EFTA01077409.pdf

ADVANCED MATERIALS vnywadvmat.de NOUVDIMIWWO) Arithmetic and Biologically-Inspired Computing Using Phase-Change Materials C. David Wright,* Yanwei Liu, Krisztian I. Kohary, Mustafa M. Aziz, and Roberti. Hicken Computers in which processing and memory functions are is higher in the amorphous than in the crystal phase. This was performed simultaneously and at the same location have long explained by an 'umbrella flip' of Ce atoms, which was put for- been a scientific "dream', since they promise dramatic improve- ward as the potential origin of ultra-fast switching. The crys- ments in performance along with the opportunity to design and talline phase of phase-change alloys is also unusual, exhibiting build 'brain-like systerns.9-31 This "dreanf has moved a step strong resonance bonding, with such bonding being suggested closer following recent investigations of so-called memristor as a 'necessary conditiorf for technologically useful phase- (memory resistor) devicesi"I However, phase-change mate- change properties.1201 The scientific and technological impor- rials also offer a promising route to the practical realisation of tance of phase-change materials is dearly high; however their new forms of general-purpose and biologically-inspired com- use for simple binary storage, the main application to date, puting.19-111 Here we provide, for the first time, an experimental barely begins to exploit their remarkable properties to the full. proof-of-principle of such a phase-change material-based "proc- As pointed out by OvshinsIcy,itml some phase-change materials, essor. We demonstrate reliable experimental execution of the such as GeSbTe, should also be capable of non-binary arith- four basic arithmetic processes of addition, multiplication, divi- metic processing, multi-value logic and biological (neuromor- sion and subtraction, with simultaneous storage of the result. phic) type processing. The origins of these exciting possibili- This arithmetic functionality is possible because phase-change ties lie in the detail of the crystallisation process in nucleation- materials exhibit a natural accumulation property, a property dominant materials1111 that can also be exploited to implement an Integrate and fire" Crystallisation can be viewed as energy-accumulation, with neuron.02.13I The ability of phase-change devices to 'remember' excitation "events" (electrical or optical pulses) as the energy previous excitations also imbues them with memristor-type source. For binary storage the aim is to ensure complete crys- functionality/ol meaning that they can also provide synaptic- tallisation with a single excitation. For phase-change based like learning.1033I Our results demonstrate convincingly these processing however, multiple excitations that exploit the nat- remarkable computing capabilities of phase-change materials. ural accumulation property are used. For example, in conven- Our experiments are performed in the optical domain, but tional (electrical) PCM devices we can control excitation voltage equivalent processing capabilities are also inherent to electrical and current such that only a partial crystallisation occurs with phase-change devices. each excitation.PII With a succession of such excitations, nano- Phase-change materials such as GeSbTe or AgInSbTe alloys crystallites are formed which may grow and merge to form con- exhibit some remarkable properties; they can be crystallised ducting pathways, at which point the cell resistance changes by pulses in the picosecond range1'4.151 yet can remain stable quite abruptly (see Figure Ia). Analogous behaviour occurs against spontaneous crystallisation for many years. They show using optical excitation (the experimental method we use here), hugely contrasting properties between amorphous and crystal and can be understood using a physically realistic crystallisa- phases, including an electrical conductivity difference of up to tion model. One such model is the rate-equation approach'11.221 five orders of magnitudel14l and a large refractive index change; that tracks both sub-critical and super-critical crystal cluster properties that have led to their application in electrical (phase- sizes during each excitation event. The ability to track sub- change RAM or PCM devices) and optical (DVD and Blu-Ray critical dusters is important since they play a significant role discs) memories.P7381 The origin of such remarkable properties in the early stages of crystallisation, as recently confirmed has been a source of much recent research. Kolobov1191 showed experimentally.1211 Our rate-equation model is discussed in that, contrary to expectations, the short-range order in GeSbTe detail elsewhereP1221 (Supporting Information); here we use it to understand the processing capability of the energy accumu- lation regime. For this we consider a region of phase-change material, here the nucleation-dominant material Ge2SbiTes, Prof. C. D. Wright, Dr. K. I. Kohary, Dr. M. M. Aziz subject to a series of optical or electrical excitations. For sim- School of Engineering plicity we assume that as a result of each excitation the entire Computing and Mathematics University of Exeter region is heated to some constant temperature for a dura- Exeter EX4 4QF, UK tion dt seconds. We calculate the population distributions of E-mail: [email protected] crystal duster sizes before, during and after each excitation and Dr. Y. Liu, Prof. R. J. Hicken track the fraction of crystallised material. We map the change School of Physics in crystal fraction to a change in electrical and optical properties University of Exeter EX4 4QF, UK using effective medium theor020-9 (Supporting Information). In Figure lb we show the calculated optical reflectivity DOl: 10.1002/adma.201101060 and electrical conductivity as a function of the number of Adv. Mores. 2011. XX. 1-6 C 2011 WILEYNCH Vedas GmbH & Co. KGaA., Weinheim 1 EFTA01077409  ADVANCED MATERIALS www.advmat.de a) sequentially (a format suited to arithmetic processing); however, for multiple weighted nn Constant amplitude chnge cell itr Cell switches parallel inputs, as shown schematically in Figure la, we can use the same accumulation, threshold and non-linear output change (in input pulses after N pulses resistance or reflectivity) to mimic an 'inte- grate and fire biological neuronlIzIll using a single phase-change cell (or spot), a far sim- Multiple weighted HsCell 'fires' on pler approach than conventional implemen- tations that use relatively complicated multi- transistor CMOS circuitslal (although we note that similarly simple neuron-like hard- parallel input pulses combination of ware can be implemented using non-phase- input pulses change based memristive systemsln al) We now implement experimentally a phase-change arithmetic processor, working in the optical regime. The optical arrange- ment is shown in Figure 2a and comprises b) a pulsed pump beam and a continuous probe beam that are overlapped on the sample surface within the focal plane of an 1.0 optical microscope. The pulsed beam excites 30 the phase-change material (here a Si/ZnS• SiO2(310 nm)/Ce2Sb2Tes (20 nin)/ZnS-SiO2 normalised reflectivity 0.8 (30 nm) sample typical of that used in optical storage discs) while the probe beam measures the reflectivity. We used 800 inn pump pulses 0.6 20 G in the range 70 fs to 500 fs and fluences from 2 mJ cm-2 to 12 mJ cm-2. The typical reflect- ance change as a function of the number of pulses is shown Figure 2b, for which case the 0.4 sample remains in the accumulation mode 10 with little or no change in reflectivity until around 150 pulses are received, whereupon 0.2 subsequent pulses cause significant increases in reflectivity. In this arrangement the system might be used to perform arithmetic com- 0.0 putations in a high-order base. More use- 0 100 200 300 400 500 600 700 800 fully, individual pulses can be combined into number of pulses groups with each group designating a single excitation event. This approach gives great Figure 1. Processing using the accumulation property ofGeSbTe. a) Schematic ofphase-change flexibility; for example if a single excitation processor for arithmetic (top) and neuron-like (bottom) processing. b) Simulated, using the comprises 25 successive 85 fs, 3.61 mJ cm-2 rate-equation and effective medium theories, change in normalized reflectivity (solid lines) in pulses of the form used in Figure 2b, then a Ge2Sb2Te5 sample as a function of the number of 700 K temperature excitations (rectangular temperature pulses) of duration 10 ns, 1 ns, and 0.3 ns. Also shown is the resulting change in a threshold between the 9th and 10th excita- sample conductivity (dashed line). The natural accumulation and threshold property of phase- tion can be readily set (suitable for base-10 change materials is clear. addition and multiplication). Combining the same individual pulses into groups of 16 would on the other hand provide a threshold excitations assuming a fully amorphous starting phase, Tem', = suitable for direct hexadecimal computations. The response 700 K (chosen to match the estimated temperature achieved curve for our base-10 scheme is thus as shown in Figure 2c; in our experimental results—see Supporting Information) and note that there is very little reflectance change for the first 6 to various pulse durations; initially there is relatively little change 7 excitations, and that the change for 10 excitations (6%) is sig- in optical reflectivity or electrical conductivity but a distinct nificantly larger than that for 9 excitations (4%) and a suitable threshold exists where a rapid change sets in, with the sud- reflectivity threshold for computations is 5% in this case. Also denness of the change in electrical properties being more pro- shown in Figures 2b and 2c for comparison is the simulated, nounced (due to percolation). The number of pulses required using the rate-equation model and effective medium theory, to reach the threshold can be controlled via the excitation dura- change in reflectivity; to evaluate the theoretical results we cal- tion (or amplitude). In this example we have applied excitations culated the temperature distribution in the Gei Sb2Tes sample 2 C 2011 WILEYNCH vadat GmbH & Ca KGa.A.. Weinbeim Alit Morn 2011. XX. 1-6 EFTA01077410  ADVANCED MATERIALS wwvAadvrnat.de NOILV)INflWWO) by analytical solution of the heat equation for an impulsive Micro- a) Pump pulses scope Detector optical source (we note that our analytical thermal model does not include phonon-carrier interaction and relaxation proc- Probe beam esses often included in more complex two-temperature type modelsI29i of fast thermal processes; however the crystallisa- tion process will be dominated by the relatively long (ns order) thermal time constant of the optical disc-like sample used here, rather than the very short thermalisation time which is typically less than 5 ps for Ge2Sb2Te59S0t — see Supporting Information for more details). b) Now we are ready to implement base-10 addition. Having already set the threshold change in optical reflectivity to occur between the 9'h and 10'h excitations as in Figure 2c, we can 20 compute a base-10 addition directly by inputting a number of a. excitations equal to the first addend, followed by excitations 15 equal in number to the second addendP-111 The phase-change 'processor' automatically sums the two addends due to its accu- mulation property, simultaneously storing the result (at the to same physical location). To access the stored result, excitations are applied until the threshold is reached, the number of excita- tions required and the calculation base revealing the result. As a threshold lever practical example, starting in the amorphous phase, we applied excitations of the form in Figure 2c (is. 25 x 85 fs pulses = I excitation) to perform the summation (7 + 2). Of course the 250 ris 500 625 750 65 1000 answer is 9 and so the result of the sum should lead to a reflec- number of pulses tivity change below the 5% threshold. This was indeed the case; after inputting the first addend (7 excitations) the experimental change in reflectivity was 2.2%; inputting excitations equal to the second addend (2) took the total reflectance change to 4.5%. To access the result of the computation we input further excita- tions until the threshold is passed; in this case only one fur- ther excitation was needed, taking the total experimental reflec- tivity change to 6.3%. comfortably above the threshold and revealing the correct result of the sum (9 in this case). A micro- scopic image of the physical mark stored in the phase-change sample as a result of this addition is shown in Figure 3 and is just about discernible to the eye. Note that should the result of the sum be greater than the base, the phase-change material is reset to amorphous each time the threshold is exceeded and the number of resets reveals the multiples of the base in the final sum. Re-aznorphization is readily achieved in the current arrangement by a single (i.e. 1 x 85 fs) 11.7 mj cm-2 pulse, as 4 6 8 number of excitations also shown in Figure 3. Since multiplication is simply sequential addition, it is dear Figure 2. Experimentally measured accumulation property of GezSb2Tes. a) that this too can be readily implemented using the process Schematic of the set up for the femtosecond laser experiments. b) Experi- described above. mentally measured (squares) change in optical reflectivity ((R—Ra)/Ft.,) where R, is amorphous phase reflectivity) of the Ge2Sb2Te5 sample as a Turning to division, this can be implemented by using function of the number of 85 fs, 3.61 mi/cm2 pulses applied. c) Experimen- the divisor to define the threshold, then applying a number tally measured (squares) change in reflectivity as a function of excitation of pulses equal to the dividend (and re-setting each time the events (for first 12 events), with a single excitation event comprising 25 x threshold is passed). For example 14410 is executed by setting 85 fs, 3.61 mycm2 pulses and chosen so that a threshold can be set for the threshold to be passed after 10 input excitations (because the implementation of base-10 addition and multiplication. Result shows this is the divisor, not because we are in base-10) and applying dearly the energy accumulation property and the threshold (at 5% change in optical reflectivity) is set between the rand 10th excitations; also shown are 14 excitations. This would require the system to be re-set once microscopic images of the mark formed after 10 excitations (6.3% change (after the 10'h excitation), leaving 4 stored in the phase-change in reflectivity) and after 12 excitations (11% change in reflectivity), as well as medium; hence the result is 1 remainder 4. We have performed the initial amorphous starting phase (white scale bar is 50 pm). Also shown exactly this computation using our phase-change processor. in 2b and 2c is the simulated change in reflectivity (solid lines), calculated Since we have already set the threshold to occur at 10, which is using the rate equation and effective medium models and a sample tem- equal to the divisor in this case, all that remains to perform the perature distribution obtained by analytical solution of the heat conduction division is to input excitations equal in number to the dividend equation for an impulsive optical source (Supporting Information). MIt Mow 2011. XX, 1-6 41 2011 WILEYNCH Vedas GmbH & Co. KGaA., Weinheim 3 EFTA01077411  ADVANCED MATERIALS we input excitations equal to the subtrahend O 7+2 14 ÷ 10 5-2 (2); the phase-change material carries out the subtraction and simultaneously stores a the result (3 in this case), which is accessed by counting the number of input pulses (3) required to reach threshold. We have re-cast the subtraction (5-2) as a division (5+2) and carried out our previous division process but this time with the dividend (5) defining the threshold (rather than the divisor). An alter- O native view of subtraction is as the addition 516+ B16 10 then reset 12 excitations algorithm but with the threshold set by the minuend, rather than by the base. To perform the calculation 5-2 experimentally we first set the threshold to be exceeded after 5 excita- tions (the minuend in this example). We can do this easily in our system by grouping the basic 85 fs, 3.61 mJ cm-2 pukes into excita- tion units of 50 pulses (i.e. one excitation event is 50 x 85 fs pulses). The typical reflec- tivity change after 4 such excitations is 3% Figure 3. Simultaneous phase-change processing and storage. Microscope images (50 pm and that for 5 excitations is 6%, thus a suit- x 42 gm in each case) of marks in the Ge25b2Tes sample after the execution of various arith- able threshold reflectivity change in this case metic processes. From left to right the first three images show the mark after computing and is 4.5%. All that remains to perform the cal- extracting the result for the base-10 computation of 7 + 2, 14+10 and 5-2. The fourth image culation is to input to the system a number shows the mark after computing and extracting the result of the base-16 addition 5164816 For of excitations equal to the subtrahend (2), the first two calculations a single excitation comprised a group of 25 x 85 fs optical pulses; the phase-change material then executes for the subtraction calculation a single excitation comprised 50 x 85 fs pulses; for the base-16 calculation a single excitation was 16 x 85 fs pulses. The extraction of the stored result for the computation and simultaneously stores each of these computations took the measured reflectivity change above the pre-determined the result (3). Experimentally the reflectivity threshold value (which was 5%, 5%, 4.5% and 5.4% respectively), so the final marks in each change obtained following the input of the case look very similar. In normal operation the phase-change material is reset to its initial state subtrahend (i.e. 2 excitations) was minimal whenever the threshold is exceeded; in our case this was carried out using a single 11.7 my (0.4%) and to extract the result of the calcula- cm2 85 h pulse that successfully reset the system to the amorphous phase, as can be seen in tion a further 3 excitations were required to the fifth image from the left which shows the result of inputting 10 (25 x 85 fs, 3.61 mJ/cm2) excitations followed by a single 11.7 mJ/cm2 85 fs reset pulse. Also shown (far right image) for exceed the threshold, as expected. The total comparison purposes is the resulting mark after 12 excitations and without resetting; in this reflectivity change following input of these case the reflectivity change is —11% and the mark is clearly different, even to the eye. 3 further excitations was 5.8%, significantly above the threshold, while the reflectivity change after inputting only 2 excitations was (14), re-setting each time the threshold is reached. Experimen- well below the threshold. An image of the mark at the end of tally the measured reflectance change after 10 excitations was this subtraction process is also shown in Figure 3. Although 6.3%; this exceeds the threshold so the system was re-set to the not demonstrated here, it is also easy to see that subtractions amorphous phase, again by a single 85 fs, 11.7 mJ cm-2 pulse. resulting in a negative difference can be directly implemented A further 4 excitations were then applied, resulting in a negli- using the same approach. gible change (0.3%) in reflectivity and leaving the remainder (4) As a further demonstration of arithznetic processing we exe- of the division calculation stored in the phase-change spot. This cute directly a hexadecimal computation, specifically the sum remainder is accessed by applying as many subsequent excita- 50-B" (= 10"; remember that the basic hexadecimial digits tions as necessary to once again reach the threshold. This was are represented by 0, 1, 2 .....9, A, B, C, D, E, F). For base-16 achieved experimentally with 6 further excitations, which gave a addition we set the threshold reflectivity change to lie between total reflectivity change of 6.0% front the re-set state. Thus the the 15th and 1616 excitations. We do this by combining the basic experimental result of the division calculation is as expected, 85 fs pulses into groups of 16 such that a single excitation event I remainder 4, and the final state of the phase-change mate- consists of 16 x 85 fs pulses and for which the threshold reflec- rial upon completion of this division process is also shown in tivity change is 5.4%. The hexadecimal addition is then carried Figure 3. out by inputting 516 excitations (i.e.. 510 x 16, 85fs pulses) fol- Finally we turn to subtraction. For conventional computing, lowed by B" (i.e. 1110 x 16, 85 fs pulses). Experimentally this division can be done using successive subtraction (e.g. 5+2 = 2, resulted in reflectivity changes of 0.4% and 6.0%, respectively, remainder 1; or 5-2-2 remainder 1); to implement subtraction providing the correct answer of 1016; the image of the mark at using a phase-change processor we do the reverse, i.e. use the the end of this process is also shown in Figure 3. A summary of division algorithm to perform subtraction. For example, to cal- all the above arithmetic computations is given in Table 1 and we culate 5-2 we use the minuend (5) to define the threshold, then note that the main source of uncertainty in such computations 4 C 2011 WILEYNGH Vedas GmbH & Ce. KGa.A. Weinbeim M Mater. 2011. XX. 1-6 EFTA01077412  ADVANCED MATERIALS veww.advmat.de NOI1V3IMIWWO3 Table 1. Summary of experimentally performed arithmetic processes including definition of a single excitation event for each calculation, the threshold reflectivity change, the excitation sequence (numbers in brackets show number of excitations applied to extract stored result) and the experimentally measured reflectivity change at each stage of the computation. Sum Exataticm Event Threshold (% R) Excitation Sequence Experimental (%R) Answer (experimental) 7+2 25 x 55 fs 5 7, 2, (1) 2.2, 4.5, (6.3) 9 14 ÷ 10 25 x 55 Is 5 10, reset, 4, (6) 6.3, reset, 0.3, (6.0) 1 remainder 4 5-2 50x85 fs 4.5 (3) 0.4, (5.5) 3 514 8If 16 x/35 fs 5.4 SIP 1110 0.4,6.0 stems from variations in the power of the probe beam used for or "memflector") in which the optical reflectivity is determined our reflectivity measurement and slight changes caused to the by excitation history. A distinctive feature of electrical meznris- optical path when moving the sample—such variations could be tance is a non-linear relationship between the integrals of cur- significantly reduced in a dedicated system, so providing for rent and voltage, which results in various fonns of hysteretic reliable computation. current-voltage (I—V) curvesf'•81 The optical equivalent of an Finally we now turn our attention to the znemristive-like I—V curve is a plot of reflected (PR) versus incident (P,) light properties of phase-change materials. It has already been intensity. In Figure 4 we show such a characteristic PR-PI curve pointed out that electrical phase-change memory cells are a (in this case simulated using an analytical model for the tem- form of memristorial (a device whose current state is deter- perature calculation, rate-equation model for calculating the mined by its excitation history) and that memristive devices can fraction of crystallised material and effective medium theory be used to implement synaptic-like processing.Pa•29•SOI Since we for calculation of optical properties-see Supporting Informa- have already shown that phase-change devices can be used to tion) for several cycles of linear up/down incident laser inten- implement a basic form of neuron (Figures 1 and 2 associated sity sweeps; here the reflected intensity continuously increases text), if we can also implement synaptic-like (memristive-like) during sweeps, and the PR-PI slope of each sweep picks up processing with phase-change materials then it should be fea- from where the last sweep left off, in direct analogy to the sible to build entire networks of neurons and their associated electrical casein' Also shown inset in Figure 4 is the laser synapses using phase-change devices and therefore implement excitation waveform and the calculated fraction of crystallised biological-inspired (neuromophic) computation/processing. material during the various cycles; note that the crystallised Indeed, our results (Figure lb and Figure 2) already demon- fraction is dependent on both temperature and time and that strate the optical analogue of a memristor (a memory-reflector relatively little crystallisation occurs during the first "up' ramp but crystallisation continues during the first "down' ramp (and cooling period) and subsequent cycles in accordance with the well-known time-temperature-transformation (Tri) character- istics of Gei Sb2Tes.131) Figure 4 shows dearly that optical and/ or electrical forms of phase-change memflector/memristor devices appear feasible, so offering a synaptic-type processing capability to add to the arithmetic and neuron-like processing already demonstrated above. The remarkable properties of phase-change materials may therefore in time lead to some truly remarkable applications. Supporting Information Supporting Information is available from the Wiley Online Library or from the author. 2 4 6 8 10 12 14 incident laser intensity (mW/µm2) Acknowledgements Figure 4. The memflector; optical analogue of the memristor. A plot of We gratefully acknowledge financial support for this work from the UK the (simulated) normalised reflected light intensity (PR x riFt/R,) versus EPSRC (grant EP/F/015046/1). We are also indebted to Dr. Andrew incident (P1) light intensity for the optical analogue of the memristor (the Pauza of Plarion (formerly Plasmon) Ltd., Cambridge, UK, for the supply memflector) as a function of the number of linear up/down sweeps of of the GeSbTe samples. the incident laser intensity (this is equivalent to memristor I—V curves). Maximum incident intensity was 13 mW/µm2 and the up/down ramp Received: March 22, 2011 timewas 20 ns in total (10 ns up and 10 ns down). Also shown inset is the Revised: April 28, 2011 incident laser waveform and resulting fraction of crystallised material. Published online: MIt Morn. 2011. XX, 1-6 49 2011 WILEYNCH Verlag GmbH Si Co. KGaA, Weinheim 5 EFTA01077413  ADVANCED MATERIALS wwwadvmatde z pj L. S. Smith, Handbook of Nature-Inspired and Innovative Computing: integrating Classical Models with Emerging Technologies; Springer: [16] G. Bruns, P. Merkelbach, C. Schlockermann, M. Salinga, M. Wuttig, T. D. Happ, J. B. Philipp, M. Kund, Appl. Phys Lett. 2009, 95, New York (2006). 043108. [2] F. M. Raymo, Adv. Mater. 2002, 14, 401. [17] M. Wuttig, N. Yamada, Nat. Mater. 2007, 6, 824. [31 T D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, [18] G. Atwood, Science 2008, 32f, 210. J. L O'Brien, Nature 2010, 464, 45. [19] A. V. Kolobov, P. Fons, A. I. Frenkel, A. L Ankudinov, J. 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