions Gate ide channel Q channel = = g = W/t = W = / t = gc t = ( gs ds /) t polysilicon gate t n+ n+ p-type body W SiO gate ide (good insulator, = 3.9) + gate g + source g gd drain - - channel n+ - + n+ s ds p-type body d 5 arrier velocity harge is carried by e Electrons are propelled by the lateral electric field between source and drain E = ds / arrier velocity v proportional to lateral E field v = E called mobility Time for carrier to cross channel: t = / v 6 3
Now we know nmos inear How much charge Q channel is in the channel How much time t each carrier takes to cross ds Qchannel t W ds gs t ds ds gs t ds W = 7 nmos Saturation f gd < t, channel pinches off near drain When ds > d = gs t Now drain voltage no longer increases current d gs t ds gs t d 8 4
harge ensity along the hannel The channel potential varies with position along the channel: Q ( y) ( y) The current flowing in the channel lis WQ ( y ) v ( y ) The carrier drift velocity at position y is v( y) ne n where n is the electron field effect mobility d ( y) dy rain urrent, (for < ) d ( y) WQ( y) v( y) WQ( y) n dy ntegrating from source to drain: W n S d W n 0 dy S W Q n ( ) d n W ( ) 5
haracteristic For a fixed value of, is a parabolic function of. reaches a maximum value at =. n W ( ) nversion ayer Pinch Off ( > ) When =, Q = 0 at the drain end of the channel. The channel is pinched off. As increases above, the pinch off point (where Q = 0) moves toward the source. Note that the channel potential is always equal to at the pinch off point. The maximum voltage that can be applied across the ersion layer channel (from source to drain) is. The drain current urates at a maximum value. 6
urrent Flow in Pinch Off Region Under the influence of the lateral electric field, carriers driftfrom from the source (through the ersion layer channel) toward the drain. A large lateral electric field exists in the pinch off region: E Once carriers reach the pinch off point, they are swept into the drain by the electric field. rain urrent Saturation (ong hannel MOSFET) For > :, n W, 7
MOSFET Regions of Operation When the potential When the potential difference between difference between the the gate and drain is gate and drain is equal greater than, the to or less than, the MOSFET is operating MOSFET is operating in in the triode region. the uration region. Triode or Saturation? n circuit analysis, when the MOSFET region of operation is not known, an intelligent guess should be made; then the resulting answer should be checked against the assumption. Example: Given n = 00 A/, = 0.4. f G increases by 0m, what is the change in? 8
The Body Effect is increased by reverse biasing the body source PN junction: FB FB B B qn qn ( A Si qn A Si( B) B SB ) qn A Si ( B) A Si 0 B SB B 0 B SB is the body effect parameter. qn ( A Si B SB B ) hannel ength Modulation The pinch off point moves toward the source as increases. The length of the ersion layer channel becomes shorter with increasing. increases (slightly) with increasing in the uration region of operation. W is the channel length modulation coefficient., n, 9
and The effect of channel length modulation is less for a longchannel MOSFET than for a short channel MOSFET. elocity Saturation n state of the art MOSFETs, the channel is very short (<0.m); hence the lateral electric field is very high and carrier drift velocities can reach their uration levels. The electric field magnitude at which the carrier velocity urates is E. v 6 80 cm/s for electrons in Si v 6 60 cm/s for holes in Si E 0
mpact of elocity Saturation Recall that WQ ( y) v( y) f > E, the carrier velocity will urate and hence the drain current will urate:, WQ v W, is proportional to rather than ( ), is notdependent on, is dependent on W v Short hannel MOSFET P. Bai et al. (ntel orp.), nt l Electron evices Meeting, 004., is proportional to rather than ( ), is smaller than hannel length modulation is apparent (?)
rain nduced Barrier owering (B) n a short channel MOSFET, the source & drain regions each support a significant fraction of the total channel depletion charge Q dep W is lower than for a long channel MOSFET As the drain voltage increases, the reverse bias on the body drain PN junction increases, and hence the drain depletion region widens. decreases with increasing drain bias. (The barrier to carrier diffusion from the source into the channel is reduced.) increases with increasing drain bias. NMOSFET in OFF State We had previously assumed that there is no channel current when <. This is incorrect! As is reduced (toward 0 ) below, the potential barrier to carrier diffusion from the source into the channel is increased. becomes limited by carrier diffusion into the channel, rather than by carrier drift through the channel. (This is similar to the case of a PN junction diode!) varies exponentially with the potential barrier height at the source, whichvaries directlywith the channel potential.
Sub Threshold eakage urrent Recall that, in the depletion (sub threshold) region of operation, the channel potential is capacitively coupled to the gate potential. A change in gate voltage tage( ( ) ) results in a change in channel voltage ( S ): S / m dep Therefore, the sub threshold current (,subth ) decreases exponentially with linearly decreasing /m log ( ) Sub threshold swing : d(log0 ) S d S m ln(0) 60m/dec T Short hannel MOSFET P. Bai et al. (ntel orp.), nt l Electron evices Meeting, 004. 3
esign Trade Off ow is desirable for high ON state current:, ( ) < < But high is needed for low OFF state current: OFF,low log ow High cannot be reduced aggressively. 0 OFF,high MOSFET arge Signal Models ( > ) epending on the value of, the MOSFET can be represented with different large signal models. << ( ) <, >, R ON W n ( ), tri n W ( ), W n, or v W ( ),, 4
MOSFET Transconductance, g m Transconductance (g m ) is a measure of how much the drain current changes when the gate voltage changes. gm For amplifier applications, the MOSFET is usually operating in the uration region. For a long channel MOSFET: W g m n, W g m n, For a short channel MOSFET: g m vw, MOSFET Small Signal Model (Saturation Region of Operation) The effect of channel length modulation or B (which cause to increase linearly with ) is modeled by the transistor output resistance, r o. ro 5
PMOS Transistor A p channel MOSFET behaves similarly to an n channel MOSFET, except the polarities for and are reversed. Schematic cross section ircuit symbol The small signal model for a PMOSFET is the same as that for an NMOSFET. The values of g m and r o will be different for a PMOSFET vs. an NMOSFET, since mobility & uration velocity are different for holes vs. electrons. PMOS Equations For <, : W, tri p ( ), For >, :,, p W v W ( or ),, for long channel for short channel 6
MOS Technology t possible to form deep n type regions ( well ) within a p type substrate to allow PMOSFETs and NMOSFETs to be co fabricated on a single substrate. This is referred to as MOS ( omplementary MOS ) technology. Schematic cross section of MOS devices omparison of BJT and MOSFET The BJT can achieve much higher g m than a MOSFET, for a given bias current, due to its exponential characteristic. 7
oltage ontrolled Attenuator As the gate voltage decreases, the output drops because the channel resistance increases. This type of gain control finds application in cell phones to avoid uration near base stations. Application of Electronic Switches n a cordless telephone system in which a single antenna is used for both transmission and reception, a switch is used to connect either the receiver or transmitter to the antenna. 8
Effects of On Resistance To minimize signal attenuation, R on of the switch has to be as small as possible. This means larger W/ aspect ratio and greater. MOSFET Biasing The voltage at node X is determined by, R, and R : Also, R X S R X R R n W R R R where W n RS 9
Self Biased MOSFET Stage Note that there is no voltage dropped across R G M is operating in the uration region. R R S MOSFETs as urrent Sources A MOSFET behaves as a current source when it is operating in the uration region. An NMOSFET draws current from a point to ground ( sinks current ), whereas a PMOSFET draws current from to a point ( sources current ). 0
MOSFET Amplifiers What next