Neuro–genetic approach for better nano device modeling A. Karmakara, S. K. Sarkarb, S. C. Dasb, T. Dattac Dept. of Electronic Science, Calcutta University, Kolkata, India E-mail: [email protected] b Dept. of Electronics and Telecommunication Engg., Jadavpur University, Kolkata, India E-mail: [email protected] c Dept. of Electronics and Communication Engg., I. E. M., Salt Lake, Kolkata, India a

Abstract – An artificial neural network is employed here to predict the best parameters for the polar semiconductor nano structures such as In0.53Ga0.47As quantum well so that the relevant device will exhibit best high frequency response characterized by a desirable cutoff frequency. The parameters to be predicted include the lattice temperature, carrier concentration, channel length, dc biasing field, frequency of the applied ac field, ac mobility and the cutoff frequency. Out of these parameters, one parameter like the ac mobility or the cutoff frequency can be taken as output parameter and the rest as input parameters. The feed-forward back propagation network has been employed for the prediction of practically realizable parameters for the best nanodevice structures. Parameter optimization is also done employing the genetic algorithm to get the desired response as an aid to the nanodevice related work. The results obtained in those two different techniques are compared to predict the flexibility of the parameter values and may be utilized during the fabrication of nanodevices. Key words: Artificial neural network, genetic algorithm, nano structures, optimization, polar semiconductors.

I. INTRODUCTION Realization of nano electric materials and devices in parallel with nano fabrication essentially required nanometer-scale evaluation of electrical characteristics as it keeps a direct relevance to the electric or electronic functionality. Electric characteristics are controlled by the system parameters, lattice temperatures, external dc biasing field and the frequency of the applied ac electric field. All these parameters are related in a complex way so that it is very difficult to predict the best parameters for the most wanted electrical characteristics. Quasi-low dimensional electric transport in nano devices has been the objects of intensive researches during the last two decades [1-5]. Some of the devices have matured into commercially useful products and form part of modern electric circuits. Some others require further development, but have the promise of being useful commercially in the near

future. Nanostructures are now recognized as a promising basis for the study of the physics of low dimensional structures (LDSs) and their future technological applications. Researches on the physics of LDSs continue to be both challenging and exiting, as novel structures with different materials having different properties are developed. Such studies also help in optimizing the performance of the structures in devices and in exploring the possibilities of new applications. A low electron effective mass, a high sheet carrier concentration, a large conduction band offset and paek drift velocity are some of the novel properties of In0.53Ga0.47As [2]. Therefore, we find here the optimized system parameters of In0.53Ga0.47As quantum well (QW) to get desired high frequency response characterized by a 3dB cutoff frequency f3dB. An artificial neural network (ANN) is a computational tool having artificial intelligence origins, also known as a ‘neural net’. ANN is a computing system made up of a number of simple, highly interconnected processing elements, which process information by their dynamic state response to external inputs. Presently they are being used for a wide range of applications covering character recognition, speech recognition, moaning from spelling to sound, motor control, data framing and many more areas of applications [6]. Genetic algorithm (GA) is a biological evolutionary process in intelligent search, machine learning and optimization problems. GAs are computationally simple but powerful in its search for an improvement [5, 7]. GAs require only payoff values (objective function values) associated with individual strings to perform an effective search for better and better structures. This characteristic makes GAs most canonical than any other search methods. In the present work, an ANN is employed to predict the best parameters for the polar semiconductor nano structures so that the relevant

device will exhibit best high frequency response characterized by a desirable cutoff frequency. The parameters to be predicted include the lattice temperature, carrier concentration, channel length, dc biasing field, frequency of the applied ac field, ac mobility and the cutoff frequency. Out of these parameters, one parameter like the ac mobility or the cutoff frequency can be taken as output parameter and the rest as input parameters. The feed-forward back propagation network has been employed for the prediction of practically realizable parameters for the best nanodevice structures. Parameter optimization is also done employing the GA to get the desired response as an aid to the nanodevice related work. The results obtained in those two different techniques are compared to predict the flexibility of the parameter values and may be utilized during the fabrication of nanodevices. II. ANALYTICAL MODEL Square QWs of In0.53Ga0.47As of infinite barrier height having channel length Lz are considered. The system parameters, namely, two dimensional (2D) carrier concentration (n2D), channel length (Lz) and lattice temperature (TL) used here, are such that the separation between the lowest and the next higher subband is sufficiently higher than the maximum average electron energy. Thus, the carrier distribution is degenerate as the electrons are assumed to populate only the lowest subband of the square QWs in the infinite barrier height approximation. In this present work, the energy exchanges with longitudinal optic (LO) phonons via polar coupling and momentum exchanges through interactions with acoustic phonons via deformation potential coupling, LO phonons, alloy disorder scattering and background-ionized impurities are incorporated. The screened scattering rates are considered except for polar optic phonons where carrier scattering is insignificant in this present investigation [8]. The scattering due to ionized impurities in the remote barrier region is not considered as it can be made substantially feeble by introducing undoped spacer layers [9]. Improved carrier confinement and reduction of the effects of ionized impurity scattering in the channel establish a strong electron-electron interaction in the QW. This interaction in energy and momentum exchanges favors a heated drifted Fermi-Dirac distribution function for the carriers characterized by an electron temperature Te and a drift crystal momentum pd [10]. The establishment of an

electron temperature in 2D systems has been demonstrated by the photo luminescent experiments [11]. Analytical details adopted here are available in Ref. [12], where net rate of increase of phonon occupation equation is solved with the help of energy and momentum balance equations together with the expressions of applied electric field, electron temperature, phonon occupation number and drift momentum [12]. III. OPTIMIZATION TECHNIQUE ANN starts with a set of equations associated with a randomly chosen group of coefficients and rules for adjusting those coefficients during ‘training’. Back propagation performs a gradient descent learning algorithm to train the network. Once an ANN is ‘trained’ to a satisfactory level it may be used as an analytical tool on other data. To do this, the user no longer specifies any training runs and instead allows the network to work in forward propagation mode only. New inputs are presented to the input pattern where they filter into and are processed by the middle layers as though training were taking place, however, at this point the output is retained and no back propagation occurs. The output of a forward propagation run is the predicted model for the data, which can then be used for further analysis and interpretation. The fitness function is the main criteria for reproduction in GA; the fitness values are set from the system parameters of In0.53Ga0.47As QWs under hot electron conditions. These fitness values are calculated from the binary strings. All the fitness values are used to form a population of strings to start the reproduction process. Then these strings are entered into a mating pool for further genetic operation. Thereafter the crossover and then mutation is done to get good results in empirical GA. After the first generation, we take the average of the newly generated strings and the original strings. Those strings, which are higher than the new average strings are suited for the next generation. According to the fitness values, from the population of the next generation, we take the first best, the second best and so on for the optimum values in our present work. IV. RESULTS AND DISCUSSIONS Artificial neural network and genetic algorithm based computations are performed with the

parameter values of In0.53Ga0.47As taken from Ref. [2] for the dc biasing field F0 of 0.75×105 V/m and the frequency of the applied ac field of 300GHz. In this present work, details studies are made for getting optimized system parameters together with the lattice temperature and electron temperature for a desired high frequency response characterized by a well defined 3dB cutoff frequency. This implies that the model so realized can predict the optimum system parameters if the cutoff frequency and the biasing field are provided. Optimized system parameters for the frequency 300GHz of the applied small-signal electric field and the dc biasing field F0 of 0.75×105 V/m are given in Table 1, which reveal that for the desired cutoff frequency at a particular dc biasing field it is possible to predict the optimum values of the system parameters like carrier concentration, channel length and electron temperature for realizing a particular high frequency response characterized by a cutoff frequency. It is found that at the lattice temperature TL of 200K, the optimized system parameters are: electron temperature Te=275K, 2D carrier concentration n2D= 8×105m−2 and the channel length Lz= 120 nm. V. CONCLUSION The optimized system parameters of In0.53Ga0.47As QWs are computed using both ANN and GA to get desired high frequency response characterized by a 3dB cutoff frequency f3dB. The results are represented in tabular form. It is observed that the system parameters are not in particular order but represent the optimized values for obtaining the desired cutoff frequency at a given dc biasing field. The optimized system parameters presented here will predict the better performance in In0.53Ga0.47As nano structures. Those parameters are not available in the current literature and the present optimized data has the potential of analyzing the experimental data when they appear in the literature. ACKNOWLEDGEMENT S. K. Sarkar thankfully acknowledges the financial support obtained from DRDO, Govt. of India.

Table 1: Comparison of optimized system parameters for frequency = 300GHz and F0= 0.75×105 V/m for In0.53Ga0.47As. ac mobility µac (m2/V.s) ANN GA

TL (K)

Te (K)

n2D (105 m−2)

Lz (nm)

1.59225 1.61 77 335 9.0 95 1.8155 1.83 100 170 5.9 90 1.89243 1.91 125 215 7.0 95 1.56193 1.60 150 190 5.0 110 1.9533 1.98 175 300 10.0 120 1.73976 1.78 200 275 8.0 120 1.6252 1.65 225 285 8.0 95 1.55781 1.56 250 305 8.0 90 1.64491 1.66 275 350 9.0 115 1.33465 1.37 300 345 7.0 110 [TL= Lattice temperature, Te= Electron temperature, n2D= Carrier concentration, Lz= Channel length]

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