Pattern recognition of messily grown nanowire morphologies applying multi-layer connected self-organized feature maps

doi:10.1016/j.jmst.2018.11.007

Abstract

Abstract:

Multi-layer connected self-organizing feature maps (SOFMs) and the associated learning procedure were proposed to achieve efficient recognition and clustering of messily grown nanowire morphologies. The network is made up by several paratactic 2-D SOFMs with inter-layer connections. By means of Monte Carlo simulations, virtual morphologies were generated to be the training samples. With the unsupervised inner-layer and inter-layer learning, the neural network can cluster different morphologies of messily grown nanowires and build connections between the morphological microstructure and geometrical features of nanowires within. Then, the as-proposed networks were applied on recognitions and quantitative estimations of the experimental morphologies. Results show that the as-trained SOFMs are able to cluster the morphologies and recognize the average length and quantity of the messily grown nanowires within. The inter-layer connections between winning neurons on each competitive layer have significant influence on the relations between the microstructure of the morphology and physical parameters of the nanowires within.

Key words: Artificial neural networks, Self-organizing feature maps, Monte Carlo simulation, Pattern recognition, Messily grown nanowire morphologies

Liu Qing, junLi He, Zhang Yulei, Zhao Zhigang. Pattern recognition of messily grown nanowire morphologies applying multi-layer connected self-organized feature maps[J]. J. Mater. Sci. Technol., 2019, 35(5): 946-956.

Figures/Tables 15

Fig. 1. Topology structure of the connected double-layer SOFMs [(a)] and numbering rules of neurons on each layer [(b)].

Fig. 2. Schematic of inter-layer learning procedure. (a)-(c) Building inter-layer connections between winning neurons and the neighbored ones representing the training samples with mapping relations; (d)-(f) boosting of the repeated connections.

Fig. 3. Model of the virtual training samples. (a) Generated virtual morphology of messily grown nanowires; (b) and (c) structure of the virtual nanowire and each line section.

Fig. 4. SEM images of messily grown Si nanowire morphologies [9]. (a) M1 synthesized at 950?°C for 2?h; (b) M2 synthesized at 1000?°C for 2?h; (c) M3 synthesized at 1100?°C for 0.5?h.

Fig. 5. Area ratios and CF histograms of experimental morphologies M1 [(a) and (b)], M2 [(c) and (d)] and M3 [(e) and (f)].

Table 1 Average converted radii, nanowire length, direction angles and growth direction change of morphology M1-M3 [9].

	ρ_A	2r_exp (nm)	r_conv	l_exp (μm)	φˉ(deg)	Δφ(deg)
M1	0.133	26.89	0.098	0.56	81.83	9.27
M2	0.273	27.74	0.085	1.80	93.29	7.85
M3	0.128	29.14	0.050	1.46	96.06	5.20

Fig. 6. Schematic of morphology recognition using the as-proposed SOFMs.

Table 2 Candidate sets including virtual training samples with similar area ratios to the experimental morphologies.

	Candidate set with nanowire quantity and length (N_sim, l_sim)
M1	UL	r_sim?=?0.1	(50,5)	(70,3.5)	(100,2.5)	-	(200,1)
	UR		(50,10)	(70,8)	(100,5)	(150,3)	(200,2.5)
	LL		(50,6)	(70,4.5)	(100,3)	(150,2)	(200,1.5)
	LR		(50,5)	(70,3.5)	(100,2.5)	-	(200,1)
M2	UL	r_sim?=?0.05	-	(70,17)	(100,10)	(150,6)	(200,4.5)
	UL	r_sim?=?0.1	-	(70,12)	(100,8)	(150,4.5)	(200,3.5)
	UR	r_sim?=?0.05	-	(70,25)	(100,13)	(150,8)	(200,6)
	UR	r_sim?=?0.1	-	(70,17)	(100,10)	(150,6)	(200,4)
	LL	r_sim?=?0.05	-	(70,17)	(100,10)	(150,6)	(200,4.5)
	LL	r_sim?=?0.1	-	(70,12)	(100,8)	(150,4.5)	(200,3.5)
	LR	r_sim?=?0.05	-	(70,15)	(100,9)	(150,6)	(200,4)
	LR	r_sim?=?0.1	-	(70,10)	(100,7)	(150,4)	(200,3)
M3	UL	r_sim?=?0.05	(50,10)	(70,6.5)	(100,4)	(150,2.5)	(200,2)
	UR		(50,10)	(70,7)	(100,4)	(150,3)	(200,2)
	LL		(50,8)	(70,5.5)	(100,4)	(150,2.5)	-
	LR		(50,7)	(70,5)	(100,3)	(150,2)	-

Fig. 7. Nanowire length predictions and neuron responses of the as-trained double-layer SOFMs. (a) Nanowire length of the experimental morphologies predicted by the as-trained SOFMs; (b) neural responses to input H(λx) of M3-UL.

Table 3 Estimated nanowire quantity and length of experimental morphologies.

	N?exp	l?exp (μm)
MM1	488	0.55
MM2	478	1.58
MM3	465	1.53

Fig. 8. H(λx) of M3-UL and the virtual training samples with similar ρA and rsim to M3-UL.

Fig. 9. Evolution of winning neuron locations with training times on layer N1. The inputs are candidate virtual training samples for M3-UL. Winning neuron locations with (a) 1 training time, (b) 10 training times, (c) 100 training times, (d) 200 training times, (e) 300 training times. (f) Final location and inter-layer connection of winning neurons.

Fig. 10. Evolution of Euclidean distance between winning neurons and the corresponding training samples. The inputs are candidate virtual training samples for M3-UL. (a) Distance evolution of X1, X3 and X5 on layer N1; (b) distance evolution of Y1, Y3 and Y5 on layer N2.

Fig. 11. Inter-layer weights of winning neurons representing Hλx and Nsim,lsim of one virtual training sample {X3(λx),Y3}. Numbers on the edges of N1 and N2 represent the sequence number of the neurons. (a) Inter-layer connections of winning neuron No.17 on layer N1; (b) inter-layer connections of winning neuron No.55 on layer N2.

Fig. 12. Evolution of inter-layer weight of winning neuron No. 55 on layer N2 representing Y3 X3.

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