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*3.2. Complexity Features Based on Huffman-Multi-Scale Entropy (HMSE)*

Sample entropy (SampEn) is a new time series complexity characterization parameter proposed by Richman et al. in 2004 [31]. The sample entropy is improved on the basis of approximate entropy, both of which measure the complexity of the time series and the probability of a new pattern generated by the sequence when the dimensionality changes. The greater the probability of generating a new pattern, the more complex the sequence and the higher the entropy value. Compared with other nonlinear dynamic methods such as Lyapunov exponent, information entropy, and correlation dimension, sample entropy has the advantages of short data, strong anti-noise and anti-interference ability, and good consistency within a large range of parameters. Therefore, it has attracted the attention of many scholars and has been frequently used in the field of mechanical signal analysis and fault diagnosis in recent years.

#### 3.2.1. Traditional Multi-Scale Sample Entropy (MSE)

Suppose a time series of length *N* is *X* = {*x*1, *x*2, ··· , *xN*−1, *xN*}, and the calculation method of sample entropy is as follows:

Step 1: Construct the time series X into an *m*-dimensional vector:

$$X(i) = \{x\_i, x\_{i+1} \cdot \dots \cdot, x\_{i+m-1}\}, \ i = 1, 2, \dots, N - m + 1\tag{9}$$

Step 2: Define the distance between *X*(*i*) and *X*(*j*) as *d*[*X*(*i*), *X*(*j*)], (*i* = *j*), which is the largest difference between the two corresponding elements:

$$d[X(i), X(j)] = \max\_{k \in (0, m-1)} \left| \mathbf{x}(i+k) - \mathbf{x}(j+k) \right|\_{\prime} \text{ ( $i \neq j$ )}\tag{10}$$

Step 3: Given a threshold *r* > 0, count the number of *d*[*X*(*i*), *X*(*j*)] < *r* and calculate the ratio to the total number of vectors *N* − *m*:

$$B\_i^m(r) = \frac{1}{N - m} num\{d[X(i), X(j)] < r\} \tag{11}$$

Step 4: Average all the results obtained by Equation (12):

$$B^{m}(r) = \frac{1}{N - m + 1} \sum\_{i=1}^{N-m+1} B\_i^{m}(r) \tag{12}$$

Step 5: Then m = m + 1, repeat Step1–Step4.

Step 6: Then theoretically the sample entropy of this sequence is:

$$SampEn(m,r) = \lim\_{N \to \infty} \left\{ -\ln(\frac{B^{m+1}(r)}{B^m(r)}) \right\} \tag{13}$$

However, *N* cannot be infinite in fact, but a finite value. The estimated value of sample entropy is:

$$Samp\mathbb{E}n(m,r,N) = -\ln(\frac{B^{m+1}(r)}{B^m(r)})\tag{14}$$

The sample entropy does not include the comparison of its own data segments, which not only improves the calculation accuracy and saves the calculation time, but also makes the calculation of the sample entropy independent of the data length. In addition, the sample entropy has better consistency. In other words, if one sequence has a higher SampEn than another sequence, then when the parameters *m* and *r* are changed, the sequence still has a relatively high SampEn value. However, the disadvantage of sample entropy is that it does not consider the different time scales that may exist in the time series.

To calculate the complexity of the signal at different time scales, Costa et al. proposed multi-scale entropy [32], which aims to extend the sample entropy to multiple time scales to provide additional observation perspectives when the time scale is uncertain. Like other entropy measurement methods, the goal of multi-scale entropy is to evaluate the complexity of time series. One of the main reasons for using multi-scale entropy is that the relevant time scale in the time series is not known. For example, when analyzing a speech signal, it is more effective to count the complexity of the signal under the word time scale than the complexity of the entire speech segment. However, the actual situation is that we often cannot know how many words a certain speech segment contains, or know what time scale should be used to obtain more useful information from the original signal. Therefore, analyzing the problem through multiple time scales will obtain more effective information.

The basic principle of multi-scale entropy (MSE) includes coarse-graining or downsampling the time series, so that the time series can be analyzed at increasingly coarse time resolutions. Given a time series *X* = {*x*1, *x*2, ··· , *xN*−1, *xN*} of length *N*, set the coarsegrained scale to *s*, then the original time series can be split into *i* consecutive segments without overlap, where *i* = *floor*(*N*/*s*), *floor*(∗) means taking the largest integer smaller than \*. The original sequence can be transformed into a new sequence by calculating the average value of each fragment by Equation (15). Then the MSE of the original sequence can be obtained by solving the sample entropy of the new sequence *Y* = {*y*1, *y*2, ··· , *yi*} obtained under different *s*. The process of coarse-graining the time series is shown in Figure 3.

$$y\_i = \frac{\sum\_{k=1}^{s} \mathcal{X}\_{(i-1)s+k}}{s} \tag{15}$$

**Figure 3.** The process of coarse-graining the time series.

#### 3.2.2. The Huffman-Multi-Scale Entropy (HMSE)

According to the process of the calculation of multi-scale sample entropy, the core of this method is to coarse-grain the original time series on different time scales by averaging. Figure 4a shows a satellite momentum wheel voltage telemetry signal with the length of 10,000. This signal is coarse-granulated and averaged on time scales *s* = 10, *s* = 50, and *s* = 100 respectively. The results are shown in Figure 4b–d. As can be seen from Figure 4, the waveform of the new signal obtained by averaging the original signal at different time scales is almost the same.

It can be seen from Figure 4 that the state of the signal changes at about the 4000th sample point in the original signal. However, the use of different coarse-grained scales cannot reflect the difference in signal changes. Therefore, this paper proposes a new improved multi-scale entropy calculation method based on the Huffman mean model. The main innovation of this method is that when the original data is coarse-grained on different time scales, the average value is not taken, but the Huffman average value is taken. This section will introduce the Huffman mean model and the improved multi-scale entropy calculation method based on the Huffman mean model in detail.

(1) Huffman Coding.

In 1952, Huffman proposed an optimum method of coding an ensemble of messages consisting of a finite number of members [33]. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized. The process of Huffman coding is as follows.

Step 1: Given a sequence containing *n* kinds of symbols. Suppose the set of symbol types is *S*0 = *s*0 1,*s*0 2, ··· ,*s*0 *i* , ···*s*0 *n* , *i* = 1, 2, ··· , *n*. The probability of each symbol appearing is *P*0 = *p*0 1, *p*0 2, ··· , *p*0 *i* , ··· *p*0 *n* , *i* = 1, 2, ··· , *n*, and *n* ∑ *i*=1 *p*0 *i* = 1.

Step 2: Set the iteration parameter to *t*, the maximum value of t is *n* − 1 and the initial value of *t* is 0. The symbol sequence and the corresponding probability at the beginning of the *k*-th iteration are *Sk*−1 and *Pk*−1. The symbol sequence and the corresponding probability at the end of the *k*-th iteration are *Sk* and *Pk*.

**Figure 4.** The average value of voltage telemetry under different scales: (**a**) original signal, (**b**) scale = 10, (**c**) scale = 50, (**d**) scale = 100.

Step 3: When *t* = *k*, arrange the symbol *Sk*−1 in ascending order of probability *Pk*−1 as *Sk*−1 = *sk*−1 1 ,*sk*−1 2 , ··· ,*sk*−1 *i* , ···*sk*−1 *n*−*k*+1 . Then the probability *Pk*−1 is also rearranged accordingly as *Pk*−1 = *pk*−1 1 , *pk*−1 2 , ··· , *pk*−1 *i* , ··· *pk*−1 *n*−*k*+1 .

Step 4: Take the two symbols *sk*−1 1 and *sk*−1 2 with the least probability in the symbols sequence. Encode the symbol *sk*−1 2 with higher probability into "1" and the symbol *sk*−1 1 with lower probability as "0". Add the probabilities *pk*−1 1 and *pk*−1 2 of the *sk*−1 1 and *sk*−1 2 as the probability *p*∗ of the new symbol *s*∗.

Step 5: Delete *sk*−1 1 and *sk*−1 2 from *Sk*−1, and add *s*∗ into *Sk*−1. Then the *Sk*−1 turns into *Sk*, and the size of *Sk* is *n* − *k*. Delete *pk*−1 1 and *pk*−1 2 from *Pk*−1, and add *p*∗ into *Pk*−1. Then the *Pk*−1 turns into *Pk*, and the size of *Pk* is also *n* − *k*.

Step 6: Repeat the Step 3 to Step 5 until *t* = *n* − 1. Then the symbols sequence will be *Sn*−1 = *sn*−1 1 and the probability will be *Pn*−1 = *pn*−1 1 , *pn*−1 1 = 1.

It can be seen from the above coding process that the symbol with the lower probability in the original signal has the longer Huffman code length. Conversely, the symbol with the higher probability has the shorter Huffman code length. The complexity of the probability distribution of the signal can be described by solving the Huffman average code length of the original signal. Based on the above-mentioned Huffman coding process, the method to further calculate the average Huffman coding length is as follows.

Backtrack from the symbol *sn*−1 1 with the probability of *pn*−1 1 = 1 to each source symbol and record 0/1 in the backtracking path. The Huffman code of *s*0 *i* is *ci*. The average Huffman coding length *L*∗ can be calculated according to the length of *ci* and the corresponding probability *p*0 *i* as Equation (16). *L*(*ci*) is the length of *ci*.

$$L^\* = \sum\_{i=1}^n p\_i^0 \ast L(c\_i) \tag{16}$$

For a set of source symbols *S*0 = {*s*1,*s*2,*s*3,*s*4,*s*5,*s*6} with probability *P*0 = {0.35,0.28, 0.14,0.13,0.07,0.03} , the process of Huffman coding is shown in Table 2. The average Huffman coding length of *S*0 can be calculated as 2.33 as follows.

$$L^\*(S\_0) = (0.35 + 0.28 + 0.14) \ast 2 + 0.13 \ast 3 + (0.07 + 0.03) \ast 4 = 2.33$$

**Table 2.** An example of the Huffman coding process.

(2) Huffman Mean Model.

The basic principle of Huffman coding and the calculation method for solving the average Huffman coding length were introduced above. In this paper, a new Huffman mean model based on the Huffman coding is proposed for the problem of satellite anomaly detection. For a sequence *T* = {*t*1, *t*2, ··· , *ti*, ··· , *tn*}, the expression of the Huffman mean model is shown in Equation (17).

$$HM(T) = \begin{cases} \begin{array}{l} T' = T/sum(T) \\ \text{C} = Huffman\\_coding(T')\\ \ell = L(\text{C}) \\\ Huffman\\_mean = sum(T\*(\ell/sum(\ell))) \end{array} \end{cases} \tag{17}$$

where *HM*(*T*) is the Huffman mean value of *T*, *T* = *T*/*sum*(*T*) means to convert the original time series into a probability series, *C* = *Huf f man*\_*coding*(*T* ) represents the Huffman coding result of the probability sequence *T* , *C* = {*c*1, *c*2, ··· , *ci*, ··· , *cn*}, *i* = 1, 2, ··· , *n*, *ci* is the Huffman code corresponding to *ti* in the original sequence, - = *L*(*C*) means to calculate the length of each *ci*, *Huf f man*\_*mean* = *sum*(*T* ∗ (-/*sum*(-))) represents the Huffman mean value of the sequence *T* considering the length weight of the Huffman code.

(3) The Improved Method of Huffman-multi-scale Entropy.

The Figure 5 shows the calculation process of Huffman-multi-scale entropy. The inputs of both two methods are original signal *X* = {*x*1, *x*2, ··· , *xN*−1, *xN*}, the scale sequence *Scale* = *s*1,*s*2, ··· ,*sp* and the parameter set *θ* = {*m*,*r*}, usually 0.1*std*(*X*) < *r* < 0.2*std*(*X*). Compared with the classic MSE, the Huffman-multi-scale entropy method proposed in this paper adopts the coarse-grained method based on the Huffman mean model.

**Figure 5.** The process of the improved method of Huffman-multi-scale Entropy.

Figure 6 shows the same satellite momentum wheel voltage telemetry signal with the length of 10,000. This signal is coarse-granulated and calculated by Huffman mean model on time scales *s* = 10, *s* = 50, and *s* = 100, respectively. Obviously, the coarse-grained method based on the Huffman mean model can enhance the difference of signal changes at different time scales.

**Figure 6.** The Huffman average code length of voltage telemetry under different scales: (**a**) original signal, (**b**) scale = 10, (**c**) scale = 50, (**d**) scale = 100.

#### **4. Anomaly Detection Method Based on Multi-Class SVM**

#### *4.1. Multi-Class SVM*

A support vector machine (SVM) is widely used in classification problems. The basic idea is to find a hyperplane so that all sample points in the positive and negative categories are farthest from the plane, and points that are far enough from the plane can basically be correctly classified. Therefore, if the points closer to the hyperplane are as far away as possible from the hyperplane, a better classification effect can be achieved.

This article uses the most interval classifier to achieve two-class SVM, and then uses the directed acyclic graph (DAG) method to achieve the multi-class SVM based on twoclass SVM.

Set the dataset as {(*xi*, *yi*)|*i* = 1, 2, ··· , *N*}, *xi* ∈ *Rn*, *y* ∈ {−1, +1}, the hyperplane is *wTx* + *b* = 0, Then the distance from the support vector to the hyperplane is *wTx* + *b* = *y*, which can be written as

$$\frac{|y(w^T\mathbf{x}+b)|}{||w||\_2} = \frac{1}{||w||\_2} \tag{18}$$

The SVM model keeps all the points on both sides of the support vector of their respective categories, while keeping away from this hyperplane. It can be seen from Equation (18) that when ||*w*||2 is the smallest, the interval is the largest. Introduce the penalty parameter *λ* for misclassification and the relaxation factor *ξ* that allows misclassification, and the objective function can be

$$\begin{array}{c} \min\_{\mathbb{Z}} \frac{1}{2}||w||\_2^2 + \lambda \sum\_{i=1}^N \mathbb{Z}\_i \\ \text{s.t.} \quad y^i(w^T x + b) \ge 1 - \mathbb{Z}\_{i\prime} i = 1, 2, \cdots, N \\ \mathbb{Z}\_i^x \ge 0, i = 1, 2, \cdots, N \end{array} \tag{19}$$

According to Lagrange's duality, the optimization objective can be converted into an equivalent dual problem. The Equation (19) can be transformed into:

$$\begin{aligned} \min\_{\boldsymbol{a}} & \frac{1}{2} \sum\_{i,j=1}^{N} y\_i y\_j \boldsymbol{a}\_i \boldsymbol{a}\_j \boldsymbol{\mathcal{K}} \langle \boldsymbol{x}\_i, \boldsymbol{x} \rangle - \sum\_{j=1}^{N} \boldsymbol{a}\_j \\ \text{s.t.} & \quad y^i (\boldsymbol{w}^T \boldsymbol{x} + \boldsymbol{b}) \ge 1 - \xi\_i, i = 1, 2, \dots, N \\ & \quad \xi\_i^z \ge 0, i = 1, 2, \dots, N \end{aligned} \tag{20}$$

where *K xi*, *x* is the kernel function. The radial basis function is used as the kernel function in this paper, *K xi*, *x* = exp −||*xi*−*x*||2 2*σ*2 , *σ* is the kernel function parameter. Then the decision function is

$$f(\mathbf{x}) = w^T \mathbf{x} + b = \text{sgn}[\sum\_{i=1}^{N} y\_i \mathbb{1}\_i \mathbb{K} \langle \mathbf{x}\_i, \mathbf{x} \rangle + b], 0 < \alpha\_i < \lambda \tag{21}$$

Among the multi-class SVM methods, one is the direct solution method, but this method has high time complexity and is difficult to implement. It is not suitable for a large amount of data. The other one is to combine multiple two-class SVM models into a multi-class SVM model. In this paper, a directed acyclic graph method is used to construct a multi-class SVM.

The DAG method uses the "competition" rule. For *n* types, the height of the decision tree is *n* − 1. Put the classes that are easy to distinguish on the upper layer, and the classes that are difficult to distinguish on the lower layer. The schematic diagram of DAG method for five-class SVM is shown in Figure 7.

**Figure 7.** The schematic diagram of DAG method for five-class SVM model.


**5. Conclusion**

344 Microelectromechanical Systems and Devices

heat dissipation to the underlying substrate, permits the single layer structure to exhibit

increased robustness to the laser irradiation compared to the multilayered structures. The optical-thermal effects can also explain the temperature discontinuities observed in the temperature measurements of laser irradiated cantilevers and actuators (Serrano & Phinney, 2007; Serrano et al., 2009), shown in Fig. 9. As predicted above, the discontinuity corresponds to the presence of the peak in the absorptance curve. The surface temperature increases rapidly by 200 K as the peak is encountered. The temperature-power relationship regains a linear relation after the temperature reaches the opposite side of the absorptance peak. Numerical simulations of this experiment, utilizing the non-linear absorptance and known material and geometrical parameters for the irradiated structure, are in good agreement with the measured values, reproducing temperature discontinuity. This type of sudden increase in the temperature makes predicting a threshold power for laser damage in polysilicon structures extremely challenging without accurate knowledge of optical and

Fig. 10. Measured and modeled temperatures of a polysilicon MEMS structure measured irradiated with an λ = 808 nm laser. The discontinuity in the temperature results from a peak in the absorptance of the irradiated layer due to thin film interference effects

dimensional properties.

(Serrano et al., 2009).

Understanding the thermal and optical response of laser-irradiated microsystems requires careful consideration of not only the individual thermal, optical, and mechanical parameters, but also the coupling that exists between them. Of particular importance is the impact that the change in the optical properties with temperature can have in the performance and reliability of these structures. To gain insight into the role that temperature and geometry play in the optical performance of these devices, one must utilize the basic optical relations in a way that is compatible with thermal analyses of a laser-heated structure. The LTR method has proven to be a very useful technique in these types of analyses since it can easily incorporate temperature dependant optical properties and readily provide the interlayer absorptances for the irradiated structures.

Once the temperature and optical fields are coupled in the analysis, a more accurate picture emerges of the thermal and optical behavior of the irradiated device. These coupled optical-thermal effects give rise to non-linear absorptance that can, in some instances, lead to increased resistance to laser damage by dynamically reducing the absorptance as the incident laser power is increased, while in other cases, the nonlinear effects compound to enhance absorptance of the incident laser energy producing rapid temperature increases that eventually lead to device damage. A quantitative estimation of device robustness to determine in which regime of damage susceptibility a particular structure resides in therefore requires a complete description of the overall irradiating conditions as well as the device composition. For polysilicon-based devices, this type of analysis has shown reasonable agreement with the experimentally-observed thermal behavior, and can explain the observed damage trends of the laser-irradiated structures.

### **6. Acknowledgment**

The authors would like to acknowledge the help and assistance of Allen Gorby, James Rogers, Wayne Trott, and Jaime Castaneda. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

### **7. References**

Optical-Thermal Phenomena in Polycrystalline Silicon MEMS During Laser Irradiation 347

Oliver, A. D., Vigil, S. R. & Gianchandani, Y. B. (2003). Photothermal surface-micromachined actuators. *IEEE Transactions on Electron Devices,* Vol. 50, No. 4, pp. 1156-1157 Phinney, L. M., Klody, K. A., Sackos, J. T. & Walraven, J. A., (2005). Damage of MEMS

Phinney, L. M. & Serrano, J. R. (2007). Influence of target design on the damage threshold for

Phinney, L. M., Spahn, O. B. & Wong, C. C. (2006). Experimental and computational study

Plass, R. A., Baker, M. S. & Walraven, J. A. (2004). Electrothermal actuator reliability studies.

Sassen, W. P., Henneken, V. A., Tichem, M. & Sarro, P. M. (2008). Contoured thermal V-

Schulz, L. G. (1954). The Optical Constants of Silver, Gold, Copper, and Aluminum. I. The

Serrano, J. R. & Phinney, L. M. (2008). Displacement and Thermal Performance of Laser-

Serrano, J. R. & Phinney, L. M. (2009). Effects of layers and vias on continuous-wave laser

Serrano, J. R., Phinney, L. M. & Brooks, C. F. (2005). Laser-Induced damage of

Serrano, J. R., Phinney, L. M. & Rogers, J. W. (2009). Temperature amplification during laser

Sun, B. K., Zhang, X. & Grigoropoulos, C. P. (1997). Spectral optical functions of silicon in

Wong, C. N. C. & Graham, S. (2003). Investigating the thermal response of a micro-optical

Xu, X. & Grigoropoulos, C. P. (1993). High temperature radiative properties of thin

*Micro/Nanolithography, MEMS and MOEMS,* Vol. 8, No. 4, pp. 043030 Serrano, J. R. & Phinney, L. M. (2007). Micro-Raman thermometry of laser heated surfaces.

*Proceedings of ASME InterPACK 2007,* Vancouver, BC, Canada

88

2, pp. 538-543

6111, pp. 611108

357-362

17, No. 1, pp. 166-174

pp. 2255-2264

pp. 324-331

*Proceedings of SPIE,* Vol. 5343, pp. 15-21

*Physical,* Vol. 144, No. 2, pp. 341-347

*InterPACK 2005,* San Franscisco, CA, USA

*Mass Transfer,* Vol. 40, No. 7, pp. 1591-1600

*Mass Transfer,* Vol. 36, No. 17, pp. 4163-4172

thermal actuators heated by laser irradiation. *Proceedings of SPIE,* Vol. 5716, pp. 81-

optically powered MEMS thermal actuators. *Sensors and Actuators A,* Vol. 134, No.

on laser heating of surface micromachined cantilevers. *Proceedings of SPIE,* Vol.

beam actuator with improved temperature uniformity. *Sensors and Actuators A:*

Absorption Coefficient k. *Journal of the Optical Society of America,* Vol. 44, No. 5, pp.

Heated Asymmetric MEMS Actuators. *Journal of Microelectromechanical Systems,* Vol.

heating and damage of surface-micromachined structures. *Journal of*

polycrystalline silicon optically powered MEMS actuators. *Proceedings of ASME*

heating of polycrystalline silicon microcantilevers due to temperature-dependent optical properties. *International Journal of Heat and Mass Transfer,* Vol. 52, No. 9-10,

the range of 1.13-4.96 eV at elevated temperatures. *International Journal of Heat and*

shutter. *IEEE Transactions on Components and Packaging Technologies,* Vol. 26, No. 2,

polysilicon films at the = 0.6328 m wavelength. *International Journal of Heat and*

Baglio, S., Castorina, S., Fortuna, L. & Savalli, N. (2002). Novel microactuators based on a

Baker, M. S., Plass, R. A., Headley, T. J. & Walraven, J. A., (2004), *Final Report: Compliant*

Born, M. & Wolf, E. (1999). Principles of Optics: Electromagnetic Theory of Propagation,

Burns, D. M. & Bright, V. M. (1998). Optical power induced damage to

Carter, J., Cowen, A., Hardy, B., Mahadevan, R., Stonefield, M. & Wilcenski, S., (2005),

Gallis, M. A., Torczynski, J. R. & Rader, D. J. (2007). A computational investigation of

Jellison Jr, G. E. & Modine, F. A. (1982a). Optical absorption of silicon between 1.6 and 4.7 eV at elevated temperatures. *Applied Physics Letters,* Vol. 41, No. 2, pp. 180-182 Jellison Jr, G. E. & Modine, F. A. (1982b). Optical constants for silicon at 300 and 10 K

Jellison Jr, G. E. & Modine, F. A. (1983). Optical functions of silicon between 1.7 and 4.7 eV at elevated temperatures. *Physical Review B,* Vol. 27, No. 12, pp. 7466-7472 Katsidis, C. C. & Siapkas, D. I. (2002). General Transfer-Matrix Method for Optical

Knoernschild, C., Changsoon, K., Gregory, C. W., Lu, F. P. & Jungsang, K. (2010).

Knoernschild, C., Kim, C., Lu, F. P. & Kim, J. (2009). Multiplexed broadband beam steering

Lubberts, G., Burkey, B. C., Moser, F. & Trabka, E. A. (1981). Optical properties of

Mazilu, M., Miller, A. & Donchev, V. T. (2001). Modular Method for Calculation of

MEMS Technologies Department, (2008), *SUMMiT V™ Five Level Surface Micromachining*

*PolyMUMPs Design Handbook, Revision 11.0,* MEMSCAP, Inc.

National Laboratories, Albuquerque, New Mexico

FL, USA

Cambridge

6-14

68

7244

No. 5, pp. 3745-3753

No. 11, pp. 6870-6878

36, pp. 6670-6676

*Applied Optics,* Vol. 41, No. 19, pp. 3978-3987

*Microelectromechanical Systems,* Vol. 19, No. 3, pp. 640-646

Sandia National Laboratories, Albuquerque, NM

photo-thermo-mechanical actuation strategy. *Proceedings of IEEE Sensors*, Orlando,

*Thermo-Mechanical MEMS Actuators LDRD #52553*, SAND2004-6635, Sandia

Interference and Diffraction of Light (7th edition), Cambridge University Press,

microelectromechanical mirrors. *Sensors and Actuators A,* Vol. 70, No. 1-2, pp.

noncontinuum gas-phase heat transfer between a heated microbeam and the adjacent ambient substrate. *Sensors and Actuators A: Physical,* Vol. 134, No. 1, pp. 57-

determined from 1.64 to 4.73 eV by ellipsometry. *Journal of Applied Physics,* Vol. 53,

Multilayer Systems with Coherent, Partially Coherent, and Incoherent Interference.

Investigation of Optical Power Tolerance for MEMS Mirrors. *Journal of*

system utilizing high speed MEMS mirrors. *Optics Express,* Vol. 17, No. 9, pp. 7233-

phosphorus-doped polycrystalline silicon layers. *Journal of Applied Physics,* Vol. 52,

Transmission and Reflection in Multilayered Structures. *Applied Optics,* Vol. 40, No.

*Technology Design Manual: Version 3.1a*, Sandia Report No. SAND2008-0659P,

**Part 4**

**MEMS Based Actuators**

Yavas, O., Do, N., Tam, A. C., Leung, P. T., Leung, W. P., Park, H. K., Grigoropoulos, C. P., Boneberg, J. & Leiderer, P. (1993). Temperature dependence of optical properties for amorphous silicon at wavelengths of 632.8 and 752 nm. *Optics Letters,* Vol. 18, No. 7, pp. 540-542

**Part 4**

**MEMS Based Actuators**

348 Microelectromechanical Systems and Devices

Yavas, O., Do, N., Tam, A. C., Leung, P. T., Leung, W. P., Park, H. K., Grigoropoulos, C. P.,

No. 7, pp. 540-542

Boneberg, J. & Leiderer, P. (1993). Temperature dependence of optical properties for amorphous silicon at wavelengths of 632.8 and 752 nm. *Optics Letters,* Vol. 18,

**14**

*Portugal*

J. Pérez de la Cruz

**Piezoelectric Thick Films:**

**Preparation and Characterization**

*INESC Porto - Institute for Systems and Computer Engineering of Porto, Porto,*

Sol-gel technology allows the deposition of 1m thick oxide films onto a variety of substrates at temperatures well below those conventionally used for bulk ceramic processing. Thin film processing temperatures as low as 500-700oC are typically used allowing ceramic materials to be incorporated into the silicon processing stages (Ohno et al., 2000; Wu et al., 1999). In addition, low processing temperatures reduce the inter-diffusion of atomic species between the different thin film layers and ionic vaporization, such as: lead in lead zirconate titanate oxide (PZT) films (Wu et al., 1999; Jeon et al., 2000). PZT thin films have been largely deposited in order to produce several types of devices, such as: membrane sensors, accelerometers and micromotors (Barrow et al., 1997). However, devices requiring larger actuation forces (i.e. high frequency transducers, vibration control devices) require thicker piezoelectric films (Tsurumi et al., 2000). In these cases, it is not practical to produce thick PZT films using standard sol-gel techniques, because of the increased cracking risk due to shrinkage nor is it desirable to produce thick films by a repetitive single layer

deposition process due to the time required (Barrow et al., 1995; Zhou et al., 2000).

thickness range that is difficult to achieve by other deposition techniques.

The interest in ferroelectric lead zirconate titanate thick films for device applications, including high-frequency ferroelectric sonar transducers (Bernstein et al., 1997), microelectromechanical system devices (Polla & Schiller, 1995; Myers et al., 2003; (Akasheh et al., 2004), elastic surface wave devices (Cicco et al., 1996), hydrophones (Chan et al., 1999) and sensors (Xia et al., 2001), has increased in the last decades because PZT ferroelectric thick films possess the merits of both bulk and thin film materials (Barrow et al., 1997; Ledermann et al., 2003). PZT thick films devices not only work at low voltage and high frequency, as they are compatible with semiconductor integrated circuit, but also possess superior electric properties approaching near-bulk values. Naturally, processing of PZT thick films has also become an increasingly popular research field. Some approaches that have recently been studied to process thick films include electrophoretic deposition (Corni et al., 2008), pulsed laser deposition (Yang et al., 2003), screen printing (Walter et al., 2002) and sol-gel (Xia et al., 2001; Wang et al., 2003; He et al., 2003). Among them, the hybrid sol-gel technique has a special interest due to its low preparation cost and excellent stoichiometric control. Sol-gel also offers the capability to lay down thick layers anywhere between 0.1m and 100m, a

**1. Introduction**


**2. Fermion Condensation**

The theory of FC has been described several times, see, e.g., [4,15,19,20]; nonetheless, for the readers' convenience, we briefly present this methodology. The usual approach to describe the ensembles of itinerant Fermi particles is the well-known Landau Fermi liquid theory [34,35]. This theory represents the real properties of a solid with itinerant electrons in terms of a Fermi gas of so-called quasiparticles with weak interaction. In this case, the quasiparticles represent the excited states of a solid or liquid states and are responsible for the low temperature thermodynamic, transport and relaxation properties of common metals. These quasiparticle excitations are characterized by the effective mass *M*∗, that is of the order of the bare mass of electron, *M*, and depends weakly on external parameters such as temperature *T*, magnetic field *B*, external pressure *P*, etc. [34,35]. However, the LFL theory cannot explain why the effective mass *M*∗ begins to depend strongly on the stimuli above and, for example, can even be a divergent function of magnetic field *B* or temperature *T*, see, e.g., [4,15,19,36]. Such a dependence is called the NFL behavior and is connected to the growth of the effective mass that occurs when the system approaches the topological fermion condensation quantum phase transition (FCQPT) leading to an FC state with flat bands [1,4,15,19]. Beyond the FCQPT, the system develops a flat band, formed by FC, and characterized by the topological charge that is different from both the topological charges of the Landau Fermi liquid (LFL) and marginal Fermi liquid, representing a new type of Fermi liquid [2,4,15,19,37]. Thus, the stability of FC is ensured by its topological charge, and it can be destroyed only by the first order phase transition, since the topological charge cannot acquire continuous values [2,15,19,37]. As a result of these unique properties of the FC state, a new state of matter is generated, represented by QSL, HF metals, quasicrystals, 2D liquids such as 3He and high-*Tc* superconductors, so that 1D, 2D and 3D strongly correlated Fermi systems exhibit universal scaling behavior irrespective of their microscopic structure [15,19,20,38,39].

The main feature of FC theory is the existence of one more instability channel (additional to those of Pomeranchuk) that cannot be described within the framework of the Landau theory of Fermi liquid [35]. Indeed, under some conditions, the effective mass *M*∗ of LFL quasiparticle diverges, see, e.g., [15,19]. As a result, to keep the finite and positive effective mass at zero and finite temperatures, the Fermi surface changes its topology: the Fermi surface transforms into a Fermi layer, as seen in Figure 1. This topological phase transition generates the effective mass dependence on temperature, magnetic field, etc. We assume, without loss of generality [15,19], that the Fermi liquid is homogeneous. That is, in our model we account for the most important and common features only, neglecting marginal effects related to the crystalline anisotropy of solids [15,19,20]. The Landau equation for the quasiparticle effective mass *M*∗ reads [15,34,35]

$$\frac{1}{M\_{\sigma}^\*(\mathbf{B}, T)} = -\frac{1}{M} + \sum\_{\sigma\_1} \int \frac{\mathbf{P}\_F \mathbf{P}}{p\_F^3} \mathbf{F}\_{\sigma, \sigma\_1}(p\_{F\_\sigma} p)$$

$$\times \quad \frac{\partial n\_{\sigma\_1}(\mathbf{p}\_\prime, T, B)}{\partial p} \frac{dp}{(2\pi)^3} \tag{3}$$

where *Fσ*,*σ*1 (*pF*, *p*) is the interaction function, introduced by Landau. The function *Fσ*,*σ*1 (*pF*, *p*), depending on momentum *p*, Fermi momentum *pF* and spin indices *σ*, *σ*1, has the form of

spherical harmonics with coefficients taken from the best fit to experiment. The fermion occupation number *n* in the Fermi–Dirac statistics reads

$$m\_{\sigma}(p,T) = \left\{ 1 + \exp\left[\frac{\left(\varepsilon\_{\sigma}(\mathbf{p}\_{\prime}T) - \mu\_{\sigma}\right)}{T}\right] \right\}^{-1},\tag{4}$$

where *εσ*(*p*, *T*) is the single-particle spectrum, and *μσ* is a spin-dependent chemical potential: *μσ* = *μ* ± *μBB* where *μB* is the Bohr magneton. The magnetic field dependence occurs due to the Zeeman splitting shifting the system from its topological FCQPT [15].

**Figure 1.** Diagram of flat bands near the FCQPT at zero temperature, *T* = 0. Panel (**a**) shows normal Fermi sphere and corresponding quasiparticles spectrum *ε*(*p*) *p*2/(2*M*) and occupation number *n*(*p*) being a step function. Panel (**b**) displays the system in the FC state after the topological FCQPT. The Fermi sphere alters its topology, which is shown schematically as an emergence of a spherical layer of the thickness *pf* − *pi*. In this case, the Fermi momentum *pF* is hidden inside the flat band, defined by the condition *ε*(*p*) = *μ* (7). This condition defines the flat band, shown as a dispersionless part of the spectrum *ε*(*p*) = *μ*, with *μ* being the chemical potential. The function *n*(*p*) decreases gradually from *n*(*pi*) = 1 to *n*(*pf*) = 0 without violating the Pauli exclusion principle.

The standard procedure for obtaining the single-particle spectrum *εσ*(*p*, *T*) in the Landau theory is to vary the system energy *E*[*nσ*(*p*, *T*)] with regard to the occupation number *n*

$$
\varepsilon\_{\sigma}(p, T) = \frac{\delta E[n(p)]}{\delta n\_{\sigma}(p)}.\tag{5}
$$

We note that the Landau interaction entering Equation (3) is not of a special form since it is fixed by the simple condition that the system is in the FCQPT point [15,19]. The explicit form of the variational Equation (5) reads

$$\frac{\partial \varepsilon\_{\sigma}(p, T)}{\partial p} = \frac{p}{M} - \sum\_{\sigma\_1} \int \frac{\partial F\_{\sigma, \sigma\_1}(p\_\prime, p\_1)}{\partial \mathbf{p}} n\_{\sigma\_1}(p\_1, T) \frac{d^3 p\_1}{(2\pi)^3 \prime} \tag{6}$$

Later on for simplicity, we omit the spin indexes *σ*. In the FC phase (i.e., beyond the FCQPT) at *T* = 0, Equation (5) takes the form [1]

$$
\varepsilon(p, T=0) = \mu, \ p\_i \le p \le p\_f; \ 0 \le n(p) \le 1. \tag{7}
$$

where *pi*, *f* stands for initial and final momenta (not to be confused with Fermi momentum *pF*), where the flat band resides, see Figure 1. Condition (7) defines the flat band since in this case the quasiparticles have no dispersion. By this virtue, quasiparticles have the Fermi velocity *VF* = 0 and at *T* = 0 are condensed with the same energy *ε*(*p*, *T* = 0) = *μ*, representing the superconducting state with the finite order parameter *κ*, while the superconducting gap Δ = 0, see Section 7. As this resembles the case of Bose condensation, the corresponding phenomenon is called fermion condensation, being separated from LFL by the first order phase transition [1,2,37]. The system with FC acquires properties, being very different from those of ordinary Fermi liquids, since the Fermi liquid with FC forms a new, topologically-protected (and thus "extremely stable") state of matter. This means that if FC is formed in a substance, it will define its properties at *T* = 0 and at elevated temperatures as well. Figure 1 visualizes (at *T* = 0) the consequences of the FCQPT on the Fermi surface, spectrum and occupation number of a Fermi liquid. The transformation from panel (a) (normal Fermi liquid) to panel (b) is represented by altering the Fermi surface topology so that in the normal Fermi liquid the layer of finite length *pf* − *pi* appears instead of the Fermi surface located at Fermi momentum *p* = *pF*. This immediately implies the emergence of the flat part of the spectrum defined by Equation (7), where all the condensed fermions are located. This, in turn, generates the gradual (instead of abrupt on the panel (a) decay of the occupation numbers *n*(*p*) from *n* = 1 at *p* < *pi* to *n* = 0 at *p* > *pf* .

Equations (3) and (7) allow one to determine the energy spectrum *εσ*(*p*, *T*) and occupation numbers *nσ*(*p*, *T*) in a self-consistent way. These quantities, in turn, permit the calculation of the effective mass, *pF*/*M*∗ = *∂ε*(*p*)/*∂p*|*p*=*pF* = *VF*. We emphasize that both magnetic field and temperature dependences of the effective mass *M*∗(*B*, *T*) in the FC phase come from Equation (3) and from the *T*, *B*-dependence of *εσ*(*p*) and *nσ*(*p*). Calculated (by Equations (3) and (7)) spectrum and occupation numbers [15] in the FC phase are reported in Figure 2. At (almost) zero temperature, the flat portion of the spectrum is clearly seen at *pi* < *p* < *pf* . This shape of the spectrum defines *n*(*p*) (Figure 2, panel (b)) in the form of "two steps", gradually decaying from one to zero. Simultaneously, at relatively high temperatures (equal to *T*/*EF* = 0.01, which at *EF* ∼ 1eV implies *T* 100 K) this part is rather strongly upward tilted. This shows that finite temperatures erode the FC state, making the effective mass *M*∗ finite, while the system acquires features similar to ordinary Fermi liquid [4,15].

To gain more insights into the physical properties of the FC state, it is helpful to explore the system behavior at *T* → 0. It was shown earlier [1,15,19] that the ground state of a system with FC is highly degenerate. In this case, the occupation numbers *n*0(*p*) of the FC state quasiparticles (i.e., having dispersionless spectrum or belonging to the flat band) change gradually from *n* = 1 to *n* = 0 at *T* = 0. This variation occurs at *pi* ≤ *p* ≤ *pf* . It is clear that such a property of the occupation numbers drastically differs from the property of the usual Fermi–Dirac function property at *T* = 0. Indeed, in that case, the Fermi–Dirac function is represented by the step function between *n* = 1 and *n* = 0 at *p* = *pF*, where *pF* stands for Fermi momentum, see Figure 1.

At *T* = 0, the infinite degeneracy of the ground state with FC leads to a *T*-independent entropy term [4,15], remaining finite at *T* = 0 in violation of the Nernst theorem

$$S\_0 = -\sum\_p [n\_0(p)\ln n\_0(p) + (1 - n\_0(p))\ln(1 - n\_0(p))].\tag{8}$$

**Figure 2.** Flat band induced by FC. The calculated single-particle spectrum (**a**) and the quasiparticle occupation number (**b**) at small but finite temperatures versus the dimensionless momentum *k* = *p*/*pF*, where *pF* is the Fermi momentum [15]. Temperature is measured in the units of *EF*. At *T* = 0.01*EF* and *T* = 0.0001*EF*, the vertical lines show the position of the Fermi level *EF* at which *n*(*k*, *T*) = 0.5 (see the horizontal line in panel (b)). At *T* = 0.0001*EF* (blue curve), the single-particle spectrum *ε*(*k*, *T*) is almost flat (marked "Flat band") in the range *k f* − *ki* (with *ki* = *pi*/*pF* and *k f* = *k f* /*pF* denoting, respectively, the initial and final momenta for FC realization, and *k* = *p*/*pF*). Thus, in the range *k f* − *ki* the density of states *N*0 → ∞, and outside the range *N*0 is finite. The distribution function *n*(*k*, *T*) becomes more asymmetric with respect to the Fermi level *EF*, generating the NFL behavior, and C invariance is broken. To illuminate the asymmetry, the area occupied by holes in panel (b) is labeled h (red) and that occupied by quasiparticles by *p* (maroon).

Thus, the infinite degeneracy of the FC ground state generated by flat bands, see Refs. [19,20] for a comprehensive discussion. We note that for systems where the Nernst theorem is violated due to the ground state degeneracy is a spin glass [40,41]. It is well known that in normal Fermi liquid the function *n*(*p*) at finite temperatures loses its steplike feature at *p* = *pF*, becoming continuous around this point. The same is valid for a Fermi liquid with flat bands; this conclusion follows from Equation (4). This means that at small but finite temperatures *T* = 0 the degeneracy of the above ground state is lifted, consequently the single-particle energy *ε*(*p*, *T* = 0) acquires a small dispersion [4]

$$
\varepsilon(p, T \to 0) = T \ln \frac{1 - n\_0(p)}{n\_0(\mathbf{p})}.\tag{9}
$$

From Equation (9), we see that the dispersion is proportional to *T* since the occupation numbers *n*0 approximately remain the same as at *T* = 0. This means that the entropy *S* in this case still remains *S*(*T*) ≥ *S*0. This situation also jeopardizes the Nernst theorem. To avoid this unphysical situation, the nearly flat bands representing the FC state should acquire dispersion in a way that the excess entropy *S*0 should "dissolve" as *T* → 0. This occurs by virtue of some additions to the FCQPT phase transition such as a ferromagnetic and/or a superconductive one, etc. [4,15,19]. Thus, at low temperatures the FC state has to be consumed by a number of phase transitions. This "consumption" can be viewed as a complicated phase diagram of an HF metal at its quantum critical point. In fact, at *T* = 0 the FC state is represented by the superconducting state with the superconducting order parameter *κ* = *n*(*p*)(1 − *n*(*p*)) that is finite in the region (*pi* − *pf*) [15,33,42], for in the region *n*(*p*) < 1, as shown in Figure 2. Nonetheless, the superconducting gap , Δ = 0, can be absent provided that the superconducting coupling constant *g* = 0. In case of finite *g*, the gap exhibits very specific non-BCS behavior [43] Δ ∝ *g*, see, e.g., [1,4,44,45] and Section 7.

#### **3. Scaling of Physical Properties**

Experimental manifestations of the FC phenomenon correspond to the universal behavior of the physical properties of HF metals [15,19,20,46]. The physical properties of HF metals are formed due to flat bands and are widespread compounds [6]. To reveal the scaling, consider now the approximate solutions of Equation (3) [15,19,20]. At *B* = 0, Equation (3) becomes strongly temperature dependent, which is a typical NFL feature and can be solved analytically [15,19,20,46]:

$$M^\*(T) \simeq a\_T T^{-2/3}.\tag{10}$$

At *T* = 0, the analytical solution is

$$M^\*(B) \cong a\_B B^{-2/3}.\tag{11}$$

Here, *aT* and *aB* are constants. Under the application of a magnetic field, the system transits to the LFL state with the effective mass becoming almost temperature independent and strongly dependent on *B*, as seen from Equation (11).

#### *3.1. Internal Variables Revealing the Scaling Behavior*

Equations (10) and (11) allow us to construct the approximate solution of Equation (3) in the form *M*∗(*B*, *T*) = *M*∗(*T*/*B*). The introduction of "internal" scales simplifies the problem of constructing the universal scaling of the effective mass *M*∗, since in that case we eliminate the microscopic structure of the compound in question [15,19,20]. From the Figure 3a, we see that the effective mass *M*∗(*B*, *T*) reaches a maximum *M*∗*M* at a certain temperature *TM* ∝ *B* [15]. Accordingly, to measure the effective mass and temperature, it is convenient to introduce the scales *M*∗*M* and *TM*. In this case, we have new variables *M*∗*N* = *M*∗/*M*∗*M* that we call normalized effective mass and *TN* = *T*/*TM* that we call normalized temperature. As a result, *M*∗*N* becomes a function of the only variable *TN* ∝ *T*/*B*, as seen from Figure 3b.

**Figure 3.** Electronic specific heat of YbRh2Si2. Panel (**a**): Specific heat *C*/*T*, versus temperature *T* as a function of magnetic field *B* [36] shown in the legend. Panel (**b**): The normalized effective mass *M*∗*N* as a function of normalized temperature *TN* ∝ *T*/*B*. *M*∗*N* is extracted from the measurements of the specific heat *C*/*T* on YbRh2Si2 in magnetic field *B* [36], see panel (**a**), listed in the legend. Approximate constant effective mass *M*∗ at *TN* < 1 is typical for the normal Landau Fermi liquids, and is shown by the arrow.

In the vicinity of the FCQPT, the normalized effective mass *M*∗*N*(*TN*) can be well approximated by a certain universal function [15,19], interpolating the solutions of Equation (3) between the LFL state, given by Equation (11), and the NFL one, given by Equation (10) [15]

$$M\_N^\*(T\_N) \approx c\_0 \frac{1 + c\_1 T\_N^2}{1 + c\_2 T\_N^{8/3}}.\tag{12}$$

Here, *TN* = *T*/*TM*, *c*0 = (1 + *c*2)/(1 + *c*1), where *c*1 and *c*2 are free parameters. Since the magnetic field *B* enters Equation (3) as *μBB*/*T*, the maximum temperature *TM* ∼ *μBB*. Consequently, from Equation (12),

$$T\_M \simeq a\_1 \mu\_B B; \quad T\_N = \frac{T}{T\_M} = \frac{T}{a\_1 \mu\_B B} \propto \frac{T}{B}.\tag{13}$$

where *a*1 is a dimensionless parameter, and *μB* is the Bohr magneton. Equation (13) shows that Equation (12) determines the effective mass as a function of the single variable *TN* ∝ *T*/*B*. That is, the curves *M*∗*N*(*T*, *B*) merge into a single one *M*∗*N*(*TN*), *TN* = *T*/*TM*, as shown in Figure 4. Since *TM* ∝ *B*, from Equation (13) we conclude that the curves *M*∗*N*(*T*, *B*) coalesce into a single one *M*∗*N*(*TN* = *T*/*B*), *TN* = *T*/*TM* = *T*/*B*, demonstrating the universal scaling in HF metals [15,19,20]. This universal scaling exhibited by *MN* is also shown in Figure 4. We note that Equations (12) and (13) allow one to describe the universal scaling behavior of HF metals, see, e.g., [15,19,20].

**Figure 4.** Scaling of the thermodynamic properties governed by the normalized effective mass *M*∗*N* in the case of the application of a magnetic field *TN* ∝ *T*/*B*, as follows from Equation (13). The solid curve depicts *M*∗*N* versus normalized temperature *TN*. It is clearly seen that at finite *TN* < 1, the normal Fermi liquid properties take place. At *TN* ∼ 1, *M*-*N* enters the crossover state, and at growing temperatures it exhibits the NFL behavior.

One more important feature of the FC state is that apart from the fact that the Landau quasiparticle effective mass starts to depend strongly on external stimuli such as *T* and *B*, all relations, inherent in the LFL theory, formally remain the same. Namely, the famous LFL relation [35],

$$M^\*(B, T) \propto \chi(B, T) \propto \frac{\mathcal{C}(B, T)}{T} \propto \gamma\_0. \tag{14}$$

still holds. Here, *γ*0 is the Sommerfeld coefficient. Expression (14) has been related to the FC case, where the specific heat *C*, magnetic susceptibility *χ* and effective mass *M*∗ depend on *T* and *B*. Taking Equation (14) into account, we obtain that the normalized values of *C*/*T* and *χ* are of the form [15,19]

$$M\_N^\*(B, T) = \chi\_N(B, T) = \left(\frac{\mathbb{C}(B, T)}{T}\right)\_N. \tag{15}$$

From Equation (15) we see that the above thermodynamic properties have the same scaling displayed in Figure 4. As a result, we shall see that the observed scaling allows us to construct a general schematic phase diagram, see Section 3.3.


**1. Introduction**

Increased industrial energy e fficiency has been a highlighted objective in political agendas in Europe, aiming at productivity gains and ecological sustainability. Small- and medium-sized enterprises (SMEs) hold a special position in this context and they are often considered the backbone of the European industrial structure [1]. In Germany in 2017, 184,667 SMEs represented about 96.9% of industrial enterprises [2]. Despite strong political e fforts in Europe, SMEs seem to be neglecting to adopt e ffective measures for energy saving and e fficiency. Thollander et al. [3] estimate the energy efficiency potential of manufacturing SMEs in the European Union at more than 25%. Why this potential remains untapped has kept policy makers and scientists occupied since the notion of the "energy e fficiency gap" [4,5] emerged; academia struggles with another empirical phenomenon often referred to as the energy "e fficiency-paradox" [6]. Despite high profitability, energy e fficiency measures are often not implemented.

The question of what constrains and drives decisions for energy e fficiency in industrial organizations represents a vast research field in energy literature [7–10]. Barriers and drivers can be defined as all factors that hamper or foster the adoption of cost-effective, energy-efficient technologies and their diffusion [11,12]. Accounting for the fact that measures representing high rates of return, or requiring no capital investment, are often not undertaken by SMEs [13,14]. A perspective solely focusing on economically rational decisions appears insufficient for a thorough understanding of the situation of SMEs.

Studies on the adoption and implementation of energy-efficient practices represent an overlapping key area of research on industrial energy efficiency [15]. Recent analyses emphasize the benefits and characteristics of measures [16], the potentials of particular technical processes [17], or beneficial intersections to other management aspects such as supply chain management [18]. Despite the theoretical importance and practical value of these approaches, a one-sided view of technical measures has been increasingly criticized in recent publications [19–23] on the barriers and adoption of energy efficiency measures. To date, practices other than technical measures have received inadequate attention in empirical studies [24], neglecting the material, social, cultural, and institutional aspects framing the decision-making processes [25,26].

Rejecting an atomistic perspective on decision making and technology, scholars of sociology, ethnology, and anthropology have drawn increasing attention to the cultural aspects of energy-related behavior in enterprises. By looking at the values, norms, laws, and everyday practices, these approaches emphasize the embeddedness of organizational decisions on energy efficiency in cultural, social, and material contexts [27–31]. Ethnographic case studies have since shown the significance of SME owners' and managers' personal values in terms of environmental decision making [32] and how energy management practices are influenced by organizational cultures, team dynamics, and individual's aspirations [33]. Despite these efforts, Andrews and Johnson [34] call for an increase in studies addressing the rules, norms, beliefs, and logics embedded in the organization's context. Fawcett and Hampton similarly argue that a "more complex understanding of SMEs, as organizations operating in a socio-technical landscape, and with varied capabilities, objectives and values" could provide a more effective policy design [35] (p. 3).

By adopting a cultural perspective [36], this empirical study on German manufacturing SMEs examined the energy efficiency climate, the energy efficiency practices, and the intersections between the enterprises and their members and their institutional environment. The purpose of this study was to investigate the establishment of energy efficiency within the SMEs and identify general drivers in promoting energy efficiency decisions, energy-saving behavior, and the general establishment of energy efficiency in SMEs. The study followed a mixed-methods approach and utilized qualitative (single case studies) and quantitative (survey) data of SMEs situated in the federal state of Baden-Wuerttemberg, southern Germany.

The study indicates the importance of everyday employee behavior in achieving energy savings. The studied enterprises value behavior-related measures as similarly important as technical measures. Raising awareness for energy issues within the organization, therefore, constitutes an essential leadership task, which is oftentimes perceived as challenging and frustrating. The results suggest the embedding of energy efficiency in corporate strategy, the use of a broad spectrum of different practices, and the empowerment and involvement of employees as major drivers in establishing energy efficiency within SMEs. Furthermore, the findings reveal external influences on shaping the meanings of energy efficiency for the SMEs by raising attention for energy efficiency in the enterprises and making energy efficiency decisions more likely.

The remainder of this study is organized as follows: The next section sets out the theoretical background and research focus. Section 3 provides a brief overview of the research strategy and the methods used. Section 4 is devoted to the main results of the study. The following section presents the discussion of the results and Section 6 provides the conclusions and implications of the study.

#### **2. Theoretical Background and Focus**

#### *2.1. The Concept of Culture in the Context of Energy E*ffi*ciency Research*

Culture is frequently explained as a constraining soft factor from an organizational perspective [37,38]. Culture can be roughly defined as the mix of knowledge, ideology, norms, values, laws, and everyday rituals that characterize a social system [39]. Sorrell et al. [40] presume that environmental values embedded in organizational cultures and practices have an essential effect on organizational decisions and behavior. However, they do not view culture to be a barrier, "but an important explanatory variable" [40] (p. 15). Although a cultural perspective on industrial energy e fficiency promises useful findings for science and politics, only a few researchers have transferred this complex to a strategy for empirical inquiry. Criticizing that "within the energy literature, the concept of culture has generally been more implied than overt", Stephenson et al. [41] (p. 6123) developed a conceptual framework of energy cultures. The so-called Energy Cultures Framework (EFC) is based on sociological theory [42,43] and represents a heuristic approach to investigate influences on energy-related behaviors in social systems to identify the "levers for change towards more energy-e fficient behaviors" [41] (p. 6123). According to the ECF, the energy cultures are constituted via the interactions between material culture, practices, and norms, all of which are affected by external influences and embedded in wider cultural spheres [44]. Since its development, the ECF has been applied to di fferent contexts, ranging from household energy-related behavior [45] to industrial sectors such as the timber processing industry [46].

König [36] introduced a similar framework addressing specifically industrial organizations. Taking a sociological perspective, he views organizations as cultural systems embedded in wider social contexts and he developed a theoretical framework addressing individual organizational and institutional dimensions, shaping decisions on energy e fficiency. The framework combines multidisciplinary concepts and theoretical approaches of organizational theory. It integrates concepts of sociological neo-institutional theory [47,48], the translation perspective on di ffusion [49], the attention-based view of the firm [50], and organizational [51] and energy culture research [41,44]. The energy e fficiency culture of an industrial organization is defined as unconscious, shared understandings, which are mutually dependent from the organizational structures, practices, environment, and individual members. Decisions on energy e fficiency in industrial enterprises are, therefore, based on a multilevel process shaped by individuals, organizations, and the environment. Referring to the attention-based view of the firm [50], the organization structures the situational context of, distributes the attention to, and shapes the focus of attention on energy e fficiency issues. This framework supports the identification of drivers and served as an anchor in conceptualizing the research design of the study.

#### *2.2. Theoretical Perspective of the Study*

The data collection and analysis were structured by the theoretical concept developed by König (Figure 1), which assumes that decisions and actions on energy e fficiency emerge at the intersection between three levels.

crucial factor of decision making. Following Denison's concept of organizational climate [57], the energy e fficiency climate represents the interpretation of the situations related to energy efficiency within the organization. The energy e fficiency practices are understood as the totality of all practices toward energy e fficiency and energy conservation by an enterprise and represent outcomes as well as inputs to decisions on energy e fficiency measures. Referring to Fiedler and Mircea [58], who view energy management as "the sum of all measures and activities which are planned or executed in order to minimize the energy consumption of a company", the energy e fficiency practices synonymously represent the energy management of an enterprise. Following Schein's concept of organizational culture [51], the basic energy assumptions and beliefs within an industrial organization are mutually dependent from the organizational structures, practices, environment, and individual members.

3. The Micro level incorporates the decision makers and members of the organization with their individual characteristics (e.g., attitudes, interests, competencies). These characteristics are mutually dependent of the positioning and socialization of individuals within the organization.

**Figure 1.** Energy e fficiency culture framework following König [36].

Decisions on energy e fficiency represent processes of theorization and problematization, linking together the issue-field (1. Macro level), the organization (2. Meso level), and the members (3. Micro level). In this sense, decision makers are not considered as atomistic units; they are members of professional groups, work groups, milieus, or families in the case of family businesses [34] (p. 198).

#### *2.3. Research Focus and Research Questions*

The research focused on manufacturing SMEs in Baden-Württemberg, Germany. This federal state constitutes the most industrial area in Germany, with about 1.3 million employees in the industry sector and around 7500 manufacturing SMEs with around 505,833 employees [59] representing the industrial backbone. Baden-Württemberg is ahead of all G-10 states (a group of the 11 leading industrial countries) with a share of manufacturing industry in the gross value added and exceeds the benchmark for industry defined by the EU for 2020 (20% share of industry in gross value added) by around 60% with 32.5% [60,61].

Referring to the framework described above, the research concentrated on four areas that were derived as crucial in answering the overarching research question: What drives the establishment of energy e fficiency in SMEs in everyday work life? The study focused on examining the energy e fficiency climate, the energy e fficiency practices, the intersection between the enterprises and their members, and the intersection to its relevant environment. These four areas were assigned the guiding research questions, which structured the data collection and analysis.

1. Energy efficiency climate:

According to the theoretical perspective taken, the energy efficiency climate reflects the interpretation of the situations related to energy efficiency within the organization, which structure the attention of its members. Correspondingly, the investigation concentrated on the following research questions:

As outlined in the introduction, the study should not only take technical measures into account. Following the classification of energy efficiency practices by König [36] (p.6), six different forms of energy efficiency practices were investigated: Technology investment-related practices (e.g., the purchase and implementation of energy-efficient technical equipment), technology organization-related practices (e.g., the enhancement and optimization of existing support or process technology), organization-related practices (e.g., corporate energy strategy, the implementation of an energy management system), information-related practices (e.g., energy monitoring, internal technical meetings), competence-related practices (e.g., workshops, trainings), and behavior-related practices (e.g., raising awareness for energy saving by personal encouragement and explicit behavior guidelines). The following research questions were focused on:

Organizational procedures and structures potentially regulate the energy-related behavior of their members and subunits [34]. Aiming at everyday work life in the enterprises, the following research questions were targeted:

As described above, it was assumed that external actors and organizations potentially exert regulative, economic–financial, normative, and cognitive–cultural influences on the SMEs regarding energy efficiency practices and decisions. Accordingly, the study focused on these questions:


3.3. Glycophosphatidylinositol

Glycosylphosphatidylinositols (GPI) are complex structures to which the C-terminus of proteins gets attached during their post-translational modification [48]. All GPI have a core glycan structure sandwiched between an ethanolamine phosphate linker, bridging the C-terminal of the protein with the highly conserved glycan core, and a phosphatidylinositol (PI) group. The fatty acids of the PI moiety attach the GPI to the cell membrane. So far more than 200 proteins have been found to be anchored by a GPI to the cell surface and more than 20 GPI structures have been elucidated [49]. Some of the proteins attached to GPI anchor are enzymes like alkaline phosphatase (APase), acetylcholinesterase (AChE) and 50 -nucleotidase, complement defense proteins like decay accelerating factor (DAF or CD55), CD59, and mammalian antigens like Thy-1, or protozoan antigens like variant surface glycoprotein (VSG) found on the cell surface of Trypanosoma [48].

Unlike GPI-anchored proteins not much is known about biological functions of GPI anchors, apart from their role as a membrane anchor for proteins. Given the complexity and diversity of their structures, they are thought of as being involved in many different biological functions but there are not sufficient experimental evidences to draw definitive conclusions [50]. However, there are several studies implicating their involvement in sorting of proteins in the lipid raft and in signal transduction [51–53]. Other studies have shown that the structure and conformation of proteins change upon binding to GPI anchors [54, 55]. Besides this physiological role, deficiency of GPI anchors on red blood cells causes a chronic pathological disorder paroxysmal nocturnal hemoglobinuria (PNH) [56].

#### 3.4. Lipopolysaccharides

Lipopolysaccharides (LPS), also referred to as endotoxins, are a major component of the outer membrane of gram negative bacteria and are essential for maintaining the structural integrity of the membrane. LPS have three components: lipid A, core oligosaccharide and O-antigen polysaccharide. Lipid A is the active component and under normal conditions consists of β(1–6) linked glucosamine disaccharides. The diglucosamine backbone is phosphorylated and decorated with multiple fatty acids anchoring them in the outer leaflet of the bacterial cell membrane. Lipid A, when released from the cell, is recognized by pattern recognition receptor TLR4 triggering cytokine synthesis. At low level of endotoxins, the innate immune system eliminates it, but at high concentrations it can prove fatal [57].


**4. Estimation of the burden of carers in Portugal**

It has been estimated that the number of people with dementia in Portugal, in 2012, was 182,526 in a population of less than 10 million people. This number represents about 1.7% of Portuguese population, and it is higher than the EU averages of 1.55% [19] (Alzheimer Europe 2019). Considering that 60–70% of those patients with dementia suffer from Alzheimer's disease, it means that currently there are more than 110,000–128,000 Alzheimer's patients in Portugal. It is estimated that in the next 20 years, the number of Alzheimer's patients in this country will be around 322,000 [9].

The current health expenditure (CHE) in Portugal directed for long-term care (LTC) has two functions, both social and health. Despite the inexistence of the EU average reference and comparing with Sweden which has some well-functioning long-term care system, Portugal presents a low share of expenditure (CHE) in long-term care expenditure for health but a reasonable level for long-term care expenditure for social support (**Figure 5**).

Public aid to informal caregivers in Portugal is in its infant stages, and the formal care is insufficient for the current demand. This national institutional framework pushes nearly all the care of Alzheimer's patients to their families, who have stood for the overwhelming task of taking care of them, even if they do it with affection and love or even if they have no conditions to do so.

#### **4.1 Method for collecting data**

To collect data for Portugal, a questionnaire based on RUD, which includes questions about the informal caregiver concerning their socio-demographic characteristics, health status, received external support, professional status, activities performed and time management, was used [20].

This questionnaire was applied over 5 months, in 2018, in the Neurology Services of the Hospital Centre of the University of Coimbra, Portugal, to informal caregivers of Alzheimer's patients. This study has been approved by the ethical commission of the hospital centre, and participants have signed an informed consent form. Confidentiality and anonymity are guaranteed to participants in this study.

#### **Figure 5.**

*Share of LTC expenditure in total current health expenditure. Note: LTC, long-term care expenditure. Source: Based on Eurostat [hlth\_sha11\_hc] [8].*

The study includes 86 Alzheimer's patients and 97 informal caregivers. The difference in these numbers is due to the fact that some patients have more than one carer.


**About the Editors**

#### **Jong Seong Kang**

Jong Seong Kang is a professor at the College of Pharmacy, Chungnam National University in Korea. He graduated in Pharmaceutical Sciences and completed his Ph.D. in Pharmaceutical Analysis at the Julius Maximilian University of Wurzburg in Germany. He has been visiting scientist at ¨ the National Institute on Alcohol Abuse and Alcoholism at NIH, USA and exchange professor at the University of Pennsylvania, USA. Dr. Kang has published in several peer-reviewed journals, book chapters, and conference papers. His research interests are mainly focused on the quality standardization in the development of herbal drugs, and the specification and test method in the new drug development.

#### **Narendra Singh Yadav**

Narendra Singh Yadav is a Researcher at the University of Lethbridge, Canada. He received his Ph.D. (2013) in Plant Biotechnology from the CSIR-Central Salt and Marine Chemicals Research Institute in Gujarat, India. He has also been a Researcher at Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Israel. His research is mainly focused on the 'genetics and epigenetics plant stress response.' Over his career so far, he has published more than 50 articles, book chapters, and conference abstracts/ papers, reviewed more than 50 manuscripts, and served as handling editor for 25 manuscripts.


**2. Role of zinc in the brain**

#### **2.1 Role of zinc in neurogenesis and synaptic transmission**

Zinc has a variety of crucial roles in neurogenesis [4]. Zinc deficiency decreases the neurogenesis process and impairs the expression of genes involved in hippocampus proliferation and neuronal development in the postnatal rat cerebellum [20]. Further, zinc deficiency reduces the proliferation of the human neuroblastoma cell line, promotes apoptosis, and inhibits retinoic-acid-induced neuronal development in cultured cells [1, 21].

Of note, zinc is found in the presynaptic glutamatergic vesicles across the brain, including the cerebral cortex, limbic system, hippocampus, and olfactory bulb [22].

It acts as a neuromodulator on a wide range of membrane receptors, ion channels, and transporters [23]. Synaptic zinc, in particular, is enhanced via a specialized zinc transporter, ZnT3, and is coreleased with glutamate during action potential-induced exocytosis [24]. These also have an impact on synaptic transmission, which interacts with receptors and channels that regulate auditory processing [25, 26]. Synaptic zinc has been discovered to inhibit NMDA receptors, GABA-A receptors, and calcium channels while activating AMPA and glycine receptors [27–30]. Zinc also has vital effects on other kinds of receptors, including serotonin, dopamine, and acetylcholine receptors, as well as voltage-gated ion channels for sodium, potassium, calcium, and chlorine [29, 31].

Synaptic zinc regulates sensory processing and improves acuity in the discrimination of different sensory stimuli. Synaptic zinc plasticity leads to prolonged adaptations and sense memories. Recently, the mechanism of this long-term synaptic

zinc plasticity has been described as being due to group 1 metabotropic glutamate receptors (G1 mGluRs)-dependent mechanism that triggers a bidirectional long-term change in synaptic zinc signaling [32].

#### **2.2 Role of zinc at depression**

No one denies that depression treatment is a gateway to overcoming many social and psychological problems that affect millions of people all over the world. Many factors play a role in depressive-like behaviors, such as impairment of functions of the hippocampus and the prefrontal cortex. These brain parts play an important role in decision-making processes, so any dysfunction at this area can induce a predisposition to negative feelings, and many glucocorticoid receptors are involved in these areas [33].

In terms of both pharmacological and clinical/epidemiological data, recent years have provided additional evidence confirming the role of zinc in depression. Zinc demonstrated antidepressant-like efficacy in preclinical studies and depressive models. Clinical evidence suggested that zinc supplementation might be beneficial in people suffering from depression. Zinc supplementation has been demonstrated to be beneficial as adjuvant therapy or as a stand-alone intervention for depression. Furthermore, zinc consumption has been linked to an increased risk of depression. Dietary zinc restriction was found to be a causal factor in the development of depressive-like symptoms or anhedonia in mouse studies [34]. Some epidemiological studies have reported that reduced nutritional zinc consumption is related to depression in females but not in males [35]. Even though the first prospective study examining the relationship between zinc intake and depression risk found a small but significant inverse correlation between them, a 20-year follow-up study found that a reduced dietary zinc intake protects from depression in men who were not previously depressed. However, because the research participants were all men with a hospital discharge diagnosis of unipolar depression, the findings cannot be applied to women or patients who did not require hospitalization. On the contrary, a reduced nutritional zinc intake was found to be a risk factor for depression in a prospective analysis of both men and women [36]. Mice missing the G-protein-coupled receptor 39 (GPR39), a zinc-activated receptor, show depressive-like behavior [37]. TC-G-1008, a GPR39 agonist, was recently discovered to have antidepressant-like effects [38]. These findings add to the growing body of evidence that zinc is useful in the treatment of depression.

Meta-analyses support the use of zinc as a supplement in the treatment of severe depression, and single research currently supports the use of zinc for psychotic symptoms [39]. Zinc deficiency has also been linked to neuropsychiatric symptoms such as altered behavior and cognition, learning difficulties, and depression [40–42].

The link between zinc dysregulation and psychiatric disorder was that zinc acts as an inhibitory modulator at the NMDA glutamate receptor [43–45]. In addition, the inhibitory effects on the nicotinic acetylcholine receptor (nAChR), GSK3 (glycogen synthase kinase 3beta), and NOS (nitric oxide synthase) are also relevant to depressive processes [46, 47].

Numerous studies show lower zinc blood levels in depressed people compared with healthy people, with a meta-analysis showing depressive symptomatology at zinc serum levels of 1.8 M or below [48]. In several investigations, zinc supplementation enhanced mood in those who were suffering from treatment-resistant depression [41, 49].

Zinc's effect on the brain-derived neurotrophic factor (BDNF), a growth factor that promotes neurogenesis and differentiation, may be connected to depression. The hippocampus is a center of lifelong neurogenesis, and periods of significant

depression are associated with reduced BDNF expression and neuro/synaptogenesis.  Zinc-rich diets, on the other hand, increased amounts of progenitor cells [3, 41]. The GPR39 receptor is most likely a critical connection in the interaction between zinc and the serotonergic system, which is required for antidepressants that affect the serotonin pathway to work [34].

#### **2.3 Zinc and neuroimmunity**

Of note, laboratory animal models showed that zinc insufficiency induces thymus and lymphoid tissue atrophy. It lowers the number of spleen cells and the sensitivity to antigens that are both T-cell-dependent and -independent [50]. Microglia is a kind of immune cell found in the central nervous system (CNS) [51]. The link between zinc and microglial activation reflects an undiscovered process that may play a role in neuropathy. However, zinc is produced by neurons under several conditions to activate microglial [52].


**Abstract**

The metabolism hypothesis of Alzheimer's disease (AD) was first proposed in 1975. In normal aging and very mild AD, the cerebral metabolic rate for oxygen (CMRO2) and cerebral blood flow (CBF) remained approximately constant, but the metabolism of glucose (CMRglu) declined markedly. This decline in CMRglu identified a specific and primary metabolic defect that triggered downstream cellular cascades evolving into AD and its characteristic neuropathological lesions. These findings led research about AD into the role of insulin resistance that foresaw modern trials of insulin for AD treatment. The metabolism hypothesis evolved over subsequent decades with improved in-vivo measurement of metabolic parameters and AD biomarkers in humans. A more recent model highlights the interrelationships between the default mode network (DMN) and biomarkers such as CMRglu, amyloid, and tau. In other words, metabolic conditions related to sustained cortical activity during aging throughout the lifetime are conducive to the deposition of amyloid. This activity is thought to underlie the "autobiographical self." These ideas and findings motivate aging and AD-research focus on the biochemistry and cell biology of cerebral metabolism.

**Keywords:** dementia, amyloid, tau, cerebral metabolism, default mode networks, cerebral energetics, aerobic glycolysis, cognitive aging, functional connectivity