The Resonant Tunnelling Transistor

Colin Moffat
Image Processing Group
Department of Physics and Astronomy
Universty College London
Gower Street
London. WC1E 6BT

Tel. 0171-209 6582
Fax. 0171-209 6580

Contents

1. Introduction 1.1 The problem with conventional transistors 2. Resonant Tunnelling Devices 2.1 The Resonant Tunnelling Diode (RTD) 2.1.1 Application of the RTD to Multiple-State Memory 2.2 Resonant Tunnelling Transistors 2.2.1 The Resonant Tunnelling Hot-Electron Transistor (RHET) 2.2.2 The Quantum Excited State Transistor (QuESTT) 3. Functional Application of Resonant Tunnelling Devices 3.1 The Bistable Pair 3.2 Memory Operation 3.3 Digital Logic Operation 3.3.1 Conventional Logic 3.3.2 Threshold Logic 4. Conclusion References

Note

This document is an edited version of an internal group report. Its primary intention is to provide background information as an aid to the understanding of the Resonant Tunnelling Transistor Demo. It is not to be taken as a complete paper detailing the workings of the resonant tunnelling transistor. If you wish to gain a quick overview of the device without reading the whole document, I suggest you refer to sections 2.1, 2.2.2, 3.1 and 3.3. Unfortunately, several of the figures had to be scanned in, and are of poor quality (though I am working on them). However, a better quality version of the document is available here in Microsoft Word 6.0 format. Please don't hesitate to mail me if you spot any errors or have any questions.

1. Introduction

There is continuous pressure on computer manufacturers to reduce the size of transistors, and there are three reasons for this: 1. A smaller transistor will switch faster, giving a speed-up in processing time. 2. Smaller transistors allow more complex processors to be built within the same area as before. 3. Alternatively, smaller transistors allow a greater number of standard processors to be built within the same area as before. However, there is a fundamental limit to how small a conventional transistor can be, and if this limit is surpassed the device will cease to be of use. Current digital computing depends on the fact that transistors can be used to switch electrical current flow on and off, but once a conventional transistor shrinks past its physical limit, it will begin to leak. The more that the transistor shrinks, the more it leaks, until eventually it becomes useless as a switching device [1]. This will signal the end of any further increase in computational power using conventional transistors. At this point, it is necessary to redesign the transistor. Conventional transistors are several microns in size, but useful new devices will eventually operate at dimensions on the nanometre scale (1 micron = 1000 nanometres). To give an idea of the scales involved, these Nanoelectronic devices are intended to have feature sizes comparable to the wavelength of an electron, and will operate at ultra-high speed with an ultra- high circuit density. Resonant tunnelling devices are especially useful because of their novel output characteristics, allowing many operations to be carried out with fewer components than usual.

1.1 The problem with conventional transistors

Conventional transistors use potential barriers to control the flow of charge. The two most common types of barrier are pn-junctions (within the bipolar transistor) and electrostatic depletion regions (within the field effect transistor). Figure 1.1 shows the energy band diagram of a bipolar transistor, with the emitter on the left, the collector on the right, and the potential barrier base region in the middle. Initially, a voltage is applied between the emitter and the collector, but not between the emitter and the base. The potential barrier at the base prevents current from passing through the transistor, so it is switched off. As the voltage across the base region is increased (with respect to the emitter), the height of the barrier on the emitter side is decreased. As it decreases, more and more electrons entering the emitter are able to cross the base and exit through the collector, as shown in figure 1.2. The transistor is now switched on. The use of a barrier to control the flow of electrons from one end of the device to the other is the basis of all transistor action, and current digital computing depends upon it. The trouble with this design is that the width of the potential barrier at the base must always be sufficiently greater than the wavelength of an electron (approx. 10nm). If it s not, electrons will actually begin to tunnel right through it (figure 1.3). This causes the transistor to leak, and the more that the width of the barrier is reduced the more it will leak. Once this happens, the transistor cannot be totally turned off and is no longer effective as a switching device. Nanoelectronic devices however, (particularly the resonant tunnelling devices described in this report) are designed to take advantage of quantum mechanical effects such as tunnelling, so the width limit does not apply.

2. Resonant Tunnelling Devices

2.1 The Resonant Tunnelling Diode (RTD)

The resonant tunnelling diode (or RTD) consists of an emitter and collector region, and a double tunnel barrier structure which contains a quantum well (as shown in the energy band diagrams of figure 2.1). This quantum well is so narrow (5-10 nm) that it can only contain a single, so called resonant, energy level. The principle of this device is that electrons wishing to travel from the emitter to the collector can only do so if they are lined up with this resonant energy level. Initially, with a low voltage across the device (at point A), the electrons are below the point of resonance, and no current can flow through the device. As the voltage increases, the emitter region is warped upwards, and the collector region is warped downwards. Eventually, the band of electrons in the emitter will line up with the resonant energy state, and are free to tunnel through to the right. This gives an increase in the current up to the peak at point B. As the voltage across the device increases, the electrons are pushed up past the resonant energy level and are unable to continue tunnelling. This can be observed by the drop in current to the valley at point C. As the voltage continues to increase, more and more electrons are able to flow over the top of the tunnel barriers, and the current flow will rise [2]. The current-voltage characteristic of this device is similar to that of the Esaki tunnel diode in that it exhibits a peak and a valley in the curve. The difference is that RTDs have a much lower device capacitance which allows them to oscillate faster, and their current-voltage characteristics (i.e. the position of the peak and the valley) can be shaped with the appropriate bandgap engineering [3].

2.1.1 Application of the RTD to Multiple-State Memory

Several resonant tunnelling diodes can be combined to generate multiple peaks on the current-voltage curve (such that n diodes will produce n peaks). For example, two RTDs connected in parallel across a voltage source which increases from 0 to Vbias will give the double peak-and-valley characteristic shown in figure 2.2a. Note that one of the RTDs must be connected in series with a suitable offset resistance (Roffset). If it is not, both RTDs will produce a peak and valley at the same time, giving the same output as a single RTD. If these RTDs are connected in series with a load resistor, RL (as shown in figure 2.2b), the load line of the resistor will intersect the positive slope of the curve at the three stable operating points Q1, Q2 and Q3 (figure 2.2a). This means that if the voltage across the RTDs is measured it can only ever be one of V1, V2 or V3 - effectively producing a 3-state memory cell. The RTDs are forced into one of these states by momentarily writing a second voltage across them (using Vwrite in figure 2.2b). For example, if Vwrite = V2 is temporarily applied across the RTDs, they will remain at V2. This system provides n+1 stable operating points from n peaks, and can be used for storing values from an n+1 state logic [4 - 7].

2.2 Resonant Tunnelling Transistors 2.2.1 The Resonant Tunnelling Hot-Electron Transistor (RHET)

A resonant tunnelling transistor (RTT) is a transistor which has a current-voltage characteristic similar to that of a resonant tunnelling diode (i.e., a peak and a valley). This characteristic may be single or multiple-peaked, depending on the type of implementation. One example of an RTT is the resonant-tunnelling hot-electron transistor (or RHET). This is effectively a conventional hot-electron transistor which contains an RTD between the emitter and the base (figure 2.3). The position of the resonant energy level (relative to the emitter) is controlled by the base voltage. When there is a zero base voltage, no current can flow through the device as the electrons in the emitter are below the resonant energy level. Increasing the base voltage pulls the resonant energy level down towards the electrons in the emitter, and only when they are lined up (or in resonance) can current flow through the device. This produces a peak in the current output. As the base voltage continues to increase, the resonant energy level is pulled down past the electrons in the emitter, and resonant tunnelling stops. This causes the valley in the current output. An important point about this device is that the resonant energy level is very high, which means that electrons can only enter the base when they have a substantial kinetic energy. These are known as hot electrons, hence the name of the device. The greater than average energy of the electrons means that they will pass through the base very quickly, possibly without scattering. This allows a very high-frequency operation (41 GHz oscillation has been demonstrated so far) [8 - 9, 3].

2.2.2 The Quantum Excited State Transistor (QuESTT)

The quantum excited state transistor, or QuESTT, is an RTD-like structure which makes direct electrical contact to the quantum well and treats it as the base (figure 2.4). As with the RTD, charge can only cross the base if the emitter is in resonance with one of the confined states of the well. In this case though, the energy levels in the well can be moved up and down independently of the emitter and the collector, giving control over the point of resonance. The potential of the quantum well is modulated by removing or injecting charge into the ground state. Normally, this charge would leak out through the tunnel barriers, but the QuESTT has a ground state which is hidden from the emitter and collector energy bands, effectively confining the charge carriers to the base. This is achieved by making the bandgaps of the emitter and collector wider than that of the well, such that tunnelling current passes through an excited state of the well. The main difficulty with this type of device is making direct electrical contact to this ultra-small well region. At the moment, this device exhibits no significant gain, but because there are no pn-junctions or depletion regions the QuESTT is potentially very scaleable [10, 11]. The ultimate scaling of this or a QuESTT-type device would be to a 1-dimensional electron gas (also known as a 1DEG or a quantum wire) for the emitter and collector, and a 0-dimensional electron gas (0DEG or quantum dot) for the base. Such a device would be ultra-fast, and have an ultra-high packing density. However, as devices increase in speed, they will eventually spend more and more of their time waiting for signals to arrive from other devices. This is a limiting factor, and means that a super- fast device could not operate at its full potential without further developments in fast interconnects. The output characteristics of both of the RTTs are identical to that of an RTD, with one important exception - the resonant point is controlled by a third terminal, the base. If the resonant energy level is moved up and down, the output peak current of the device moves up and down as well. This is because the resonant energy level is the point at which the maximum number of electrons can pass through the device (figure 2.5). It will be shown in section 3 that this fact makes resonant tunnelling devices ideal for use in threshold logic applications. Note that the circuit symbol used in this report for an RTT is the same as that of an RTD, but with three or more terminals (where the third and later terminals represent base contacts).

3. Functional Application of Resonant Tunnelling Devices

3.1 The Bistable Pair

All resonant tunnelling logic families depend upon the principle of voltage stability. This was touched upon in section 2.1.1 with the ternary (3-state) memory cell, which requires three stable output voltage states (tristability). The logic families covered in this report are all binary, so require only two stable states (bistability). However many states are required, the heart of any resonant tunnelling logic element (be it a memory cell or a digital gate) consists of two devices - the load and the driver. The load can either be a resistor (as in section 2.1.1), a transistor, an RTD or an RTT (depending on the implementation), whilst the driver is almost always an RTD or an RTT. With binary devices the load and the driver are referred to as a bistable pair. Figure 3.1 shows bistable pairs with the different load devices. Each load device intersects the driver at two stable points, Q1 and Q2, and the unstable point, P. Ignoring the unstable point for now, this means that if the voltage across the resonant tunnelling driver device is measured, it can only ever be equal to V1 or V2. In binary logic, voltage V1 will represent binary state 0, and voltage V2 will represent binary state 1.

3.2 Memory Operation

If the bistable pair is being used as a memory cell, a value is stored by temporarily applying the appropriate voltage (V1 for state 0 or V2 for state 1) across the driver device (as in section 2.1.1). The pair will latch into the required state, and will remain there until a different voltage is applied. Whether a resistor, transistor or resonant tunnelling device is being used as the load does not make any difference to the logical operation of the memory cell. However, it is preferable to use a pair of resonant tunnelling devices as resistors and conventional transistors are not nanoelectronic components. Since the bistable pair must always be at V1 or V2, what happens if a voltage not equal to V1 or V2 is applied to the memory cell? The answer is that the pair of devices will resolve themselves into one of the allowed states, unless the voltage is very close to the unstable point, P. Which of the states is chosen depends on the following rules: 1. If applied voltage, Vwrite <= V1, voltage resolves to V1, state = 0. 2. If V1 >= Vwrite < P, voltage resolves to V1, state = 0. 3. If P < Vwrite <= V2, voltage resolves to V2, state = 1. 4. If Vwrite >=V2, voltage resolves to V2, state = 1. 5. If Vwrite = P, intersection will remain at P, state = ?. The intersection at P is not useful as a third logical state because of its unstability. If the write voltage is slightly greater or less than P, or if the cell receives sufficient thermal noise (both of which are very likely), it will latch into state 0 or 1. Because of this natural tendency to slip into one of two states, the memory cell is very tolerant of noise. If a 0 is to be stored in the cell, the write line can take any voltage less than P. If a 1 is to be stored, the write line can take any voltage greater than P. Once the value is stored, it is very difficult to accidentally flip the cell into a different state.

3.3 Digital Logic Operation

A bistable pair can also be used to perform digital logic operations. The output of the pair will always correspond to a binary 0 or 1, so to carry out a logical function it is necessary that this output be a function of one or more inputs. The only way that the bistable pair can receive inputs is if the load and driver devices each have three or more terminals (two for the positive and negative contacts, and the rest for functional control - figure 3.3). For simplicities sake, the remainder of this section will assume that the load and driver devices are both resonant tunnelling transistors. Other configurations are possible, but these are outside of the scope of this document. This circuit contains only nanoelectronic devices, and is the most general example for explaining the logical methods upon which all the resonant tunnelling logic families are based. Note that this configuration corresponds to the ideal form of the MOBILE (monostable-bistable transition logic element) logic family [12 - 17]. As was shown in figure 2.5, the base inputs to an RTT allow the position of the peak current output to be moved up and down. Figure 3.4 shows the set of possible outputs from a bistable pair of two RTTs, each with two base inputs (as in figure 3.3 above). Each of the RTTs has three possible output curves, corresponding to the sum of the base inputs. This is assuming that a base input is represented by a binary 0 or 1 (corresponding to a low or high input voltage signal), and that the influence of each input on the RTT is the same. Note that one of the output sets is always offset by half a step from the other. This is an essential part of the logical operation of these devices, as the output depends on the relative position of the two curves selected by the inputs. The output of this logical element is dependent on the following two rules: 1. If Load Peak > Driver Peak, Output state = 1. 2. If Load Peak < Driver Peak, Output state = 0. where the output states correspond to the two stable voltage states, V1 and V2, mentioned previously. This method of deriving the output from a greater than or less than comparison of two values is called threshold logic [18]. It is a superset of ordinary Boolean logic, and allows many conventional functions to be implemented with a reduced number of logical elements. This will be explored in greater detail in section 3.3.2, but first the implementation of conventional functions (AND, OR etc.) will be explained.

3.3.1 Conventional Logic

The functions AND, OR, Buffer (i.e. output = input), NAND, NOR and Inverter can all be implemented with a single bistable pair of resonant tunnelling devices (hereon referred to as a logical element). Depending on the operation, either the load or the driver device is given a constant base input which will fix its peak height at a constant threshold value. The other device receives the binary inputs, the sum of which will set its peak height. According to the rules above, the output will then depend on which device has the highest peak. From figure 3.5, the load peak can take three positions, corresponding to the sum of the A and B inputs (A+B = 0, A+B = 1, A+B = 2). The driver device has a single base input which is used to fix its peak height between A+B = 1 and A+B = 2 (i.e. at position 1.5). A comparison of the curves shows that the output will only be equal to 1 if both A and B are equal to 1. This is the AND function. In order to make a comparison between the two curves, the load curve has to be swept across the driver. Initially, the three base inputs are applied and held at the appropriate settings, and the bias voltage, VBIAS, is steadily increased from 0 volts. Figures 3.6a and 3.6b show the progression of the intersection of the two curves as VBIAS is increased. The load peak in figure 3.6a is lower than the driver, and as the two peaks cross, the intersection drops back down the slope, giving a final output state of 0. The load peak in figure 3.6b is higher than the driver, so when the two peaks cross, the intersection is able to make it across the top. This gives a final output state of 1. The OR function is implemented by shifting the threshold to position 0.5 (i.e. between the curves A+B = 0 and A+B = 1). The threshold is exceeded if either or both of the inputs is equal to 1, which produces a high output state. The single input Buffer function is also implemented with a threshold of 0.5, so that if A = 0, the output = 0, and if A = 1, the output = 1. The inverse set of functions, NAND, NOR and Inversion are implemented in a similar way, except the variable inputs are applied to the driver, and the threshold to the load. For example, figure 3.7 shows the NAND implementation. The function of the logical element is dependent on the threshold value. If this input is variable instead of fixed, it is possible to construct circuitry from variable function logic elements. This can add to the flexibility of a system.

3.3.2 Threshold Logic

The set of functions just described can be expanded to include all of those within threshold logic. This system takes the weighted sum of a set of inputs and thresholds it to produce the binary output. All of the standard Boolean functions can be implemented within it. More importantly, threshold logic allows many Boolean functions to be minimised, reducing the complexity of a system [18]. The notation of threshold logic differs from Boolean in that only the plus and minus operators are used. To avoid confusion between the two logics (such as the dual meaning of +), any Boolean operators mentioned will be spelled out in capital letters (e.g. AND). A threshold logic expression is contained within angle brackets, and the threshold is given as a subscript to the closing bracket. Note that the threshold is not given as a fraction (such as 1.5 for the AND gate above). Instead, the upper and lower bounds are given, separated by a colon (so 1.5 becomes 2:1, meaning the threshold is between 2 and 1).

Example 3.1 The AND function

Boolean: Q = A AND B Threshold: Q = < A + B >2:1

Example 3.2 The OR function

Boolean: Q = A OR B Threshold: Q = < A + B >1:0 A slightly more complex operation, such as the inclusion of an inversion, is simplified with the minus operator.

Example 3.3 The NOT function

Boolean: Q = A AND NOT B Threshold: Q = < A - B >1:0 Boolean: Q = A OR NOT B Threshold: Q = < A - B >0:-1 These functions require two Boolean operations, but can be achieved with only one threshold operation. In fact, out of the sixteen possible Boolean operations on two variables, fourteen can be implemented with one threshold logic element. The other two, exclusive-or and exclusive-nor, still only require two logic elements (four components). Many more complex Boolean operations can be simplified, as the following examples show:

Example 3.4

Boolean: Q = A OR B AND ( C OR D AND ( E OR F )) Threshold: Q = < 8A + 5B + 3C + 2D + E + F >8:7

Example 3.5

Boolean: Q = A AND ( B AND C OR D AND E ) Threshold: Q = < 3A + 2< B + C >2:1 + D + E >5:4 Threshold expressions are implemented according to the following rules: 1. Positive inputs are applied to the load device. 2. Negative inputs are applied to the driver device. 3. Weights are implemented by increasing the relative effect of the relevant base contact. 4. The threshold is set with the driver device. Figure 3.8 shows the circuit implementation of example 3.5, and tables 3.1a and 3.1b run through the Boolean and threshold logic to show that they are correct.

4. Conclusion

The eventual implementation of a bistable pair of reliable and ideal resonant tunnelling transistors offers a real alternative to digital design with conventional transistors. Unfortunately, good RTTs are still some way off, but the logical principles of the device can still be implemented with alternative configurations, such as hybrid MOSFET and RTD combinations. These principles can allow conventional Boolean logic to be expanded into threshold logic, which allows many digital functions to be implemented with fewer operations. This in turn leads to a requirement for fewer components than the equivalent Boolean implementation. Given that a normal Boolean function can be implemented with fewer RTTs than conventional transistors anyway, the saving in components is even greater. The implementation of resonant tunnelling devices in GaAs and similar materials is a problem because the investment and experience gained from device fabrication in silicon is far higher. At the moment, the types of device mentioned cannot be manufactured using silicon materials. However, some research is being carried out in this area so the situation may change in the future [19]. This would bring these devices into the mainstream of digital computing manufacture, and would help to drive down the cost of the components. Another problem is the non-zero power consumption of the components. When a bistable pair latches into a state, it will always be drawing current in order to maintain that state. This is unlike CMOS for instance, which requires power only to switch from one state to another. However, as the resonant tunnelling devices continue to decrease in size, so will their current density. This will drive the current required into the microamp rather than the milliamp scale, and reduce the power consumption accordingly. The state latched into by a bistable pair is discovered by checking the voltage on the output, so the current is able to decrease almost indefinitely. By far the greatest advantage of resonant tunnelling devices is their potential for shrinkage. The active region of the device is the quantum well surrounded by the two barriers, each of which can be implemented with a few atomic layers. The problem is that the quantum well region is very difficulty to contact in isolation (for the manufacture of an RTT), and that the emitter and collector regions on either side of the active region may be very deep and broad. This pushes the total size of the device into the micron rather than the nanometre scale. However, as fabrication technology continues to improve, these obstacles will hopefully fall away. At that time, the implementation of extremely complex, yet ultra-small and fast, computer systems will be possible.

References

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Last updated: July 24, 1996 by Colin Moffat