\r\n\tThe outcome of cancer therapy with radiation has been improving over the years due to technological progress. However, due to the biological property of cancer, current radiotherapy has limitations. Therefore, in consideration of the dynamics of tumor cells caused by radiation irradiation, attempts are being made to overcome the current drawbacks and to improve radiotherapy. It is expected that carbon ion beams, hyperthermia, oxygen effect, blood flow control, etc. will be used in the future in order to improve the treatments. This book aims to introduce research results of various radioprotective agent development research and hypoxia sensitizers.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"c574888a21d8152f6b25191ea63af008",bookSignature:"Prof. Yeunhwa Gu and Dr. Jin Ho Song",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9388.jpg",keywords:"Oxygen Effective Ratio, Low LET, Therapeutic Ratio, Radioresistance, Radiation Sensitivity, PLD Recovery, Enzyme Target, Oxygen Effective Ratio, Radioprotective Agent, Dose Reduction Factor",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 3rd 2019",dateEndSecondStepPublish:"September 24th 2019",dateEndThirdStepPublish:"November 23rd 2019",dateEndFourthStepPublish:"February 11th 2020",dateEndFifthStepPublish:"April 11th 2020",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"248214",title:null,name:"Yeun-Hwa",middleName:null,surname:"Gu",slug:"yeun-hwa-gu",fullName:"Yeun-Hwa Gu",profilePictureURL:"https://mts.intechopen.com/storage/users/248214/images/system/248214.jpg",biography:"Dr. Yeun-Hwa Gu is working as a Professor for the Department of Radiation Oncology, Graduate School of Health Science, Junshin Gakuen University, Japan. 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\n\t\t\t
1. Introduction
\n\t\t\t
In VLSI circuit design, nonlinear signals processing circuits such as minimum (MIN), maximum (MAX), median (MED), winner-take-all (WTA), loser-take-all (LTA), k-WTA, and arbitrary rank-order extraction are useful functions (Lippmann, 1987; Lazzaro et al., 1989). In general, median filter is used to filtering impulse noise so as to suppress the impulsive distortions. The MAX and MIN circuits are important elements in fuzzy logic design. With regard to WTA application, it is the major function in pattern classification and artificial neural networks. Thus, design of these nonlinear signal-processing circuits to integrate smoothly within SoC (System-on-a-chip) applications becomes an important research. Recently, complementary metal-oxide-semiconductor (CMOS) technology is widely used to fabricate various chips. In this chapter, the designs of all circuits are realized by using CMOS process. However, since CMOS transistor is continuously scaled down via thinner gate oxides and reduced device size, supply voltage is necessary to reduce in order to improve device reliability. Therefore, a high reliable WTA/LTA circuit, a simple MED circuit, and a low-voltage rank-order extractor are addressed in the chapter. The organization of this chapter is as follows. Section 1 introduces the background of these nonlinear functions, including definitions and applications. Section 2 describes conventional WTA/LTA architectures and presents a high reliable winner-take-all/loser-take-all circuit. Section 3 shows an analog median circuit, with advantage of simple circuit. Section 4 describes a CMOS circuit design for arbitrary rank order extraction. Restrictions and design techniques of low voltage CMOS circuit are also addressed. Section 5 will briefly conclude this chapter.
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Given a set of external input n variables a\n\t\t\t\t1, …, an\n\t\t\t\t, the operation of MAX (or MIN) circuit determines the maximum (or minimum) value. A median filter puts out the median variable among a window of input samples. The function of a WTA network is to select and identify the largest variable from a specified set of variables. A counter part of WTA, LTA identifies the smallest input variable and inhibits remain ones. Instead of choosing only one winner, the k-WTA network selects the largest k numbers among n competing variables (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t), which allows for more flexibility in applications. For arbitrary rank order identification, a rank-order filter (extractor) is designed to select the k-th largest element ak\n\t\t\t\t among n variables a\n\t\t\t\t1, …, an\n\t\t\t\t. Depending on application requirements, these input variables are either voltage, or current signals.
\n\t\t\t
In order to clearly describe these nonlinear functions, taking one example indicates these definitions. Two output responses of a circuit corresponding to a set of input currents Iin1, Iin2, …, and IinN : one is analog output current Io, the other one is digital outputs set Vo1(rank), Vo2(rank), …, and VoN(rank). Assuming five external input currents are 9, 7, 10, 5, and 3 μA. Depending on various functions requirement, the output current Io and the corresponding digital outputs responses are as follows.
\n\t\t\t\t\t\tWTA: Output voltages Vo1(rank), Vo2(rank), …, and Vo5(rank) respond to logic high to identify which one is the maximum value among Iin1, Iin2, …, and IinN. In this case, (Vo1(rank), Vo2(rank), …, Vo5(rank))= (0, 0, 1, 0, 0), where “0” and “1” are the logic low and logic high, respectively.
\n\t\t\t\t\t\tLTA: A reverse operation of WTA function, and outputs set is (0, 0, 0, 0, 1) for this case.k-WTA: Depending on k value, k winners are selected. The function has more flexible in application than WTA. For example, the outputs of 2-WTA is (Vo1(rank), Vo2(rank), …, Vo5(rank))= (1, 0, 1, 0, 0) in this case.
\n\t\t\t\t\t\tRank order: The function of the rth rank-order extraction identifies the rth largest magnitude among Iin1, Iin2, …, and IinN. For example, outputs of the 2nd and 3rd rank order are (1, 0, 0, 0, 0) and (0, 1, 0, 0, 0) in this case, respectively.
\n\t\t\t
Figure 1.
Applications of MIN and MAX operations in fuzzy inference.
\n\t\t\t
Figure 2.
Application of MED filter.
\n\t\t\t
Figure 3.
Two-dimension application of MED filter.
\n\t\t\t
Figure 4.
Applications of WTA/LTA function in artificial neural network.
\n\t\t\t
Various applications for these nonlinear functions are described as follows. The MAX and MIN circuits are important elements in fuzzy logic design (Yamakawa, 1993). Figure 1 shows the MAX and MIN operations in fuzzy inference. Variables “x” and “y” are inputs; variable “z” is the corresponding output response. In a specific status, either rule 1 or rule 2 is satisfied. MIN function realizes the “and” operation in fuzzy rules, and MAX function realizes the “or” operation. In image signal processing, MED function in general is used to filtering impulse noise so as to suppress the impulsive distortions. Figure 2 shows a one-dimension application for noise cancellation. Figure 2(a) shows a Vpp 1.2 V sinusoidal signal corrupted by noise, and Figure 2(b) shows the processed signal after MED filtering with a window of size five. In addition, Figure 3 shows a two-dimension application also for noise cancellation of image. With regard to WTA application, it is the major function in pattern classification, vector quantization, data compression, and self-organization neural networks. Figure 4 shows WTA application for pattern identification. Commonly, an analogue rank order filter is widely used in signals sorting and classification.
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In general, these nonlinear functions are achieved either by using digital or analog implementations. Under digital implementation, since most of signals obtained from the real world are continuous forms, the continuous inputs must first be transferred to digital type by using one-or-multiple analog-to-digital converter (A/D). As a result, the circuit complexity, chip area, and power consumption are increased due to the extra data converters in digital realization. Whereas for analog implementation, the circuit accuracy is slightly lost than digital operation and there is weaker tolerance to fabricate process variation. However, without extra data transfer, the analog operation is with many advantages such as saving time, bandwidth, and computation at the system level. Considering the practicality and flexibility, design issues of a CMOS analog signal processing circuit therefore must include 1) precision; 2) speed; 3) high tolerance to fabrication process variation; 4) wide range of supply voltage; 5) wide input range; 6) low circuit complexity; 7) low power consumption; 8) scalability; 9) programmability, and so forth, to allow these functions easily integration within various system-embedded chips. Additionally, when the device size of CMOS transistor is shrunk thinner and smaller, supply voltage is necessary to scale down in order to improve device reliability. A forecast of high-performance CMOS circuit operated within low voltage had been reported (Semiconductor Industry Association, 2008). Figure 5 shows the trend of CMOS supply voltage and physical gate length. Moreover, portable equipments such as biomedical electronics, computer, and portable telecommunication equipments are common used recently. Battery operation and low-power consumption are also important design requirements for these circuits.
\n\t\t\t
Figure 5.
Trend for supply voltage and physical gate length by ITRS 2008 update.
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\n\t\t
\n\t\t\t
2. Winner-Take-All and Loser-Take-All circuit
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\n\t\t\t\t
2.1 Architectures of WTA/LTA circuits
\n\t\t\t\t
Based on different circuit structures, conventional WTA/LTA circuits are roughly cataloged into four types: 1) global-inhibition structure, in which the connectivity increases linearly with the number of inputs (Lazzaro et al., 1989; Starzyk & Fang, 1993); 2) cell-based tree-topology (Smedley et al., 1995; Demosthenous et al., 1998); 3) excitatory/inhibitory connection (He & Sanchez-Sinencio, 1993); and 4) serial cascade structure (Aksin, 2002). Figure 6(a-d) shows the conceptual diagrams of these topologies. In Figure 6(a), each cell receives the same global inhibition, and a common current Icomn or voltage Vcomn is shared by all the competing cells. The cells represented in a square block are nonlinear signal processing elements. Therefore, the precision of the circuit is degraded as the number of inputs increases. Since the operation of this circuit relies on the cells matching, a stable fabrication process is required for manufacturing a high-precision system. The complexity of the connectivity of the circuit is O(N), where N is the number of inputs. Figure 6(b) shows a cell-based tree-topology, with N-1 cells arranged in a tree topology for N inputs. Each cell receives two input variables to compare and outputs the larger (or smaller) of the two input signals. The backward digits in the bottom cell are then successive feedback to 1st-layer cells to identify the maximum (or minimum) input. The precision of this circuit is also sensitive to cell matching. With this circuit design, the device sizes must be rescaled when the supply voltage is modified.
\n\t\t\t\t
Figure 6.
Conventional architectures. (a) Global-inhibition structure. (b) Cell-based tree topology. (c) Excitatory/inhibitory connection. (d) Serial cascade.
\n\t\t\t\t
\n\t\t\t\t\tFigure 6(c) shows an excitatory/inhibitory connection with an O(N2) connectivity complexity. Each cell receives the inhibited signals from other cells and an excitatory signal from itself. With this design, chip area increases with the square of the number of inputs. Based on comparators operation, Figure 6(d) shows an N-1 analog comparison blocks and N-1 digital blocks cascaded in serial. Within a comparison time Tcomp, the larger magnitude of inputs in each analog block is sent to next stage to compare with other inputs. The result of the each comparison is then sent to the corresponding digital block, and a decision digit is feedback from right block to left block to identify the maximum input. As a result, the response time of the circuit is approximated to\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t⋅\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tg\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, where Tdig is the total propagation time of the digital part. The offset voltage of each comparator dominates the precision of the architecture. Circuit implementation of Figure 6(d) is also sensitive to process variation. For a high precision application, identical internal circuit blocks shown in Figure 6(a-d) are necessary. The primary limitations of accuracy for the conventional architectures are fabricated process variations and matching requirement of internal cells. The variations of CMOS fabricated process include transistor threshold voltage, actual device size, thinness of the gate oxide, and other variety of factors. In a common process, threshold voltage in general varies from –10% to +10% of its nominal value. Due to the non-uniform etch and diffusion procedures, actual device sizes are also varied. In a real CMOS process, these variations are hard to eliminate completely. How can we improve the accuracy of analog circuit in a conventional process?
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\n\t\t\t
\n\t\t\t\t
2.2 A high reliable WTA/LTA circuit
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In the section, a highly reliable CMOS signal processing circuit with a programmable capability for WTA function and LTA function is described (Hung & Liu, 2004). A symbol \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\tO\n\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t (1≦j, k≦N and N is the number of inputs) is defined such that the ith comparator cell receives two input variables (Vinj and Vink ) to compare in magnitude at time t, and the output \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tZ\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t of the cell is the larger variable or a binary value. For a \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\tO\n\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t operation, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tZ\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis defined as
After time O(\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tlog\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tN\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) the maximum (or the minimum) input variable is obtained. Total N-1 identical comparators are necessary for this operation.
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Figure 7.
A high reliable WTA/LTA architecture.
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To reduce the matching requirement of internal cell, Figure 7 shows a conceptual diagram of high reliable circuit. In the scheme, there are N identical ‘digital’ control cells and a single comparator for N input variables. A single comparator block multiplexes in time to achieve all inputs comparisons. The operating procedures are described as follows:
The strategy adopted to find the maximum/minimum among a set of variables is that two variables are first compared; then the result of this comparison is compared with the next input variable using the same comparator. The procedure continues until the comparisons of all input variables are completed. Conceptually, circuit operation is similar to a serial comparison. Unlike the traditional architectures that require N-1 analogue comparators; this architecture requires only a single comparator to eliminate sensitivity to component matching requirements. Using the same algorithm, the LTA function is easily obtained by only reversing the output state \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tZ\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the same architecture.
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Figure 8.
Comparison block and control signals.
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The key block in this architecture is the comparator cell. Comparator performance is a crucial factor for realizing high-speed data conversion systems and telecommunication interfaces. The precision of a comparator is usually defined as the minimum identifiable differential voltage (or current) between inputs, that is, the comparator’s resolution capability. A comparator design from (Hosotani et al., 1990) is used herein; the schematic diagram is shown in Figure 8. Transistors Msw1, Msw2, Msw3 are used as switches. The circuit operates on two phases, auto-zero phase and comparison phase. Assuming the voltage at node B is Vx. Based on charge conservation, after the comparison phase, Vx arrives at the following:
The effect of the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tC\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t term in (1) represents a degrading factor. To reduce the decision time, the succeeding inverters amplify the different voltage (Vin2 - Vin1) to pull node D up to high (logic 1) or push it down to 0 V (logic 0). The functions of the N-latch are to sample the voltage at node D as latch_clk turns high and to hold the comparison result as latch_clk turns low. Ultimately, the output polarity of the N-latch will be changed according to the max/min selector setting. The max/min selector signal modifies the polarity of the compared result; therefore, without the need for structural modification, this circuit possesses win/lose configurable capability. The comparison block shown in Figure 8 is reused during all comparison procedures. The architecture of N-inputs circuit is shown in Figure 9, in which Control_Celln (1≦ n ≦N) are identical. N cells are required for N input variables. Each cell contains a status block, a control_switch block, and two latch blocks.
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Figure 9.
The block diagram of the high reliable WTA/LTA.
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\n\t\t\t\t\tFigure 10 shows the clocks for the whole circuit. Signal reset and clock reg_clk must be generated externally; other clocks are produced by reg_clk and some logic gates.
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To describe the operations of the entire circuit, the circuit architecture in Figure 9 and the clock waveform in Figure 10 are referred. First, at t1, reset signal is used to initiate the status blocks, control_switch blocks and latch blocks. The N-latch in the status block and Ro1, Ro2, …, RoN are reset to zero by reset signal. Based on max/min selector signal, the MOS transistors Ms1, Ms2, Ms3 and Ms4 preset the initial sampling voltage (0 V or VDD) at node cap_comn. Despite the magnitude of input-1 variable, the input-1 variable must be a winner during an initial interval for a serial comparison. The initial sampling voltage at node cap_comn is thus set as 0 V when the max/min selector signal is set to logic 1 for WTA operation, and vice versa.
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Figure 10.
Clock waveforms.
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Then, at t2, the Vs1 clock turns high (auto-zero phase) to sample the initial voltage (0 V or VDD) at node cap_comn. Next, at t3, Ro1 turns high to sample voltage Vin1. At this time, the clock Vs1 turns low (comparison phase) to compare the Vin1 with the initial sampling voltage, and the compared result is stored in the N-latch of the first status block. The state of the N-latch is logic 1 if the variable is the winner. At t4, the present winner Vin1 is sampled again. At t5, a new comparison between previous winner Vin1 and Vin2 is performed. At t6, the winner (the result for the Vin1 and Vin2 comparison) is sampled again. After this procedure, a new comparison between the present winner and Vin3 is performed. The procedure continues until comparison of all the input voltages is completed. Ultimately, only one state Vosn (n=1,..., N) in these cells is logic 1 for WTA/LTA indication; others are logic 0. Therefore, a WTA or a LTA operation has been accomplished.
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\n\t\t\t\t\tFigure 11 shows the status block. Figure 12 shows the control_switch block. It receives an input variable and controls the transmission gate to sample input level. A true single-phase latch composed of an N-latch and a P-latch is used to reduce the clock skew issue (Yuan & Stensson, 1989).
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Figure 11.
Status block.
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Figure 12.
Control_switch block.
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2.3 Simulation results and reliability test
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With regard to the high reliable WTA/LTA circuit, an experimental chip with six inputs was also fabricated using a 0.5-μm CMOS technology. The sampling capacitance Cs implemented by using two-layer polysilicon is set to be 3 pF. The period of reg_clk clock is 100 ns with a 50% duty cycle. WTA/LTA functions, supply-voltage range, and Monte Carlo analysis of transistor variation by simulation were also tested.
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1) WTA/LTA functions
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To test the function of the circuit, each example takes ten input voltages for the WTA/LTA operation. For supply voltage VDD=3.3 V, the input variables Vin1, Vin2, …, and Vin10 are 0.003, 0.006, 1.000, 0.997, 2.000, 2.003, 2.000, 3.297, 3.300, and 3.297 V for testing WTA function, respectively, and 3.297, 3.294, 2.000, 1.997, 2.000, 1.000, 0.997, 0.006, 0.009, and 0.003 V for testing LTA function. During the WTA operation, the logic state Vosn of each cell at each time slice becomes:
When all comparisons are finished, the outputs Vos1, Vos2, Vos3,..., and Vos10 respond as logic 0, 0, 0, 0, 0, 0, 0, 0, 1, and 0, respectively. Therefore, among these ten inputs, input variable Vin9 is the maximum. Figure 13 shows the results of HSPICE simulation for the WTA operation. The time period of the latch clock (top trace) is 100 ns. In the same operation, Figure 14 shows the results for the LTA operation. The final outputs Vos1, Vos2, Vos3, …, and Vos10 are logic 0, 0, 0, 0, 0, 0, 0, 0, 0, and 1, respectively, and the input variable Vin10 is the minimum one. Choice for the above tested voltages was based on the followings: 1) input voltages of neighbor cells should be as close as possible to test discrimination capabilities; 2) input voltages are distributed from 0 V to 3.3 V to test for wide dynamic range.
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2) Supply voltage range
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All circuit parameters such as transistor dimensions, clock periods and sampling capacitance Cs are held constant. A supply voltage VDD varies from 2 V to 5 V, and the logic high of these clocks are also modified when the supply voltage alters. The supply voltage VDD for each iteration increases in 0.1 V steps. The simulation results show that the circuit operates successfully within 3-mV discrimination when the supply voltage ranges from 2.7 V to 5 V. Without any procedure for rescaling the device size, the circuit works under various commonly used supply voltages.
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Figure 13.
Simulation results of the WTA operation.
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Figure 14.
Simulation results of the LTA operation.
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3) Process variations
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A statistical distribution of manufacturing parameters often occurs during CMOS fabrication. Wafer-to-wafer, run-to-run and transistor-to-transistor process variations determine the electrical yield and critical second-order effects. Threshold voltage, channel widths, and channel lengths of all MOS transistors were set to nominal values with ±5 % variation at the 3 sigma level, and each transistor was given an independent random Gaussian distribution. After 30 Monte Carlo iterations, HSPICE results indicate that circuit precision and speed are not degraded over this range. In addition, to verify the circuit with multi-technology support capability, using various CMOS fabrication parameters also simulates the circuit performance. The results show that the performance of the circuit under various fabrication processes is functional work, without needing to tune any device dimension. The following reasons contribute to the robustness of this circuit: 1) the circuit is designed with only a single analog cell (comparator), while the other active components are digital; 2) the comparator itself is designed with a auto-zero property, therefore, the operation of the comparator is more tolerant to manufacturing process variation.
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4) Circuit precision
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The accuracy of the comparator cell dominates the identified precision. The comparator accuracy is dependent on two factors. One is the clock feed-through error and charge-injection error in transistor Msw3, shown in Figure 8; the other is the degrading factor in Eq. (1). Charge-injection error is a complicated function of substrate doping concentration, load capacitor, input level, clock voltage, clock falling rate, MOS channel dimension, and the threshold voltage. Therefore, this error is difficult to be completely eliminated. In general, complementary clock, transmission gates, and dummy transistor are adopted for a switch realization to reduce the error.
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3. CMOS analogue median cell
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Median (MED) filter is a useful function in image processing application to eliminate pulse noise. Given a set of external input n variables a1, …, an, the operation of MED circuit determines the median value. The extracted median operation is a nonlinear function. The MED circuit realizations can be classified as analog filtering and digital filtering depending upon what type of input signals are. The digital filtering architecture has a variety of sophisticated algorithms to support the circuit realization so as with advantages of higher flexible and higher reliability. For power consumption and chip area considerations, however, it is costly expensive than analog architecture. In 1994, without using an operational amplifier, an analogue median extractor with simple structure and high sharp DC transfer characteristic was presented (Opris & Kovacs, 1994). The circuit expects to reduce the errors in the transition region. In 1997, for the same authors, an improved version with high speed operation was proposed. The median circuit has transient recovery less than 200 ns by using 2-um CMOS process (Opris & Kovacs, 1997). In 1999, a current-input analog median filter composed of absolute value and minimum circuits was proposed (Vlassis & Siskos, 1999). The operational amplifier and transconductor are also not needed in design of the circuit. Based on transconductance comparators and analog delay elements, a fully continuous-time analog median filter is presented in 2004 (Diaz-Sanchez et al., 2004). By using the median filter cells, an image of 91×80 pixels can be processed in less than 8 μs to remove salt and pepper noise. In the section, an intuitional and simple CMOS analog median cell is described (Hung et al., 2007). Based on current-mirror, current comparison, and some basic digital logics, a simple analog median filter cell is achieved. By using TSMC 0.35 μm CMOS technology, simulation shows that the median filter provides a 0.4-μA discriminability and well tracked the median value among input currents.
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\n\t\t\t\tFigure 15 shows a basic one-input current cell composed of current mirror and control logic circuits. The cell has one signal input (is), a current source (is_src) output and a current sink (is_sink) output, a control signal Vctr., and an output current (iout). Transistors M1-M12 are cascode current mirrors. Mswp and Mswn constitute transmission gate for analog switch function. Mdummy is designed to compensate the Mswn and Mswp loading to improve the accuracy of output current. Miso is used to isolate the clock noise from transmission gate. Mdis1-2 and Mres are used to speedup transmission operation and control the discharge timing. Corresponding to Figure 15(a), Figure 15(b) is a symbol representation, which is named as current signal control unit and is abbreviated as CSCU.
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Figure 15.
Current signal control unit (CSCU): (a) circuit and (b) symbol representation.
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Three input signals is1, is2, and is3, how can circuit extract the median value? Assuming is2 is a median current. The criteria must be satisfied.
As a result, current level comparison and logic decision are required to realize the function. Figure 16 shows a three-input median circuit composed of three CSCU cells and three decision logic blocks. The decision logic circuit is simply realized by AND-OR gate circuit to perform
where (1), (2), (3) and (4) represent the corresponding the logic inputs, that is, these signals come from comparison results signals. Depending on the output status of each decision logic, Eq. (3) determines Vctr a low level or a high level, respectively. A low Vctr will turn on the transmission gate of corresponding CSCU cell to switch on the input current; otherwise, the input current is prohibited. As a result, three-input MED filter cell is successfully arrived. Due to the transition pulse noise, a capacitor Cfilter is used to suppress the switch noise.
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In the circuit, NMOS transistor size (W/L)N=5μ/1μ and PMOS transistor size (W/L)P=10μ/1μ are used for M1-M12. The sizes of inverters are (W/L)N=5μ/0.35μ and (W/L)P=20μ/0.35μ. The device site of switch transistors Mswn and Mswp are equal to (W/L)N-P=20μ/0.35μ. All transistors in decision logic block are sizing (W/L)N=5μ/0.35μ and (W/L)P=10μ/0.35μ. The filter capacitance Cfilter is designed as 10 pF. The supply voltage VDD is commonly used as 3.3 V. Input current signals is1, is2, is3 have 10 μA peak value at different 5 μs, 10 μs, and 15 μs time slot, respectively. Figure 17 shows three triangle waves and the corresponding median output. The red line represents the MED output. The output is tracked well with the median value of the three inputs current. By observing Figure 17, when two input values are closed to each other, the minimum difference must be larger than 0.4 μA. That is the discriminability of the MED filter. However, there are some little spike occurs in the transition point.
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Figure 16.
Three-input median cell.
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Figure 17.
The output response of the median filter for triangle waveforms.
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Inspecting Figure 16, the proposed three-input median cell has three input pins (is1, is2, and is3) and a common output pin (iout). By modifying the switch transistors and decision logic, the MED cell can be easily modified as three inputs and three outputs. The modified MED cell will have maximum value imaxmin, median value imedian, and minimum value iminmum outputs, simultaneously. As a result, the multiple modified MED cells can be organized cooperation to perform the ‘sorting’ function. In the design, no critical components such as operational amplifier and precise voltage reference are required in the MED cell. These properties are useful for the MED cell simply embedded into a larger system.
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4. Low-voltage arbitrary rank order extraction
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4.1 Principle of rank-order extraction
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Ether WTA, LTA, or MED function, however, is only a single order operation. In 2002, a low-voltage rank-order filter with compact structure was designed (Cilingiroglu & Dake, 2002). The filter is based on a pair of multiple-winners-take-all and a set of logic gates. In the section, a new architecture for with both arbitrary rank-order extraction and k-WTA functionalities is described (Hung & Liu, 2002). An rth rank-order extraction is defined that identifies the rth largest magnitude of input variables. In the design, the circuit locates an arbitrary rank order among a set of input voltages by setting different binary signals. A set of output voltages Vo_1, Vo_2, …, and Vo_M corresponds to the output voltages of a rank-order extractor for inputting of a set of variables V1, V2, …, and VM. The output status Dij of a comparator with two-input terminals is defined as
where M is the number of the input variables. For convenience of description, a temporal index Si defines the total number of winners for the ith input variable compared with the others. Thus, Si is represented as
Thus, from the left-hand side of (6), M(M-1) comparators’ cooperation is required for M input variables to identify the rank order. Since Dji is the complementary of Dij ( Dji=\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tthe expression is replaced by \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tD\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t¯\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tin the right-hand side of (6). The physical meaning is that if both the output of the comparator and its complementary are given, the total number of comparators can be reduced from M(M-1) to M(M-1)/2.
\n\t\t\t\t
In this section, the comparator generates a unit current Iunit when input variable Vi is larger than Vj. Thus, the index Si in (5) is rewritten as
where n is the number of the winner in comparison. If the inputs are arranged in ascending order of magnitude, V1, V2, …, VM, which satisfy V1<V2< … <VM, then\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t...,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tM\n\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tObviously, the minimum, next minimum, …, maximum input variables can be found by checking the index\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tThe k-WTA function is defined so that the outputs must be logic high when
For example, if the input variables are (0.5, 0.6, 0.9, 0.2, 0.4), the first variable 0.5 is larger than variables 0.2 and 0.4. Thus, the index \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is 2Iunit; the meaning is that the variable wins two other input variables among all comparisons. For the same reason, the\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t4\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t4\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t5\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tTherefore, the rank order is found among the input variables by checking the index\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. In this example, the output voltages (Vo_1, Vo_2, …, Vo_5) of the extractor respond to be (0, 0, 1, 0, 0), (0, 1, 0, 0, 0), (1, 0, 0, 0, 0), (0, 0, 0, 1, 0) for the maximum operation, next maximum operation, median operation, and the minimum operation, respectively. The “0” and “1” are the logic low and high. Similarity, if the extractor is configured as k-WTA function, the output voltages (Vo_1, Vo_2, …, Vo_5) of the circuit respond to be (1, 1, 1, 1, 1), (1, 1, 1, 0, 1), (1, 1, 1, 0, 0), …, and (0, 0, 1, 0, 0) for 5-WTA, 4-WTA, 3-WTA, …, and 1-WTA operations, respectively.
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4.2 Architecture of rank-order extraction
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The structure of the extractor is shown in Figure 18 for five input variables (Hung & Liu, 2002). There are a total of M(M – 1)/2 comparators and M evaluation cells for M input variables. Each comparator cell accepts two input signals, and the results of each comparison are fed into the individual evaluation cell. In the first row of Figure 18, the input V1 is compared with other input variables. In addition, the results of the comparison will generate the proper unit currents Iunit. Then, these currents will be summed up in Eval-1 cell if V1 is larger than the other samples; otherwise, the result of the comparison will be fed into the corresponding evaluation cell. The connecting strategy is the same for other input variables. Therefore, equation (7) have been realized in this architecture.
\n\t\t\t\t
The signal Vchoice in Figure 18 is used to decide the function of the circuit. Vchoice is preset at logic high to allow the rank-order operation; otherwise, the k-WTA function is enabled. The binary signals sel_1, sel_2, and sel_3 are used to determine which rank-order/k-WTA will be located. Based on the select signals (sel_1-3) setting, the logic states of the evaluating cells indicate which input variable belongs to this rank order. For example, in the seven inputs rank-order operation, the (sel_1, sel_2, sel_3) signals are set to logic (0, 0, 0) to find the minimum variable; the logic (0, 1, 1) and (1, 1, 0) setting are the median and maximum functions, respectively. Similarity, in the k-WTA operation, the (sel_1, sel_2, sel_3) is set as (0, 0, 1) and (1, 1, 0); therefore, the 6-WTA and 1-WTA are obtained, respectively.
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Figure 18.
The architecture of arbitrary rank-order extractor for five input variables.
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4.3 Circuit design
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4.3.1 1.2-V comparator
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Comparator is a key element in Figure 18. An auto-zero comparator shown in Figure 19 is designed to operate at low voltage supply. To improve the speed of the comparator, the succeeding gain stage is designed to operate in dynamic mode. First, in the auto-zero phase, the input V1 is sampled at the top plate of the capacitor Cs, and the MOS transistor M11 is biased at Vbias voltage. In next phase, the voltage at node E is Vbias+(V2-V1)(Cs/Cs+Cp) during the comparison phase. Then, a deviation voltage is amplified by transistors M11 and M12. To reduce the power dissipation, the adjustable biasing voltage Vbias is chosen simply to overcome the threshold voltage of a MOS transistor, and the biasing voltage is also adjusted for the comparator operation in different voltage supplies. The succeeding transistors M13 and M14 provide the current to generate the proper voltage at node F. Depending on which input voltage is larger, either the voltage at node H or node G will be at logic high. The output node G of the comparator and its complementary node H are fed into next stage to generate unit currents Ilarge_1, Ilarge_2, Ismall_1, and Ismall_2. During the evaluation phase, the unit currents Ilarge_1 and Ilarge_2 will be presented when V1 is larger than V2. Otherwise, the Ismall_1, Ismall_2 are generated. The symbol representation of the comparator cell is shown in the right-bottom of Figure 19.
\n\t\t\t\t\t
The function of the comparator shown in Figure 19 is summarized as
where \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t is the unit current of the PMOS transistor Mbase.
\n\t\t\t\t
\n\t\t\t\t
Figure 19.
V auto-zero comparator, clock, and symbol representation.
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4.3.2 Evaluation cell
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Figure 20.
Evaluation cell.
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The circuit of the evaluation cell is shown in Figure 20. The MOS transistors Mgen and Munit reproduce the same unit current. The unit current is equal to the Ilarge_1, Ilarge_2, Ismall_1, and Ismall_2 in Figure 19. In order to find the various rank orders for all input signals, the cell must identify that the unit-current summation in (7) comes from Out_com1 and Out_com2 terminals. It is not easy to identify the exact current value in the VLSI circuit. However, whether the summation current \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tS\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t*\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t lies inside a valid range or not can be checked by the criterion,
It is a reasonable and safe design to choose\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tI\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tu\n\t\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t/\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\tTherefore, the dimensions of these MOS transistors are designed as
where W is a channel width and L is a channel length. MOS transistors Madd1 and M4 realize the \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t effect, and the M8 realizes the \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t one. Depending on the sel_1-3 signals setting, the transistors Mcnt_1-6 enable the corresponding binary-weight current. The inverters inv4-7 support sufficient gain to amplify the current difference between the currents which come from Out_com1-2 terminals and the binary-weight currents. This mechanism is similar to a current comparator. In the upper row of Figure 20, the extra PMOS transistor Madd1 generates an extra unit current; therefore, the voltage Vout-h is always larger or equal to Vout-l. If the Vchoice is preset to 0, the dash block in Figure 20 resets the Vout-l to 0. Then the effect of lower row in Figure 20 is disabled. At this time, the function of the cell resembles performing only the
Take an example to describe the function of the evaluation cell. The number of input variables is seven, and the sel_1-3 signals are set as (0, 0, 1) to find the next minimum input variable. Since the next minimum is only larger than the minimum one, only a single unit current comes from Out_com1-2 terminals of the corresponding evaluation cell. In the upper row of Figure 20, the summation of one unit current and the extra unit current (Madd1) is larger than binary weight current 1.5Iunit; therefore, Vout_h is logic 1. In contrast with the upper row, in the lower row the unit current Iunit (which comes from Out_com1-2 terminals) is smaller than the binary weight current 1.5Iunit; therefore, Vout_l is logic 0. Thus, the transistors Mid1 and Mid2 only allow the situation (Vout_h, Vout_l)= (1, 0) to pull up the corresponding output (Vo_n, n=1, …, 7) to logic 1. Otherwise, the status of Vo_n will be logic 0 or open state for other cases. Therefore, by inspecting the logic state of Vo_n, it is found which input variable belongs to this desired rank order.
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4.4 Measured results and design consideration
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A seven-input experimental chip was fabricated using a 0.5 μm CMOS technology. Bias voltage Vbias is set to 0.9 V in this design. The sampling capacitor Cs is 0.8 pF, and these analog switches in this circuit are implemented by CMOS transmission gates. The micrograph of the experimental chip is shown in Figure 21, and the active area is 610 × 780 μm2. An individual comparator cell was built in this chip for measuring the accuracy. The supply voltages of the core circuit and the input/output pads were all set as 1.2 V. The accuracy of the individual comparator was measured roughly as 40 mV, that is, the resolution of the comparator was near five bits under a 1.2 V supply voltage. Figure 22(a)
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Figure 21.
Micrograph of the 1.2-V rank-order chip.
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Figure 22.
The measurement results of (a) rank-order (b) k-WTA operations.
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shows the rank-order function, whereas Figure 22(b) shows the function of the k-WTA. On the average, the accuracy of whole circuit was approximated 150 mV. The performance of the chip was degraded by many factors such as the mismatch in comparator cells, the different capacitance at input terminals of the evaluation cells, and the clock feed-through error. Due to these non-ideal effects, each rank-order function was finished in 20 μs. After increasing supply voltage up to 1.5 V and proper biasing voltage Vbias adjusting, the performance of the circuit can be improved. Including power consumption of the input/output pads, the static power consumption of the chip was 1.4 mW.
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Many factors such as precision, speed, process variation, and chip area must be considered for design of a low-power low-voltage rank order extractor.
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Limitations of low voltage and low power
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The average power consumption of the circuit is expressed by
where f is the frequency, C is the capacitance in the circuit, VDD is the voltage supply, Io is the standby current, Ileakage is the leakage current, and the Qsc is the short-current charge during the clock transient period. In order to reduce the power consumption, the voltage supply VDD must be reduced, and the standby current in the comparator and evaluation cell must be designed as small as possible. In mask layout, the clock and its complementary are generated locally to reduce delay and mismatch. Thus, the probability of a short current occurring in the circuit is minimized.
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Speed and precision
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The accuracy of the comparators determines the resolution of the circuit. For the comparator design, the smallest differential voltage, that is, distinguished correctly is influenced by two factors. One is the charge-injection error in analog switches, and the other is the parasitic capacitor Cp effect. The effect is reduced by enlarging the sampling capacitor Cs and making the switches dimension as small as possible. In the design, the response time \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t of the extractor is the summation of the auto-zero time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t the comparison time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, and the evaluation time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
Reducing\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t will improve the response time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tThe minimum auto-zero time \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is required to sample the input voltage correctly at sampling capacitor Cs and to bias the inverter properly at high gain region. The switches shown in Figure 19 with larger dimension reduce auto-zero time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tHowever, the clock feed-through error and charge injection error will also be enlarged during the clock transition. In the same situation, the smaller sample capacitor Cs will reduce the time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tz\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tUnfortunately, it will reduce the effective magnitude of the difference voltage; thus, the comparator accuracy is degraded. The comparison time \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t dominates the response time\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tespecially when the input levels are close each other. Since the amplification in the transition region of a CMOS inverter operated at low voltage supply is not high enough, the comparator must take a long time to identify which input variable has a larger level. The evaluation time \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is defined so that the time interval between the comparator cells generates the proper currents and the extractor has finished finding the desired rank order. Time \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is a function of the current Iunit. The maximum number M of input variables is also influenced by the current Iunit. Although reducing the magnitude of the current Iunit is able to reduce the power consumption, however, the relationship among\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, Iunit, and M in this architecture is a complicated function.
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Process variation analysis
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With contemporary technology, process variation during fabrication cannot be completely eliminated; as a result, mismatch error must be noticed in VLSI circuit design. The match in dimension of the binary-weight MOS in the evaluation cell (M1 - M8 in Figure 20) is an important factor for the circuit operation. If the mismatch error induces an error current Ierr larger (or smaller) than half of the unit current Iunit, decision of the evaluation cell fails. Thus, a rough estimated constraint for Ierr is
The chapter describes various nonlinear signal processing CMOS circuits, including a high reliable WTA/LTA, simple MED cell, and low-voltage arbitrary order extractor. We focus the discussion on CMOS analog circuit design with reliable, programmable capability, and low voltage operation. It is a practical problem when the multiple identical cells are required to match and realized within a single chip using a conventional process. Thus, the design of high-reliable circuit is indeed needed. The low-voltage operation is also an important design issue when the CMOS process scale-down further. In the chapter, Section 1 introduces various CMOS nonlinear function and related applications. Section 2 describes design of highly reliable WTA/LTA circuit by using single analog comparator. The analog comparator itself has auto-zero characteristic to improve the overall reliability. Section 3 describes a simple analog MED cell. Section 4 presents a low-voltage rank order extractor with k-WTA function. The flexible and programmable functions are useful features when the nonlinear circuit will integrate with other systems. Depend on various application requirements, we must have different design strategies for design of these nonlinear signal process circuits to achieve the optimum performance. In state-of-the-art process, small chip area, low-voltage operation, low-power consumption, high reliable concern, and programmable capability still have been important factors for these circuit realizations.
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\n\t\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/9847.pdf",chapterXML:"https://mts.intechopen.com/source/xml/9847.xml",downloadPdfUrl:"/chapter/pdf-download/9847",previewPdfUrl:"/chapter/pdf-preview/9847",totalDownloads:3053,totalViews:304,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:1,dateSubmitted:null,dateReviewed:null,datePrePublished:null,datePublished:"April 1st 2010",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/9847",risUrl:"/chapter/ris/9847",book:{slug:"advances-in-solid-state-circuit-technologies"},signatures:"Hung, Yu-Cherng",authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Winner-Take-All and Loser-Take-All circuit",level:"1"},{id:"sec_2_2",title:"2.1 Architectures of WTA/LTA circuits",level:"2"},{id:"sec_3_2",title:"2.2 A high reliable WTA/LTA circuit",level:"2"},{id:"sec_4_2",title:"2.3 Simulation results and reliability test",level:"2"},{id:"sec_6",title:"3. CMOS analogue median cell",level:"1"},{id:"sec_7",title:"4. Low-voltage arbitrary rank order extraction",level:"1"},{id:"sec_7_2",title:"4.1 Principle of rank-order extraction",level:"2"},{id:"sec_8_2",title:"4.2 Architecture of rank-order extraction",level:"2"},{id:"sec_9_2",title:"4.3 Circuit design",level:"2"},{id:"sec_9_3",title:"4.3.1 1.2-V comparator",level:"3"},{id:"sec_10_3",title:"4.3.2 Evaluation cell",level:"3"},{id:"sec_12_2",title:"4.4 Measured results and design consideration",level:"2"},{id:"sec_14",title:"5. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAksin\n\t\t\t\t\t\t\tD. Y.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 A high-precision high-resolution WTA-MAX circuit of O(N) complexity. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., 49\n\t\t\t\t\t1 2002, 48\n\t\t\t\t\t53 .\n\t\t\t'},{id:"B2",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCilingiroglu\n\t\t\t\t\t\t\tU.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDake\n\t\t\t\t\t\t\tL. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 Rank-order filter design with a sampled-analog multiple-winners-take-all core. IEEE J. Solid-State Circuits,\n\t\t\t\t\t37 Aug. 2002, 978\n\t\t\t\t\t984 .\n\t\t\t'},{id:"B3",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDemosthenous\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSmedley\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTaylor\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1998 A CMOS analog winner-take-all network for large-scale applications. IEEE Trans. Circuits Syst. I, Fundam. 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Lett., 29\n\t\t\t\t\t14 1993, 1237\n\t\t\t\t\t1239 .\n\t\t\t'},{id:"B6",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHosotani\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMiki\n\t\t\t\t\t\t\tT.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMaeda\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYazawa\n\t\t\t\t\t\t\tN.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1990 An 8-bit 20-MS/s CMOS A/D converter with 50-mW power consumption. IEEE J. Solid-State Circuits,\n\t\t\t\t\t25\n\t\t\t\t\t1 Feb. 1990, 167\n\t\t\t\t\t172 .\n\t\t\t'},{id:"B7",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHung\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLiu\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\tD.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2002 A 1.2-V rail-to-rail analog CMOS rank-order filter with k-WTA capability. Analog Integr. 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Proceedings of IEEE Conference on Electron Devices and Solid-State Circuits (EDSSC), 361\n\t\t\t\t\t364 , Dec. 2007, Tainan, Taiwan.\n\t\t\t'},{id:"B10",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLazzaro\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRyckebusch\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMahowald\n\t\t\t\t\t\t\tM. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMead\n\t\t\t\t\t\t\tC. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 Winner-take-all networks of O(N) complexity. Advances in Neural Inform. Processing Syst., 1 1989, 703\n\t\t\t\t\t711 .\n\t\t\t'},{id:"B11",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tLippmann\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1987 An introduction to computing with neural nets. IEEE Acoust., Speech, Signal Processing Mag.,\n\t\t\t\t\t4\n\t\t\t\t\t2 Apr. 1987, 4\n\t\t\t\t\t22 .\n\t\t\t'},{id:"B12",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tOpris\n\t\t\t\t\t\t\tI. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKovacs\n\t\t\t\t\t\t\tG. T. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1994 Analogue median circuit. Electron. Lett., 30\n\t\t\t\t\t17 Aug. 1994, 1369\n\t\t\t\t\t1370 .\n\t\t\t'},{id:"B13",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tOpris\n\t\t\t\t\t\t\tI. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tKovacs\n\t\t\t\t\t\t\tG. T. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1997 A high-speed median circuit. IEEE J. Solid-State Circuits, 32 June 1997, 905\n\t\t\t\t\t908 .\n\t\t\t'},{id:"B14",body:'\n\t\t\t\t\n\t\t\t\t\tSemiconductor Industry Association.\n\t\t\t\t\t2008 International technology roadmap for semiconductors 2008 update. [Online]. Available: http://public.itrs.net/.\n\t\t\t\t\n\t\t\t'},{id:"B15",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSmedley\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTaylor\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWilby\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1995 A scalable high-speed current mode winner-take-all network for VLSI neural applications. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 42\n\t\t\t\t\t5 1995, 289\n\t\t\t\t\t291 .\n\t\t\t'},{id:"B16",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tStarzyk\n\t\t\t\t\t\t\tJ. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tFang\n\t\t\t\t\t\t\tX.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1993 CMOS current mode winner-take-all circuit with both excitatory and inhibitory feedback. Electron. Lett., 29\n\t\t\t\t\t10 1993, 908\n\t\t\t\t\t910 .\n\t\t\t'},{id:"B17",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tVlassis\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSiskos\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1999 CMOS analogue median circuit. Electron. Lett., 35\n\t\t\t\t\t13 June 1999, 1038\n\t\t\t\t\t1040 .\n\t\t\t'},{id:"B18",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYamakawa\n\t\t\t\t\t\t\tT.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1993 A fuzzy inference engine in nonlinear analog mode and its applications to a fuzzy logic control. IEEE Trans. Neural Netw., 4\n\t\t\t\t\t3 May 1993, 496\n\t\t\t\t\t522 .\n\t\t\t'},{id:"B19",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYuan\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tStensson\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1989 High- speed CMOS circuit technique. IEEE J. Solid-State Circuits, 24\n\t\t\t\t\t1 Feb. 1989, 62\n\t\t\t\t\t69 .\n\t\t\t'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Hung Yu-Cherng",address:null,affiliation:'
National Chin-Yi University of TechnologyTaiwan, R.O.C.
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1. Introduction
Diamond has been an attractive semiconductor in the fields of power electronics [1], valleytronics [2], optoelectronics [3, 4], and quantum information technology [5, 6] in recent years. Such application-oriented studies have been arising from the outstanding values of breakdown voltage, thermal conductivity, carrier mobility, and spin relaxation time in a diamond. This direction is accelerated due to the progress of crystal growth technique by the chemical vapor deposition (CVD) in these decades [7], by which a highly pure diamond becomes commercially available.
To design diamond-based devices, the knowledge of transport parameters, such as effective mass, scattering time, and drift mobility, is necessary. The effective mass is an important parameter in the band theory of a semiconductor, governing the transport properties, density of states, and the phase boundary of high-density carriers. The drift mobility involving the values of the effective mass and scattering time is a direct index of carrier transport. However, in the past when only natural crystals or impurity-rich synthesized crystals were available, limited information about intrinsic carrier properties had been reported [8, 9, 10, 11, 12, 13, 14]. This historical situation is in contrast to the current materials, silicon, and germanium. In silicon or germanium, a cyclotron resonance method played a significant importance to determine the effective masses for doped crystals under activation by light at low temperature in the 1950s [15, 16]. Such accurate measurements at low temperature had been impossible in diamond due to deep dopant states in the wide energy bandgap. Therefore, most of previous measurements were performed at temperatures higher than 80 K, where a carrier transport was limited by phonon scatterings. A part of anisotropic hole masses were obtained from unresolved spectra at higher temperature than 300 K [11, 12]. Information on the electron was much less, because most of the semiconducting diamond was of p-type.
Recently, measurements of time-of-flight (TOF) transport [2, 10, 17, 18] and optical transient grating [19, 20] have been performed with the highly pure crystals. However, the measured carrier mobility varied from sample to sample depending on the surface termination condition, the crystal supplier, and experimental conditions. A high-density injection under high electric field, the space charge-limited transport condition under higher dopant concentration, and non-Ohmic contact caused extrinsic effects on transport behaviors. To clarify intrinsic carrier properties in a diamond, a measurement should be achieved at low temperature under a low carrier density.
In this chapter, our recent experimental contributions to clarify the basic and intrinsic carrier parameters in a diamond will be introduced [21, 22, 23, 24, 25, 26, 27]. The measurement has been performed by a time-resolved cyclotron resonance method under optical carrier injection in pure diamond crystals. The concept of our measurement is shown in Figure 1: carriers are injected optically with ultra-violet laser pulses through the band-to-band transition or exciton creation with an assistance of phonon emission/absorption in the indirect band structure (Figure 1a). Although the created exciton is an electrically neutral binding state of electron and hole, free charge carriers are dissociated from excitons via two-body collision of excitons or thermal dissociation as described in Section 3.2. During the long lifetime of the free carriers in the indirect band structure, we can observe the cyclotron resonance under the external magnetic field (Figure 1b). Keys to realize our measurements in an intrinsic semiconductor diamond are the optical carrier injection technique and using of highly pure diamond. As in the case of pure silicon [28], which had been applied to a light-triggered thyristor as a successful power device, optical carrier injection is a promising technique to control a carrier density by a sophisticated way. The spectroscopic way of the optical carrier injection in a diamond at device-operating temperature as well as at low temperature will also be introduced.
Figure 1.
Schematic experimental concept. (a) Energy diagrams of valence and conduction bands for indirect semiconductor diamond and exciton band and (b) cyclotron motion of optically injected free carriers converted from excitons.
2. Experimental method
The time-resolved cyclotron resonance (TRCR) method was performed for optically injected transient carriers in high-purity diamond crystals in X band (microwave frequency at ν= 9.6 GHz) with a time resolution of a few nanoseconds. The well-resolved CR spectrum can be observed under the condition, ωτ≫1, where ω=2πν is the angular frequency of applied microwave and τ is the carrier scattering time. As the ω is selected by a used equipment, it is necessary to make τ longer by lowering the temperature at cryogenic ones and using pure crystals in order to determine the effective mass in good accuracy.
Highly pure diamond crystals of type-IIIa grown by the CVD method were used. A typical concentration of nitrogen and boron atoms was less than 5 and 1 ppb, respectively ([N] < 9 × 1014 cm−3, [B] < 2 × 1014 cm−3). For crystals of higher impurity concentration, it was difficult to obtain the TRCR spectrum at 10 K because of the broader spectral width due to the higher carrier scattering rate. A typical crystal dimensions were of 3 × 2 × 0.5 mm3 with the largest plane of the crystalline (001). A crystal was attached on a 2 × 8 mm2 face of a right-angle prism by a small amount of vacuum grease for better coupling with the optical excitation (see Figure 2a). The sample was mounted in a dielectric microwave cavity (Bruker, MD5W1, TE011) that is developed for the pulsed electron paramagnetic resonance (EPR) in X band with a high filling factor, in which a microwave’s electric field packed in a round mode resonates with the cyclotron motion of free carriers under an external magnetic field.
Figure 2.
Schematic drawings of experimental method: (a) the equipment and inside of a microwave cavity, (b) a temporal response of continuously applied microwave to transiently generated carrier by laser pulse at an external magnetic field, and (c) an example of a CR peak in spectrum at a delay time.
The sample was irradiated by 5-ns pulses at wavelength selected in the range from 219.4 to 226.4 nm at low temperatures or from 219.4 to 235.6 nm at room temperature from an optical parametric oscillator (Spectra Physics, MOPO with frequency doubler option) pumped by THG of a Nd:YAG laser. Temporal responses of continuous microwave power were measured in a quadrature detection using microwave mixers and a two-channel oscilloscope of a system (Bruker, ELEXSYS E580) (Figure 2b). Inphase and out-of-phase signals to the input microwave were obtained as real and imaginary parts. The cavity’s quality factor Q was set at less than 800, corresponding to a time resolution of less than 13 ns by a formula, Δt=Q/ω. By sweeping the external magnetic field step-by-step, we obtained the set of the temporal response curves, from which a CR spectrum at a delay time was extracted as a function of the magnetic field as described in Section 3.1. Excitation spectra were also obtained by measuring the signal intensity at an external magnetic field as a function of the excitation wavelength at 10, 80, and 300 K. Although the CR spectrum was too broad to resolve any carrier species at higher temperatures, the amount of free carrier was estimated from the intensity of temporal response under the magnetic field. In addition, the signal intensity was measured according to the rise of temperature.
Important carrier parameters were extracted from a resonance peak in the CR spectrum (Figure 2c): the effective mass m∗ from the resonance magnetic field B0 by m∗=eB0/ω=eB0/2πν, the carrier scattering time τ from the spectral half width at half maximum Γ by 1/τ=ωΓ/B0, and carrier drift mobility μ=eτ/m∗, where e is the elementary charge of electron. The carrier scattering time is also called as momentum relaxation time. For the analysis of effective masses, CR spectra were measured as a function of the magnetic field orientation, where the crystal was rotated about [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] crystalline axis so that the external magnetic field was oriented in the (1–10) plane or rotated about [100] axis with the external magnetic field in the (100) plane. Temperature dependence of CR spectral width provides the aspects of carrier scattering mechanism.
In addition to the abovementioned parameters, although we will not describe details here, important properties of carrier generation and decay can be unveiled from the time-resolved cyclotron resonance method: analysis of the rise time of the temporal curve and the signal intensity depending on excitation laser intensity can reveal a carrier generation mechanism [22, 29]. A lifetime of the carrier in a rotating motion is extracted from the decay time of a temporal curve. Temporal variation of carrier density is also estimated based on the plasma shift analysis [16, 30, 31]. Here, to study the basic properties of carriers, we paid careful attention to minimize plasma shifts of the resonance peaks, with the incident pulse energy less than 5.8 μJ which ensures the carrier density at the delay times later than 600 ns is less than 1011 cm−3.
3. Results
3.1 Time-resolved cyclotron method
Figure 3a shows a colored contour map of a real part of TRCR signal measured at 7.3 K excited by laser pulses at photon energy of 5.50 eV. Temporal profiles at the magnetic fields of 0.089, 0.122, 0.162, and 0.230 T are shown in Figure 3b. CR spectra at the delay times of 60, 200, and 600 ns are shown in Figure 3c, by slicing the data set at the delay times. The magnetic field was applied to an angle of 40° from the crystal axis of [001] in the (1–10) plane. In this orientation, four carrier species, light hole, heavy hole, and two electrons in inequivalent conduction valleys, indicated by lh, hh, e1, and e2, respectively, were distinguishable as shown in Figure 3a and c.
Figure 3.
(a) A colored contour map of a real part of TRCR signal at 7.3 K excited by laser pulses of photon energy at 5.50 eV; (b) temporal profiles at 0.089, 0.122, 0.162, and 0.230 T denoted by vertical lines in (a); (c) CR spectra at the delay times of 60, 200, and 600 ns denoted by horizontal lines in (a).
3.2 Optical carrier injection
Optical carrier injection is a key technique in our nanosecond TRCR method. As a diamond has an indirect band structure as shown in Figure 1a, the optical carrier injection at the lowest photon energy is established with the assistance of phonon emission/absorption to satisfy the energy and momentum conservations. The lowest excited state is an exciton band located below the indirect band edge by a binding energy larger than 80 meV [32, 33], whose fine structures were recently clarified [34]. To clarify the spectroscopic way of carrier injection, an excitation spectrum of TRCR signal at the fixed resonant magnetic field was measured with a thin CVD crystal of 70-μm in thickness to suppress the saturation by exciton absorption.
Figure 4 shows the TRCR excitation spectra obtained at 10, 80, and 300 K. The signals were averaged at the time windows, (a) 80–280 ns at 10 K, (b) 352–552 ns at 80 K, and (c) 156–356 ns at 300 K, after the signal decayed to the 1/e of the peak intensity [26]. For such late times, we observed that carriers were dominantly generated by dissociation of excitons [27]. The onset energy of the excitation spectra (a, b) at 5.493 eV coincides with the exciton generation edge assisted by emission of a transverse acoustic (TA) phonon (Eex+ℏωTA), where Eex = 5.406 eV is the exciton energy and ℏωTA = 87 meV is the TA phonon energy [35] (see the inset). The second onset at 5.547 eV is assigned to exciton generation assisted by emission of a transverse optical (TO) phonon (Eex+ℏωTO), where ℏωTO = 141 meV is the TO phonon energy [35]. Therefore, in the range of the excitation photon energy above 5.493 eV, free carriers can be generated via excitons that are generated by the assistance of phonon emission. At the lower temperatures as 10 K, free carriers were generated by two-body collision of excitons, as the CR signal intensity was proportional to the square of excitation intensity [22].
Figure 4.
CR excitation spectra at (a) 10 K, (b) 80 K, and (c) 300 K. Vertical broken lines indicate the energy positions of Eex±ℏωTA, Eex±ℏωTO, and Eex. The inset shows schematic of phonon-assisted transitions to the exciton band. This figure was taken from [26] with a slight modification.
On the other hand, the signal at 300 K arose at the lower energy side with the onset at 5.265 eV. The onset energy coincides with the threshold for exciton generation assisted by absorption of a TO phonon (Eex−ℏωTO) (see the inset). The onset energy for TA phonon absorption (Eex−ℏωTA) is higher as indicated by the vertical broken line (the second one from the left) in Figure 4c. In the range of the excitation photon energy from 5.265 to 5.493 eV, free carriers can be generated only at higher temperatures via excitons that are generated by the assistance of phonon absorption. As the CR signal intensity measured at 300 K was proportional to the excitation intensity, the carriers are generated dominantly via a one-body process, such as thermal ionization of excitons [26].
Under the excitation in the range from 5.265 to 5.493 eV, where only the phonon absorption assists the process, the carrier number should increase with rising of the temperature according to the activation of phonons. The lower panel of Figure 5 shows temperature dependence of the temporal response intensity excited by laser pulse at 5.335 eV. Solid curves in the upper panel are the temperature dependence of the quantum statistical numbers n=1/expℏωi/kBT−1 of TA and TO phonons, where ℏωi, kB, and T are the phonon energies for i = TA or TO, Boltzmann constant, and temperature, respectively. The observed signal intensity rose around 150 K in coincidence to the appearance of TA phonon. This suggests that the phonon-assisted optical carrier injection is effective at device-operating temperatures.
Figure 5.
Temperature dependence of the temporal response signal intensity at 0.16 mT due to free carriers generated by laser pulse at 5.335 eV via phonon absorption. A broken curve in the lower panel is a guide to eyes. Solid curves in the upper panel show the temperature dependence of the quantum statistical number 〈n〉 of TA or TO phonon.
In the subsequent Sections 3.3–3.5, we focus on the carrier properties at temperatures below 50 K. This temperature range is uniquely reached by our method owing to the optical carrier injection without the need of thermal activation of carriers from deep levels. For an efficient carrier generation at these temperatures, the excitation wavelength was chosen in the range of 219.4–226.4 nm. Furthermore, we discuss the CR spectra at the later delay times after 600 ns (see Figure 3) by eliminating the plasma shift effect at the earlier delay times depending on experimental conditions [16, 31].
3.3 Determination of effective masses
Both CR spectra of real and imaginary parts were well fitted by the formula for the complex conductivity [15]:
SB=∑j1−iBj/Γj1−iBj/Γj2+B2/Γj2,E1
where Γj is a half width and Bj is a central magnetic field at the resonance taken to be common for both real and imaginary parts, B is an external magnetic field, and j represents each resonant component (j=lh,hh,e1,e2). We can obtain the effective mass mj∗ and momentum relaxation time τj from these fitting parameters by using the relations, m∗=eB0/ω and 1/τj=ωΓj/Bj. Figure 6 plots the extracted effective masses mj∗ at the magnetic field orientations: the positive angles indicate the magnetic field in the (1–10) plane for the rotation axis along [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], whereas the negative angles indicate the magnetic field in the (100) plane for the rotation axis along [100].
Figure 6.
Angular dependence of effective masses, taken from Ref. [21].
The effective masses of electrons were simulated according to the following equation [15]:
mei∗=mt2mlmt1−giθ2+mlgiθ2,i=1,2,3,E2
where g1θ=±sinθ/2,g2θ=g3θ=±cosθ on (1–10) plane and g1θ=±sinθ,g2θ=±cosθ,g3θ=0 on (100) plane. The curves calculated with parameters mt/m0=0.280 and ml/m0=1.560[21] trace the data points very well. The curves of e1 and e2 in the (1–10) plane originate from two and four equivalent valleys, respectively. The curve of e2 splits into two curves in the (100) plane, where electron of a constant effective mass is referred as e3.
On the other hand, the effective masses of holes were simulated according to the equation for light (−) and heavy (+) holes [15]:
mh∗~−1A±B′1±1A±B′C2B′116fθ,E3
where fθ=1−3cos2θ2/4 in the (1–10) plane and fθ=1−3cos2θsin2θ in the (100) plane. The thick lines for lh and hh were calculated with parameters A=−2.670,B′=1.245,C=1.898 [21]. The thin lines are calculated with the upper and lower limit of errors, ΔA=±0.020,ΔB′=±0.025,ΔC=±0.048. Moreover, the split-off hole mass calculated from the parameter as mso/m0≈ℏ2/2m0A is also plotted by a broken red line. These parameters give band dispersion at the Γ point,
Ek=Ak2±B2k4+C2kx2ky2+ky2kz2+kz2kx2E4
with a transformation by B′=B2+C2/4. The finite value of Cgives rise to the warping of the valence band.
As we report in detail in Ref. [21], it is experimentally figured out that the electrons are in highly asymmetric valleys along the <001> directions, that is, at the △ points, with the transverse effective mass (mt=0.280m0) and longitudinal effective mass (ml=1.560m0). And, the doubly degenerate valence-band maxima are located at the Γ point and warping. The values of effective masses were listed in Table 1 in comparison to those of silicon and germanium [15]. The calculated values of the density of mass for electron med=mt2ml1/3 and hole mhd=mlh3/2+mhh3/2+mSO3/22/3 were also listed with the value of direct bandgap energy at Γ point.
Comparison of effective mass in group-IV semiconductor.
Values of germanium and silicon were taken from Ref. [15].
Sample
Growth
Boron
Nitrogen
Dislocation
A
CVD (001)-sector
<1 ppb
<5 ppb
–
B
CVD (001)-sector
<50 ppb
<100 ppb
–
C
HPHT+neutron irrad.
–
51 ppm
–
D
HPHT (001)-sector
<0.8 ppb
<45 ppb
Free
E
HPHT (111)-sector
<0.8 ppb
<45 ppb
Free
Table 2.
Specification of used samples.
“-” means unknown.
Figure 7 compares the angular dependence of effective masses of diamond with those of silicon and germanium [15] with the same angular definition as in Figure 6. The conduction-band minimum in silicon is located at the △ points as in a diamond, while that in germanium is located at the L points. It is easily recognized that the effective masses in diamond are largest among group-IV semiconductors, reflecting the largest direct bandgap energy at the Γ point which causes relatively larger contribution of the first perturbation term in the k·p theory to the effective mass of an energy band.
Figure 7.
Comparison of effective mass in group-IV semiconductor: angular dependence of effective masses simulated with the experimentally obtained parameters, in (a) diamond [21], (b) silicon [15], and (c) germanium [15]. Three electrons (blue lines) and light and heavy holes (red lines) are plotted for two rotation planes; the negative angles mean the magnetic field in the (100) plane for the rotation axis along [100], whereas the positive angles mean the magnetic field in the (1–10) plane for the rotation axis along [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
3.4 Sample dependence of carrier lifetime
A well-resolved spectrum of TRCR at the lower temperatures allows extracting the effective masses in good accuracy as described in Section 3.3. We compared the TRCR signals in different samples as reported in Refs. [24, 25]. The sample showed the narrower spectral width as presented in Figure 3 possesses the smaller concentration of donor and acceptor, that is, nitrogen and boron. Figure 8 shows temporal profiles of five different samples. The sample displayed a slow rise and decay in a couple of hundred nanoseconds (sample A) which is identical to that in Figure 3. The narrow spectral width is caused by the long carrier scattering time. From the comparison of CR spectra of CVD diamonds to those of dislocation-free HPHT diamonds, we found the fact that the TRCR detection is rather insensitive to crystalline dislocations [24]. It is known that a typical dislocation density in CVD diamond is lower than 104 cm−2 [36], corresponding to dislocation periods larger than 100 μm. On the other hand, the cyclotron radii in the measurement with X band microwave were 86 and 55 nm for light and heavy holes, respectively. As the carriers rotate in the much smaller spatial extension than the typical dislocation period in CVD samples, the CR detection is rather insensitive to dislocations. Instead, impurity scattering by neutral nitrogen atoms is found to be dominant at low temperatures (as described in Section 3.5), because their average separations are comparable to the cyclotron radii in the present case.
Figure 8.
Temporal profiles at the resonance of light hole in different five samples listed in Table 2, taken from Ref. [25].
From these facts, we emphasize that the accurate determination of effective masses as described in Section 3.3 became possible, since we could use a highly pure diamond produced by the CVD method under the optical carrier injection.
The rise time and decay time in the temporal profile of TRCR in Figures 3b and 8 reveal carrier generation and trapping mechanism. The finite rise time reflects the time required for carrier creation by exciton collision. A detailed formula giving an approximate rise time in connection with the lifetime is described in Refs. [22, 29]. The shorter decay time is probably caused by the higher density of impurity concentrations (in comparison among samples A–C) and by the higher density of stacking faults and substitutional impurities (in comparison samples E–D). It has been known that incorporation of defects occurs more easily in a (111)-oriented diamond than in an (001)-oriented diamond.
3.5 Carrier scattering time and drift mobility
The temperature dependence of TRCR spectrum provides the aspect of carrier scattering mechanisms. Figure 9a shows the normalized temporal curves measured at 0.16 mT at various temperatures. The rise time and the decay time of the signal increased as the temperature is rising. The longer rise and decay times at higher temperatures indicate elongating of the carrier lifetime [22]. This is probably caused by trapping of carriers into impurity states at lower temperatures. Similar shortening of the exciton lifetime at low temperatures was clarified in Ref. [37] by comparing exciton lifetimes in samples containing different concentrations of impurities.
Figure 9.
Temperature variation of temporal curves at 0.16 mT (a) and spectrum at the delay time 1 μs averaged for ±40 ns (b), adapted from Ref. [23].
Figure 9b shows the CR spectra at 7.3, 10, 20, 30, and 40 K taken at a delay time of 1 μs after the laser pulse with averaging window for ±40 ns [23]. The four peaks were separately observed up to 20 K and the width broadened with increasing temperature. These spectra were analyzed by the abovementioned spectrum fitting. The carrier scattering times τj’s, in other words, momentum relaxation times, were taken from the width Γj as a function of temperature. The fitting of the structureless spectra at the higher temperatures was possible by fixing the resonance field of the four components. The fitting curve of each spectrum is shown by the thin red lines.
The spectral width Γj at low temperature sharply depends on the impurity concentration as mentioned in Section 3.4. The carrier scattering at low temperature is mainly governed by the neutral impurity scattering instead of the ionized impurity, because the optically injected carriers neutralize ionized impurity centers. Figure 10a shows the temperature dependence of the inverse carrier scattering times 1/τj extracted from the spectra measured with a CVD diamond shown in Figure 9b. The data points are well reproduced by the sum of the longitudinal acoustic (LA) phonon scattering rate 1/τacj and a constant term bj (solid lines). The LA phonon scattering rate 1/τacj (broken lines) was calculated for electrons and holes by using Eq. (6) in Ref. [38] with a deformation potential of 8.7 eV [35] (6.8 eV) for e1 (e2) electrons or 10.0 eV for both types of holes in diamond. Deviation from the straight line of the T3/2 law which was known for acoustic phonon scattering appeared below 40 K due to inhibition of LA phonon emission at low temperatures. The constant terms were attributed to neutral impurity scattering rates. The best fit values were be1=1.4×109s−1, be2=1.3×109s−1, blh=2×109s−1, and bhh=8×109s−1. As discussed in Ref. [23], these values were larger than the values calculated by modified Erginsoy’s formulas, βe=3.4nAaA+20nDaDℏ/me∗ for the electron [39] and βh=20nAaA+3.4nDaDℏ/mh∗ for the hole, where aAD is a Bohr radius and nAD is the concentration of acceptors (donors). This fact indicates that the estimated nIaII=A,D were smaller than those in the actual situations probably owing to the too much simplified estimation of the Bohr radius by the hydrogenic model.
Now as the parameters of the effective mass m∗ and carrier scattering time τ were individually obtained from the analysis of CR spectra, we can derive the drift mobility by the relation μ=eτ/m∗. Figure 10b shows the drift mobilities of electron and hole. We used a conductivity mass for the electron, me∗=3/1/ml+2/mt=0.386±0.026m0. For the valence bands, effective masses were averaged for the warped energy surfaces mlh∗/m0=0.261±0.005 for the light hole and mhh∗/m0=0.663±0.032 for the heavy hole. The total hole mobility was obtained by weighting the light and heavy hole mobilities as μ=plhμlh+phhμhh/plh+phh=μlh+rμhh/1+r with the ratio r=phh/plh=mhh/mlh3/2=4.05 derived from the density-of-state ratio for the degenerate energy bands [40]. The drift mobility at 10 K was obtained as μe=1.52±0.27×106cm2/Vs for electrons and μlh=2.26±0.38×106 and μhh=0.24±0.03×106cm2/Vs for the light and heavy holes. The ratio of light to heavy hole mobilities μlh/μhh≅9.35 is in better agreement with the ratio of mhh∗/mlh∗5/2=10.3 than mhh∗/mlh∗=2.54. This fact indicates that light and heavy holes in ultrapure diamond relax inside each band. This is in contrast to the case in p-type germanium [40], where the intra-/inter-band scattering is dominant for the heavy-/light-hole and then μlh/μhh is proportional to mhh∗/mlh∗.
Figure 10.
Temperature dependences of carrier scattering time (a) and drift mobility (b), taken from Ref. [23].
We evaluated the mobility up to 300 K by extrapolating the T3/2 relation as shown by the solid lines, because the optical phonon process dominates carrier scattering only above 400 K in diamond [41]. The values of the mobility at 300 K were derived as μe=7.3×103cm2/Vs for electron and 5.3×103cm2/Vs for total hole. The values are higher than those evaluated by Reggiani et al. [8] and Nava et al. [9] for a natural n(p)-type diamond crystal or by Isberg et al. [10, 17] with the CVD diamond crystals. The values are summarized in Table 3 in comparison to those in silicon and germanium at 300 K [42]. The highest mobility of both electron and hole responsive to 10 GHz at 300 K indicates the outstanding possibility of a diamond in the field of power electronics and optoelectronics.
Recently developed experimental method, the nanosecond time-resolved cyclotron resonance, was introduced to clarify the basic carrier transport parameters in an intrinsic diamond. A sophisticated optical carrier injection technique in a highly pure diamond crystal realized the measurement at low temperature. The extracted effective masses, carrier scattering times, and mobilities unveiled the supreme carrier transport properties of a highly pure diamond, which indicate a large application-oriented advantage especially in power electronics and optoelectronics fields. The introduced optical carrier injection is a promising technique to control a carrier density in future devices.
Acknowledgments
The authors thank J.H. Kaneko (Hokkaido University) for providing the diamond sample grown by the CVD method and Ms. S. Hamabata (Wakayama University) for the experiments described in Section 3.2. This work was supported by JSPS KAKENHI (Grant Nos. 15 K05129 and 17H02910) and the Murata Science Foundation.
\n',keywords:"effective mass, scattering time, mobility, cyclotron resonance, optical carrier injection",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/66896.pdf",chapterXML:"https://mts.intechopen.com/source/xml/66896.xml",downloadPdfUrl:"/chapter/pdf-download/66896",previewPdfUrl:"/chapter/pdf-preview/66896",totalDownloads:249,totalViews:0,totalCrossrefCites:0,dateSubmitted:"November 20th 2018",dateReviewed:"March 23rd 2019",datePrePublished:"April 25th 2019",datePublished:"July 8th 2020",dateFinished:"April 25th 2019",readingETA:"0",abstract:"Diamond attracts increasing attentions as a semiconductor, since high-purity synthesized diamonds have become commercially available in these decades. For appropriate design of any devices, the basic carrier transport parameters should be known. However, it has been difficult to determine carrier parameters in diamond, because the controlled doping and Ohmic contact formation have been hard to achieve. In this chapter, a modern experimental method to measure basic carrier parameters, such as the effective mass, scattering times, and mobility of intrinsic diamonds, is introduced. The method, i.e., nanosecond time-resolved cyclotron resonance (TRCR), is applicable to optically injected carriers in intrinsic diamonds without wire connection. Following the key technique of optical carrier injection, detailed analysis methods for the cyclotron resonance spectra are introduced. The extracted basic parameters of diamond are summarized in comparison to those of silicon and germanium in the same group-IV semiconductor family. This is worthy for triggering further ideas in application-oriented researches using widespread materials.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/66896",risUrl:"/chapter/ris/66896",signatures:"Ikuko Akimoto and Nobuko Naka",book:{id:"8506",title:"Some Aspects of Diamonds in Scientific Research and High Technology",subtitle:null,fullTitle:"Some Aspects of Diamonds in Scientific Research and High Technology",slug:"some-aspects-of-diamonds-in-scientific-research-and-high-technology",publishedDate:"July 8th 2020",bookSignature:"Evgeniy Lipatov",coverURL:"https://cdn.intechopen.com/books/images_new/8506.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"21254",title:"Mr.",name:"Evgeniy",middleName:null,surname:"Lipatov",slug:"evgeniy-lipatov",fullName:"Evgeniy Lipatov"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"187905",title:"Dr.",name:"Ikuko",middleName:null,surname:"Akimoto",fullName:"Ikuko Akimoto",slug:"ikuko-akimoto",email:"akimoto@sys.wakayama-u.ac.jp",position:null,institution:{name:"Wakayama University",institutionURL:null,country:{name:"Japan"}}},{id:"287232",title:"Dr.",name:"Nobuko",middleName:null,surname:"Naka",fullName:"Nobuko Naka",slug:"nobuko-naka",email:"naka@scphys.kyoto-u.ac.jp",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Experimental method",level:"1"},{id:"sec_3",title:"3. Results",level:"1"},{id:"sec_3_2",title:"3.1 Time-resolved cyclotron method",level:"2"},{id:"sec_4_2",title:"3.2 Optical carrier injection",level:"2"},{id:"sec_5_2",title:"3.3 Determination of effective masses",level:"2"},{id:"sec_6_2",title:"3.4 Sample dependence of carrier lifetime",level:"2"},{id:"sec_7_2",title:"3.5 Carrier scattering time and drift mobility",level:"2"},{id:"sec_9",title:"4. Conclusion",level:"1"},{id:"sec_10",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Hiraiwa A, Kawarada H. Figure of merit of diamond power devices based on accurately estimated impact ionization processes. Journal of Applied Physics. 2013;114:034506. DOI: 10.1063/1.4816312'},{id:"B2",body:'Isberg J, Gabrysch M, Hammersberg J, Majdi S, Kovi KK, Twitchen DJ. Generation, transport and detection of valley-polarized electrons in diamond. Nature Materials. 2013;12:760. 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Condensed Matter. 2009;21:364221. DOI: 10.1088/0953-8984/21/36/364221'},{id:"B8",body:'Reggiani L, Bori S, Canali C, Nava F, Kozlov SF. On the lattice scattering and effective mass of holes in natural diamond. Solid State Communications. 1979;30:333. DOI: 10.1016/0038-1098(79)90645-8'},{id:"B9",body:'Nava F, Canali C, Jacobini C, Reffiani L, Kozlov SF. Electron effective masses and lattice scattering in natural diamond. Solid State Communications. 1980;33:475. DOI: 10.1016/0038-1098(80)90447-0'},{id:"B10",body:'Isberg J, Hammersberg J, Johansson E, Wilstroem T, Twitchen DJ, Whitehead AJ, et al. High carrier mobility in single-crystal plasma-deposited diamond. Science. 2002;297:1670. DOI: 10.1126/science.1074374'},{id:"B11",body:'Kono J, Takeyama S, Takamasu T, Miura N, Fujimori N, Nishibayashi Y, et al. High-field cyclotron resonance and valence-band structure in semiconducting diamond. Physical Review B. 1993;48:10917. DOI: 10.1103/PhysRevB.48.10917'},{id:"B12",body:'Rauch CJ. Millimeter cyclotron resonance experiment in diamond. Physical Review Letters. 1961;7:83. DOI: 10.1103/PhysRevLett.7.83'},{id:"B13",body:'Redfield AG. Electronic hall effect in diamond. Physics Review. 1954;94:526. DOI: 10.1103/PhysRev.94.526'},{id:"B14",body:'Denham P, Lightowlers EC, Dean PJ. Ultraviolet intrinsic and extrinsic photoconductivity of natural diamond. Physics Review. 1967;161:762. DOI: 10.1103/PhysRev.161.762'},{id:"B15",body:'Dresselhaus G, Kip AF, Kittel C. Cyclotron resonance of electrons and holes in silicon and germanium crystals. Physics Review. 1955;98:368. DOI: 10.1103/PhysRev.98.368'},{id:"B16",body:'Dresselhaus G, Kip AF, Kittel C. Plasma resonance in crystals: Observations and theory. Physics Review. 1955;100:618. DOI: 10.1103/PhysRev.100.618'},{id:"B17",body:'Gabrysch M, Majdi S, Twitchen DJ, Isberg J. Electron and hole drift velocity in chemical vapor deposition diamond. Journal of Applied Physics. 2011;109:063719. DOI: 10.1063/1.3554721'},{id:"B18",body:'Majdi S, Kovi KK, Hammersberg J, Isberg J. Hole transport in single crystal synthetic diamond at low temperatures. Applied Physics Letters. 2013;102:152113. DOI: 10.1063/1.4802449'},{id:"B19",body:'Ščajev P, Gudelis V, Ivakin E, Jarašiünas K. Nonequilibrium carrier dynamics in bulk HPHT diamond at two-photon carrier generation. Physica Status Solidi A: Applications and Materials Science. 2011;208:2067. DOI: 10.1002/pssa.201100006'},{id:"B20",body:'Nesladek M, Bogdan A, Deferme W, Tranchant N, Bergonzo P. Charge transport in high mobility single crystal diamond. Diamond and Related Materials. 2008;17:1235. DOI: 10.1016/j.diamond.2008.03.015'},{id:"B21",body:'Naka N, Fukai K, Handa Y, Akimoto I. Direct measurement via cyclotron resonance of the carrier effective masses in pristine diamond. Physical Review B. 2013;88:035205. DOI: 10.1103/PhysRevB.88.035205'},{id:"B22",body:'Naka N, Fukai K, Handa Y, Akimoto I. Nanosecond cyclotron resonance in ultrapure diamond. Journal of Luminescence. 2014;152:93. DOI: 10.1016/j.jlumin.2013.12.055'},{id:"B23",body:'Akimoto I, Handa Y, Fukai K, Naka N. High carrier mobility in ultrapure diamond measured by time-resolved cyclotron resonance. Applied Physics Letters. 2014;105:032102. DOI: 10.1063/1.4891039'},{id:"B24",body:'Akimoto I, Naka N, Tokuda N. Time-resolved cyclotron resonance on dislocation-free HPHT diamond. Diamond and Related Materials. 2016;63:38. DOI: 10.1016/j.diamond.2015.08.013'},{id:"B25",body:'Naka N, Morimoto H, Akimoto I. Excitons and fundamental transport properties of diamond under photo-injection. Physica Status Solidi A: Applications and Materials Science. 2016;213:2551. DOI: 10.1002/pssa.201600237'},{id:"B26",body:'Hamabata S, Akimoto I, Naka N. Temperature-dependent carrier injection routes under optical excitation in high-purity diamond crystals. Journal of Physics: Conference Series; accepted'},{id:"B27",body:'Akimoto I, Hamabata S, Kaneko JH, Naka N. in preparation'},{id:"B28",body:'Akimoto I, Naka N. Two optical routes of cold carrier injection in silicon revealed by time-resolved excitation spectroscopy. Applied Physics Express. 2017;10:061301. DOI: 10.7567/APEX.10.061301'},{id:"B29",body:'Naka N, Akimoto I, Shirai M. Free-carrier generation by two-photon resonant excitation to the excitonic states in cuprous oxide. Physica Status Solidi B. 2013;250:1773. DOI: 10.1002/pssb.201200713'},{id:"B30",body:'Naka N, Akimoto I, Shirai M, Kan’no K. Time-resolved cyclotron resonance in cuprous oxide. Physical Review B. 2012;85:035209. DOI: 10.1103/PhysRevB.85.035209'},{id:"B31",body:'Akimoto I, Torai S, Naka N, Shirai M. Temporal shift from magnetoplasma resonance to cyclotron resonance of photo carriers generated from 1 s-exciton on cuprous oxide crystal. European Physical Journal B. 2012;85:374. DOI: 10.1140/epjb/e2012-30618-8'},{id:"B32",body:'Clark CD, Dean PJ, Harris PV. Intrinsic edge absorption in diamond. Proceedings of the Royal Society A. 1964;277:312. DOI: 10.1098/rspa.1964.0025'},{id:"B33",body:'Dean PJ, Male JC. Luminescence excitation spectra and recombination radiation of diamond in the fundamental absorption region. Proceedings of the Royal Society A. 1964;277:330. DOI: 10.1098/rspa.1964.0026'},{id:"B34",body:'Hazama Y, Naka N, Stolz H. Mass-anisotropy splitting of indirect excitons in diamond. Physical Review B. 2014;90:045209. DOI: 10.1103/PhysRevB.90.045209'},{id:"B35",body:'Jacoboni C, Reggiani L. The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Reviews of Modern Physics. 1983;55:645. DOI: 10.1103/RevModPhys.55.645'},{id:"B36",body:'Martineau PM, Gaukroger MP, Guy KB, Lawson SC, Twitchen DJ, Friel I, et al. High crystalline quality single crystal chemical vapour deposition diamond. Journal of Physics. Condensed Matter. 2009;21:364205. DOI: 10.1088/0953-8984/21/36/364205'},{id:"B37",body:'Naka N, Omachi J, Sumiya H, Tamasaku K, Ishikawa T, Kuwata-Gonokami M. Density-dependent exciton kinetics in synthetic diamond crystals. Physical Review B. 2009;80:035201. DOI: 10.1103/PhysRevB.80.035201'},{id:"B38",body:'Trauernicht DP, Wolfe JP. Drift and diffusion of paraexcitons in Cu2O: Deformation-potential scattering in the low-temperature regime. Physical Review B. 1986;33:8506. DOI: 10.1103/PhysRevB.33.8506'},{id:"B39",body:'Erginsoy C. Neutral impurity scattering in semiconductors. Physics Review. 1950;79:1013. DOI: 10.1103/PhysRev.79.1013'},{id:"B40",body:'Brown DM, Bray R. Analysis of lattice and ionized impurity scattering in p-type Germanium. Physics Review. 1962;127:1593. DOI: 10.1103/PhysRev.127.1593'},{id:"B41",body:'Pernot J, Volpe PN, Omnes F, Muret P, Mortet V, Haenen K, et al. Hall hole mobility in boron-doped homoepitaxial diamond. Physical Review B. 2010;81:205203. DOI: 10.1103/PhysRevB.81.205203'},{id:"B42",body:'Sze SM, Ng KK. Physics of Semiconductor Devices. 3rd ed. New York: Wiley-Interscience; 1981. ISBN-10: 0471143235'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Ikuko Akimoto",address:"akimoto@sys.wakayama-u.ac.jp",affiliation:'
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Sudden death is the major cause of death in patients with Ch. Objective: To compare the circadian rhythm of sudden death in Ch vs. non-Ch patients. Methods: Retrospective analysis of all the cases of sudden death (SD) is recorded in our department, including autopsied patients from 1963 until 2011. Pattern of death of 266 patients (116 Ch and 146 non-Ch), 56.7% men, average age 54, 6 years old, divided into four groups: Group A: Ch with SD (n = 38), Group B: non-Ch with SD (n = 58), Group C: Ch with non-SD (n = 81), and Group D: non-Ch with non-SD (n = 89). Results: 44.7% (17/38) of sudden deaths in Group A (Ch) occurred between 6 am and 5:59 pm, while for Group B (not Ch) 70.7% (41/58) died in that time (p < 0.005). Between 6 pm and 5:59 am occurred 55.3% (21/38) of the SD in Group A (Ch) compared with 29.3% (17/58) in Group B (p < 0.005). Conclusions: Circadian rhythm of SD in patient with Ch differs from those patients with non-CH. In CH patients, SD occurs predominantly during the night compared with non-Ch SD that occurs predominantly during the morning.",signatures:"Juan Marques, Iván Mendoza and Claudia Suarez",authors:[{id:"231833",title:"Dr.",name:"Juan",surname:"Marques",fullName:"Juan Marques",slug:"juan-marques",email:"juan.alberto.marques@gmail.com"},{id:"240352",title:"Dr.",name:"Ivan",surname:"Mendoza",fullName:"Ivan Mendoza",slug:"ivan-mendoza",email:"imivanjm@gmail.com"},{id:"240712",title:"Dr.",name:"Claudia",surname:"Suarez",fullName:"Claudia Suarez",slug:"claudia-suarez",email:"claudia1937@gmail.com"}],book:{title:"Circadian Rhythm",slug:"circadian-rhythm-cellular-and-molecular-mechanisms",productType:{id:"1",title:"Edited Volume"}}}],collaborators:[{id:"169212",title:"Dr.",name:"Pavol",surname:"Svorc",slug:"pavol-svorc",fullName:"Pavol Svorc",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/169212/images/system/169212.jpg",biography:"Dr. Pavol Švorc is an Associate Professor, Doctor of the Natural Sciences, Philosophe Doctor. In 1982 he became a Doctor of the Natural Sciences from General Biology, Natural Faculty, Šafarik’s University in Košice. In 1995 he received a PhD. – Physiology and Patophysiology, Natural Faculty Šafarik’s University in Košice. In 2005 he became an Associate Professor from Normal and Patological Physiology, Medical Faculty, Šafarik’s University in Košice. From 1982 to 1983 Dr.Švorc worked as an independent specialist in the local museum in Poprad, Slovakia. In 1983 he started working as a lecturer at the Department of Physiology, Šafarik’s University in Kosice, Slovakia. From\r\n2011 until 2014 he was a Head of the Institute of Physiology and Pathophysiology, Medical Faculty, University of Ostrava, Czech Republic. His research interest includes:\r\nChronobiology of cardiovascular system, respiratory system and autonomic nervous system.",institutionString:"Pavol Josef Safarik University",institution:{name:"University of Pavol Jozef Šafárik",institutionURL:null,country:{name:"Slovakia"}}},{id:"190636",title:"Associate Prof.",name:"Hülya",surname:"Çakmur",slug:"hulya-cakmur",fullName:"Hülya Çakmur",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/190636/images/system/190636.jpeg",biography:"Hülya Çakmur graduated from medical school at the Atatürk\nUniversity in Turkey. She completed her residency training in\nFamily Medicine at the Trakya University. She has a PhD degree in Public Health from the Dokuz Eylül University. She has\n25 years of practical experience as a specialist in family medicine, including 10 years of experience in public health as a PhD\nprepared professional. She studied sleep medicine at the UPMC\nin the USA, attended narrative medicine education at the STU in Canada, studied\nvoluntarily in geriatrics, and published several studies in the field of elderly health.\nShe is an active member of the Turkish Medical Association and European Academy\nof Teachers in General Practice/Family Medicine. She has eight years of teaching experience as an associate professor at the University of Kafkas and she is the Director\nof the Department of Family Medicine. She has published more than 30 papers in\nreputed journals.",institutionString:"Kafkas University",institution:{name:"Kafkas University",institutionURL:null,country:{name:"Turkey"}}},{id:"231117",title:"Prof.",name:"Olivier",surname:"Le Bon",slug:"olivier-le-bon",fullName:"Olivier Le Bon",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"231833",title:"Dr.",name:"Juan",surname:"Marques",slug:"juan-marques",fullName:"Juan Marques",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:null,institutionString:null,institution:{name:"Central University of Venezuela",institutionURL:null,country:{name:"Venezuela"}}},{id:"234339",title:"Dr.",name:"Ruben",surname:"Fossion",slug:"ruben-fossion",fullName:"Ruben Fossion",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"National Autonomous University of Mexico",institutionURL:null,country:{name:"Mexico"}}},{id:"234383",title:"Dr.",name:"Jie",surname:"Liu",slug:"jie-liu",fullName:"Jie Liu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"234388",title:"Dr.",name:"Hua",surname:"Li",slug:"hua-li",fullName:"Hua Li",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"241937",title:"Dr.",name:"Ana Leonor",surname:"Rivera",slug:"ana-leonor-rivera",fullName:"Ana Leonor Rivera",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"241938",title:"Dr.",name:"Juan Claudio",surname:"Toledo-Roy",slug:"juan-claudio-toledo-roy",fullName:"Juan Claudio Toledo-Roy",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"241939",title:"Prof.",name:"Maia",surname:"Angelova",slug:"maia-angelova",fullName:"Maia Angelova",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null}]},generic:{page:{slug:"OA-publishing-fees",title:"Open Access Publishing Fees",intro:"
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If a manuscript requires Heavy Editing or Language Polishing, this will incur additional fees.
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\\n\\n
Your Author Service Manager will inform you of any items not covered by the OAPF and provide exact information regarding those additional costs before proceeding.
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Open Access Funding
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To explore funding opportunities and learn more about how you can finance your IntechOpen publication, go to our Open Access Funding page. IntechOpen offers expert assistance to all of its Authors. We can support you in approaching funding bodies and institutions in relation to publishing fees by providing information about compliance with the Open Access policies of your funder or institution. We can also assist with communicating the benefits of Open Access in order to support and strengthen your funding request and provide personal guidance through your application process. You can contact us at oapf@intechopen.com for further details or assistance.
\\n\\n
For Authors who are still unable to obtain funding from their institutions or research funding bodies for individual projects, IntechOpen does offer the possibility of applying for a Waiver to offset some or all processing feed. Details regarding our Waiver Policy can be found here.
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Added Value of Publishing with IntechOpen
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Choosing to publish with IntechOpen ensures the following benefits:
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\\n\\t
Indexing and listing across major repositories, see details ...
\\n\\t
Long-term archiving
\\n\\t
Visibility on the world's strongest OA platform
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Live Performance Metrics to track readership and the impact of your chapter
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Dissemination and Promotion
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\\n\\n
Benefits of Publishing with IntechOpen
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\\n\\t
Proven world leader in Open Access book publishing with over 10 years experience
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+5,200 OA books published
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Most competitive prices in the market
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Fully compliant with OA funding requirements
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Optimized processes, enabling publication between 8 and 12 months
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Personal support during every step of the publication process
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+146,150 citations in Web of Science databases
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Currently strongest OA platform with over 150 million downloads
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The Open Access Publishing Fee (OAPF) is payable only after your full chapter, monograph or Compacts monograph is accepted for publication.
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OAPF Publishing Options
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1,400 GBP Chapter - Edited Volume
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10,000 GBP Monograph - Long Form
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4,000 GBP Compacts Monograph - Short Form
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\n\n
*These prices do not include Value-Added Tax (VAT). Residents of European Union countries need to add VAT based on the specific rate in their country of residence. Institutions and companies registered as VAT taxable entities in their own EU member state will not pay VAT as long as provision of the VAT registration number is made during the application process. This is made possible by the EU reverse charge method.
\n\n
Services included are:
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An online manuscript tracking system to facilitate your work
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Personal contact and support throughout the publishing process from your dedicated Author Service Manager
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Assurance that your manuscript meets the highest publishing standards
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English language copyediting and proofreading, including the correction of grammatical, spelling, and other common errors
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XML Typesetting and pagination - web (PDF, HTML) and print files preparation
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Discoverability - electronic citation and linking via DOI
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Permanent and unrestricted online access to your work
What isn't covered by the Open Access Publishing Fee?
\n\n
If your manuscript:
\n\n
\n\t
Exceeds 20 pages (for chapters in Edited Volumes), an additional fee of 40 GBP per page will be required
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If a manuscript requires Heavy Editing or Language Polishing, this will incur additional fees.
\n
\n\n
Your Author Service Manager will inform you of any items not covered by the OAPF and provide exact information regarding those additional costs before proceeding.
\n\n
Open Access Funding
\n\n
To explore funding opportunities and learn more about how you can finance your IntechOpen publication, go to our Open Access Funding page. IntechOpen offers expert assistance to all of its Authors. We can support you in approaching funding bodies and institutions in relation to publishing fees by providing information about compliance with the Open Access policies of your funder or institution. We can also assist with communicating the benefits of Open Access in order to support and strengthen your funding request and provide personal guidance through your application process. You can contact us at oapf@intechopen.com for further details or assistance.
\n\n
For Authors who are still unable to obtain funding from their institutions or research funding bodies for individual projects, IntechOpen does offer the possibility of applying for a Waiver to offset some or all processing feed. Details regarding our Waiver Policy can be found here.
\n\n
Added Value of Publishing with IntechOpen
\n\n
Choosing to publish with IntechOpen ensures the following benefits:
\n\n
\n\t
Indexing and listing across major repositories, see details ...
\n\t
Long-term archiving
\n\t
Visibility on the world's strongest OA platform
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Live Performance Metrics to track readership and the impact of your chapter
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Dissemination and Promotion
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\n\n
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Proven world leader in Open Access book publishing with over 10 years experience
\n\t
+5,200 OA books published
\n\t
Most competitive prices in the market
\n\t
Fully compliant with OA funding requirements
\n\t
Optimized processes, enabling publication between 8 and 12 months
\n\t
Personal support during every step of the publication process
\n\t
+146,150 citations in Web of Science databases
\n\t
Currently strongest OA platform with over 150 million downloads
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