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https://nptel.ac.in/courses/117103066/17

UNIT-I

Introduction to VLSI Technology

Introduction:

The invention of the transistor by William B. Shockley, Walter H. Brattain and John Bardeen of

Bell Telephone Laboratories drastically changed the electronics industry and paved the way for

the development of the Integrated Circuit (IC) technology. The first IC was designed by Jack

Kilby at Texas Instruments at the beginning of 1960 and since that time there have already been

four generations of ICs .Viz SSI (small scale integration), MSI (medium scale integration), LSI

(large scale integration), and VLSI (very large scale integration). Now we are ready to see the

emergence of the fifth generation, ULSI (ultra large scale integration) which is characterized by

complexities in excess of 3 million devices on a single IC chip. Further miniaturization is still to

come and more revolutionary advances in the application of this technology must inevitably

occur.

Over the past several years, Silicon CMOS technology has become the dominant fabrication

process for relatively high performance and cost effective VLSI circuits. The revolutionary

nature of this development is understood by the rapid growth in which the number of transistors

integrated in circuits on a single chip.

METAL-OXIDE-SEMICONDUCTOR (MOS) AND RELATED VLSI TECHNOLOGY:

The MOS technology is considered as one of the very important and promising technologies in

the VLSI design process. The circuit designs are realized based on PMOS, NMOS, CMOS and

BiCMOS devices.

The PMOS devices are based on the p-channel MOS transistors. Specifically, the PMOS channel

is part of a n-type substrate lying between two heavily doped p+ wells beneath the source and

drain electrodes. Generally speaking, a PMOS transistor is only constructed in consort with an

NMOS transistor.

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The NMOS technology and design processes provide an excellent background for other

technologies. In particular, some familiarity with NMOS allows a relatively easy transition to

CMOS technology and design.

The techniques employed in NMOS technology for logic design are similar to GaAs technology..

Therefore, understanding the basics of NMOS design will help in the layout of GaAs circuits

In addition to VLSI technology, the VLSI design processes also provides a new degree of

freedom for designers which helps for the significant developments. With the rapid advances in

technology the size of the ICs is shrinking and the integration density is increasing.

The minimum line width of commercial products over the years is shown in the graph below.

The graph shows a significant decrease in the size of the chip in recent years which implicitly

indicates the advancements in the VLSI technology.

BASIC MOS TRANSISTORS:

The MOS Transistor means, Metal-Oxide-Semiconductor Field Effect Transistor which is the

most basic element in the design of a large scale integrated circuits(IC).

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These transistors are formed as a ``sandwich'' consisting of a semiconductor layer, usually a

slice, or wafer, from a single crystal of silicon; a layer of silicon dioxide (the oxide) and a layer

of metal. These layers are patterned in a manner which permits transistors to be formed in the

semiconductor material (the ``substrate''); a diagram showing a MOSFET is shown below in

Figure .

Silicon dioxide is a very good insulator, so a very thin layer, typically only a few hundred

molecules thick, is used. In fact , the transistors which are used do not use metal for their gate

regions, but instead use polycrystalline silicon (poly). Polysilicon gate FET's have replaced

virtually all of the older devices using metal gates in large scale integrated circuits. (Both metal

and polysilicon FET's are sometimes referred to as IGFET's (insulated gate field effect

transistors), since the silicon dioxide under the gate is an insulator.

MOS Transistors are classified as n-MOS, p-MOS and c-MOS Transistors based on the

fabrication .

NMOS devices are formed in a p-type substrate of moderate doping level. The source and drain

regions are formed by diffusing n- type impurities through suitable masks into these areas to give

the desired n-impurity concentration and give rise to depletion regions which extend mainly in

the more lightly doped p-region . Thus, source and drain are isolated from one another by two

diodes. Connections to the source and drain are made by a deposited metal layer. In order to

make a useful device, there must be the capability for establishing and controlling a current

between source and drain, and .this is commonly achieved in one of two ways, giving rise to the

enhancement mode and depletion mode transistors.

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Enhancement Mode Transistors:

In an enhancement mode device a polysilicon gate is deposited on a layer of insulation over the

region between source and drain. In the diagram below channel is not established and the device

is in a non-conducting condition, i.e VD = Vs = Vgs = 0. If this gate is connected to a suitable

positive voltage with respect to the source, then the electric field established between the gate

and the substrate gives rise to a charge inversion region in the substrate under the gate insulation

and a conducting path or channel is formed between source and drain.

ENHANCEMENT MODE TRANSISTOR ACTION :

To understand the enhancement mechanism, let us consider the enhancement mode device. In

order to establish the channel, a minimum voltage level called threshold voltage (Vt) must be

established between gate and source. Fig. (a) Shows the existing situation where a channel is

established but no current flowing between source and drain (Vds = 0 ).

Let us now consider the conditions when current flows in the channel by applying a voltage Vds

between drain and source. The IR drop = Vds along the channel. This develops a voltage

between gate and channel varying with distance along the channel with the voltage being a

maximum of Vgs at the source end. Since the effective gate voltage is Vg= Vgs - Vt, (no current

flows when Vgs < Vt) there will be voltage available to invert the channel at the drain end so

long as Vgs - Vt ~ Vds· The limiting condition comes when Vds= Vgs - Vt. For all voltages Vds

< Vgs - Vt, the device is in the non-saturated region of operation which is the condition shown in

Fig. (b) below.

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Let us now consider the situation when Vds is increased to a level greater than Vgs - Vt. In this

case, an IR drop equal to Vgs – Vt occurs over less than the whole length of the channel such

that, near the drain, there is insufficient electric field available to give rise to an inversion layer

to create the channel. The .channel is, therefore, 'pinched off as shown in Fig. (c). Diffusion

current completes the path from source to drain in this case, causing the channel to exhibit a high

resistance and behave as a constant current source. This region, known as saturation, is

.characterized by almost constant current for increase of Vds above Vds = Vgs - Vt. In all cases,

the channel will cease to exist and no current will flow when Vgs < Vt. Typically, for

enhancement mode devices, Vt = 1 volt for VDD = 5 V or, in general terms, Vt = 0.2 VDD.

DEPLETION MODE TSANSISTOR ACTION

N-MOS Depletion mode mosfets are built with P-type silicon substrates, and P-channel versions

are built on N-type substrates. In both cases they include a thin gate oxide formed between the

source and drain regions. A conductive channel is deliberately formed below the gate oxide layer

and between the source and drain by using ion-implantation. By implanting the correct ion

polarity in the channel region during fabrication determines the polarity of the threshold voltage

(i.e. -Vt for an N channel transistor, or +Vt for an P-channel transistor). The actual concentration

of ions in the substrate-to-channel region is used to adjust the threshold voltage (Vt) to the

desired value. Depletion-mode devices are a little more difficult to manufacture and their

characteristics harder to control than enhancement types, which do not require ion implantation.

In depletion mode devices the channel is established, due to the implant, even when Vgs = 0,

and to cause the channel to cease a negative voltage Vtd must be applied between gate and

source.

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Vtd is typically < - 0.8 VDD, depending on the implant and substrate bias, but, threshold voltage

differences apart, the action is similar to that of the enhancement mode transistor.

CMOS FABRICATION :

CMOS fabrication is performed based on various methods , including the p-well, the n-well, the

twin-tub, and the silicon-on-insulator processes .Among these methods the p-well process is

widely used in practice and the n-well process is also popular, particularly as it is an easy

retrofit to existing NMOS lines.

(i) The p-well Process:

The p-well structure consists of an n-type substrate in which p-devices may be formed by

suitable masking and diffusion and, in order to accommodate n-type devices, a deep p-well is

diffused into the n-type substrate as shown in the Fig.below.

This diffusion should be carried out with special care since the p-well doping concentration and

depth will affect the threshold voltages as well as the breakdown voltages of the n-transistors. To

achieve low threshold voltages (0.6 to 1.0 V) either deep-well diffusion or high-well resistivity is

required. However, deep wells require larger spacing between the n- and p-type transistors and

wires due to lateral diffusion and therefore a larger chip area. The p-wells Act as substrates for

the n-devices within the parent n-substrate, and, the two areas are electrically isolated.

Except this in all other respects- like masking, patterning, and diffusion-the process is similar to

NMOS fabrication.

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P-well fabrication process(Figs 1,2,3 & 4)

The diagram below shows the CMOS p-well inverter showing VDD and Vss substrate

connections

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The n-well Process : Though the p-well process is widely used in C-MOS fabrication the n-well

fabrication is also very popular because of the lower substrate bias effects on transistor threshold

voltage and also lower parasitic capacitances associated with source and drain regions.

The typical n-well fabrication steps are shown in the diagram below.

Fig. n-well fabrication steps

The first mask defines the n-well regions. This is followed by a low dose phosphorus implant

driven in by a high temperature diffusion step to form the n-wells. The well depth is optimized to

ensure against-substrate top+ diffusion breakdown without compromising then-well to n+ mask

separation. The next steps are to define the devices and diffusion paths, grow field oxide, deposit

and pattern the poly silicon, carry out the diffusions, make contact cuts, and finally metalize as

before. Lt will be seen that an n+ mask and its complement may be used to define the n- and p-

diffusion regions respectively. These same masks also include the VDD and Vss contacts

(respectively). It should be noted that, alternatively, we could have used a p+ mask and its

complement since the n + and p + masks are generally complementary.

The diagram below shows the Cross-sectional view of n-well CMOS Inverter.

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Due to the differences in charge carrier mobilities, the n-well process creates non-optimum p-

channel characteristics. However, in many CMOS designs (such as domino-logic and dynamic

logic structures), this is relatively unimportant since they contain a preponderance of n-channel

devices. Thus then-channel transistors are mainly those used to form1ogic elements, providing

speed and high density of elements.

However, a factor of the n-well process is that the performance of the already poorly performing

p-transistor is even further degraded. Modern process lines have come to grips with these

problems, and good device performance may be achieved for both p-well and n-well fabrication.

BICMOS Technology:

A Bi-CMOS circuit of both bipolar junction transistors and MOS transistors on a single

substrate. The driving capability of MOS transistors is less because of limited current sourcing

and sinking capabilities of the transistors. To drive large capacitive loads Bi-CMOS technology

is used. As this technology combines Bipolar and CMOS transistors in a single integrated circuit,

it has the advantages of both bipolar and CMOS transistors. Bi-CMOS is able to achieve VLSI

circuits with speed-power-density performance previously not possible with either technology

individually. The diagram given below shows the cross section of the Bi-CMOS process which

uses an NPN transistor

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Fig. Arrangement of Bi-CMOS npn transistor

The lay-out view of Bic-MOS transistor is shown in the figure below. The fabrication of Bi-

CMOS is similar to CMOS but with certain additional process steps and additional masks are

considered. They are (i) the p+ base region; (ii) n+ collector area; and (iii) the buried sub

collector (BCCD).

IDS-VDS characteristics of MOS Transistor:

The graph below shows the ID Vs VDS characteristics of an n- MOS transistor for several values

of VGS .It is clear that there are two conduction states when the device is ON. The saturated state

and the non-saturated state. The saturated curve is the flat portion and defines the saturation

region. For Vgs < VDS + Vth, the NMOS device is conducting and ID is independent of VDS. For

Vgs > VDS + Vth, the transistor is in the non-saturation region and the curve is a half parabola.

When the transistor is OFF (Vgs < Vth), then ID is zero for any VDS value.

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The boundary of the saturation/non-saturation bias states is a point seen for each curve in the

graph as the intersection of the straight line of the saturated region with the quadratic curve of

the non-saturated region. This intersection point occurs at the channel pinch off voltage called

VDSAT. The diamond symbol marks the pinch-off voltage VDSAT for each value of VGS. VDSAT is

defined as the minimum drain-source voltage that is required to keep the transistor in saturation

for a given VGS .In the non-saturated state, the drain current initially increases almost linearly

from the origin before bending in a parabolic response. Thus the name ohmic or linear for the

non- saturated region.

The drain current in saturation is virtually independent of VDS and the transistor acts as a current

Source. This is because there is no carrier inversion at the drain region of the channel. Carriers

are pulled into the high electric field of the drain/substrate pn junction and ejected out of the

drain terminal.

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Drain-to-Source Current IDS versus Voltage VDS Relationships:

The working of a MOS transistor is based on the principle that the use of a voltage on the gate

induce a charge in the channel between source and drain, which may then be caused to move

from source to drain under the influence of an electric field created by voltage Vds applied

between drain and source. Since the charge induced is dependent on the gate to source voltage

Vgs then Ids is dependent on both Vgs and Vds.

Let us consider the diagram below in which electrons will flow source to drain .So, the drain

current is given by

Charge induced in channel (Qc)

Ids =-Isd = _____________________

Electron transit time(τ)

Length of the channel

Where the transit time is given by τsd = ------------------------------

Velocity (v)

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But velocity v= µeds

Where µ =electron or hole mobility and Eds = Electric field

Also , Eds = Vds/L

So, v = µ.Vds/L

And τds = L2 / µ.Vds

The typical values of µ at room temperature are given below.

The Non-saturated Region:

Let us consider the Id vs Vd relationships in the non-saturated region .The charge induced in the

channel due to due to the voltage difference between the gate and the channel, Vgs (assuming

substrate connected to source). The voltage along the channel varies linearly with distance X

from the source due to the IR drop in the channel .In the non-saturated state the average value is

Vds/2. Also the effective gate voltage Vg = Vgs – Vt where Vt, is the threshold voltage needed

to invert the charge under the gate and establish the channel.

Hence the induced charge is Qc = Eg εins εow. L

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Where

Eg = average electric field gate to channel

Εins = relative permittivity of insulation between gate and channel

Εo = permittivity of free space.

So, we can write that

Here D is the thickness of the oxide layer. Thus

So, by combining the above two equations ,we get

Or the above equation can be written as

In the non-saturated or resistive region where Vds < Vgs – Vt and

Generally ,a constant β is defined as

So that ,the expression for drain –source current will become

The gate /channel capacitance is

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Hence we can write another alternative form forthe drain current as

Some time it is also convenient to use gate –capacitance per unit area ,Cg

So,the drain current is

This is the relation between drain current and drain-source voltage in non-saturated region.

The Saturated Region

Saturation begins when Vds = Vgs - V, since at this point the IR drop in the channel equals the

effective gate to channel voltage at the drain and we may assume that the current remains fairly

constant as Vds increases further. Thus

Or we can also write that

Or it can also be written as

Or

The expressions derived above for Ids hold for both enhancement and depletion mode devices.

Here the threshold voltage for the NMOS depletion mode device (denoted as Vtd) is negative.

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MOS Transistor Threshold Voltage Vt :

The gate structure of a MOS transistor consists, of charges stored in the dielectric layers and in

the surface to surface interfaces as well as in the substrate itself. Switching an enhancement

mode MOS transistor from the off to the on state consists in applying sufficient gate voltage to

neutralize these charges and enable the underlying silicon to undergo an inversion due to the

electric field from the gate. Switching a depletion mode NMOS transistor from the on to the off

state consists in applying enough voltage to the gate to add to the stored charge and invert the 'n'

implant region to 'p'.

The threshold voltage Vt may be expressed as:

Where QD = the charge per unit area in the depletion layer below the oxide

Qss = charge density at Si: sio2 interface

Co =Capacitance per unit area.

Φns = work function difference between gate and Si

Φfn = Fermi level potential between inverted surface and bulk Si

For polynomial gate and silicon substrate, the value of Φns is negative but negligible and the

magnitude and sign of Vt are thus determined by balancing the other terms in the equation.

To evaluate the Vt the other terms are determined as below.

Body Effect :

Generally while studying the MOS transistors it is treated as a three terminal device. But ,the

body of the transistor is also an implicit terminal which helps to understand the characteristICs of

the transistor. Considering the body of the MOS transistor as a terminal is known as the body

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effect. The potential difference between the source and the body (Vsb) affects the threshold

voltage of the transistor. In many situations, this Body Effect is relatively insignificant, so we

can (unless otherwise stated) ignore the Body Effect. But it is not always insignificant, in some

cases it can have a tremendous impact on MOSFET circuit performance.

Body effect - NMOS device

Increasing Vsb causes the channel to be depleted of charge carriers and thus the threshold

voltage is raised. Change in Vt is given by δvt = γ.(Vsb)1/2 where γ is a constant which depends

on substrate doping so that the more lightly doped the substrate, the smaller will be the body

effect

The threshold voltage can be written as

Where Vt(0) is the threshold voltage for Vsd = 0

For n-MOS depletion mode transistors ,the body voltage values at different VDD voltages are

given below.

VSB = 0 V ; Vsd = -0.7VDD (= - 3.5 V for VDD =+5V )

VSB = 5 V ; Vsd = -0.6VDD (= - 3.0 V for VDD =+5V )

The NMOS INVERTER :

An inverter circuit is a very important circuit for producing a complete range of logic circuits.

This is needed for restoring logic levels, for Nand and Nor gates, and for sequential and memory

circuits of various forms .

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A simple inverter circuit can be constructed using a transistor with source connected to ground

and a load resistor of connected from the drain to the positive supply rail VDD· The output is

taken from the drain and the input applied between gate and ground .

But, during the fabrication resistors are not conveniently produced on the silicon substrate and

even small values of resistors occupy excessively large areas .Hence some other form of load

resistance is used. A more convenient way to solve this problem is to use a depletion mode

transistor as the load, as shown in Fig. Below.

The salient features of the n-MOS inverter are

• For the depletion mode transistor, the gate is connected to the source so it is always on .

• In this configuration the depletion mode device is called the pull-up (P.U) and the

enhancement mode device the pull-down (P.D) transistor.

• With no current drawn from the output, the currents Ids for both transistors must be

equal.

NMOS Inverter transfer characteristic.

The transfer characteristic is drawn by taking Vds on x-axis and Ids on Y-axis for both

enhancement and depletion mode transistors. So,to obtain the inverter transfer characteristic for

Vgs = 0 depletion mode characteristic curve is superimposed on the family of curves for the

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enhancement mode device and from the graph it can be seen that , maximum voltage across the

enhancement mode device corresponds to minimum voltage across the depletion mode transistor.

From the graph it is clear that as Vin(=Vgs p.d. Transistor) exceeds the Pulldown threshold

voltage current begins to flow. The output voltage Vout thus decreases and the subsequent

increases in Vin will cause the Pull down transistor to come out of saturation and become

resistive.

CMOS Inverter :

The inverter is the very important part of all digital designs. Once its operation and properties

are clearly understood, Complex structures like NAND gates, adders, multipliers, and

microprocessors can also be easily done. The electrical behavior of these complex circuits can be

almost completely derived by extrapolating the results obtained for inverters. As shown in the

diagram below the CMOS transistor is designed using p-MOS and n-MOS transistors.

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In the inverter circuit ,if the input is high .the lower n-MOS device closes to discharge the

capacitive load .Similarly ,if the input is low,the top p-MOS device is turned on to charge the

capacitive load .At no time both the devices are on ,which prevents the DC current flowing from

positive power supply to ground. Qualitatively this circuit acts like the switching circuit, since

the p-channel transistor has exactly the opposite characteristICs of the n-channel transistor. In the

transition region both transistors are saturated and the circuit operates with a large voltage gain.

The C-MOS transfer characteristic is shown in the below graph.

Considering the static conditions first, it may be Seen that in region 1 for which Vi,. = logic 0,

we have the p-transistor fully turned on while the n-transistor is fully turned off. Thus no current

flows through the inverter and the output is directly connected to VDD through the p-transistor.

Hence the output voltage is logic 1 . In region 5 , Vin = logic 1 and the n-transistor is fully on

while the p-transistor is fully off. So, no current flows and a logic 0 appears at the output.

In region 2 the input voltage has increased to a level which just exceeds the threshold voltage of

the n-transistor. The n-transistor conducts and has a large voltage between source and drain; so it

is in saturation. The p-transistor is also conducting but with only a small voltage across it, it

operates in the unsaturated resistive region. A small current now flows through the inverter from

VDD to VSS. If we wish to analyze the behavior in this region, we equate the p-device resistive

region current with the n-device saturation current and thus obtain the voltage and current

relationships.

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Region 4 is similar to region 2 but with the roles of the p- and n-transistors reversed.However,

the current magnitudes in regions 2 and 4 are small and most of the energy consumed in

switching from one state to the other is due to the larger current which flows in region 3.

Region 3 is the region in which the inverter exhibits gain and in which both transistors are in

saturation.

The currents in each device must be the same ,since the transistors are in series. So,we can write

that

Since both transistors are in saturation, they act as current sources so that the equivalent circuit in

this region is two current sources in series between VDD and Vss with the output voltage coming

from their common point. The region is inherently unstable in consequence and the changeover

from one logic level to the other is rapid.

Determination of Pull-up to Pull –Down Ratio (Zp.uZp.d.)For an NMOS Inverter driven

by another NMOS Inverter :

Let us consider the arrangement shown in Fig.(a). In which an inverter is driven from the output

of another similar inverter. Consider the depletion mode transistor for which Vgs = 0 under all

conditions, and also assume that in order to cascade inverters without degradation the condition

Fig.(a).Inverter driven by another inverter.

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For equal margins around the inverter threshold, we set Vinv = 0.5VDD · At this point both

transistors are in saturation and we can write that

Where Wp.d , Lp.d , Wp.u. And Lp.u are the widths and lengths of the pull-down and pull-up

transistors respectively.

So,we can write that

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The typical, values for Vt ,Vinv and Vtd are

Substituting these values in the above equation ,we get

Here

So,we get

This is the ratio for pull-up to pull down ratio for an inverter directly driven by another inverter.

Pull -Up to Pull-Down ratio for an NMOS Inverter driven through one or more Pass

Transistors

Let us consider an arrangement in which the input to inverter 2 comes from the output of

inverter 1 but passes through one or more NMOS transistors as shown in Fig. Below (These

transistors are called pass transistors).

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The connection of pass transistors in series will degrade the logic 1 level / into inverter 2 so that

the output will not be a proper logic 0 level. The critical condition is , when point A is at 0 volts

and B is thus at VDD. But the voltage into inverter 2at point C is now reduced from VDD by the

threshold voltage of the series pass transistor. With all pass transistor gates connected to VDD

there is a loss of Vtp, however many are connected in series, since no static current flows

through them and there can be no voltage drop in the channels. Therefore, the input voltage to

inverter 2 is

Vin2 = VDD- Vtp

Where Vtp = threshold voltage for a pass transistor.

Let us consider the inverter 1 shown in Fig.(a) with input = VDD· If the input is at VDD , then the

pull-down transistor T2 is conducting but with a low voltage across it; therefore, it is in its

resistive region represented by R1 in Fig.(a) below. Meanwhile, the pull up transistor T1 is in

saturation and is represented as a current source.

For the pull down transistor

Since Vds is small, Vds/2 can be neglected in the above expression.

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So,

Now, for depletion mode pull-up transistor in saturation with Vgs = 0

The product I1R1 = Vout1

So,

Let us now consider the inverter 2 Fig.b .when input = VDD- Vtp.

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Whence,

If inverter 2 is to have the same output voltage under these conditions then Vout1 = Vout2. That is

I1R1=I2R2 , therefore

Considering the typical values

Therefore

From the above theory it is clear that, for an n-MOS transistor

(i). An inverter driven directly from the output of another should have a Zp.u/ Zpd. Ratio

Of ≥ 4/1.

(ii).An inverter driven through one or more pass transistors should have a Zp.u./Zp.d ratio of ≥8/1

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ALTERMTIVE FORMS OF PULL –UP

Generally the inverter circuit will have a depletion mode pull-up transistor as its load. But there

are also other configurations .Let us consider four such arrangements.

(i).Load resistance RL : This arrangement consists of a load resistor as apull-up as shown in the

diagram below.But it is not widely used because of the large space requirements of resistors

produced in a silicon substrate.

2. NMOS depletion mode transistor pull-up : This arrangement consists of a depletion mode

transistor as pull-up. The arrangement and the transfer characteristic are shown below.In this

type of arrangement we observe

(a) Dissipation is high , since rail to rail current flows when Vin = logical 1.

(b) Switching of output from 1 to 0 begins when Vin exceeds Vt, of pull-down device.

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NMOS depletion mode transistor pull-up and transfer characteristic

(c) When switching the output from 1 to 0, the pull-up device is non-saturated initially and this

presents lower resistance through which to charge capacitive loads .

3. NMOS enhancement mode pull-up :This arrangement consists of a n-MOS enhancement

mode transistor as pull-up. The arrangement and the transfer characteristic are shown below.

NMOS enhancement mode pull-up and transfer characteristic

The important features of this arrangement are

(a) Dissipation is high since current flows when Vin =logical 1 (VGG is returned to VDD) .

(b) Vout can never reach VDD (logical I) if VGG = VDD as is normally the case.

(c) VGG may be derived from a switching source, for example, one phase of a clock, so that

Dissipation can be greatly reduced.

(d) If VGG is higher than VDD then an extra supply rail is required.

4. Complementary transistor pull-up (CMOS) : This arrangement consists of a C-MOS

arrangement as pull-up. The arrangement and the transfer characteristic are shown below

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The salient features of this arrangement are

(a) No current flows either for logical 0 or for logical 1 inputs.

(b) Full logical 1 and 0 levels are presented at the output.

(c) For devices of similar dimensions the p-channel is slower than the n-channel device.

THE BiCMOS INVERTER :

A BiCMOS inverter, consists of a PMOS and NMOS transistor ( M2 and M1), two NPN

bipolar junction transistors,( Q2 and Q1), and two impedances which act as loads( Z2 and Z1) as

shown in the circuit below.

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When input, Vin, is high (VDD), the NMOS transistor ( M1), turns on, causing Q1 to

conduct,while M2 and Q2 are off, as shown in figure (b) . Hence , a low (GND) voltage is

translated to the output Vout. On the other hand, when the input is low, the M2 and Q2 turns on,

while m1and Q1 turns off, resulting to a high output level at the output as shown in Fig.(b).

In steady-state operation, Q1 and Q2 never turns on or off simultaneously, resulting to a lower

power consumption. This leads to a push-pull bipolar output stage. Transistors m1and M2, on

the other hand, works as a phase-splitter, which results to a higher input impedance.

The impedances Z2 and Z1 are used to bias the base-emitter junction of the bipolar transistor and

to ensure that base charge is removed when the transistors turn off. For example when the input

voltage makes a high-to-low transition, M1 turns off first. To turn off Q1, the base charge must

be removed, which can be achieved by Z1.With this effect, transition time reduces. However,

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there exists a short time when both Q1 and Q2 are on, making a direct path from the supply

(VDD) to the ground. This results to a current spike that is large and has a detrimental effect on

both the noise and power consumption, which makes the turning off of the bipolar transistor

fast .

Comparison of BiCMOS and C-MOS technologies

The BiCMOS gates perform in the same manner as the CMOS inverter in terms of power

consumption, because both gates display almost no static power consumption.

When comparing BiCMOS and CMOS in driving small capacitive loads, their performance are

comparable, however, making BiCMOS consume more power than CMOS. On the other hand,

driving larger capacitive loads makes BiCMOS in the advantage of consuming less power than

CMOS, because the construction of CMOS inverter chains are needed to drive large capacitance

loads, which is not needed in BiCMOS.

The BiCMOS inverter exhibits a substantial speed advantage over CMOS inverters, especially

when driving large capacitive loads. This is due to the bipolar transistor’s capability of

effectively multiplying its current.

For very low capacitive loads, the CMOS gate is faster than its BiCMOS counterpart due to

small values of Cint. This makes BiCMOS ineffective when it comes to the implementation of

internal gates for logic structures such as alus, where associated load capacitances are small.

BiCMOS devices have speed degradation in the low supply voltage region and also BiCMOS is

having greater manufacturing complexity than CMOS.

UNIT II

VLSI CIRCUIT DESIGN PROCESSES

In this chapter we will be studying how to get the schematic into stick diagrams or layouts.

MOS circuits are formed on four basic layers:

N-diffusion

P-diffusion

Poly silicon

Metal

These layers are isolated by one another by thick or thin silicon dioxide insulating

layers. Thin oxide mask region includes n-diffusion / p-diffusion and transistor channel.

Stick diagrams:

Stick diagrams may be used to convey layer information through the use of a color code.

For example:

N-diffusion -green

poly -- red

Blue -- metal

yellow --implant

Black --contact area

Encodings for NMOS process:

Figure shows the way of representing different layers in stick diagram notation and

mask layout using nmos style.

Figure1 shows when a n-transistor is formed: a transistor is formed when a green line

(n+ diffusion) crosses a red line (poly) completely. Figure also shows how a depletion

mode transistor is represented in the stick format.

Encodings for MOS process:

figure 2 shows when a n-transistor is formed: a transistor is formed when a green line

(n+ diffusion) crosses a red line (poly) completely.

Figure 2 also shows when a p-transistor is formed: a transistor is formed when a yellow

line (p+ diffusion) crosses a red line (poly) completely.

Encoding for BJT and MOSFETs:

There are several layers in an nMOS chip:

Paths of metal (usually aluminum) a further thick layer of silicon dioxide with contact cuts

through the silicon dioxide where connections are required.

The three layers carrying paths can be considered as independent conductors that only

interact where polysilicon crosses diffusion to form a transistor. These tracks can be drawn

as stick diagrams with

Diffusion in green

Polysilicon in red

Metal in blue

Using black to indicate contacts between layers and yellow to mark regions of implant in the

channels of depletion mode transistors. With CMOS there are two types of diffusion: n-type

is drawn in green and p-type in brown. These are on the same layers in the chip and must not

meet. In fact, the method of fabrication required that they be kept relatively far apart. Modern

CMOS processes usually support more than one layer of metal. Two are common and three

or more are often available. Actually, these conventions for colors are not universal; in

particular, industrial (rather than academic) systems tend to use red for diffusion and green

for polysilicon. Moreover, a shortage of colored pens normally means that

both types of diffusion in CMOS are colored green and the polarity indicated by drawing a

circle round p-type transistors or simply inferred From the context. Colorings for

multiple layers of metal are even less standard.

There are three ways that an nMOS inverter might bedrawn:

Figure 4 shows schematic, stick diagram and corresponding layout of nMOS depletion

Load inverter

Figure 7 shows the stick diagram nMOS implementation of the function f=[(xy)+z]

Figure 8: stick diagram of CMOS NAND and NOR

Figure 8 shows the stick diagram CMOS NOR and NAND, where we can see that the p

diffusion line never touched the n diffusion directly, it is always joined using a blue color

metal line.

NMOS and CMOS Design style:

In the NMOS style of representing the sticks for the circuit, we use only NMOS transistor, in

CMOS we need to differentiate n and p transistor, that is usually by the color or in

monochrome diagrams we will have a demarcation line. Above the demarcation line are the

p transistors and below the demarcation are the n transistors.

Following stick shows CMOS circuit example in monochrome where we utilize the

demarcation line.

Figure 9 shows the stick diagram of dynamic shift register using CMOS style. Here the output of

the TG is connected as the input to the inverter and the same chain continues depending the

number of bits.

Design Rules:

Design rules include width rules and spacing rules. Mead and Conway developed a set of

simplified scalable λ -based design rules, which are valid for a range of fabrication

technologies. In these rules, the minimum feature size of a technology is characterized as 2 λ

. All width and spacing rules are specified in terms of the parameter λ . Suppose we have

design rules that call for a minimum width of 2 λ , and a minimum spacing of 3 λ . If

we select a 2 um technology (i.e., λ = 1 um), the above rules are translated to a

minimum width of 2 um and a minimum spacing of 3 um. On the other hand, if a 1 um

technology (i.e., λ = 0.5 um) is selected, then the same width and spacing rules are now

specified as 1 um and 1.5 um, respectively.

Figure 10 shows the design rule n diffusion, p diffusion, poly, metal1 and metal 2. The n and

p diffusion lines is having a minimum width of 2λand a minimum spacing of 3λ. Similarly

we are showing for other layers

.

Figure shows the design rule for the transistor, and it also shows that the poly should

extend for a minimum of 2λbeyond the diffusion boundaries.(gate over hang distance)

What is Via?

It is used to connect higher level metals from metal1 connection. The cross section and

layout view given figure 13 explain via in a betterway.

Figure shows the design rules for contact cuts and Vias. The design rule for contact

is minimum 2λx2λand same is applicable for a Via.

Buried contact: The contact cut is made down each layer to be joined and it is shown

in figure 14.

Butting contact: The layers are butted together in such a way the two contact cuts become

contiguous. We can better under the buttingcontact from figure

CMOS LAMBDA BASED DESIGN RULES:

Till now we have studied the design rules wrt only NMOS , what are the rules to be followed

if we have the both p and n transistor on the same chip will be made clear with the diagram.

Figure 16 shows the rules to be followed in CMOS well processes to accommodate both n

and p transistors.

Orbit 2µm CMOS process:

In this process all the spacing between each layersand dimensions will be in terms

micrometer. The 2µm here represents the feature size. All the design rules what ever we have

seen will not have lambda instead it will have the actual dimension in micrometer.

In one way lambda based design rules are better compared micrometer based design

rules, that is lambda based rules are feature size independent.

Figure 17 shows the design rule for BiCMOS process using orbit 2um process.

The following is the example stick and layout for 2way selector with enable (2:1 MUX).

Scaling of MOS Circuits:

What is Scaling?

Proportional adjustment of the dimensions of an electronic device while maintaining

the electrical properties of the device, results in a device either larger or smallerthan

the un-scaled device. Then Which way do we scale the devices for VLSI?

BIG and SLOW … or SMALLand FAST? What do we gain?

Why Scaling?...

Scale the devices and wires down, Make the chips ‘fatter’ – functionality, intelligence,

memory – and – faster, Make more chips per wafer – increased yield, Make the end user

Happy by giving more for less and therefore, make MORE MONEY!!

FoM for Scaling

Impact of scaling is characterized in terms of several indicators:

Minimum feature size

Number of gates on one chip

Power dissipation

Maximum operational frequency

Die size

Production cost

Many of the FoMs can be improved by shrinking the dimensions of transistors and

interconnections. Shrinking the separation between features – transistors and wires

Adjusting doping levels and supply voltages.

Technology Scaling :

Goals of scaling the dimensions by 30%:

Reduce gate delay by 30% (increase operating frequency by

43%) Double transistor density

Reduce energy per transition by 65% (50% power savings @ 43% increase in frequency)

Die size used to increase by 14% per generation

Technology generation spans 2-3 years

Figure1 to Figure 5 illustrates the technology scaling in terms of minimum feature

size, transistor count, prapogation delay, power dissipation and density and technology

generations.

Scaling Models

Full Scaling (Constant Electrical Field)

Ideal model – dimensions and voltage scale together by the same scale factor Fixed Voltage

Scaling

Most common model until recently – only the dimensions scale, voltages remain

constant General Scaling

Most realistic for today’s situation – voltages and dimensions scale with different factors

Scaling Factors for Device Parameters

Device scaling modeled in terms of generic scaling factors: 1/αand 1/β

• 1/β: scaling factor for supply voltage VDD, and gate oxide thickness D

• 1/α: linear dimensions both horizontal and vertical dimensions

Why is the scaling factor for gate oxide thickness different from other linear horizontal

and vertical dimensions? Consider the cross sectionof the device as in Figure 6,various

parameters derived are as follows.

Limitations of Scaling:

Effects, as a result of scaling down- which eventually become severe enough to prevent further

miniaturization.

• Substrate doping

• Depletion width

• Limits of miniaturization

• Limits of interconnect and contact resistance

• Limits due to sub threshold currents

• Limits on logic levels and supply voltage due to noise

• Limits due to current density

UNIT-III

GATE LEVEL DESIGN

LOGIC GATES AND OTHER COMPLEX GATES:

Invert(nmos, cmos, Bicmos) NAND Gate(nmos, cmos, Bicmos) NOR Gate(nmos, cmos, Bicmos)

The module (integrated circuit) is implemented in terms of logic gates and interconnections

between these gates. Designer should know the gate-level diagram of the design. In general, gate-level modeling is used for implementing lowest level modules in a design like, full-adder, multiplexers, etc.

nmos Inverter : The logic symbol and truth table of ideal inverter is shown in figure given below.

Here A is the input and B is the inverted output represented by their node voltages. Using positive logic,

the Boolean value of logic 1 is represented by Vdd and logic 0 is represented by 0. Vth is the inverter

threshold voltage, which is Vdd /2, where Vdd is the output voltage.

The output is switched from 0 to Vdd when input is less than Vth. So, for 0<Vin<Vth output is equal to logic 0

input and Vth<Vin< Vdd is equal to logic 1 input for inverter.

The characteristics shown in the figure are ideal. The nmos inverter is as shown

Let us consider the nmos inverter with 8:1 pull up transistors and 1:1 pull down transistors. Using this data,

the power dissipated by the inverter is obtained as

Rpu = Zpu * Rs = 8*10Kohms = 80 kΩ

Rpd = Zpd * Rs = 1*10Kohms = 10 kΩ

Assuming Vdd = 5V

(Power dissipated) Pd = V2/(Rpu + Rpd)

=25/(90 K Ω)

=o.28 nW

Further, as the pull down transistors shape-factor is ‘1’, the input capacitance is 1 Cg.

cmos Inverter : The CMOS inverter circuit is shown in the figure. Here, nMOS and pMOS transistors

work as driver transistors; when one transistor is ON, other is OFF.

This configuration is called complementary MOS (CMOS). The input is connected to the gate terminal of

both the transistors such that both can be driven directly with input voltages. Substrate of the nMOS is

connected to the ground and substrate of the pMOS is connected to the power supply, VDD.

So VSB = 0 for both the transistors.

VGS,n=VinVGS,n=Vin

VDS,n=VoutVDS,n=Vout

And,

VGS,p=Vin−VDDVGS,p=Vin−VDD

VDS,p=Vout−VDDVDS,p=Vout−VDD

When the input of nMOS is smaller than the threshold voltage (Vin < VTO,n), the nMOS is cut – off and

pMOS is in linear region. So, the drain current of both the transistors is zero.

ID,n=ID,p=0ID,n=ID,p=0

Therefore, the output voltage VOH is equal to the supply voltage.

Vout=VOH=VDDVout=VOH=VDD

When the input voltage is greater than the VDD + VTO,p, the pMOS transistor is in the cutoff region and the

nMOS is in the linear region, so the drain current of both the transistors is zero.

ID,n=ID,p=0ID,n=ID,p=0

Therefore, the output voltage VOL is equal to zero.

Vout=VOL=0Vout=VOL=0

The nMOS operates in the saturation region if Vin > VTO and if following conditions are satisfied.

VDS,n≥VGS,n−VTO,nVDS,n≥VGS,n−VTO,n

Vout≥Vin−VTO,nVout≥Vin−VTO,n

The pMOS operates in the saturation region if Vin < VDD + VTO,p and if following conditions are satisfied.

VDS,p≤VGS,p−VTO,pVDS,p≤VGS,p−VTO,p

Vout≤Vin−VTO,p

bicmos Inverter : A BiCMOS inverter, consists of a PMOS and NMOS transistor ( M2 and M1), two

NPN bipolar junction transistors,( Q2 and Q1), and two impedances which act as loads( Z2 and Z1) as shown in the circuit below.

When input, Vin, is high (VDD), the NMOS transistor ( M1), turns on, causing Q1 to conduct,while M2 and

Q2 are off, as shown in figure (b) . Hence , a low (GND) voltage is translated to the output Vout. On the

other hand, when the input is low, the M2 and Q2 turns on, while M1and Q1 turns off, resulting to a high

output level at the output as shown in Fig.(b). In steady-state operation, Q1 and Q2 never turns on or off

simultaneously, resulting to a lower power consumption. This leads to a push-pull bipolar output stage.

Transistors M1and M2, on the other hand, works as a phase-splitter, which results to a higher input

impedance.

The impedances Z2 and Z1 are used to bias the base-emitter junction of the bipolar transistor and to

ensure that base charge is removed when the transistors turn off. For example when the input voltage

makes a high-to-low transition, M1 turns off first. To turn off Q1, the base charge must be removed, which

can be achieved by Z1.With this effect, transition time reduces. However, there exists a short time when

both Q1 and Q2 are on, making a direct path from the supply (VDD) to the ground. This results to a current

spike that is large and has a detrimental effect on both the noise and power consumption, which makes

the turning off of the bipolar transistor fast .

nmos NAND Gate : vout <= vt = 0.2vdd

Vout = (vdd*n*zpd)/(nzpd+zpu) = 0.2vdd

= (nzpd)/(nzpd+zpu) = 0.2

Consider zpd = 1

(2)/(2+zpu) = 0.2

0.2zpu = 2-0.4

Zpu= 8

(zpu)/(2*zpd) = 8/2 = 4

nmos NAND geometry reveals two significant factors:

--nmos NAND gate area requirements are greater than those of a corresponding nmos inverter, pull

down transistors must be added in series to provide no.of inputs, as inputs are added there must be

corresponding length adjustment of pull up transistor, channel to maintain required overall ratio.

--nmos NAND gate delays are also increased in direct proportion to the members of required added.

If pull down transistor are kept at minimum size (2λx2λ) each will present 10’s CG at its inputs. But if their

n such inputs then the length and resistance by a factor n to keep correct ratio. Thus the delay associated

with nmos NAND are

ƬNAND = ƞ Tinv

Where , n- No. Of inputs

Tinv - Inverted delay

Other approach, keeping Zpu constant and widening pull down channels.

Nmos NAND gate is used only where absolutely necessary and when the number of inputs are restricted.

cmos NAND Gate : The two input NAND function is expressed by Y=A.B

Step 1 Take complement of Y

Y= A.B = A.B

Step 2 Design the PDN

In this case, there is only one AND term, so there will be two nMOSFETs in series as shown in figure.

Step 3 Design the PUN. In PUN there will be two pMOSFETs in parallel , as shown in figure

Finally join the PUN and PDN as shown in figure which realizes two –input NAND gate. Note that we have

realized y, rather tat Y because the inversion is automatically provided by the nature of the CMOS circuit

operation,

Working operation

1) Whenever at least one of the inputs is LOW, the corresponding pMOS transistor will conduct

while the corresponding nMOS transistor will turn OFF. Subsequently, the output voltage will be HIGH.

2) Conversely, if both inputs are simultaneously HIGH, then both pMOS transistors will turn

OFF, and the output voltage will be pulled LOW by the two conducting nMOS transistors.

The cmos NAND gate has no such restrictions but, bearing in mind the remarks are asymmetry,

it is necessary to allow for extended fall times on capacitive loads owing to the no.of n-transistors in series

forming the pull down. Some adjustments of transistor geometry is necessary for this reason and to keep

the transfer characteristics symmetrical above vdd/2.

bicmos NAND Gate : The bicmos gate is shown in practical version and is thus more complex than

the simple intuitive version. However, it has considerable load driving capabilities and is most useful

where a large fan out is required or where there is some other form of high capacitance load on the

output. A typical mask layout for this gate, using orbitTM 2μm design rules, is given in monochrome form.

nmos NOR Gate :

NOR gate can be used to accommodate any reasonable number of inputs (preferred over nand gate).

Both legs of two input nmos nor gate provided.

The ratio must be such that one conducting pull down leg will give inverted line transfer characteristics.

Ares occupied by nmos NOR gate is reasonable since the pull up transistor dimensions are unaffected by

the number of inputs accommodate.

NOR gate is as fast as the inverter and is the preferred inverted based nmos logic.

cmos NOR Gate : The two input NOR function is expressed by

Y=A+B

Step 1: Take complement of Y

Y= A+B = A+B

Step 2: Design the PDN

In this case, there is only one OR term, so there will be two nMOSFETs connected in parallel, as shown in figure. Step 3: Design the PUN

In PUN there will be two pMOSFETs in series , as shown in figure NRI Institute of Technology

Finally join the PUN and PDN as shown in figure which realizes two –input NAND gate. Note that we have

realized y, rather tat Y because the inversion is automatically provided by the nature of the cMOS circuit

operation,

Working operation

1) Whenever at least one of the inputs is LOW, the corresponding pMOS transistor will conduct

while the corresponding nMOS transistor will turn OFF. Subsequently, the output voltage will be HIGH.

2) Conversely, if both inputs are simultaneously HIGH, then both pMOS transistors will turn

OFF, and the output voltage will be pulled LOW by the two conducting nMOS transistors.

Two pull up transistors are required to implement the logic ‘1’ condition and two pull down transistors

are required to implement logic ‘0’.

Pmos are connected in series, nmos are connected in parallel.

Predominant resistance of the p-devices is aggravated in its effect by the number connected in series.

Raise and fall time asymmetry on capacity load is increased and there will be a shift in the transfer

characteristics which will reduce noise immunity.

For these reasons CMOS NOR gate with more than 2 inputs may require adjustment if p,n transistors

geometry.

SWITCH LOGIC:

1) Switch logic is mainly based on pass transistor or transmission gate.

2) It is fast for small arrays and takes no static current from the supply, VDD. Hence power dissipation of such arrays is small since current only flows on switching.

3) Switch (pass transistor) logic is analogous to logic arrays based on relay contacts, where in path through each switch is isolated from the logic levels activating the switch.

PASS TRANSISTOR:

1) This logic uses transistors as switches to carry logic signals from node to node instead of connecting output nodes directly to VDD or ground(GND)

2) If a single transistor is a switch between two nodes, then voltage degradation.equal to Vt(threshold voltage) for high or low level depends up on nMOS or pMOS logic.

3) When using nMOS switch logic no pass transistor gate input may be driven through one or more pass transistors as shown in figure.

4) Since the signal out of pass transistor T1 does not reach a full logic 1 by threshold voltage effects signal is degraded by below a true logic 1, this degraded voltage would not permit the output of T2 to reach an acceptable logic 1 level.

Advantages

They have topological simplicity.

1) Requires minimum geometry.

2) Do not dissipate standby power, since they do not have a path from supply to ground.

Disadvantages

1) Degradation in the voltage levels due to undesirable threshold voltage effects.

2) Never drive a pass transistor with the output of another pass transistor.

TRANSMISSION GATE :

1) It is an electronic element, good non-mechanical relay built with CMOS technology.

2) It is made by parallel combination of an nMOS and pMOS transistors with the input at gate of one transistor being complementary to the input at the gate of the other as shown in figure.

3) Thus current can flow through this element in either direction.

4) Depending on whether or not there is a voltage on the gate, the connection between the input and output is either low resistance or high-resistance, respectively Ron = 100Ω and Roff > 5 MΩ.

Operation

• When the gate input to the nMOS transistor is ‘0’ and the complementary ‘1’ is gate input to the pMOS , thus both are turned off.

• When gate input to the nMOS is ‘1’ and its complementary ‘0’ is the gate input to the pMOS , both are turned on and passes any signal ‘1’ and ‘0’ equally without any degradation.

• The use of transmission gates eliminates the undesirable threshold voltage effects which give rise to loss of logic levels in pass-transistors as shown in figure.

Advantages

1) Transmission gates eliminates the signal degradation in the output logic levels.

2) Transmission gate consists of two transistors in parallel and except near the positive and negative

rails.

Disadvantages

1) Transmission gate requires more area than nMOS pass circuitry.

2) Transmission gate requires complemented control signals.

CMOS DOMINO LOGIC

Standard CMOS logic gates need a PMOS and an NMOS transistor for each logic input. The pMOS

transistors require a greater area tan the nMOS transistors carrying the same current. So, a large chip area is

necessary to perform complex logic operations. The package density in CMOS is improved if a dynamic

logic circuit, called the domino CMOS logic circuit, is used.

Domino CMOS logic is slightly modified version of the dynamic CMOS logic circuit. In this case, a

static inverter is connected at the output of each dynamic CMOS logic block. The addition of the inverter

solves the problem of cascading of dynamic CMOS logic circuits.

The circuit diagram of domino CMOS logic structures as shown in figure as follows

A domino CMOS AND-OR gate that realizes the function y = AB + CD is depicted in fugure . The left hand

part of the circuit containing Mn,Mp, T1,T2,,T3,and T4 forms and AND-ORINVERTER (AOI) gate. It

derives the static CMOS inverter formed by N2 and P2 in the right

hand part of the circuit. The domino gate is activated by the single phase clock ø applied to the NMOS (Mn)

and the PMOS (Mp) transistors. The load on the AOI part of the circuits is the parasitic load capacitance.

Working

• When ø = 0, is ON and Mn is OFF, so that no current flows in the AND-OR paths of the AOI. The

capacitor CL is charged to VDD through Mp since the latter is ON. The input to the inverter is high, and

drives the output voltage V0 to logic-0.

• When ø = 1, Mp is turned OFF and Mn is turned ON. If either (or both) A and B or C and D is at logic-1,

CL discharges through either T2,T1 and Mn or T3,T4 and Mp. So , the inverter input is driven to logic-0 and

hence the output voltage V0 to logic-1. The Boolean expression for the output voltage is Y = AB + CD.

Note : Logic input can change only when ø = 0. No changes of the inputs are permitted when ø = 1 since a

discharge path may occur.

Advantages

1) Smaller areas compared to conventional CMOS logic.

2) Parasitic capacitances are smaller so that higher operating speeds are possible.

3) Operation is free of glitches since each gate can make one transition.

Disadvantages

1) Non inverting structures are possible because of the presence of inverting buffer.

2) Charge distribution may be a problem.

CLOCKED CMOS LOGIC :

The clocked CMOS logic is also referred as C2MOS logic. Figure shows the general arrangement of a

clocked CMOS (C2MOS) logic. A pull-up p-block and a complementary n-block pull-down structure

represent p and n-transistors respectively and are used as implement clocked CMOS logic shown in figure.

However, the logic in this case is connected to the output only during the ON period of the clock. Figure

shows a clocked inverter circuit which is also belongs to clocked CMOS logic family. The slower rise times

and fall times can be expected due to owing of extra transistors in series with the output.

Working

• When ø = 1 the circuit acts an inverter , because transistors Q3 and Q4 are ‘ON’ . It is said to be in the

“evaluation mode”. Therefore the output Z changes its previous value.

• When ø = 0 the circuit is in hold mode, because transistors Q3 and Q4 becomes ‘OFF’ . It is said to be in

the “precharge mode”. Therefore the output Z remains its previous value

n-p CMOS LOGIC :

Figure shows the another variation of basic dynamic logic arrangement of CMOS logic called as n-p CMOS

logic. In this, logic the actual logic blocks are alternatively ‘n’ and ‘p’ in a cascaded structure. The clock ø

and ø- are used alternatively to fed the precharge and evaluate transistors. However, the functions of top and

bottom transistors are also alternate between precharge and evaluate transistors.

Working

• During the pre charge phase ø = 0 , the output of the n-tree gate, OUT 1 OUT3 , are charged to VDD,

while the output of the p-tree gate OUT2 is pre discharged to 0V. Since the n-tree gate connects pMOS

pull-up devices, the PUN of the p-tree is turned off at that time.

• During the evaluation phase ø = 1, the outputs (OUT1,OUT3) of the n-tree gate can only make a 1-Æ0

transition, conditionally turning on some transistors in the p-tree. This ensures that no accidental discharge

of OUT 2 can occur.

• Similarly n-tree blocks can follow p-tree gates without any problems, because the inputs to the n-gate are

pre charged to 0.

Disadvantages

Here, the p-tree blocks are slower than the n-tree modules, due to the lower current drive of the pMOS

transistors in the logic network.

UNIT-IV

ADDERS:

Binary Adder Notations and Operations:

As mentioned previously, adders in VLSI digital systems use binary notation.

In that case, add is done bit by bit using Boolean equations.

1-bit Half Adder.

Consider a simple binary add with two n-bit inputs A;B and a one-bit carry-in

cin along with n-bit output S.

S = A + B + Cin

Where A = an-1, an-2……a0; B = bn-1, bn-2……b0.

The + in the above equation is the regular and operation. However, in the

binary world, only Boolean algebra works. For add related operations, AND, OR and

Exclusive-OR (XOR) are required. In the following documentation, a dot between

two variables (each with single bit), e.g. a _ b denotes 'a AND b'. Similarly, a + b

denotes 'a OR b' and a _ b denotes 'a XOR b'. Considering the situation of adding two

bits, the sum s and carry c can be expressed

using Boolean operations mentioned above.

Si = ai ^ bi

Ci + 1 = ai . bi

The Equation of Ci+1 can be implemented as shown in Fig.2.1. In the figure,

there is a Half adder, which takes only 2 input bits. The solid line highlights the

critical path, which indicates the longest path from the input to the output. Equation of

ci+1 can be extended to perform full add operation, where there is a carry input.

Si = ai ^ bi ^ ci

Ci + 1 = ai . bi + ai . ci + bi . ci

1-bit Full Adder.

A Full adder can be built based on Equation above. The block diagram of a 1-

bit full adder is shown in Fig.2.2. The full adder is composed of 2 half adders and an

OR gate for computing carry-out. Using Boolean algebra, the equivalence can be

easily proven. To help the computation of the carry for each bit, two binary literals are

introduced. They are called carry generate and carry propagate, denoted by gi and pi.

Another literal called temporary sum ti is employed as well. There is relation between

the inputs and these literals.

Gi = ai . bi

Pi = ai + bi

Ti = ai ^ bi

Where i is an integer and 0 _ i < n.

With the help of the literals above, output carry and sum at each bit can be

written as:

Ci + 1 = gi + pi . ci

Si = ti ^ ci

In some literatures, carry-propagate pi can be replaced with temporary sum ti

in order to save the number of logic gates. Here these two terms are separated in order

to clarify the concepts. For example, for Ling adders, only pi is used as carry-

propagate.

The single bit carry generate/propagate can be extended to group version G

and P. The following equations show the inherent relations.

Gi : k = Gi : j + Pi : j . Gj – 1 : k

Pi : k = Pi : j . Pj-1:k

Where i : k denotes the group term from i through k.

Using group carry generate/propagate, carry can be expressed as expressed in

the following equation.

Ci + 1 = Gi : j + Pi : j . Cj

Ripple carry adder

Ripple carry adder is an n-bit adder built from full adders. Fig 2.1 shows a 4-bit ripple

carry adder. One full adder is responsible for the addition of two binary digits at any

stage of the ripple carry. The carryout of one stage is fed directly to the carry-in of

the next stage. Even though this is a simple adder and can be used to add unrestricted

bit length numbers, it is however not very efficient when large bit numbers are used.

4-b Ripple Carry Adder

One of the most serious drawbacks of this adder is that the delay increases

linearly with the bit length. The worst-case delay of the RCA is when a carry

signal transition ripples through all stages of adder chain from the least significant

bit to the most significant bit, which is approximated by:

T = (n-1) tc + ts

Delay :

The latency of a 4-bit ripple carry adder can be derived by considering the

worst-case signal propagation path. We can thus write the following

expressions:

TRCA-4bit = TFA(A0,B0→Co)+T FA (C in→C1)+TFA (Cin→C2)+ TFA

(Cin→S3)

And, it is easy to extend to k-bit RCA:

TRCA-4bit = TFA(A0,B0→Co)+(K-2)* TFA (Cin→Ci)+ TFA (Cin→Sk-1).

Drawbacks :

Delay increases linearly with the bit length and Not very efficient when large

bit numbers are used.

Carry Look-Ahead Adder

Lookahead carry algorithm speed up the operation to perform addition,

because in this algorithm carry for the next stages is calculated in advance based on

input signals. In CLA, the carry propagation time is reduced to O(log2(Wd)) by using

a tree like circuit to compute the carry rapidly. Fig. shows the 4-bit Carry Look-Ahead

Adder.

4-bit Carry Look Ahead Adder

The CLA exploits the fact that the carry generated by a bit-position depends

on the three inputs to that position. If ‘X’ and ‘Y‘ are two inputs then if X=Y=1, a

carry is generated independently of the carry from the previous bit position and if

X=Y= 0, no carry is generated. Similarly if X ≠ Y, a carry is generated if and only if

the previous bit-position generates a carry. ‘C’ is initial carry, “S” and “Cout” are

output sum and carry respectively, then Boolean expression for calculating next carry

and addition is:

Pi = Xi xor Yi -- Carry Propagation

Gi = Xi and Yi -- Carry Generation

Ci + 1 = Gi or (Pi and Ci) -- Next Carry

Si = Xi xor Yi xor Ci -- Sum Generation

Thus, for 4-bit adder, we can extend the carry, as shown below:

C1 = G0 + P0 · C0

C2 = G1 + P1 · C1 = G1 + P1 · G0 + P1 · P0 · C0

C3 = G2 + P2 · G1 + P2 · P1 · G0 + P2 · P1 · P0 · C0

C4 = G3 + P3 · G2 + P3 · P2 · G1 + P3 · P2 · P1 · G0+ P3 · P2 · P1 · P0 · C0

As with many design problems in digital logic, we can make tradeoffs

between area and performance (delay). In the case of adders, we can create faster (but

larger) designs than the RCA. The Carry Look ahead Adder (CLA) is one of these

designs (there are others too, but we will only look at the CLA).

Drawbacks :

For long bit length, a carry look-ahead adder is not practical, but a hierarchical

structure one can improve much. The disadvantage of CLA is that the carry logic

block gets very complicated for more than 4-bits. For that reason, CLAs are usual

implemented as 4-bit modules and are used in a hierarchical structure to realize adders

that have multiples of 4-bits.

Carry Save Adder

The carry-save adder reduces the addition of 3 numbers to the addition of 2

numbers. The propagation delay is 3 gates regardless of the number of bits. The carry-

save unit consists of n full adders, each of which computes a single sum and carries

bit based solely on the corresponding bits of the three input numbers.

The entire sum can then be computed by shifting the carry sequence left by

one place and appending a 0 to the front (most significant bit) of the partial sum

sequence and adding this sequence with RCA produces the resulting n+1-bit value.

This process can be continued indefinitely, adding an input for each stage of

full adders, without any intermediate carry propagation. These stages can be arranged

in a binary tree structure, with cumulative delay logarithmic in the number of inputs

to be added, and invariant of the number of bits per input. The main application of

carry save algorithm is, well known for multiplier architecture is used for efficient

CMOS implementation of much wider variety of algorithms for high speed digital

signal processing .CSA applied in the partial product line of array multipliers will

speed up the carry propagation in the array.

4-bit Carry Save Adder

Basically, carry save adder is used to compute sum of three or more n-bit

binary numbers. Carry save adder is same as a full adder. As shown in the Fig.2.4,

here we are computing sum of two 4-bit binary numbers, so we take 4 full adders at

first stage. Carry save unit consists of 4 full adders, each of which computes single

sum and carry bit based only on the corresponding bits of the two input numbers. Let

X and Y are two 4-bit numbers and produces partial sum and carry as S and C as

shown in the below :

Si = Xi xor Yi ; Ci = Xi and Yi

The final addition is then computed as:

1. Shifting the carry sequence C left by one place.

2. Placing a 0 to the front (MSB) of the partial sum sequence S.

3. Finally, a ripple carry adder is used to add these two together and computing the

resulting sum.

Carry Save Adder Computation :

X: 1 0 0 1 1

Y: 1 1 0 0 1

Z: + 0 1 0 1 1

S: 0 0 0 0 1

C: + 1 1 0 1 1

SUM: 1 1 0 1 1 1

In this design 128 bit carry save adder is used since the output of the multiplier

is 128 bits (2N). The carry save adder minimize the addition from 3numbers to 2

numbers. The propagation delay is 3gates despite of the number of bits. The carry

save adder contains n full adders, computing a single sum and carries bit based mainly

on the respective bits of the three input numbers. The entire sum can be calculated by

shifting the carry sequence left by one place and then appending a 0 to most

significant bit of the partial sum sequence. Now the partial sum sequence is added

with ripple carry unit resulting in n + 1 bit value. The ripple carry unit refers to the

process where the carryout of one stage is fed directly to the carry in of the next stage.

This process is continued without adding any intermediate carry propagation. Since

the representation of 128 bit carry save adder is infeasible, hence a typical 8 bit carry

save adder is shown in the figure 3.Here we are computing the sum of two 128 bit

binary numbers, then 128 half adders at the first stage instead of 128 full adder.

Therefore , carry save unit comprises of 128 half adders, each of which computes

single sum and carry bit based only on the corresponding bits of the two input

numbers.

bit carry save adder

If x and y are supposed to be two 128 bit numbers then it produces the partial

products and carry as S and C respectively.

Si = xi 1\ yi (4)

Ci = xi & yi (5)

During the addition of two numbers using a half adder, two ripple carry adder

is used. This is due the fact that ripple carry adder cannot compute a sum bit without

waiting for the previous carry bit to be produced, and hence the delay will be equal to

that of n full adders. However a carry-save adder produces all the output values in

parallel, resulting in the total computation time less than ripple carry adders. So,

Parallel In Parallel Out (PIPO) is used as an accumulator in the final stage.

2.5. Carry Select Adder

A carry-select adder is divided into sectors, each of which – except for the

least-significant –performs two additions in parallel, one assuming a carry-in of zero,

the other a carry-in of one. A four bit carry select adder generally consists of two

ripple carry adders and a multiplexer. The carry-select adder is simple but rather fast,

having a gate level depth of O(√n) . Adding two n-bit numbers with a carry select

adder is done with two adders (two ripple carry adders) in order to perform the

calculation twice, one time with the assumption of the carry being zero and the other

assuming one.

After the two results are calculated, the correct sum, as well as the correct

carry, is then selected with the multiplexer once the correct carry is known. The

design schematic of Carry Select Adder is shown in Fig.

The N-bit Ripple Carry Adder constructed by N set single bit Full-adder

In the N-bit carry ripple adder, the delay time can be expressed as:

TCRA = (N-1) Tcarry + Tsum

In the N-bit carry select adder, the delay time is:

TCSA = Tsetup + (N/M) Tcarry + MTmux + Tsum

In our proposed N-bit area-efficient carry select adder, the delay time is:

Tnew = Tsetup + (N-1) Tmux + Tsum

The carry select adder comes in the category of conditional sum adder.

Conditional sum adder works on some condition. Sum and carry are calculated by

assuming input carry as 1 and 0 prior the input carry comes. When actual carry input

arrives, the actual calculated values of sum and carry are selected using a multiplexer.

The conventional carry select adder consists of k/2 bit adder for the lower half

of the bits i.e. least significant bits and for the upper half i.e. most significant bits

(MSB’s) two k/bit adders. In MSB adders one adder assumes carry input as one for

performing addition and another assumes carry input as zero. The carry out calculated

from the last stage i.e. least significant bit stage is used to select the actual calculated

values of output carry and sum. The selection is done by using a multiplexer. This

technique of dividing adder in two stages increases the area utilization but addition

operation fastens.

2.6 Ripple Carry Adder

The basic addition operation at the bit level can be accomplished with a Full

Adder (FA) circuit. FA adds two input bits Xi and Yi along with an input carry Cin ,

resulting in a sum Si and a carry-out bit Cout as shown in Figure 3(b). The operation

preformed by the FA is defined by the following boolean equations for the sum and

the carry-out bits:

Si = Xi ⊕ Yi ⊕ Cin

Cout = (Xi ∧ Yi) ∨ (Cin ∧ (Xi ⊕ Yi))

= Majority(Xi, Yi, Cin)

The following notation for various Boolean operators will be used in this work to

avoid ambiguity

x ∨ y ↔ x OR y

x ∧ y ↔ x AND y

x ⊕ y ↔ x XOR y

x ↔ NOT x

It is apparent from equations 2.4 and 2.5 that the realization of the sum function

requires two XOR logic gates, while two AND and one OR logic gates are needed for

the carry-out function. Despite that, FA sum and carry-out functions can be

represented in many different logic expressions and, thereby, determine the structure

of the circuit. Based upon those different logic expressions, many full-adder cells and

modules can be conceived. This provides the digital designer with various alternatives

for the FA adder implementations to choose from and to investigate. Recently Shams

et al. carried out detailed performance analysis of twenty three 1-bit FA. Their study

showed that each adder cell exhibits it own figurers of power consumption, delay and

area.the area and power-delay product performance of six existing 1-bit FA adders

and proposed a new design based on XOR/XNOR. proposed five different FA

expressions based on XOR/XNOR implementation to explore different performance

tradeoffs. Then, they used their proposed FA cells to improve the area and power of

an array tree multiplier.

The 1-bit FA is cascaded as illustrated in Figure 4 to create n-bit wide operand adder

known as Ripple Carry Adder (RCA). The sum at each bit position i is determined by

the corresponding bit values of the operands at that position and the incoming carry

bit value from (i − 1)th position. The addition is completed once the carry value

propagates along the entire structure to the most significant bit (MSB) position.

Ripple carry adder block diagram.

The area and delay of this adder can be roughly estimated using the unit-gate delay

and area model. This model is technology independent and assumes that each gate,

excluding exclusive-OR, counts as one elementary gate for both area and delay. An

exclusive-OR gate counts for two elementary gates for both area and delay.

Complex gates as well as multi-input gates are built from 2-input basic gates and their

gate count equals the sum of gate counts of the composing cells. Thus, RCA delay is

estimated as 2n unit-gate delay while its area is 7n unit-gate area, where n is the

operand size. The main advantage of RCA implementation is that it is area efficient

and easy to construct. However, its linear delay characteristics makes it less suitable

for high-speed implementations. An improved addition approach in given next.

Multipliers

Introduction

Multiplication is important fundamental function in arithmetic logic operation. A

system’s performance is generally determined by the performance of the multiplier

because the multiplier is generally the slowest clement in the system. The objective of

good multiplier to provide a physically compact high speed and low power

consumption unit.To reduce significant power consumption of multiplier design it is a

good direction to reduce number of operations thereby reducing a dynamic power

which is a major part of total power dissipation.

An efficient multiplier should have following characteristics:-

Accuracy:- A good multiplier should give correct result.

Speed:- Multiplier should perform operation at high speed.

Area:- A multiplier should occupies less number of slices and LUTs.

Power:- Multiplier should consume less power.

Multiplication process or A multiplier can be divided into three steps-

1. Partial product generation-The first is radix 4 booth encoding in which a partial

product is produced from the multiplier and multiplicand.

2. Partial product reduction-The second is adder array or partial product compression

to add all partial products and convert them into the form of sum and carry.

3. Final addition-The last is the final addition in which the final multiplication result

is generated by adding the sum and carry . Z=A*B+Z.

For the multiplication of an n-bit multiplicand with an m bit multiplier, m partial

products are generated and products formed is n + m bits long.

A=(an an-1 an-2.......................a0) B=(bn bn-1 bn-2.....................b0)

AB= ( A2nbn+A2n-1bn-1+A2n-2bn-2+...................................+A20b0 )

Types of Multipliers

The common multiplication method is “add and shift” algorithm.

1.) In parallel multipliers number of partial products to be added is the main

parameter that determines the performance of the multiplier.

2.)To reduce the number of partial products to be added, Modified Booth algorithm is

one of the most popular algorithms.

3.)To achieve speed improvements Wallace Tree algorithm can be used to reduce the

number of sequential adding stages.

4.) On the other hand “serial-parallel” multipliers compromise speed to achieve better

performance for area and power consumption. The selection of a parallel or serial

multiplier actually depends on the nature of application.

Applications

1.)Multiplication is a heavily used arithmetic operation that figures prominently in

signal processing and scientific applications

2.)Multipliers are key components of many high performance systems such as FIR

filters, microprocessors, digital signal processors, etc.

3.) Multipliers play an important role in today’s digital signal processing and various

other applications.

Types of Multipliers

Serial-Parallel Multiplier

The serial multiplier uses successive addition algorithm, where both operands are

entered in serial manner, which leads to poor speed performance. However in the

parallel multiplier both operands are entered in parallel manner, which gives high

speed but occupies much larger area when compared to serial multiplier.Hence, we go

for serial-parallel multiplier.

The serial-parallel multiplier serves as a good trade-off between the time consuming

serial multiplier and area consuming parallel multipliers. These multipliers are used

when there is demand for both high speed and small area. In a device using the serial-

parallel multiplier, one operand is entered serially and the other operand is stored in

parallel with a fixed number of bits. The resultant enhancement in the processing

speed and the chip area will become more significant when a large number of

independent operations are performed.

1.)This multiplier is the simplest one, the multiplication being considered as a

succession of additions.

If A=(an an-1 an-2.......................a0)

B=(bn bn-1 bn-2..............b0)

then the product A.B may be expressed as

AB= ( A2nbn+A2n-1bn-1+A2n-2bn- 2+...................................+A20b0 )

2.)To implement this we use D flip-flop and full adder .

3.)In this D flip-flop acts as a memory to store the data values and full adder circuit

is used for adding the partial products.

4.)A possible form of this multiplier for multiplying 4- bit quantities based on this

expression is shown in figure (1). The operation of the multiplier is as follows-

i.)'Number A' is entered in the 4 right most bits of the top row of D flip-flop, which

are further connected to three D flip-flops to form a 7-bit shift register. The first left

most column of D flip-flops holds B values.

ii.) The number A( a3 a2 a1 a0 ) is then multiplied with the least significant bit of

B( b0 ). Later the number A is shifted and then multiplied with the other bits of B one

after the other simultaneously.The partial products are then added using full adders.

iii.)This is done to allow the multiplication of 'number A' by 21 22..................2n, thus

forming the partial product at each stage of the process.

5.)This approach can be used to eliminate the least significant bits of the product.

6.)A further reduction in hardware can be done by using 3 additional D flip-flops

( which were earlier used as shifting of A proceeds ) for holding b values.

7.)This structure is suited only for positive or unsigned operands. If the operands are

negative and 2's compliment encoded then -

i.) The most significant bit of B will have a negative weight and so a subtraction must

be performed as the last step.

ii.) The most significant bit of A must be replicated since operand A must be

expanded to 2N bits.

Figure (1): 4- bit Serial and Parallel Multiplier

Braun Multiplier

Braun Edward Louis proposed the braun multiplier in 1963. It is the simplest parallel

multiplier, that is commonly known as the Carry Save Array Multiplier.

This multiplier consists of an array of AND gates and adders arranged in an iterative

structure that does not require logic registers. This is also known as the non-additive

multiplier since it does not add an a operand to result of the multiplication. The

completion time is limited by the depth of the Carry Save Array, and by the Carry

propagation in the adder.This multiplier is suited only for positive operands. This

multiplier is restricted to performing multiplication of two unsigned numbers.

Architecture

1.)An n*n bit Braun multiplier is constructed with n (n-1) adders, n2 AND gates and

(n-1) rows of Carry Save Adder .

2.)In the first rows there is no Carry propagation ( using Carry Save adder).At the

bottom of the array, the output of the array is noted in Carry Save, so an adder

converts it ( by mean of a Carry propagation) into the classical notation.

3.)Each products can be generated in parallel with the AND gates. Each partial

product can be added to the previous sum of partial products.(which has produced by

using the row of adders).

4.)The carry out will be shifted one bit to the left or right and then are added to the

sum of first adder and the newly generated partial product.

5.)The shifting would carry out with the help of Carry Save Adder (CSA) and the

Ripple carry adder should be used for the final stage of the output.

6.)The schematic diagram is as shown figure(4.2).

Figure - Carry save adder

Figure - Ripple Carry adder

Performance of Braun Multiplier

1.)Braun multiplier performs well for the unsigned operands that are less than 16 bits

in terms of speed, power and area.But it is simple structure when compared to the

other multipliers.

2.)The number of components required in building the Braun multiplier increases

quadratically with the number of bits, which makes it inefficient.

3.)The main drawback of this multiplier is that the potential susceptibility of glitching

problem due to the Ripple Carry Adder in the last stage. The delay depends on the

delay of the Full Adder and also a final adder in the last stage.

To overcome drawback

1.)The internal structure of the full adder can be realized using FPGA. The power and

area can also be reduced by using two bypassing techniques called Row bypassing

technique and Column bypassing technique.

2.)Delay due to the final ripple adder can be minimized by using very fast one of a

Parallel Prefix Adder “KOGGE STONE ADDER” which is a type of Carry Look

Head Adder.

Speed consideration:

1.)The delay of the Braun multiplier is dependent on the delay of the full Adder cell

and also on the final Adder in the last row.

2.)In the multiplier array, a full Adder with balanced Carry and sum delays is

desirable because the sum and carry signals are both in the critical path.

3.)The speed and power of the full Adder is very important for large arrays.

Enhanced Braun Multipliers

1.)The performance of Braun Multiplier can be enhanced by replacing full adders

with half adder, which will result in saving three logic gates, but regularity of

structure gets disturbed.

2.)The another way to do this is by optimising the interconnection between the adders,

so that delay through out each adders path is approximately same.

Baugh-Wooley multiplier

In signed multiplication the length of the partial products and the number of partial

products will be very high. So an algorithm was introduced for signed multiplication

called as Baugh- Wooley algorithm. The Baugh-Wooley multiplication is one

amongst the cost-effective ways to handle the sign bits. This method has been

developed so as to style regular multipliers, suited to 2's compliment numbers.

Baugh-Wooley Two’s compliment Signed multipliers is the best known algorithm for

signed multiplication because it maximizes the regularity of the multiplier and allow

all the partial products to have positive sign bits.

Figure- unsigned 4-

bit multiplication

Figure-signed 4-bit multiplication

Figure-Baugh-Wooley 4-bit algorithm

When multiplying two’s compliment numbers directly, each of the partial products to

be added is a signed numbers. Thus each partial product has to be sign extended to the

width of the final product in order to form a correct sum by the Carry Save Adder

(CSA) tree. According to Baugh-Wooleyapproach, an efficient method of adding

extra entries to the bit matrix suggested to avoid having deal with the negatively

weighted bits in the partial product matrix.

Baugh-Wooley algorithm

Here are using fewer steps and also lesser adders. Here a0, a1, a2, a3& b0, b1, b2, b3

are the inputs. I am getting the outputs that are p0, p1... p7. As I am using pipelining

resister in this architecture ,so it will take less time to multiply large number of 2’s

compliment.

Let us consider two numbers A and B ( 2's compliment number )

The product of two numbers is

--->(3)

The first two terms of above equation are positive and last two terms are negative.

The last two terms are n-1 bits that extend in binary weight from 2n-1 upto 22n-3.O n

the other hand, the final product is 2n bits that extends in binary weight from 20 to

22n-1 . In order to calculate the product, instead of subtracting the last two terms, it is

possible to add the opposite values.

We see that subtractor cells must be used. In order to use only adder cells, the

negative terms may be rewritten as :

----->(4)

Then A.B becomes

---->(5)

The final equation is

----->(6)

The above equation signifies the Baugh-Wooley algorithm for multiplication process

in two’s compliment form.

Baugh-Wooley Multiplier provides a high speed, signed multiplication algorithm . It

uses parallel products to complement multiplication and adjusts the partial products to

maximize the regularity of multiplication array . When number is represented in two’s

complement form, sign of the number is embedded in Baugh-Wooley multiplier.This

algorithm has the advantage that the sign of the partial product bits are always kept

positive so that array addition techniques can be directly employed.In the two’s

complement multiplication, each partial product bit is the AND of a multiplier bit and

a multiplicand bit, and the sign of the partial product bits are positive .In this scheme ,

a total of n(n - 1) + 3 full adders are required. Hence, for the case of n = 4, the array

requires 15 adders.

FPGA AND CPLDS

Integrated circuits (IC) technology is the enabling technology for a whole host

of innovative devices and systems that have changed the way of living. VLSI systems

are much smaller and consume less power than discrete components used to built

electronic systems before 1960’s. The electronics industry has achieved a phenomenal

growth over the last two decades, mainly due to the rapid advances in integration

technologies, large-scale systems design in short, due to the advent of VLSI. The

number of applications of integrated circuits in high-performance computing,

telecommunications, and consumer electronics has been rising steadily, and at a very

fast pace. Typically, the required computational power (or, in other words, the

intelligence) of these applications is the driving force for the fast development of this

field. Below figure gives an overview of the prominent trends in information

technologies over the next few decades. The current leading-edge technologies (such

as low bit-rate video and cellular communications) already provide the end-users a

certain amount of processing power and portability.

Trends of VLSI

This trend is expected to continue, with very important implications on VLSI

and systems design. One of the most important characteristics of information services

is their increasing need for very high processing power and bandwidth (in order to

handle real-time video, for example). The other important characteristic is that the

information services tend to become more and more personalized (as opposed to

collective services such as broadcasting), which means that the devices must be more

intelligent to answer individual demands, and at the same time they must be portable

to allow more flexibility/mobility. As more and more complex functions are required

in various data processing and telecommunications devices, the need to integrate

these functions in a small system/package is also increasing. The level of integration

as measured by the number of logic gates in a monolithic chip has been steadily rising

for almost three decades, mainly due to the rapid progress in processing technology

and inter connect technology.

Figure 6.2: Evolution of integration density and minimum feature size, as seen in the

early 1980s.

2. VLSI Design Flow

The design process at various levels is usually evolutionary in nature. It starts

with a given set of requirements. Initial design is developed and tested against the

requirements. When requirements are not met, the design has to be improved. If such

improvement is either not possible or too costly, then the revision of requirements and

its impact analysis must be considered. The three important domains in VLSI are

Behavioral domain, Structural domain, Geometrical layout domain. The design flow

starts from the algorithm that describes the behavior of the target chip. The

corresponding architecture of the processor is first defined. It is mapped onto the chip

surface by floor planning. The next design evolution in the behavioral domain defines

finite state machines (FSMs) which are structurally implemented with functional

modules such as registers and arithmetic logic units (ALUs).

These modules are then geometrically placed onto the chip surface using CAD

tools for automatic module placement followed by routing, with a goal of minimizing

the interconnects area and signal delays. The third evolution starts with a behavioral

module description. Individual modules are then implemented with leaf cells. At this

stage the chip is described in terms of logic gates (leaf cells), which can be placed and

interconnected by using a cell placement & routing program. The last evolution

involves a detailed Boolean description of leaf cells followed by a transistor level

implementation of leaf cells and mask generation. In standard-cell based design, leaf

cells are already pre-designed and stored in a library for logic design use.

3. Design Hierarchy

The use of hierarchy, or divide and conquer technique involves dividing a

module into sub- modules and then repeating this operation on the sub-modules until

the complexity of the smaller parts becomes manageable. This approach is very

similar to the software case where large programs are split into smaller and smaller

sections until simple subroutines, with well-defined functions and interfaces, can be

written. The design of a VLSI chip can be represented in three domains.

Correspondingly, a hierarchy structure can be described in each domain separately.

However, it is important for the simplicity of design that the hierarchies in different

domains can be mapped into each other easily.

In the physical domain, partitioning a complex system into its various

functional blocks will provide a valuable guidance for the actual realization of these

blocks on chip. Obviously, the approximate shape and size (area) of each sub-module

should be estimated in order to provide a useful floor plan. This physical view

describes the external geometry of the adder, the locations of input and output pins,

and how pin locations allow some signals (in this case the carry signals) to be

transferred from one sub-block to the other without external routing.

4.VLSI Design Styles

Several design styles can be considered for chip implementation of specified

algorithms or logic functions. Each design style has its own merits and shortcomings,

and thus a proper choice has to be made by designers in order to provide the

functionality at low cost.

Field Programmable Gate Array (FPGA)

Fully fabricated FPGA chips containing thousands of logic gates or even more,

with programmable interconnects, are available to users for their custom hardware

programming to realize desired functionality. This design style provides a means for

fast prototyping and also for cost-effective chip design, especially for low-volume

applications. A typical field programmable gate array (FPGA) chip consists of I/O

buffers, an array of configurable logic blocks (CLBs), and programmable interconnect

structures. The programming of the inter connects is implemented by programming of

RAM cells whose output terminals are connected to the gates of MOS pass

transistors.

Performance of the design can be simulated and verified before downloading

the design for programming of the FPGA chip. The programming of the chip remains

valid as long as the chip is powered-on or until new programming is done. In most

cases, full utilization of the FPGA chip area is not possible - many cell sites may

remain unused.

The largest advantage of FPGA-based design is the very short turn-around

time, i.e., the time required from the start of the design process until a functional chip

is available. Since no physical manufacturing step is necessary for customizing the

FPGA chip, a functional sample can be obtained almost as soon as the design is

mapped into a specific technology. The typical price of FPGA chips are usually higher

than other realization alternatives (such as gate array or standard cells) of the same

design, but for small-volume production of ASIC chips and for fast prototyping,

FPGA offers a very valuable option.

General architecture of Xilinx FPGA.

Gate Array Design

In view of the fast prototyping capability, the gate array (GA) comes after the

FPGA. While the design implementation of the FPGA chip is done with user

programming, that of the gate array is done with metal mask design and processing.

Gate array implementation requires a two-step manufacturing process: The first phase,

which is based on generic (standard) masks, results in an array of uncommitted

transistors on each GA chip. These uncommitted chips can be stored for later

customization, which is completed by defining the metal interconnects between the

transistors of the array. Since the patterning of metallic interconnects is done at the

end of the chip fabrication, the turn-around time can be still short, a few days to a few

weeks.

Basic processing steps required for gate array implementation.

Figure above shows a magnified portion of the internal array with metal mask

design (metal lines highlighted in dark) to realize a complex logic function. Typical

gate array platforms allow dedicated areas, called channels. The availability of these

routing channels simplifies the interconnections, even using one metal layer only. The

interconnection patterns to realize basic logic gates can be stored in a library, which

can then be used to customize rows of uncommitted transistors according to the net

list. While most gate array platforms only contain rows of uncommitted transistors

separated by routing channels, some other platforms also offer dedicated memory

(RAM) arrays to allow a higher density where memory functions are required.

Layout views of a conventional GA chip and a gate array with two memory banks.

Metal mask design to realize complex logic function on channeled GA

In general, the GA chip utilization factor, as measured by the used chip area

divided by the total chip area, is higher than that of the FPGA and so is the chip speed,

since more customized design can be achieved with metal mask designs. The current

gate array chips can implement as many as hundreds of thousands of logic gates.

Standard-Cells Based Design

The standard-cells based design is one of the most prevalent full custom

design styles which require development of a full custom mask set. For instance, the

inverter gate can have standard size transistors, double size transistors, and quadruple

size transistors so that the chip designer can choose the proper size to achieve high

circuit speedandlayoutdensity.

The standard cell is also called the poly cell. In this design style, all of the

commonly used logic cells are developed, characterized, and stored in a standard cell

library. A typical library may contain a few hundred cells including inverters, NAND

gates, NOR gates, complex AOI, OAI gates, D-latches, and flip-flops. Each gate type

can have multiple implementations to provide adequate driving capability for

different fan outs.

VHDL contains constructs that are more specific to simulation and verification

than for synthesis. Synthesis software may ignore such constructs or rules. However,

the goal is to match the simulation specification with the codes for synthesis.

Depending on tools, the goal may (or usually) not be achievable. For example, the

following two VHDL codes are different but describe the same design - one for

simulation (cannot be synthesized efficiently) and the other for synthesis.

A standard cell layout example.

After chip logic design is done using standard cells in the library, the most

challenging task is to place individual cells into rows and interconnect them in a way

that meets stringent design goals in circuit speed, chip area, and power consumption.

Many advanced CAD tools for place-and-route have been developed and used to

achieve such goals.

Full Custom Design Full custom design, in a strict sense, it is somewhat less than fully custom

since the cells are pre-designed for general use and the same cells are utilized in many

different chip designs. In a fuller custom design, the entire mask design is done anew

without use of any library. However, the development cost of such a design style is

becoming prohibitively high. Thus, the concept of design reuse is becoming popular

in order to reduce design cycle time and development cost.

Simplified floor plan consisting of two separate blocks and a common signal bus.

The most rigorous full custom design can be the design of a memory cell, be it

static or dynamic. Since the same layout design is replicated, there would not be any

alternative to high density memory chip design. For logic chip design, a good

compromise can be achieved by using a combination of different design styles on the

same chip, such as standard cells, data-path cells and PLAs. In real full-custom layout

in which the geometry, orientation and placement of every transistor is done

individually by the designer, design productivity is usually very low - typically 10 to

20 transistors per day, per designer. In digital CMOS VLSI, full-custom design is

rarely used due to the high labor cost. Exceptions to this include the design of high-

volume products such as memory chips, high- performance microprocessors and

FPGA masters.

Cost of Manufacturing

IC manufacturing plants are extremely expensive. A single plant costs as

much as $4 billion. Given that a new state –of-the-art manufacturing process is

developed every three years that is a sizeable investment. The investment makes sense

because s single plant can manufacture so many chips and can easily be switched to

manufacture different types of chips. In early years of the IC business companies

focused on building large quantities of a few standard parts. These parts are

commodities one 80 ns, 256 MB dynamic RAM is one more or less the same as any

other regardless of the manufacturer. Companies concentrated on commodity parts

because manufacturing variations are easier to keep track of when the same part is

being fabricated day after day. Standard parts also made sense because designing

integrated circuits was hard not only the circuit but the layout had to be designed, and

there were few computer programs to help automate the design process.

UNIT-5

CIRCUIT SYNTHESIS AND DESIGNFLOW:

SIMULATION: