NUSOD Blog

Connecting Theory and Practice in Optoelectronics

Testing an Artificial Neural Network (ANN)

On an almost daily basis, NUSODnews tweets about new publications in our field. The paper our readers visited most often in 2019 is about a machine learning approach to photonic crystal fiber (PCF) design. The authors employ an artificial neural network (ANN) to predict a set of fiber properties (output) based on a set of input design parameters (see picture). This looks like a reasonable project, I thought, and a good chance to test an ANN, since the correct output can be obtained by numerical simulation using PCF theory.

ANN connecting optical fiber design parameters (input) to fiber properties (output).

The basic math behind ANNs is actually not that complicated, if you are familiar with matrix calculus. An instructive animated ANN introduction is available on YouTube. The ANN simply transforms a set of input numbers into a set of output numbers, as illustrated in the picture. Initially, this output is arbitrary and meaningless. But its deviation from a known correct output is used to adjust internal matrix coefficients (“training”). Such adjustments are repeated many times until the output error (“cost”) is small enough. A large number of examples with known output is needed to train an ANN for any given purpose.

In the above paper, more than 1000 different fiber designs have been first simulated numerically to provide training examples. For each set of input design parameters, the four fiber properties are calculated based on PCF theory. During the subsequent ANN training, up to 5000 adjustment cycles (“epochs”) are performed per example. After the training is completed, the ANN is tested by predicting the fiber properties for new sets of design parameters, for which the correct output was also calculated for comparison. However, this initial ANN test delivered mixed results.

The effective index predicted by the ANN was fairly close to the exact calculation. But poor agreement was observed for the three other fiber properties, even after 5000 adjustment cycles, which was attributed to insufficient training examples. Better ANN predictions are achieved by adding specific training examples or by restructuring some training data. The authors point out that quite accurate ANN predictions are finally obtained within milliseconds while exact simulations require several minutes of computing time. But they seem to neglect the many hours of simulation time necessary to generate more than 1000 training examples.

My main conclusion is that any user of an ANN should have access to correct results for ANN testing and be able to re-train the ANN if needed. Well-trained ANNs enable very fast design optimizations in a multi-dimensional parameter space. But the time-consuming ANN training only makes sense, in my view, if such optimizations are routinely performed within the exact same design space. However, scientific discoveries seem impossible this way because ANNs simply interpolate between known results.

Reference: Sunny Chugh, Aamir Gulistan, Souvik Ghosh, and B. M. A. Rahman: Machine learning approach for computing optical properties of a photonic crystal fiber, Optics Express, Vol. 27, Issue 25, pp. 36414-36425 (2019)

UPDATE 1/15/20: The authors provide more details about their methods here, as well as insight into ANN pitfalls.

Energy Efficiency Comparison of GaN-based Light Sources

GaN-based blue light emitters are in demand for applications in lighting, displays, communication, data storage, medical equipment and other fields. High energy efficiency is a key requirement in many cases. GaN-based light emitting diodes (LEDs) can transform more than 80% of the electrical input power into light output power. GaN-based laser diodes reach about half that value. But less than 10% energy efficiency is reported for blue superluminescent LEDs (SLEDs) which are attractive light sources, e.g., for virtual / augmented reality displays.

Most publications focus on the efficiency droop, i.e., the relative efficiency reduction with rising input current (see figure). However, the absolute efficiency is often of greater importance. We recently investigated limitations of the peak efficiency in order to explain the surprising discrepancy between different emitter types.[1,2]

Our analysis reveals that the peak energy efficiency is strongly influenced by the input current. Lasers and SLEDs require a much higher current density so that their electrical efficiency is lower (see figure).[2] In other words, the electrical resistance causes a severe energy loss of injected electrons on their way to the light-generating quantum wells. In addition, SLEDs suffer more than laser diodes from Auger recombination due to their higher quantum well carrier density.[1] Remedies are discussed in the references below.

[1] Optical and Quantum Electronics 51:382 (2019)

[2] Journal of Solid State Science and Technology 9:015008 (2020)

Should we trust artificial intelligence?

Artificial intelligence (AI) is gaining increasing control over our lives. ‘Intelligence’ suggest trustworthiness, but hardly anyone understands how these AI systems work, including myself. Benefits & risks are being debated and recent airplane crashes intensify this discussion.

In order to gather some insight, I started looking at AI methods in my own field, numerical simulation of optoelectronic devices (NUSOD). At first, I assumed that traditional NUSOD is a good example for AI, since it enables computers to predict the performance of real devices. However, I was skeptical about the term ‘intelligence’ because experts know that such predictions can easily be wrong if models or input data are incorrect.

Fortunately, our 2019 NUSOD conference featured several AI papers as well as a rump session about AI methods. To my surprise, the discussion revealed that modern AI often ignores much of our existing know-how. Instead, AI is required to learn from scratch how to find a specific answer, based on artificial neural networks (ANNs) which are inspired by the human brain. But an ANN only handles numbers and does not understand their meaning. Many examples are needed to train an ANN. If trained well, ANNs find answers much faster than traditional methods. They are also able to analyze huge data sets. In fact, ANNs represent a modern type of statistics. The output is solely determined by the training and it may suffer, e.g., from overfitting or underfitting. But the ANN decision process remains in the dark. Results are not explained.

In my view, all this makes ANNs less reliable than conventional numerical methods. In other words, I think we should never give up on our own intelligence.

UPDATE 11/8/19: AI’s dramatic social implications are investigated in this PBS report.

UPDATE 11/25/19: The difference between machine learning and AI is discussed here.

On a Database of Simulated TEM Images for In(Ga)As/GaAs Quantum Dots with Various Shapes

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Quantum dot geometry and FEM mesh (top) and simulated TEM image (bottom)

The fabrication of semiconductor quantum dots (QDs) with desired electronic properties would highly benefit from the assessment of QD geometry, distribution, and strain profile in a feedback loop between epitaxial growth and analysis of their properties. In [1, 2] we introduced a novel concept for 3D model-based geometry reconstruction (MBGR) of QDs from TEM imaging (see NUSOD 2018 blog). The approach is based on (a) an appropriate model for the QD configuration in real space including a categorization of QD shapes (e.g., pyramidal or lens-shaped) and continuous parameters (e.g., size, height), (b) a database of simulated TEM images covering a large number of possible QD configurations and image acquisition parameters (e.g. bright field/dark field, sample tilt), as well as (c) a statistical procedure for the estimation of QD properties and classification of QD types based on acquired TEM image data.
Here we present a database of simulated transmission electron microscopy (TEM) images for In(Ga)As quantum dots (QDs) embedded in bulk-like GaAs samples. The database contains series of TEM images for QDs with various shapes, e.g. pyramidal and lens-shaped, depending on the size and indium concentration as well as on the excitation conditions of the electron beam.
For the generation of TEM images for the database we use a parametric geometry description of the QD shape, e.g. using base length and height of the QD. In the database the geometrical model, the computed strain profile, the multi-beam solution as obtained by the solution of the Darwin-Howie-Whelan equations and the resulting TEM images are stored together with necessary meta data. Our aim is a comprehensive database covering all the different types and shapes of QDs as introduced in [3].

More details will be presented at the NUSOD 2019 conference in Ottawa (paper MB2).

References

  1. T. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow and J. Polzehl, Towards Model-Based Geometry Reconstruction of Quantum Dots from TEM, 2018 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), pp. 115-116, 2018. DOI: 10.1109/NUSOD.2018.8570246
  2. A. Maltsi, T. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, Proc. Appl. Math. Mech., vol. 18, e201800398, 2018. DOI: 10.1002/pamm.201800398
  3. A. Schliwa, M. Winkelnkemper, D. Bimberg, Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots,
    Phys. Rev. B, vol. 76, 205324, 2007. DOI: 10.1103/PhysRevB.76.205324

Atomistic Analysis of transport properties of InGaN/GaN multi-quantum wells

InGaN/GaN based devices are of interest for realizing light emitting diodes (LEDs) that emit in the visible spectral range. However, even though InGaN based LEDs have some widespread applications, several underlying physical phenomena are still not fully understood, for instance, the “droop” effect [1]. Therefore, the full potential of these LEDs for energy efficient lighting applications has yet to be exploited.

Often, when investigating transport through such systems, the device is described by average parameters and the underlying microscopic structure is neglected. Both experimental and theoretical studies have shown that alloy fluctuations have a significant influence on the electronic and optical properties of these systems [2]. Standard approaches do not capture these phenomena. Therefore, we aim to investigate the impact of the underlying alloy microstructure on transport properties of nitride-based devices in a combined atomistic and quantum mechanical picture.

Figure 1. (a) Side view of model system. (b) Dimensions of the supercell used.

The electronic structure calculations are performed using an sp3 TB model [3]. This allows us to capture fluctuations due to a (random) Indium atom distribution in the QW regions in a 3-dimensional frame. The resulting Hamiltonian is used as input to the Non-Equilibrium Green’s function solver OMEN [4] in order to compute transport properties in a quantum mechanical framework. Figure 1 shows a model system used containing two InGaN/GaN QWs with 15% Indium content.

We focus our attention on transmission probabilities and how this changes with alloy composition. More specifically, we compare results from virtual crystal approximation (VCA) calculations with then outcome of atomistic calculations in which the “level of randomness” changes. We turn our attention initially to electrons and later to hole transport properties.

Our calculations show that random alloy fluctuations can significantly affect transmission probabilities, leading for instance to a broadening and a reduction of these probabilities when compared to VCA calculations.

More details will be presented at the NUSOD 2019 conference in Ottawa (paper MB4).

References

[1] J. Piprek, “How to decide between competing efficiency droop models for GaN-based light- emitting diodes” Appl. Phys. Lett. 107, 031101 (2015)

[2] P. Dawson, et al., “The nature of carrier localisation in polar and nonpolar InGaN/GaN quantum wells”, J. Appl. Phys. 119, 181505 (2016)

[3] S. Schulz, et al., “Atomistic analysis of the impact of alloy and well-width fluctuations on the electronic and optical properties of InGaN/GaN quantum wells”, Phys. Rev. B. 91 035439 (2015)

[4] M. Luisier, et al., “Atomistic simulation of nanowires in the sp3d5s* tight-binding formalism: From boundary conditions to strain calculation”, Phys. Rev. B. 74, 205323, (2006)