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1 λ i d displaystyle r_ text out frac 1 lambda i_ text d note r out is the inverse of g ds where g ds i ds v ds displaystyle g_ text ds frac partial i_ text ds partial v_ text ds i d is the expression in the saturation region if λ is taken as zero an infinite output resistance of the device results that leads to unrealistic circuit predictions particularly in analog circuits as the channel length becomes very short these equations become quite inaccurate new physical effects arise for example carrier transport in the active mode may become limited by velocity saturation when velocity saturation dominates the saturation drain current is more nearly linear than quadratic in v gs at even shorter lengths carriers transport with near zero scattering known as quasi ballistic transport in the ballistic regime the carriers travel at an injection velocity that may exceed the saturation velocity and approaches the fermi velocity at high inversion charge density in addition drain induced barrier lowering increases off state cutoff current and requires an increase in threshold voltage to compensate which in turn reduces the saturation current 48 49 verification needed body effect main article body effect band diagram showing body effect v sb splits fermi levels f n for electrons and f p for holes requiring larger v gb to populate the conduction band in an nmos mosfet the occupancy of the energy bands in a semiconductor is set by the position of the fermi level relative to the semiconductor energy band edges application of a source to substrate reverse bias of the source body pn junction introduces a split between the fermi levels for electrons and holes moving the fermi level for the channel further from the band edge lowering the occupancy of the channel the effect is to increase the gate voltage necessary to establish the channel as seen in the figure this change in channel strength by application of reverse bias is called the body effect using an nmos example the gate to body bias v gb positions the conduction band energy levels while the source to body bias v sb positions the electron fermi level near the interface deciding occupancy of these levels near the interface and hence the strength of the inversion layer or channel the body effect upon the channel can be described using a modification of the threshold voltage approximated by the following equation v tb v t 0 γ v sb 2 φ b 2 φ b displaystyle v_ text tb v_ t0 gamma left sqrt v_ text sb 2 varphi _ b sqrt 2 varphi _ b right where v tb is the threshold voltage with substrate bias present and v t0 is the zero v sb value of threshold voltage γ displaystyle gamma is the body effect parameter and 2 φ b is the approximate potential drop between surface and bulk across the depletion layer when v sb 0 and gate bias is sufficient to ensure that a channel is present 50 as this equation shows a reverse bias v sb 0 causes an increase in threshold voltage v tb and therefore demands a larger gate voltage before the channel populates the body can be operated as a second gate and is sometimes referred to as the back gate the body effect is sometimes called the back gate effect 51 circuit symbols a variety of symbols are used for the mosfet the basic design is generally a line for the channel with the source and drain leaving it at right angles and then bending back at right angles into the same direction as the channel sometimes three line segments are used for enhancement mode and a solid line for depletion mode see depletion and enhancement modes another line is drawn parallel to the channel for the gate a 4 terminal nmos has two intrinsic body diodes due to the body to drain and body to source p n junctions in pmos these diodes are reversed the body to source diode is made irrelevant by shorting the body to the source in 3 terminal devices the remaining body to drain diode prevents the nmos from blocking source to drain current and is used in some dc to dc converters 52 the bulk or body connection if shown is shown connected to the back of the channel with an arrow indicating pmos or nmos this arrow always points from p to n so an nmos n channel in p well or p substrate has the arrow pointing from the bulk to the channel typically the bulk is internally connected to the source as is generally the case with discrete devices in which case the bulk end of the arrow will have a line drawn between it and the source to explicitly show this connection some symbols will also explicitly show the mosfet s intrinsic body diode along an outer and sometimes dotted as may be done for parasitic elements path between drain and source note that tying the bulk to the source is by no means the only important configuration in general the mosfet is a four terminal device in integrated circuits many of the mosfets share a body connection not necessarily connected to the source terminals of all the transistors if the bulk is not shown as is often the case in ic design as they are generally common bulk an inversion symbol is sometimes used to indicate pmos alternatively as is done with bipolar transistors an arrow on the mosfet s source may indicate the direction of conventional current pointing out for nmos in for pmos in the following symbols for jfets enhancement mode mosfets and depletion mode mosfets the orientation of the symbols most significantly the position of source relative to drain is such that more positive voltages appear higher on the page than less positive voltages implying conventional current flowing down the page 53 54 55 jfet enhancement mode mosfet depletion mode mosfet bulk explicitly tied to source exposed bulk terminal bulk connection not shown note 1 bulk explicitly tied to source p channel n channel in schematics where g s d are not labeled the detailed features of the symbol indicate which terminal is source and which is drain for enhancement mode and depletion mode mosfet symbols in columns two and five the source terminal is the one connected to the triangle additionally in this diagram the gate is shown as an l shape whose input leg is closer to s than d also indicating which is which however these symbols are often drawn with a t shaped gate as elsewhere on this page so it is the triangle which must be relied upon to indicate the source terminal applications digital integrated circuits such as microprocessors and memory devices contain thousands to billions of integrated mosfets on each device providing the basic switching functions required to implement logic gates and data storage discrete devices are widely used in applications such as switch mode power supplies variable frequency drives and other power electronics applications where each device may be switching thousands of watts radio frequency amplifiers up to the uhf spectrum use mosfet transistors as analog signal and power amplifiers radio systems also use mosfets as oscillators or mixers to convert frequencies mosfet devices are also applied in audio frequency power amplifiers for public address systems sound reinforcement and home and automobile sound systems citation needed mos integrated circuits following the development of clean rooms to reduce contamination to levels never before thought necessary and of photolithography 56 and the planar process to allow circuits to be made in very few steps the si sio 2 system possessed the technical attractions of low cost of production on a per circuit basis and ease of integration largely because of these two factors the mosfet has become the most widely used type of transistor in the institution of engineering and technology iet citation needed general micro electronics introduced the first commercial mos integrated circuit in 1964 57 additionally the method of coupling two complementary mosfets p channel and n channel into one high low switch known as cmos means that digital circuits dissipate very little power except when actually switched the earliest microprocessors starting in 1970 were all mos microprocessors fabricated entirely from pmos logic or fabricated entirely from nmos logic in the 1970s mos microprocessors were often contrasted with cmos microprocessors and bipolar bit slice processors 58 cmos circuits the mosfet is used in digital complementary metal oxide semiconductor cmos logic 59 which uses p and n channel mosfets as building blocks overheating is a major concern in integrated circuits since ever more transistors are packed into ever smaller chips cmos logic reduces power consumption because no current flows ideally and thus no power is consumed except when the inputs to logic gates are being switched cmos accomplishes this current reduction by complementing every nmos fet with a pmos fet and connecting both gates and both drains together a high voltage on the gates will cause the nmos fet to conduct and the pmos fet not to conduct and a low voltage on the gates causes the reverse during the switching time as the voltage goes from one state to another both mosfets will conduct briefly this arrangement greatly reduces power consumption and heat generation digital the growth of digital technologies like the microprocessor has provided the motivation to advance mosfet technology faster than any other type of silicon based transistor 60 a big advantage of mosfets for digital switching is that the oxide layer between the gate and the channel prevents dc current from flowing through the gate further reducing power consumption and giving a very large input impedance the insulating oxide between the gate and channel effectively isolates a mosfet in one logic stage from earlier and later stages which allows a single mosfet output to drive a considerable number of mosfet inputs bipolar transistor based logic such as ttl does not have such a high fanout capacity this isolation also makes it easier for the designers to ignore to some extent loading effects between logic stages independently that extent is defined by the operating frequency as frequencies increase the input impedance of the mosfets decreases analog the mosfet s advantages in digital circuits do not translate into supremacy in all analog circuits the two types of circuit draw upon different features of transistor behavior digital circuits switch spending most of their time either fully on or fully off the transition from one to the other is only of concern with regards to speed and charge required analog circuits depend on operation in the transition region where small changes to v gs can modulate the output drain current the jfet and bipolar junction transistor bjt are preferred for accurate matching of adjacent devices in integrated circuits higher transconductance and certain temperature characteristics which simplify keeping performance predictable as circuit temperature varies nevertheless mosfets are widely used in many types of analog circuits because of their own advantages zero gate current high and adjustable output impedance and improved robustness vs bjts which can be permanently degraded by even lightly breaking down the emitter base vague the characteristics and performance of many analog circuits can be scaled up or down by changing the sizes length and width of the mosfets used by comparison bipolar transistors follow a different scaling law mosfets ideal characteristics regarding gate current zero and drain source offset voltage zero also make them nearly ideal switch elements and also make switched capacitor analog circuits practical in their linear region mosfets can be used as precision resistors which can have a much higher controlled resistance than bjts in high power circuits mosfets sometimes have the advantage of not suffering from thermal runaway as bjts do dubious discuss this means that complete analog circuits can be made on a silicon chip in a much smaller space and with simpler fabrication techniques mosfets are ideally suited to switch inductive loads because of tolerance to inductive kickback some ics combine analog and digital mosfet circuitry on a single mixed signal integrated circuit making the needed board space even smaller this creates a need to isolate the analog circuits from the digital circuits on a chip level leading to the use of isolation rings and silicon on insulator soi since mosfets require more space to handle a given amount of power than a bjt fabrication processes can incorporate bjts and mosfets into a single device mixed transistor devices are called bi fets bipolar fets if they contain just one bjt fet and bicmos bipolar cmos if they contain complementary bjt fets such devices have the advantages of both insulated gates and higher current density analog switches this section does not cite any sources please help improve this section by adding citations to reliable sources unsourced material may be challenged and removed september 2016 learn how and when to remove this message bidirectional analog switches pass analog signals when on or block them by presenting a high impedance when off the mosfets used are typically symmetrical such that their drain and source exchange places depending on the relative voltages of their electrodes at any moment the source would be the more negative side for an nmos or the more positive side for a pmos all of these switches are limited on what signals they can pass or stop by their gate source gate drain and source drain voltages exceeding the voltage current or power limits will potentially damage the switch see power mosfet subsection down below single type this analog switch uses a four terminal symmetrical mosfet of either p or n type in the case of an n type switch the body is connected to the most negative supply usually gnd and the gate is used as the switch control whenever the gate voltage exceeds the source voltage by at least a threshold voltage the mosfet conducts the higher the voltage the more the mosfet can conduct an nmos switch passes all voltages less than v gate v threshold_nmos but passes lower voltages better than higher ones when the switch is conducting it typically operates in the linear or ohmic mode of operation since the source and drain voltages will typically be nearly equal in the case of a pmos the body is connected to the most positive voltage and the gate is brought to a lower potential to turn the switch on the pmos switch passes all voltages higher than v gate v threshold_pmos note enhancement mode pmos fets have a negative threshold voltage but passes higher voltages better than lower ones dual type cmos main article transmission gate electronic switch the cmos analog switch passes the signal through both a pmos qp and an nmos qn when st is high the switch provides a low resistance between ua and ub either of which could be considered the input or output this complementary or cmos type of switch uses one pmos and one nmos fet connected in parallel to counteract the limitations of the single type switch 61 when used in digital logic it is called a transmission gate the...
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