COMPUCOM INSTITUTE OF TECHNOLOGY & MANAGEMENT, JAIPUR (DEPARTMENT OF ELECTRONICS & COMMUNICATION) Notes VLSI DESIGN NOTES (Subject Code: 7EC5) Prepared By: MANVENDRA SINGH Class: B. Tech. IV Year, VII Semester
Syllabus UNIT 2: - Ids versus Vds relationship, Aspects of threshold voltage, Transistor Transconductance gm. The nmos inverter, Pull up to Pull-down ratio for a NMOS Inverter and CMOS Inverter (Bn/Bp), MOS transistor circuit Model, Noise Margin. Prepared By: MANVENDRA SINGH Page 2
Unit -2 Derivation of the i D -v DS relationship Now that we have developed the essential physical intuition underlying MOSFET operation, we derive a mathematical description (equations) of operation. In other words, i-v curves that are pretty much shaped correctly are good, but exact equations for these lines are even better. Consider an NMOS operating in triode mode: vgs > Vt and vds < vgs Vt (1) Consider an infinitesimal segment of the channel of length dx at a point x from the source and let the channel voltage at this point be v(x). Figure: Illustration to aid in the derivation of the id - vds characteristic of the NMOS transistor. Fig. 1 vds characteristic of the NMOS Prepared By: MANVENDRA SINGH Page 3
The gate to channel voltage at this point is vgs v(x). The electron charge dq(x) in this infinitesimal portion of the channel is: dq(x) = CoxW dx [vgs v(x) Vt] (2) where: Recall good old Q = CV? The negative sign is due to negative electron charge. Cox is the capacitance per unit area of the parallel-plate capacitor formed by the gate electrode and the channel, and is given by: Cox =(1/ tox) (3) ox is the permittivity of SiO2 (3.5 10 13F/cm). tox is the thickness of the oxide layer (0.02 to 0.1 µm). Recall good old C= d for a parallel plate A capacitor? W (channel width) times dx (infinitesimal length along channel) has units of area. [vgs v(x) Vt] is the voltage driving charge aggregation on the capacitor plates. vds produces an electric field (E ) along the channel in the negative x direction (leftward). Recall that electric field is the negative gradient of the potential: E (x) = - (dv(x)/dx) (4) Prepared By: MANVENDRA SINGH Page 4
Also recall that electrons (negative charge carriers) move against the electric field. An electron located at x will, therefore, move with a velocity dx/dt Thus, we can relate electron velocity to channel potential: dx/dt= µne (x) (5) dx/dt = µn(dv(x)/dx) (6) where µn is the electron mobility in the channel. Charged carriers moving by virtue of electric fields constitutes drift current. Drift current (i) can be found by multiplying the charge per unit length dq(x)/dx by the drift velocity: i = µncoxw[vgs v(x) Vt] (dv(x)/dx) (7) Note that current is constant at all points along the channel (due to conservation of charge). Thus we can write the drain-to-source current (id ) is simply the negative of i (which is positive for current flowing from source-to-drain): id = µncoxw[vgs v(x) Vt] (dv(x)/dx) (8) Solving this differential equation is quite simple. First, rearrange as: iddx = µncoxw[vgs Vt v(x)] (dv(x)/dx) (9) Second, integrate both sides along the channel (e.g., from x = 0 where v(0) = 0 to x = L where v(l) = vds : iddx = µncoxw[vgs Vt v(x)] (dv(x)/dx) (10) Finally, evaluating the integral yields: Prepared By: MANVENDRA SINGH Page 5
id = (µncox) (W/L)(Vgs-Vt)Vds-Vds/2 (11) This is the id vds characteristic in the triode region. The expression for the saturation region is found by substituting vds = vgs - Vt into the triode equation, yielding: id= 1/2(µnCox) W/L(vGS Vt)2 (12) Note that saturation current is independent of vds as expected. Note that current is proportional to the MOSFET channel aspect ratio ( W/L ); both parameters can be specified during circuit design in order to achieve the desired i v characteristic. µncox is a constant determined by the process technology and is known as the process transconductance parameter (k nwith units A/V2): k n= µncox (13) Cutoff region (vgs < Vt) id = 0 (14) Saturation region (vds vgs Vt): id= 1/2k n W/L(vGS Vt)2 (15) Aspects of threshold voltage The threshold voltage of a MOSFET is usually defined as the gate voltage where an inversion layer forms at the interface between the insulating layer (oxide) and the substrate (body) of Prepared By: MANVENDRA SINGH Page 6
the transistor. The purpose of the inversion layer's forming is to allow the flow of electrons through the gate-source junction. The creation of this layer is described next. Fig. 2 When VGS > VTHN (nmosfet), the semiconductor/oxide interface is inverted, i.e., the inversion layer is formed. In an n-mosfet the substrate of the transistor is composed of p-type silicon (see doping (semiconductor)), which has positively charged mobile holes as carriers. When a positive voltage is applied on the gate, an electric field causes the holes to be repelled from the interface, creating a depletion region containing immobile negatively charged acceptor ions. A further increase in the gate voltage eventually causes electrons to appear at the interface, in what is called an inversion layer, or channel. Historically the gate voltage at which the electron density at the interface is the same as the hole density in the neutral bulk material is called the threshold voltage. Practically speaking the threshold voltage is the voltage at which there are sufficient electrons in the inversion layer to make a low resistance conducting path between the MOSFET source and drain. In the figures, the source (left side) and drain (right side) are labeled n+ to indicate heavily doped (blue) n-regions. The depletion layer dopant is labeled N A to indicate that the ions in the (pink) depletion layer are negatively charged and there are very few holes. In the (red) bulk the number of holes p = N A making the bulk charge neutral. If the gate voltage is below the threshold voltage (top figure), the transistor is turned off and ideally there is no current from the drain to the source of the transistor. In fact, there is a current Prepared By: MANVENDRA SINGH Page 7
even for gate biases below threshold (subthreshold leakage) current, although it is small and varies exponentially with gate bias. If the gate voltage is above the threshold voltage (lower figure), the transistor is turned on, due to there being many electrons in the channel at the oxide-silicon interface, creating a low-resistance channel where charge can flow from drain to source. For voltages significantly above threshold, this situation is called strong inversion. The channel is tapered when V D > 0 because the voltage drops due to the current in the resistive channel reduces the oxide field supporting the channel as the drain is approached. Transistor Transconductance gm The small-signal drain current due to vgs is therefore given by Prepared By: MANVENDRA SINGH Page 8
Evaluating the partial derivative: Fig. 3 Transistor Model and Characteristics of MOS In order to find a simple expression that highlights the dependence of gm on the DC drain current, we neglect the (usually) small error in writing: For typical values and what find that An NMOS inverter In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. The truth table is shown on the right. Prepared By: MANVENDRA SINGH Page 9
This represents perfect switching behavior, which is the defining assumption in Digital electronics. In practice, actual devices have electrical characteristics that must be carefully considered when designing inverters. In fact, the non-ideal transition region behavior of a CMOS inverter makes it useful in analog electronics as a class A amplifier (e.g., as the output stage of an operational amplifier) Figure: 4 An NMOS inverter The gate of the depletion mode transistor is connected to its drain, to keep the transistor permanently turned on. The depletion mode transistor is used as a ``pull-up'' resistor, and the enhancement mode transistor is used as a switch to ``pull down'' the output when the switch is turned on. Note that in this technology, the resistance of the permanently turned on depletion mode transistor must be large compared with the ``on'' resistance of the enhancement mode transistor, but small compared with the ``off'' resistance of the transistor. This type of logic is often called a ``ratioed logic'', since the ratio of the pull-up resistance to the pull-down resistance effectively determines the voltage at which the output of the device changes state. Typically, with this technology:. The large resistive pull-up transistor causes three particular problems 1. The depletion mode transistor must be made large ( i.e., long and thin) to create the large ``on'' resistance. Prepared By: MANVENDRA SINGH Page 10
2. When driving a capacitive output load such as the gate of another transistor, the charging time (proportional to ) will be long compared to the discharging time (proportional to ). This effect is clearly evident in Figure 2.7 (c). 3. The device consumes DC power whenever the enhancement mode pull down device is turned on, due to the resistive losses in the pull-up transistor. The third problem becomes more serious as feature sizes for transistors decrease, because the number of such resistors per unit area increases, and the devices may not dissipate the heat as well, resulting in device failure due to overheating. Pull up to Pull-down ratio for a NMOS Inverter and CMOS Inverter (Bn/Bp) Inverter : basic requirement for producing a complete range of Logic circuits Fig. 5 Inverter Basic Inverter: Transistor with source connected to ground and a load resistor connected from the drain to the positive Supply rail Output is taken from the drain and control input connected Prepared By: MANVENDRA SINGH Page 11
between gate and ground Resistors are not easily formed in silicon they occupy too much area Transistors can be used as the pull-up device. Fig. 6 Pull UP & Pull down Network NMOS Depletion Mode Transistor Pull - Up Pull-Up is always on Vgs = 0; depletion Pull-Down turns on when Vin > Vt With no current drawn from outputs, Ids for both transistors is equal Prepared By: MANVENDRA SINGH Page 12
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Fig. 7 Characteristics of MOS Point where Vo = Vin is called Vinv Transfer Characteristics and Vinv can be shifted by altering ratio of pull-up to Pull down impedances MOS transistor circuit Model These devices are known as FET s (Field effect transistors), which consist of three regions source, drain and gate. The resistance path between the drain and source is, controlled by applying a voltage to the gate. This varies the depletion layer under the gate and thus reduces or increases the conductance path. The FET input impedance (unlike the BJT which is a few KΩ) is very high (~MΩ s) and as a result the gate current can be considered as zero. Prepared By: MANVENDRA SINGH Page 14
Fig. 8 MOS Transistor Circuit Model As per the BJT the FET is best described by it s Output I-V DC characteristics (N-type enhancement characteristics shown below), however things are complicated by the fact there are two types of FET depletion and enhancement that are both available as N-type or P-type devices. For low frequencies the enhancement devices are more commonly used (Depletion mode types will be described when discussing microwave devices). Prepared By: MANVENDRA SINGH Page 15
(1) Cut-Off Region In this region the gate voltage is less than the pinch-off voltage Vp and therefore very little current flows. (2) Triode Region In this mode the device is operating below pinch-off and is effectively a variable resistor. R OUT is ~ linear but only over a small range of V DS. (3) Saturation Region This is the main operating region for the device. The drain voltage has to be greater than the gate voltage less the pinch-off voltage this sets the minimum supply voltage. The curves in the saturation region can be extrapolated to a point 1/λ, where λ is known as the Channel length modulation parameter, (units V -1 ), - this is analogous to the BJT Early voltage. Non saturation/ non linear region only Prepared By: MANVENDRA SINGH Page 16
CMOS Inverter Noise MarginsCMOS Margins Prepared By: MANVENDRA SINGH Page 17
Fig. 9 Gain Point V IL and V IH measure effect of input voltage on inverter output VIL= largest input voltage recognized as logic 0 VIH= smallest input voltage recognized as logic 1 Defined as point on VTC where slope = -1 Prepared By: MANVENDRA SINGH Page 18
Fig. 10 Noise margin is a measure of the robustness of an inverter NML= VIL-VOL Prepared By: MANVENDRA SINGH Page 19
NMH= VOH-VIH Models a chain of inverters. Fig. 11 output characteristics and input characteristics (Transistor) Beyond the Syllabus: A transistor is a semiconductor device used to amplify and switch electronic signals and electrical power. It is composed of semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current flowing through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits. The transistor is the fundamental building block of modern electronic devices, and is ubiquitous in modern electronic systems. Following its development in the early 1950s the transistor revolutionized the field of electronics, and paved the way for smaller and cheaper radios, calculators, and computers, among other things. Prepared By: MANVENDRA SINGH Page 20
Fig. 12 Assorted discrete transistors Simplified operation This section does not cite any references or sources. (November 2010) Fig.13 BJT A simple circuit diagram to show the labels of a NPN bipolar transistor. The essential usefulness of a transistor comes from its ability to use a small signal applied between one pair of its terminals to control a much larger signal at another pair of terminals. This property is called gain. A transistor can control its output in proportion to the input signal; that is, it can act as an amplifier. Alternatively, the transistor can be used to turn current on or off in a Prepared By: MANVENDRA SINGH Page 21
circuit as an electrically controlled switch, where the amount of current is determined by other circuit elements. There are two types of transistors, which have slight differences in how they are used in a circuit. A bipolar transistor has terminals labeled base, collector, and emitter. A small current at the base terminal (that is, flowing between the base and the emitter) can control or switch a much larger current between the collector and emitter terminals. For a field-effect transistor, the terminals are labeled gate, source, and drain, and a voltage at the gate can control a current between source and drain. The image to the right represents a typical bipolar transistor in a circuit. Charge will flow between emitter and collector terminals depending on the current in the base. Since internally the base and emitter connections behave like a semiconductor diode, a voltage drop develops between base and emitter while the base current exists. The amount of this voltage depends on the material the transistor is made from, and is referred to as V BE. Transistor as a switch Fig. 14 Transistor as a switch BJT used as an electronic switch, in grounded-emitter configuration. Transistors are commonly used as electronic switches, both for high-power applications such as switched-mode power supplies and for low-power applications such as logic gates. In a grounded-emitter transistor circuit, such as the light-switch circuit shown, as the base voltage rises, the emitter and collector currents rise exponentially. The collector voltage drops because of the collector load resistance (in this example, the resistance of the light bulb). If the collector voltage were zero, the collector current would be limited only by the light bulb resistance and the supply voltage. The transistor is then said to be saturated - it will have a very small voltage from collector to emitter. Providing sufficient base drive current is a key problem in the use of bipolar transistors as switches. The transistor provides current gain, allowing a relatively large current in the collector to be switched by a much smaller current into the base terminal. The ratio of these currents varies depending on the type of transistor, and even for a particular type, varies depending on the collector current. In the example light-switch circuit shown, the resistor is chosen to provide enough base current to ensure the transistor will be saturated. Prepared By: MANVENDRA SINGH Page 22
In any switching circuit, values of input voltage would be chosen such that the output is either completely off, or completely on. The transistor is acting as a switch, and this type of operation is common in digital circuits where only "on" and "off" values are relevant. Transistor as an amplifier Fig. 15Amplifier circuit, common-emitter configuration with a voltage-divider bias circuit. The common-emitter amplifier is designed so that a small change in voltage (V in ) changes the small current through the base of the transistor; the transistor's current amplification combined with the properties of the circuit mean that small swings in V in produce large changes in V out. Various configurations of single transistor amplifier are possible, with some providing current gain, some voltage gain, and some both. From mobile phones to televisions, vast numbers of products include amplifiers for sound reproduction, radio transmission, and signal processing. The first discrete transistor audio amplifiers barely supplied a few hundred milliwatts, but power and audio fidelity gradually increased as better transistors became available and amplifier architecture evolved. Modern transistor audio amplifiers of up to a few hundred watts are common and relatively inexpensive. Comparison with vacuum tubes Prior to the development of transistors, vacuum (electron) tubes (or in the UK "thermionic valves" or just "valves") were the main active components in electronic equipment. Advantages The key advantages that have allowed transistors to replace their vacuum tube predecessors in most applications are Prepared By: MANVENDRA SINGH Page 23
Small size and minimal weight, allowing the development of miniaturized electronic devices. Highly automated manufacturing processes, resulting in low per-unit cost. Lower possible operating voltages, making transistors suitable for small, battery-powered applications. No warm-up period for cathode heaters required after power application. Lower power dissipation and generally greater energy efficiency. Higher reliability and greater physical ruggedness. Extremely long life. Some transistorized devices have been in service for more than 50 years. Complementary devices available, facilitating the design of complementary-symmetry circuits, something not possible with vacuum tubes. Insensitivity to mechanical shock and vibration, thus avoiding the problem of microphonics in audio applications. Limitations Silicon transistors typically do not operate at voltages higher than about 1000 volts (SiC devices can be operated as high as 3000 volts). In contrast, vacuum tubes have been developed that can be operated at tens of thousands of volts. High-power, high-frequency operation, such as that used in over-the-air television broadcasting, is better achieved in vacuum tubes due to improved electron mobility in a vacuum. Silicon transistors are much more vulnerable than vacuum tubes to an electromagnetic pulse generated by a high-altitude nuclear explosion. Sensitivity to radiation and cosmic rays (special radiation hardened chips are used for spacecraft devices). Vacuum tubes create a distortion, the so-called tube sound, that some people find to be more tolerable to the ear. Prepared By: MANVENDRA SINGH Page 24
Types PNP P-channel NPN N-channel BJT JFET Fig. 16 BJT and JFET symbols P-channel N-channel JFET MOSFET enh MOSFET dep Fig. 17JFET and IGFET symbols Transistors are categorized by Semiconductor material (date first used): the metalloids germanium (1947) and silicon (1954) in amorphous, polycrystalline and monocrystalline form; the compounds gallium arsenide (1966) and silicon carbide (1997), the alloy silicon-germanium (1989), the allotrope of carbon graphene (research ongoing since 2004), etc. see Semiconductor material Structure: BJT, JFET, IGFET (MOSFET), IGBT, "other types" Electrical polarity (positive and negative) : NPN, PNP (BJTs); N-channel, P-channel (FETs) Prepared By: MANVENDRA SINGH Page 25
Maximum power rating: low, medium, high Maximum operating frequency: low, medium, high, radio frequency (RF), microwave (The maximum effective frequency of a transistor is denoted by the term, an abbreviation for transition frequency the frequency of transition is the frequency at which the transistor yields unity gain) Application: switch, general purpose, audio, high voltage, super-beta, matched pair Physical packaging: through-hole metal, through-hole plastic, surface mount, ball grid array, power modules see Packaging Amplification factor h fe or β F (transistor beta) [23] Thus, a particular transistor may be described as silicon, surface mount, BJT, NPN, low power, high frequency switch. Bipolar junction transistor Bipolar transistors are so named because they conduct by using both majority and minority carriers. The bipolar junction transistor (BJT), the first type of transistor to be mass-produced, is a combination of two junction diodes, and is formed of either a thin layer of p-type semiconductor sandwiched between two n-type semiconductors (an n-p-n transistor), or a thin layer of n-type semiconductor sandwiched between two p-type semiconductors (a p-n-p transistor). This construction produces two p-n junctions: a base emitter junction and a base collector junction, separated by a thin region of semiconductor known as the base region (two junction diodes wired together without sharing an intervening semiconducting region will not make a transistor). The BJT has three terminals, corresponding to the three layers of semiconductor an emitter, a base, and a collector. It is useful in amplifiers because the currents at the emitter and collector are controllable by a relatively small base current." In an NPN transistor operating in the active region, the emitter-base junction is forward biased (electrons and electron holes recombine at the junction), and electrons are injected into the base region. Because the base is narrow, most of these electrons will diffuse into the reverse-biased (electrons and holes are formed at, and move away from the junction) base-collector junction and be swept into the collector; perhaps onehundredth of the electrons will recombine in the base, which is the dominant mechanism in the base current. By controlling the number of electrons that can leave the base, the number of electrons entering the collector can be controlled. Collector current is approximately β (commonemitter current gain) times the base current. It is typically greater than 100 for small-signal transistors but can be smaller in transistors designed for high-power applications. Unlike the FET, the BJT is a low input-impedance device. Also, as the base emitter voltage (V be ) is increased the base emitter current and hence the collector emitter current (I ce ) increase exponentially according to the Shockley diode model and the Ebers-Moll model. Because of this exponential relationship, the BJT has a higher transconductance than the FET. Prepared By: MANVENDRA SINGH Page 26
Bipolar transistors can be made to conduct by exposure to light, since absorption of photons in the base region generates a photocurrent that acts as a base current; the collector current is approximately β times the photocurrent. Devices designed for this purpose have a transparent window in the package and are called phototransistors. Field-effect transistor The field-effect transistor (FET), sometimes called a unipolar transistor, uses either electrons (in N-channel FET) or holes (in P-channel FET) for conduction. The four terminals of the FET are named source, gate, drain, and body (substrate). On most FETs, the body is connected to the source inside the package, and this will be assumed for the following description. In a FET, the drain-to-source current flows via a conducting channel that connects the source region to the drain region. The conductivity is varied by the electric field that is produced when a voltage is applied between the gate and source terminals; hence the current flowing between the drain and source is controlled by the voltage applied between the gate and source. As the gate source voltage (V gs ) is increased, the drain source current (I ds ) increases exponentially for V gs below threshold, and then at a roughly quadratic rate ( ) (where V T is the threshold voltage at which drain current begins) [25] in the "space-charge-limited" region above threshold. A quadratic behavior is not observed in modern devices, for example, at the 65 nm technology node. [26] For low noise at narrow bandwidth the higher input resistance of the FET is advantageous. FETs are divided into two families: junction FET (JFET) and insulated gate FET (IGFET). The IGFET is more commonly known as a metal oxide semiconductor FET (MOSFET), reflecting its original construction from layers of metal (the gate), oxide (the insulation), and semiconductor. Unlike IGFETs, the JFET gate forms a p-n diode with the channel which lies between the source and drain. Functionally, this makes the N-channel JFET the solid-state equivalent of the vacuum tube triode which, similarly, forms a diode between its grid and cathode. Also, both devices operate in the depletion mode, they both have a high input impedance, and they both conduct current under the control of an input voltage. Metal semiconductor FETs (MESFETs) are JFETs in which the reverse biased p-n junction is replaced by a metal semiconductor junction. These, and the HEMTs (high electron mobility transistors, or HFETs), in which a two-dimensional electron gas with very high carrier mobility is used for charge transport, are especially suitable for use at very high frequencies (microwave frequencies; several GHz). Unlike bipolar transistors, FETs do not inherently amplify a photocurrent. Nevertheless, there are ways to use them, especially JFETs, as light-sensitive devices, by exploiting the photocurrents in channel gate or channel body junctions. Prepared By: MANVENDRA SINGH Page 27
FETs are further divided into depletion-mode and enhancement-mode types, depending on whether the channel is turned on or off with zero gate-to-source voltage. For enhancement mode, the channel is off at zero bias, and a gate potential can "enhance" the conduction. For depletion mode, the channel is on at zero bias, and a gate potential (of the opposite polarity) can "deplete" the channel, reducing conduction. For either mode, a more positive gate voltage corresponds to a higher current for N-channel devices and a lower current for P-channel devices. Nearly all JFETs are depletion-mode as the diode junctions would forward bias and conduct if they were enhancement mode devices; most IGFETs are enhancement-mode types. Prepared By: MANVENDRA SINGH Page 28