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T FLIP FLOP IMPLEMENTATION USING SIMON

T FLIP FLOP IMPLEMENTATION USING SIMON


 

ABSTRACT:

             This project aims in designing a T Flip Flop using SIMON software. It mainly works on the use of single electron transistor for making the basic gates, whose performance is evaluated through single electron tunnelling across the junction or so called the channel. The working of such kind of junctions is due to the coulomb blockade and tunnelling process which allows only one electron to exist in the transistor at particular instant of time.

The basic building blocks of combinational logic circuits are gates. In particular, AND, OR, and NOT gates (however, there are also, XOR, NAND, NOR, XNOR gates too). The basic building blocks of sequential logic circuits are flip flops. Flip flops are devices that use a clock. Each flip flop can store one bit.

INTRODUCTION:

            When we talk about the single electron transistors we must first understand how it works. So the details below depict the functioning of a single electron transistor.

            Before getting into the functional details of a SET (single electron transistor) lets discuss what is coulomb blockade and tunnelling.

·         COULOMB BLOCKADE:

            In physics, a Coulomb blockade (abbreviated QB), named after Charles-Augustin de Coulomb, is the increased resistance at small bias voltages of an electronic device comprising at least one low-capacitance tunnel junction. Because of the QB, the resistances of devices are not constant at low bias voltages, but increase to infinity for zero bias (i.e. no current flows).

 

Schematic representation of an electron tunnelling through a barrier

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COULOMB BLOCKADE IN A TUNNEL JUNCTION:

            A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting electrodes. If the electrodes are superconducting, Cooper pairs with a charge of two elementary charges carry the current. In the case that the electrodes are normal conducting, i.e. neither superconducting nor semiconducting, electrons with a charge of one elementary charge carry the current. The following reasoning is for the case of tunnel junctions with an insulating barrier between two normal conducting electrodes (NIN junctions).

            According to the laws of classical electrodynamics, no current can flow through an insulating barrier. According to the laws of quantum mechanics, however, there is a nonvanishing (larger than zero) probability for an electron on one side of the barrier to reach the other side (see quantum tunnelling). When a bias voltage is applied, this means that there will be a current. In first-order approximation, that is, neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical terms, the tunnel junction behaves as a resistor with a constant resistance, also known as an ohmic resistor. The resistance depends exponentially on the barrier thickness. Typical barrier thicknesses are on the order of one to several nanometers.

           An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite capacitance. The insulator is also called dielectric in this context, the tunnel junction behaves as a capacitor.

            Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in which exactly one electron passes (tunnels) through the tunnel barrier (we neglect cotunneling, in which two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementary charge by the tunnelling electron, causing a voltage buildup U = e / C, where e is the elementary charge of 1.6×10−19 coulomb and C the capacitance of the junction. If the capacitance is very small, the voltage buildup can be large enough to prevent another electron from tunnelling. The electrical current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the differential resistance around zero bias is called the Coulomb blockade.

OBSERVING THE COULOMB BLOCKADE:

            In order for the Coulomb blockade to be observable, the temperature has to be low enough so that the characteristic charging energy (the energy that is required to charge the junction with one elementary charge) is larger than the thermal energy of the charge carriers. For capacitances above 1 femtofarad (10−15 farad), this implies that the temperature has to be below about 1 kelvin. This temperature range is routinely reached for example by dilution refrigerators.

            To make a tunnel junction in plate condenser geometry with a capacitance of 1 femtofarad, using an oxide layer of electric permittivity 10 and thickness one nanometer, one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by electron beam lithography and appropriate pattern transfer technologies, like the Niemeyer-Dolan technique, also known as shadow evaporation technique.

 

            Another problem for the observation of the Coulomb blockade is the relatively large capacitance of the leads that connect the tunnel junction to the measurement electronics.

·        SINGLE ELECTRON TRANSISTOR:

The simplest device in which the effect of Coulomb blockade can be observed is the so-called single electron transistor. It consists of two tunnel junctions sharing one common electrode with a low self-capacitance, known as the island. The electrical potential of the island can be tuned by a third electrode (the gate), capacitively coupled to the island.

            In the blocking state no accessible energy levels are within tunneling range of the electron (red) on the source contact. All energy levels on the island electrode with lower energies are occupied.

 

Schematic of a single electron transistor

 

            When a positive voltage is applied to the gate electrode the energy levels of the island electrode are lowered. The electron (green 1.) can tunnel onto the island (2.), occupying a previously vacant energy level. From there it can tunnel onto the drain electrode (3.) where it inelastically scatters and reaches the drain electrode Fermi level (4.).

            The energy levels of the island electrode are evenly spaced with a separation of ΔE. ΔE is the energy needed to each subsequent electron to the island, which acts as a self-capacitance C. The lower C the bigger ΔE gets. To achieve the Coulomb blockade, three criteria have to be met:

1.      The bias voltage can't exceed the charging energy divided by the capacitance Vbias = e/C ;

2.      The thermal energy kBT must be below the charging energy EC = e2/C, or else the electron will be able to pass the QB via thermal excitation; and

3.      The tunneling resistance (Rt) should be greater than h/e2 , which is derived from Heisenberg's Uncertainty principle.

 

 

T FLIP FLOP:

The memory elements in a sequential circuit are called flip-flops. A flip-flop circuit has two outputs, one for the normal value and one for the complement value of the stored bit. Binary information can enter a flip-flop in a variety of ways and gives rise to different types of flip-flops

The basic building blocks of sequential logic circuits are flip flops. Flip flops are devices that use a clock. Each flip flop can store one bit.

Here's how a flip flop looks:

Basically, a flip flop has two inputs. One input is a control input. For a D flip flop, the control input is labelled D. For a T flip flop, the control input is labelled T. The other input is the clock. You can read about clock from the class notes on clock.

The clock input is usually drawn with a triangular input. These flip-flops are positive edge-triggered flip flops. This means that the flip flops can only change output values when the clock is at a positive edge. There are also negative edge triggered flip flops, which change on a negative edge, and level-triggered flip flops, that change only when the value is 1. We consider only positive edge-triggered flip flops. When the clock is not at a positive edge, then the output value is held. That is, it does not change.

A flip flop also has two outputs, Q and Q'. The output is really the bit that's stored. Thus, the flip flop is always outputting the one bit of information. But you might wonder "Doesn't it have two bits of information? Q and Q'?". If you have two bits, you have four possible values. However, Q' is the negation of Q which means you only have two possible outputs: Q = 0, Q' = 1, Q = 1, Q' = 0. Since the second output is always negated from the first, you don't get any additional storage.

You might wonder why flip flops have two outputs, Q and Q'. It turns out you can design flip flops with NOR gates or NAND gates, with cycles (which is not allowed for combinational circuits). The design gives you Q' basically for free, so that's why flip flops have both the regular output and the negated output.

Although I rarely draw it, flip flops often have one additional input called asynchronous clear. It's drawn at the top of the flip flop. This is an active low asynchronous clear. "Asynchronous" means "without a clock" (usually). Active low, means you need to set the value to 0, to make it active.

Thus, if you set the asynchronous clear to 0, it causes Q to be automatically set to 0. It does this, even if the clock has not reached a positive edge. That is, it sets Q to zero as fast as it can. The asynchronous clear is often used to reset flip flops to some initial value. Often, you see active low inputs because it consumes less power.

The flip flops have additional inputs you don't see (so do logic gates for that matter). Flip flops and logic gates are powered devices. They need an input for ground and usually 5 volts (although there are low voltage versions of the flip flops). However, they're not drawn because they don't affect how the flip flop behaves.

·         Characteristic Tables:

The behavior of a flip flops can be described by a characteristic table which is basically a truth table.

·         T Flip Flop Characteristic Table:

Here's the characteristic table for a T flip flop.

  T  

  Q  

  Q+

  Operation  

0

0

0

Hold

0

1

1

Hold

1

0

1

Toggle

1

1

0

Toggle

 

The T flip flop characteristic table has 3 columns. The first column is the value of T, a control input. The second column is the current state, that is the current value being output by Q. The third column is the next state, that is, the value of Q at the next positive edge. It's labelled with Q and the superscript, + (the plus sign).

The T flip flop has two possible values. When T = 0, the flip flop does a hold. A hold means that the output, Q is kept the same as it was before the clock edge. When T = 1, the flip flop does a toggle, which means the output Q is negated after the clock edge, compared to the value before the clock edge.

Thus, in a T flip flop, you can either maintain the current state's value for another cycle, or you can toggle the value (negate it) at the next clock edge.

·         Triggering of Flip-flops:

The state of a flip-flop is changed by a momentary change in the input signal. This change is called a trigger and the transition it causes is said to trigger the flip-flop. The basic require an input trigger defined by a change in signal level. This level must be returned to its initial level before a second trigger is applied. Clocked flip-flops are triggered by pulses.

The feedback path between the combinational circuit and memory elements can produce instability if the outputs of the memory elements (flip-flops) are changing while the outputs of the combinational circuit that go to the flip-flop inputs are being sampled by the clock pulse. A way to solve the feedback timing problem is to make the flip-flop sensitive to the pulse transition rather than the pulse duration.

The clock pulse goes through two signal transitions: from 0 to 1 and the return from 1 to 0. As shown in Figure the positive transition is defined as the positive edge and the negative transition as the negative edge.

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Definition of clock pulse transition

The clocked flip-flops already introduced are triggered during the positive edge of the pulse, and the state transition starts as soon as the pulse reaches the logic-1 level. If the other inputs change while the clock is still 1, a new output state may occur. If the flip-flop is made to respond to the positive (or negative) edge transition only, instead of the entire pulse duration, then the multiple-transition problem can be eliminated.

SIMON SOFTWARE:

The SIMON symbolises SIMulation On Nanostructures. It is a single-electron tunnelling device and circuit simulator created at the Institute of Microelectronics TU, Vienna by Christoph Wasshuber.

SIMON is a sophisticated multipurpose simulator for single-electron devices and circuits. It features a graphical circuit editor embedded in a graphical user interface as well as the simulation of co-tunnel events and a single step interactive analyses mode. It supports energy dependent density of states and is able to calculate stability plots.

 

 

 

FEATURES OF SIMON 2.0:

·         STABILITY PLOT

Traditional stability plot with two voltages as x- and y-axis

One axis can be the temperature

One or both axis can be a capacitance or resistance

Differentiation in x or y direction possible

·         NORMAL RESISTORS

Normal resistors allow the modeling of more complex and realistic circuits

·         CURRENT SOURCES

Current sources can be specified with a certain charge-granularity, which allows the modeling of electron injectors/pumps/turnstiles in a very easy manner

·         ENERGY DEPENDENT DENSITY OF STATES

The tunnel model has been improved by incorporating three kinds of density of states functions

Constant with optional bandgap (metallic)

Square-root with bandgap (semiconductor-like)

x/(x2-1)1/2 with bandgap (superconductor-like)

Discrete energy levels are modeled as gaussian functions, with mean, width, and height.

·         SUPPORT FOR SUPERCONDUCTING TUNNEL JUNCTIONS

quasiparticle tunneling

·         FULL SUPPORT FOR LINUX

SIMON is shipped in a software package where all necessary libraries (tcl/tk) are wrapped into the application. Hence no need to install any 3rd party tools to run SIMON on Linux. The installation is as easy as copying a file into a subdirectory.

·         EASY TO USE

Simple automatic installation for Windows operating systems

Graphical user interface

Graphical circuit editor (drag and drop assembly of circuits; few mouse clicks and your circuit is assembled)

Graphical visualization of simulation results (you can plot many graphs in one diagram; compare results from different simulations)

·         CO-TUNNELING

Co-tunneling is simulated up to a user specified order

Two different co-tunnel simulation algorithms are available

·         INTERACTIVE SINGLE-STEP MODE

Single electrons can be forced to tunnel through particular tunnel junctions in an interactive fashion

The system energy, all node voltages, and all node charges are updated automatically

SIMULATION OF T FLIP FLOP:

 Now let’s design the T flip flop as discussed earlier. For designing the Flip flop we have to construct the related circuit elements like the AND gate and the NOR gate as shown in the diagram below.


 



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