Sarkar, Subir Kumar

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imiian 1  Phys. T l \  (1), 23-26 (2003)U P  Aan international journalGA based parameter optimizations for better mSlimeter and sub-millimeter wave response characteristics of GaA  ^ quantum wellsSubir Kumar Sarkar IDepartment of Electronics and Tclecommuniiation Engineering, Jadavpur University, Kolkatu 7(K) c|l2. IndiaE-mail : $u_sarkar@hotmail.<|>mReceived 6 May 2002. aicepted JH Seffember 2002Abstract . The aim of this work is to predict the optimum values of the system parameters of GaAs quantum wells incor|)orating the relevant scattering mechanisms for getting better millimeter and sub-rnillimeier wave response characteristics and to explore the possibilities of new applications ot Mich nanostructures Optimized parameters have been computed by employing the Genetic Algorithms to get the desired response as an aid to the device related work The optimized parameters like phase angle, ac mobility, channel width, carrier concentration, lattice teinperuture and electron icinpeiaiure will obviously save the search time for the technologists involved in the fabrication of devicesKeywords Genetic algorithm, optimization, quantum wells, ac mobility, hot electron, probabilistic rules, carrier transportPACS Nos. 72 10.- d; 72.20. Dp, 73.63.Hs1. IntroductionThere has been considerable interest in the study of the physical properties of the two-dimensional (2D) quantum wells [1-2]. Investigations on such two-dimensional (2D) quantum wells are already started and some of these devices are ready for commercial use in many applications [3-6]. Yet, there arc many scopes for further investigation to improve the operations of such two-dimensional (2D) quantum structures [7-10], In our work, wc want to find out the optimized system parameters for the two-dimensional (2D) quantum wells for high frequency under hot electron condition. When a thin layer of lower handgap semiconductor such as GaAs, is sandwiched between the layers of higher bandgap semiconductor such as (Al, Ga)As, then a quantum well (QW) is formed. In these structures, the two dimensional (2D) electronic transport parallel to the mterfacial planes is allowed due to the layer thickness t^omparable to the de Broglie wavelength. Electron mobility in QWs is particularly high at low temperatures as modulation <ioping separates the electrons from their parent doner atoms reducing thereby the influence of ionized impurity scattering 16]. The main advantage of the quantum well (QW) over a single heierojunction is that the modulation doping on both sides ofCorresponding Authorthe quantum well is possible, so that higher electron concentrations are possible in quantum wells than the single hctcrojunctions [11-13]. The properties like electron mobility. Hall mobility. Hall to drift mobility ratio, etc are the main criteria for the study of two-dimensional (2D) quantum wells. Due to the dependence of these properties on the various system parameters, namely, the channel width, carrier concentration, lattice temperature, electron temperature, etc, the optimization of these system parameters of the two dimensional quantum wells (QWs) is very essential for suitable application in commercial market.For the optimization, the various methods are already used, but due to some important advantages, genetic algorithm is used successfully in our work. It is a biological evolutionary process in intelligent search, machine learning and optimization problems and this algorithm is based on the mechanics of natural selection and natural genetics. In every generation, a new set of artificial creatures is created using bits and pieces of the fittest of the old; an occasional new part is tried for good measure. While randomized, genetic algorithms (GA) are no simple random walk. They efficiently exploit historical information to speculate on new search points with expected improved performance. The main theme of this algorithm is robustness. It is the balance©2003IACS24 Subir Kumar Sarkarbetween efficiency and efficiency necessary for survival in many different environments. GAs arc theoretically and empirically proven to provide robust search in complex spaces. So GAs are now finding more widespread application in business* scientific and engineering circles. The reasons behind the growing numbers of applications arc clear. These algorithms arc computationally simple yet powerful in their search for improvement. In order for GA to surpass their more traditional in the quest for robustness. GAs must differ in some fundamental ways. (14) GA provides most canonical meth(xl than many search schemes.In the present work, we intend to compute the optimized parameters using GA to get desired millimeter and sub millimeter wave response characteristics of GaAs quantum wells.2. Method of approachWe consider square QWs of GaAs of infinite barrier height having channel width L For the 2D carrier concentration channel length (L_), and the lattice temperature (7^) used here, the separation between the lowest and the next higher subband is at least four times the average carrier energy. The electrons are, therefore, assumed to populate only the lowest subband of the square QWs in the infinite barrier height approximation. The carrier distribution is thus degenerate.In the present work, we include the carrier scattering via deformation potential acoustic phonons, polar optic phonons, and ioni/cd impurities. The effect of screening on the scattering rate for polar optic phonons is insignificant over the temperature range of interest (15] and hence not included in the present calculations. Screening is, however, incorporated for other scattering processes. Reduced ionized impurity scattering and improve carrier confinement establish a strong electron-electron interaction in the QW structure. Tliis strong interaction in energy and momentum exchanges favours a heated drifted Fermi-Dirac distributibn function for the carriers characterized by an electron temperature and a drifted crystal momentum p^. The establishment of an electron temperature is demonstrated by the photoluminesccnce experiment [ 16J. In presence of a healing electric field F applied parallel to the heterojunction interfaces, the carrier distribution in the QW is thus :n k )  = /o (E ) + (hpj Im*) k if^  / E) C O S 0  , ( 1)where fo (^ )  is the Fermi-Dirac distribution function for the carriers, ft is the Plank’s constant divided by 2;r, m* is the electronic effective mass and 6 is the angle between F and the 2D wave vector k of the carriers with energy E.An ac electric field of amplitude F, and frequency (O superimposed on dc biasing field is applied. So the net field lakes the formF = Fq + F, sin to r .Detailed mathematical calculation utilized in this article is available in Ref. (17). Electron temperature model is employed here together with energy and momentum balance equation for the carriers. Other relevant material parameters are used in the present calculations arc represented in section 4. Empirical relations are established here in this work in the same way as done in Ref. (17).In many optimization methods, we move gingerly from u single point in the decision space to the next using some transition rule to determine the next point. This point-to-point method is dangerous because it is a perfect prescription for locating false peaks in multimodal search spaces. By contrast, GAs work from a rich database of points simultaneouslv, climbing many peaks in parallel; thus, the probability of finding a false peak is reduced over methods that go point to point.GAs require the natural parameter set of optimization problem to be coded as a finite-length siring over some finite alphabet With GAs, the first step of our optimization process to code llic parameter as a finite length string. Tliere are many ways to code the parameter. At the moment, let’s consider an optimization problem where the coding comes a bit more naturally.A simple Genetic Algorithm is composed of three operators:- Reproduction, Cros.sovcr and Mutation.Reproduction is a process in which individual strings aic copied according to their objective function values. Copying strings according to their fitness values means that strings with a higher value have a higher probability of contributing one or more offspring in the next generation. This operator, of course, is an artificial version of natural selection, a Darwinian survival of the fittest among string creatures.After reproduction, simple crossover may proceed in the following steps. First, members of newly reproduced strings in the mating pool are mated at random. Second, each pair of strings undergoes crossing over as follows.An integer position t along the strings is selected uniformly at random between 1 and the siring length less one [ 1, P -  11 Two new strings are created by swapping all characters between positions (/ + I) and P inclusively. For example, consider two strings X  and Y.I100111 ion,Y=001I0I0010.ISuppose in choosing a random number between 1 and S (9 -  I ), as P = 9 as indicated in the above by dotted line. Then the result of cross over which produces two new strings indicated by Xj and Yj (say).X , = 100110010,Y, =001101011.GA based parameter optimizations fo r  better millimeter and sub-millimeter wave etc 25The mutation operator plays a secondary role in the simple GA. Wc simply note that the frequency of mutation to obtain good results in empirical Genetic Algorithm studies is on the order of one mutation per thousand bit transfers. Mutation rates arc simply small in natural population. Thus mutation is considered as a secondary mechanism of Genetic Algorithm adaption.3. Method of optimizatioiiPresent work declares that a soft computing tool, GA is used to get the optimized system parameters of GaAs QW for a desired high frequency response characterized by a cutoff frequency present work, a model of optimized system parameters of GaAs QW is obtained for a high frequency under hot electron condition. In GA, a fitness function is the main criteria for reproduction. The fitness values are u.scd to favc)ur high fitness individuals over low fitness individuals to take part in the process of reproduction. In the present application of GA, we find the f,^ g for a semiconductor quantum structure for Its different system parameters. So we find the variation of f^  (cut off frequency at which the mobility falls to 0.707 of its lowfrequency value) and one particular parameter of the system where the other parameters are optimized by the Genetic Algorithm. By taking the other parameters in one form, wc can be able to find the fitness values. These fitness values are converted to binary form and then proceed for further Genetic Algorithm operation.4. Numerical results and discussionIn this optimization technique, wc consider a square quantum well of GaAs and electron temperature model is employed for numerical calculations with the following system parameters : KlecU'on effective ma.ss /;/ * = 0.61033x 10'' kg, kingitudinal clastic constant, = 14.03x 10“’ N.m % acoustic deformation potential. £, = 17.6x10 “ J, Static dielectric constant, £ =  12.52, optic dielectric constant, = 10.82, LO phonon angular frequency, = 5 .37x l0 ’'ra d  s ' ,  background loni/ed impurity concentration 6.0 X !()-' m ' longitudinal acou.stic velocity = 5.22 X logins '. The frequency of the applied is varied and at each frequency the optimum parameters are determined by employing the Genetic algorithm for a particular dc biasing field. For a particular dc biasing field, it is possible to prqdict theTabic 1. Optimized parameters tor dc bias field F„ = I 0 x 10^  v/mFrequency Phase Ac Carrier ChannelGH/ mobility concentration width(inVv.s) N7/J ( lO '^in-) C. (nm)Lattice H ied runtem pe t a I u re t e in pe rat u re 7/ (A') 7; (A)10 6 76 5 06 9.0 120 77 3272 0 13 68 4.54 10 0 120 100 31850 30.01 4 43 9 0 120 87 305100 49.24 3.60 10.0 120 1 10 302200 56.94 1.88 8.0 105 150 240250 67 19 1 68 9.0 100 150 268:^oo 68 74 1.37 8 0 85 200 290400 66.70 0 99 8 0 120 250 322500 63 18 0 75 5.0 100 300 336600 67.16 0 65 5 0 100 300 336Tabic 2. Optimized parameters for dc bias field F„ = 0 5 X 10^  v/mFrequencyGHzPhase Acmobility(mVv.s)Carrierconcentration /i2/> (lO'^'m ')Channel width L. (nm)1.alt ICCtemperatureTi_{K)Electron icmperaiiire /;  (A)10 7 58 5.62 10 0 1 15 11 17320 9.89 3.79 9.0 120 100 14850 23.94 3.54 9.0 105 125 163100 37.24 2 60 lO.O 120 150 184200 49.41 1.60 8.0 115 200 222300 68.77 1.31 9.0 85 225 255400 72.71 1.01 10.0 100 250 284500 73.18 0.81 9.0 1 10 270 298600 75.89 0.68 9.0 1 10 300 330700 80.29 0.59 7.0 80 150 17426 Subir Kumar Sarkaroptimum values of the system parameters like electron temperature, channel width, carrier concentration, for the realization of a desired high frequency response and ac mobility. Optimized parameters have been computed by employing the Genetic Algorithms to get the desired high frequency response as an aid to the device related work. The optimized parameters will obviously save the search time for the technologists involved in the fabrication of the devices. The application of GA will enable the technologists involved in the fabrication to predict directly the system parameters for a device to be operated at a desired frequency with required ac mobility. The methexi of optimization studies how to dc.scribe and attain what is the best. Optimization theory encompasses the quantitative study of optima and methods for finding them. Optimization ensures performance toward some optimal point or points. There arc several other optimization techniques, but they need auxiliary information for proper working. As for an example, gradient methods require derivatives in order to be able to climb to the current peak, and other local search procedures like the greedy methods of combinatorial optimization need access to most if not all. On the other hand, GAs have no requirements for all these auxiliary information. GAs are more canonical method than many schemes. Moreover, GA based techniques enable the lechnologi.sts to determine the suitable optimized parameters directly to get the desired ac mobility and can be utilized during fabrication. Prom the Tables 1 and 2, it is revealed that for a frequency of200GHz and for ac mobility of 1.88 mVv.s (Table 1) and 1.60 mVv.s (Table 2) the optimized system parameters arc presented by the various columns of row 5 for both the tables. Tlie optimized parameters fur the biasing fields of 1.0 x 105 v/m and 0.5 x 105 v/m are represented in the tabular form in Table I and Table 2, respectively. This work has the potential of predicting the optimized system parameters, which will surely save the search time for the technologists involved in the fabrication of high frequency devices.5. ConclusionWe have computed the optimized parameters using GA to get desired millim eter and sub-m illim eter wave response characteristics. The application of GA in the device parameteroptimization for getting the best performance is a new area of re.search. The optimized system parameters pre.sented here, predict the better performance of GaAs QWs in the microwave and millimeter wave regime and can be used to analyse the experimental data when they appear in the literature. This is actually an application of a specialized soft computing tool and it is expected that the present model is capable of predicting the optimized parameters, which will surely save the search time for the technologists involved in the fabrication of high frequency devices.AcknowledgmentS K Sarkar thankfully acknowledges the financial support obtained from All India Council of Technical Education vide Older no. 8018/RlI/BOR/R&D( 199V99-2000dated 24.03.2000.References[ IJ K Kanisawa, H Yamaguchi and Y Hirayama Appi Phys, Leti 76 589 (2000)[2] F Uonard and R C Desai Phy. Rew B 57 4805 (1998)(3J W A Jessor, J H Van der Merwc and P M Stoop J. Appi Phys. 85 2129 (1999)(4j H Seng Wu. X Xiang Huang and M Weng Phys, Stai Sol (b). 204 747 (1997)(51 J C Kim al Appi Phys Lett Vol. 75 214 (1999)(6) S K Sarkar and D Chattopadhyay Phys, Rev B 62 15331 ( 2000)(7) Junichi Sonc Semkonci Sn. Technol 7 B2K) (1992).(8) T Yamada and J Sonc Phys Rev, B 40 6165 (1989)(9) J F Miller, P Thomson and P V G Bradbcr Eyolutwnur\ Computmfi Vol 93. 181 (1995)(10] P Thomson and J F Miller IEEE Piov, Comp and Tech (1996)[I I I  F M Yeh and C S Lin Electronics Lett. 29 1540 (1993)(12) F Como et al Inti Test Conf, 1 p 39 (1996)(13) T Sosao IEEE Trans, On CAO of Integrated Ct/cuits and Systems 12 621 (1993)(14) J F Miller and P Thomson Int. J. of Electronics 76 37 (1994)115] S K Sarkar et al Phys. Stat. Sol (b) 207 125 (1998)[16] S K Sarkar and D Chattopadhyay Nanotechnology 2 (1998)[I7J S K Sarkar et al J. Appi Phys. 78 283 (1995)(18] J P Uburton J. Appi Phys 56 2850 (1984)

GA Based Parameter Optimizations for Better Millimeter and Sub-Millimeter Wave Response Characteristics of GaAs Quantum Wells

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GA Based Parameter Optimizations for Better Millimeter and Sub-Millimeter Wave Response Characteristics of GaAs Quantum Wells

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