Patent Publication Number: US-2022237358-A1

Title: Method of and system for manufacturing semiconductor device

Description:
PRIORITY CLAIM AND CROSS-REFERENCE 
     This application claims priority to U.S. Provisional Application No. 63/142,769 filed Jan. 28, 2021, the disclosure of which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Electronic equipment involving semiconductor devices is essential for many modern applications. Technological advances in materials and design have produced generations of semiconductor devices, in which each generation includes smaller and more complex circuits than the previous generation. In the course of advancement and innovation, functional density (i.e., the number of interconnected devices per chip area) has generally increased while geometric size (i.e., the smallest component that can be created using a fabrication process) has decreased. Such advances have increased complexity of processing and manufacturing semiconductor devices. Therefore, there is a continuous need to modify the structure and manufacturing method of the devices in order to improve device robustness as well as reducing manufacturing cost and processing time. Among the various studies of the semiconductor devices, advanced types of field-effect transistors (FET), such as nanosheet FET, have attracted a great deal of attentions for their superior performance, e.g., better gate control and improved short channel effect. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects of the present disclosure are best understood from the following detailed description when read with the accompanying figures. It should be noted that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion. 
         FIG. 1A  is a perspective view of a nanosheet field-effect transistor (FET) device, in accordance with some embodiments of the present disclosure. 
         FIG. 1B  is a cross-sectional view of the nanosheet FET device shown in  FIG. 1A , in accordance with some embodiments of the present disclosure. 
         FIG. 2  is a schematic diagram of a design layout, in accordance with some embodiments of the present disclosure. 
         FIGS. 3A and 3B  are schematic diagrams of design layouts for standard cells, in accordance with various embodiments of the present disclosure. 
         FIG. 3C  includes tables for determining widths and spacings of active regions in various standard cells, in accordance with some embodiments of the present disclosure. 
         FIGS. 4A, 4B, 4C and 4D  are schematic diagrams of design layouts for standard cells, in accordance with various embodiments of the present disclosure. 
         FIGS. 5A, 5B, 5C, 5D and 5E  are schematic diagrams of design layouts for standard cells, in accordance with various embodiments of the present disclosure. 
         FIG. 6A  is a flowchart of a layout method, in accordance with some embodiments. 
         FIG. 6B  is a flowchart of a layout method, in accordance with some embodiments. 
         FIG. 7A  is a schematic diagram showing an integrated circuit (IC) manufacturing system, in accordance with some embodiments. 
         FIG. 7B  is a schematic diagram of a design subsystem in the IC manufacturing system shown in  FIG. 7A  for generating a design layout, in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following disclosure provides many different embodiments, or examples, for implementing different features of the provided subject matter. Specific examples of components and arrangements are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. For example, the formation of a first feature over or on a second feature in the description that follows may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed between the first and second features, such that the first and second features may not be in direct contact. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. 
     Further, spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly. 
     Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the deviation normally found in the respective testing measurements. Also, as used herein, the terms “about,” “substantial” or “substantially” generally mean within 10%, 5%, 1% or 0.5% of a given value or range. Alternatively, the terms “about,” “substantial” or “substantially” mean within an acceptable standard error of the mean when considered by one of ordinary skill in the art. Other than in the operating/working examples, or unless otherwise expressly specified, all of the numerical ranges, amounts, values and percentages such as those for quantities of materials, durations of times, temperatures, operating conditions, ratios of amounts, and the likes thereof disclosed herein should be understood as modified in all instances by the terms “about,” “substantial” or “substantially.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the present disclosure and attached claims are approximations that can vary as desired. At the very least, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Ranges can be expressed herein as being from one endpoint to another endpoint or between two endpoints. All ranges disclosed herein are inclusive of the endpoints, unless specified otherwise. 
     The term “standard cell” or “cell” used throughout the present disclosure refers to a group of circuit patterns in a design layout to implement specific functionalities of a circuit. A standard cell is comprised of various patterns in one or more layers and may be expressed as unions of polygons. A design layout may be initially constructed through placement of a combination of identical or different standard cells during the layout design stage. The geometries of the patterns in the cells may be adjusted at different stages of layout design in order to compensate for design and process effects. A standard cell may cover circuits corresponding to a portion or an entirety of a die to be manufactured. The standard cells may be accessible from cell libraries provided by semiconductor circuit manufacturers or designers. 
     Some embodiments of the present disclosure discuss methods of generating standard cells associated with nanosheet field-effect transistor (FET) devices. Due to the fact that the widths and spacings of the nanosheets are irregular discrete numbers, it may involve a great deal of work in a layout revision stage to modify the design layout for fulfilling design rules while maintaining circuit efficiency in area and power. Through the design methodology of the proposed scheme, a set of standard cells associated with nanosheets is generated. In this set, the standard cells are provided with individual nanosheet widths and spacings selected from a finite set of widths and spacings for nanosheets to achieve the goal of equal cell heights among the standard cells, thereby simplifying efforts and cost of modifying the layout of the standard cells in a layout revision stage. 
     Some embodiments of the present disclosure also discuss layout methods and associated structures of semiconductor devices based on one or more nanosheet field-effect transistor (FET) devices. Through the proposed layout scheme, a semiconductor device is configured to accommodate different types of nanosheet FETs with different device size and capabilities. For example, different standard cells associated with nanosheet FETs can be designed having equal cell heights with different nanosheet sizes and spacings to fulfill design rules of nanosheet dimensions. In this way, the design cycle can be improved in searching for compliant nanosheet sizes and spacings while a better balance between area, power and performance is achieved. 
       FIG. 1A  is a perspective view of a semiconductor device  100 , in accordance with some embodiments of the present disclosure. Referring to  FIG. 1A , the semiconductor device  100  is a nanosheet FET device. However, other types of semiconductor device are also possible for the semiconductor device  100 , such as nanowire FET, fin-type FET, or the like. Referring to  FIG. 1A , the semiconductor device  100  includes substrates  102  and  112 , an isolation region  104 , gate electrodes  106  and  108  and nanosheet stacks  114  and  124 . 
     The substrates  102  and  112  are formed from a same substrate wafer (not shown) and can be seen as two protrusive portions of the substrate wafer. In some embodiments, the substrates  102  and  112  are in a strip shape extending in the x-axis. The substrates  102  and  112  may be formed from a semiconductor substrate, such as a bulk semiconductor, a semiconductor-on-insulator (SOI) substrate, or the like, which may be doped (e.g., with a p-type or an n-type dopant) or undoped. Generally, an SOI substrate comprises a layer of a semiconductor material formed on an insulator layer. The insulator layer may be, for example, a buried oxide (BOX) layer, a silicon oxide layer, or the like. The insulator layer is provided on a substrate, typically a silicon or glass substrate. Other substrates, such as a multi-layered or gradient substrate, may also be used. In some embodiments, the semiconductor material of the substrates  102  and  112  may include silicon; germanium; a compound semiconductor including silicon germanium, silicon carbide, gallium arsenic, gallium phosphide, indium phosphide, indium arsenide, and/or indium antimonide; an alloy semiconductor including SiGe, GaAsP, AlInAs, AlGaAs, GaInAs, GaInP, and/or GaInAsP; combinations thereof, or the like. 
     The isolation region  104  is formed in trenches between the substrates  102  and  112 . In some embodiments, the isolation region  104  has an upper surface level with the upper surfaces of the substrates  102  and  112 . The isolation regions  114  may include insulating materials, such as a dielectric material, e.g., silicon oxide, silicon nitride, silicon oxynitride, a combination thereof, or the like. The isolation region  114  may be formed by chemical vapor deposition (CVD), high-density plasma CVD (HDP-CVD), flowable CVD (FCVD), atomic layer deposition (ALD), physical vapor deposition (PVD), a combination thereof, or the like. Other insulation materials formed by any suitable process may be also used. In some embodiments, an annealing process may be performed after the insulation material of the isolation region  114  is deposited. 
     The gate electrodes  106  and  108  are formed over the substrates  102  and  112  and the isolation region  104 . The gate electrodes  106  and  108  may extend in a direction, e.g., the y-axis, perpendicular to the direction in which the substrates  102  and  112  extend. In some embodiments, each of the gate electrodes  106  and  108  is made of one or more layers of conductive materials, such as doped polysilicon or metallic materials, e.g., Co, Ru, Al, Ag, Au, W, Ni, Ti, Cu, Mn, Pd, Re, Ir, Pt, Zr, alloys thereof, combinations thereof, or the like, and may further include other work function adjusting metals, diffusion barrier materials or glue layers. 
     The nanosheet stacks  114  and  124  each includes a plurality of separated nanosheets in a stacked form and is arranged over the substrates  102  and  112  and the isolation region  104 . A nanosheet in the nanosheet stack  114  or  124  generally refers to a two-dimensional semiconductor slab with a length or width greater than about 100 nm and a thickness less than about 20 nm. The nanosheet stacks  114  and  124  may extend in a direction, e.g., the x-axis, in which the substrates  102  and  112  extend. In some embodiments, the nanosheet stacks  114  and  124  extend in a direction perpendicular to the direction in which the gate electrodes  106  and  108  extend. The nanosheet stacks  114  and  124  may overlap the gate electrodes  106  and  108 . In some embodiments, a portion of each nanosheet of the nanosheet stacks  114  and  124  is surrounded by the electrodes  106  and  108 . 
     In some embodiments, the nanosheet stacks  114  and  124  and the substrates  102  and  112  are formed from the same substrate wafer using photolithography and etching operations on this substrate wafer. The nanosheet stack  114  or  124  may be doped with an n-type impurity, e.g., arsenic, phosphorus, or the like, to form an n-type nanosheet FET, or may be doped with a p-type impurity, e.g., boron or the like, to form a p-type nanosheet FET. The stacked nanosheets of a same nanosheet stack  114  or  124  are configured to form a combined channel region or a combined source/drain region of a nanosheet FET. For example, the portion of each nanosheet of the nanosheet stack  114  which overlaps the gate electrode  106  serves as a combined channel region of a first nanosheet FET, while the other portions of each nanosheet of the nanosheet stack  114  on two sides of the channel region serves as the source/drain regions of the first nanosheet FET. Similarly, the portion of each nanosheet of the nanosheet stack  124  which overlaps the gate electrode  106  serves as a combined channel region of a second nanosheet FET, while the other portions of each nanosheet of the nanosheet stack  114  on two sides of the channel region of the second nanosheet FET serves as the source/drain regions of the second nanosheet FET. 
     In the depicted example, the number of nanosheet stacks  114 ,  124  is set as two. However, the present disclosure is not limited thereto, and the number of the nanosheet stacks of the semiconductor device  100  can be less than or more than two. In the depicted example, each of the nanosheet stacks  114  and  124  has four nanosheet stacked over another. However, the present disclosure is not limited thereto, and the nanosheet stacks  114  and  124  can have an arbitrary number of nanosheets. In the depicted example, the number of gate electrodes is two. However, the present disclosure is not limited thereto, and the number of the gate electrodes of the semiconductor device  100  can be less than or more than two. 
     In some embodiments, the nanosheets in a same stack  114  or  124  are formed to have substantially equal dimensions, such as the nanosheet length measured in the x-axis, the nanosheet width measured in the y-axis and the nanosheet thickness measured in the z-axis. In some embodiments, the nanosheet dimensions of one nanosheet stack, e.g., the nanosheet stack  114 , may be different to those of another nanosheet stack, e.g., the nanosheet stack  124 . In some embodiments, the nanosheet stacks  114  and  124  have substantially equal nanosheet thicknesses and different nanosheet widths or nanosheet lengths. 
       FIG. 1B  is a cross-sectional view of the nanosheet FET  100  shown in  FIG. 1A , in accordance with some embodiments of the present disclosure. The cross-sectional view of  FIG. 1B  is taken along the sectional line AA cutting through the gate electrode  108  of  FIG. 1A . Referring to  FIG. 1A  and  FIG. 1B , the nanosheet FET device  100  further includes a gate insulating layer  116  or  126  between the gate electrode  108  and each nanosheet of the nanosheet stack  114 ,  124 . The gate insulating layer  116  or  126  may be formed of one or more dielectric materials, such as oxide, nitride, oxynitride, or high-k dielectric materials, such as Al 2 O 3 , HfO 2 , ZrO 2 , HfO x N y , ZrO x N y , HfSi x O y , ZrSi x O y , HfSi x O y N z , ZrSi x O y N z , TiO 2 , Ta 2 O 5 , La 2 O 3 , CeO 2 , Bi 4 Si 2 O 12 , WO 3 , Y 2 O 3 , LaAlO 3 , Ba 1-x Sr x TiO 3 , PbTiO 3 , BaTiO 3  (BTO), SrTiO 3  (STO), BaSrTiO 3  (BST), PbZrO 3 , lead-strontium-titanate (PST), lead-zinc-niobate (PZN), lead-zirconate-titanate (PZT), lead-magnesium-niobium (PMN), yttria-stabilized zirconia (YSZ), ZnO/Ag/ZnO (ZAZ), a combination thereof, or the like. 
     In some embodiments, the nanosheet FET  100  further includes a work function adjusting layer  118 ,  128  between the gate electrode  108  and each of the gate insulating layer  116 ,  126 . In embodiments of an n-type nanosheet FET  100 , the work function adjusting layer  118 ,  128  is formed of Ti, Ag, Al, TiAl, TiAlN, TiAlC, TaC, TaCN, TaSiN, TaAlC, Mn, Zr, a combination thereof, or the like, and may be formed to wrap around the gate insulating layer  116 ,  126  by a deposition method such as atomic layer deposition (ALD), chemical vapor deposition (CVD), physical vapor deposition (PVD), combinations thereof, or the like. In embodiments of a p-type nanosheet FET  100 , the work function adjusting layer  118 ,  128  is formed of TiN, WN, TaN, Ru, Co, a combination thereof, or the like, and may be formed to wrap around the gate insulating layer  116 ,  126  by ALD, CVD, PVD, combinations thereof, or the like. 
       FIG. 2  is a schematic diagram  200  of a design layout, in accordance with some embodiments of the present disclosure. The design layout  200  may include at least one semiconductor device, e.g., a complementary metal-oxide-semiconductor (CMOS) device, and can be implemented using a FET device, e.g., the nanosheet FET  100  as shown in  FIG. 1A . In some other embodiments, the design layout  200  includes a gate-all-around (GAA) device, a nanowire device, or the like. 
     The design layout  200  includes two exemplary rows R 1  and R 2  extending in a row direction along the x-axis. In the depicted example, only two rows are arranged in a column direction along the y-axis (perpendicular to the row direction) in the design layout  200 . However, the disclosure is not limited thereto and more than two rows are possible. The design layout  200  further includes first power rails V 1  and second power rails V 2  are alternatingly arranged and extend in the row direction (only one second power rail V 2  is illustrated in  FIG. 2  for brevity). Each of the first power rails V 1  and the second power rail V 2  is arranged on an upper side or lower side of one of the rows R 1 , R 2 . In some embodiments, the center line of each of the first power rails V 1  and the second power rails V 2  is aligned with the upper side or lower side of the row R or R 2 . In some embodiments, the first power rails V 1  are configured to supply first voltage while the second power rails V 2  are configured to supply second voltage different from the first voltage. In some embodiments, the first voltage is VDD and the second voltage is ground, or vice versa. 
     Referring to  FIG. 2 , the design layout  200  includes a plurality of standard cells, for example, standard cells SC 1 , SC 2 , SC 3 , SC 4  and SC 5 . The standard cells SC 1 , SC 2  and SC 3  may be predetermined and stored in a cell library and accessible by a circuit designer. During a placement operation, the standard cells SC 1 , SC 2  and SC 3  are arranged in the row R 1  and the standard cells SC 4  and SC 5  are arranged in the row R 2 . Although  FIG. 2  shows only two or three standard cells in one row, the number of standard cells arranged in one row may be greater than three. Further, in some embodiments some of the standard cells contact each other, e.g., the standard cells SC 1  and SC 2 ; in some other embodiments, the standard cells are separate from each other, e.g., the standard cells SC 4  and SC 5 . 
     The dimensions of the standard cells SC 1  through SC 5  are defined by their respective cell boundaries, in which each cell boundary includes an upper cell side and a lower cell side (both extending in the row direction) and a left cell side and a right cell side (both extending in the column direction). The standard cells SC 1  through SC 5  may be separated from one another or share at least one cell side. In some embodiments, the standard cells SC 1  through SC 5  have respective upper cell sides and lower cell sides aligned with the center lines of either the first power rails V 1  or the second power rails V 2 . Each standard cell SC 1  through SC 5  may have the same or different cell lengths in the row direction. 
     In some embodiments, a row height RH 1  of the first row R 1  is defined as a distance in the column direction between a center line CL 1 , extending in the row direction, of the lower first power rail V 1  and the center line CL 2 , extending in the row direction, of the second power rail V 2 . In some embodiments, a cell height CH 1  is determined based on a pitch between the lower first power rail V 1  and the second power rail V 2 . Similarly, a row height RH 2  of the second row R 2  is defined as a distance in the column direction between a center line CL 2  and a center line CL 3  of the upper first power rail V 1 . In some embodiments, the row height RH 2  is determined based on a pitch between the second power rail V 2  and the upper first power rail V 1 . In some embodiments, the row height RH 1  is the same as or different from the row height RH 2 . 
     In some embodiments, the cell height CH 1  of the standard cell SC 1 , SC 2  or SC 3  is determined based on the row height RH 1 . In some embodiments, the cell height CH 1  is determined based on a pitch between the lower first power rail V 1  and the second power rail V 2 . In some embodiments, the cell height CH 1  is equal to the row height RH 1 . Similarly, the cell height CH 4  of the standard cell SC 4  or SC 5  is equal to the row height RH 2 . 
     Each of the rows R 1  and R 2  defines one or more (row) active regions NOD and POD (indicated by dashed line boxes) along the row direction, in which the active regions POD and NOD have opposite conductivities. For example, the active region NOD denotes an active region doped with n-type dopants while the active region POD denotes an active region doped with p-type dopants. Each of the standard cells SC 1  through SC 5  includes one or more (cell) active regions (indicated by solid line boxes) with the dimensions defined by the cell boundaries of the respective standard cells and the boundaries of the respective (row) active region NOD or POD. For example, the standard cell SC 1  includes an n-type active region NOD 1  and a p-type cell active region POD 1 , where the n-type active region NOD 1  is defined by the cell boundary of the standard cell SC 1  and the boundary of the row active region NOD in the row R 1 , while the p-type active region POD 1  is defined by the cell boundary of the standard cell SC 1  and the boundary of the row active region POD in the row R 1 . The (cell) active region NODxy or PODxy (x denotes the index of the standard cell, and y is optionally used to denote the ordinal number to distinguish more than one similar active regions) within each standard cell SC 1  through SC 5 , e.g., the active regions NOD 1  and POD 1 , illustrated in the design layout  200  correspond to a top view of a nanosheet stack, e.g., nanosheet stack  114  or  124 , of the semiconductor device in the respective standard cell SC 1  through SC 5 . As a result, the configurations of the aforesaid (cell) active regions will determine the planar dimensions of the nanosheets in the nanosheet FET of the respective standard cell SC 1  through SC 5 . 
     Referring to  FIG. 2 , the standard cells SC 1 , SC 2 , SC 3  include respective n-type active regions NOD 1 , NOD 2 , NOD 3  that are overlapped with each other in the row direction within the row active region NOD. In some embodiments, the active regions NOD 1 , NOD 2  and NOD 3  have different active region widths, referred to as OD (oxide definition) widths herein, measured in the column direction. In some embodiments, although the widths of the active regions NOD 1 , NOD 2  and NOD 3  are different, each of these active regions has at least one side, e.g., an upper side, aligned with one side of other active regions. 
     Similarly, the standard cells SC 1 , SC 2 , SC 3  include respective n-type active regions POD 1 , POD 2 , POD 3  overlapped with each other in the row direction within the row active region POD. In some embodiments, the active regions POD 1 , POD 2  and POD 3  have different OD widths. In some embodiments, although the widths of the active regions POD 1 , POD 2  and POD 3  are different, each of these active regions has at least one side, e.g., a lower side, aligned with a side of other active regions. 
     With respect to the standard cells SC 1  through SC 5  illustrated in  FIG. 2 , only the (cell) active regions are shown for clarity. Other cell features, such as gate electrodes, are described in greater detail below. 
       FIG. 3A  is a schematic diagram of design layouts for standard cells  300 A and  300 B, in accordance with various embodiments of the present disclosure. In some embodiments, the standard cells  300 A and  300 B correspond to the standard cells arranged in a same row, e.g., row R 1  or R 2 . The standard cells  300 A and  300 B are defined by their respective cell boundaries CB, and have cell heights CH 1  equal to a row height, e.g., RH 1  or RH 2  in  FIG. 2 . 
     The standard cells  300 A and  300 B include respective electrode gates GT 1  and GT 2  extending over a substrate (not shown) in the column direction. The materials of the electrode gates GT 1 , GT 2  are similar to the electrode gates  106 ,  108  shown in  FIG. 1 . The standard cell  300 A further includes two active regions (OD) OD 11  and OD 12  extending in the row direction, in which channel regions of the active regions OD 11  and OD 12  are surrounded by the electrode gates GT 1 . Similarly, the standard cell  300 B further includes two active regions (OD) OD 21  and OD 22  extending in the row direction, in which channel regions of the active regions OD 21  and OD 22  are and wrapped around by the electrode gates GT 2 . 
     The standard cells  300 A and  300 B also include respectively conductive lines MD 1  and MD 2  extending in the column direction between adjacent gate electrodes GT 1 , GT 2 . The conductive lines MD 1 , MD 2  are arranged in a layer overlapping the gate electrodes GT 1 , GT 2 , and electrically coupled to the active regions OD 11 , OD 12 , OD 21  and OD 22 . The conductive lines MD 1 , MD 2  are configured to electrically couple source/drain regions of the active regions OD 11 , OD 12 , OD 21 , OD 22  in the standard cells  300 A,  300 B, to overlying or underlying layers of the standard cells  300 A,  300 B. The conductive lines MD 1 , MD 2  may be formed of doped polysilicon or metallic materials, such as copper, tungsten, titanium, titanium nitride, tantalum, tantalum nitride, or the like. 
     The standard cell  300 A or  300 B further includes a line separation pattern CMD, referred to herein as a “cut-MD pattern” extending in the row direction on an upper cell side and a lower cell side of the standard cell  300 A or  300 B. The cut-MD pattern CMD is used to signify an MD separation step during the semiconductor fabrication process, by which the contiguous conductive lines MD 1  or MD 2  extending in the column direction are segmented into aligned conductive line segments MD 1  or MD 2  with predetermined line lengths, as shown in the standard cell  300 A or  300 B. The positions of the cut-MD patterns CMD are shown in  FIG. 3A  for illustrational purposes. The cut-MD patterns CMD can also be arranged in other locations of the standard cell  300 A or  300 B for segmenting the conduction lines MD 1  or MD 2  extending through the standard cell  300 A or  300 B. 
     The standard cells  300 A and  300 B each includes a nanosheet FET formed of two active regions OD 11  and OD 12  or OD 21  and OD 22 . In some embodiments, the two active regions OD 11  and OD 12  (or OD 21  and OD 22 ) are grouped and formed of one n-type active region and one p-type active region, or vice versa, as a basic unit to construct a semiconductor logic gate device, such as a NAND gate, an inverter gate, an XOR gate, an AND gate, a NOR gate, an AOI gate, or another suitable logic gate devices. 
     The grouped active regions OD 11  and OD 12  have equal nanosheet lengths L 1  measured in the row direction, and the grouped active regions OD 21  and OD 22  have equal nanosheet lengths L 2  measured in the row direction. In some embodiments, the nanosheet lengths L 1  and L 2  may be equal or different depending on various design requirements. 
     The grouped active regions OD 11  and OD 12  have nanosheet widths W 11  and W 12 , respectively, measured in the column direction, and the grouped active regions OD 21  and OD 22  have nanosheet widths W 21  and W 22 , respectively, measured in the column direction. The boundaries of these grouped active regions in each standard cell  300 A or  300 B are defined by lines K 1  and K 2 . The lines K 1  and K 2  are defined as lines extending in the row direction parallel to the upper or lower cell side of the standard cells  300 A,  300 B, in which the line K 1  is distant from the upper cell side by a marginal distance M 1  while the line K 2  is distant from the lower cell side by a marginal distance M 2 . The lines K 1  and K 2  define a flexibility width T 1  measured in the column direction. The upper sides of the active region OD 11  and OD 21  are aligned with each other at the line K 1 , while the lower sides of the active regions OD 12  and OD 22  are aligned with each other at the line K 2 . In some embodiments, the marginal distances M 1  and M 2  and the flexibility width T 1  are predetermined cell parameters that obey the constraint of the cell height CH 1  of the standard cell  300 A or  300 B as follows: 
       CH1= M 1+ T 1+ M 2. 
     A spacing in the standard cell  300 A between the grouped active regions OD 11  and OD 12  has a spacing width S 11 , and a spacing in the standard cell  300 B between the grouped active region OD 21  and OD 22  has a spacing width S 21 , in which the following formula holds: 
         T 1= S 11+ W 11+ W 12= S 21+ W 21+ W 22. 
     In some embodiments, the widths and spacings of active regions, e.g., the widths W 11 , W 12 , W 21  and W 22  and spacings S 11  and S 21 , are not only specifically determined according to the designer, but also are subject to the manufacturing capability. In some embodiments, although the values of the widths W 11 , W 12 , W 21  and W 22  and spacings S 11  and S 21  can be arbitrary in certain ranges for a designer, these value ranges may not pass the design rule check due to manufacturing limitations. In some embodiments, the active regions of the standard cells  300 A and  300 B adopt nanosheets, and the widths and spacings of the associated nanosheets as provided include only a predetermined set of numbers compliant with manufacturers&#39; requirements. In some embodiments, these numbers are neither related to each other nor unpredictable in terms of an equation or formula. 
     In view of the unpredictable nature of the selected widths and spacings of the nanosheets, it may be a time-consuming work in tuning the dimensions of the nanosheets in a layout revision stage. This is because a small increment of an originally selected nanosheet width (spacing) picked from the set may not be included in the same set, and a greater incremental increase may be necessary, which usually exceeds the cell height of the standard cell at issue. As a result, an attempt to tune the width of a single nanosheet may inevitably involve alteration of cell heights across a large area of the design layout. The design cycle, area and power of the revised design layout may not be optimized due to the revised design layout in the context of nanosheet FETs. 
     In view of the above, some embodiments of the present disclosure propose a procedure to provide a standard cell library by generating a plurality of standard cells for nanosheet FETs with different selected nanosheet widths and spacings selected from a predetermined set of widths and spacings while ensuring that these standard cells have equal cell heights for the convenience of design layout. 
       FIG. 3C  includes tables for determining widths and spacings of active regions in various standard cells, in accordance with some embodiments. For the description of  FIG. 3C , widths and spacings of active regions are correspondingly referred to as nanosheet widths and nanosheet spacings. Tables (a) and (b) include example formulas for determining combinations of nanosheet widths and nanosheet spacings that will result in cells having different nanosheet widths but the same cell height. Tables (c) and (d) include specific examples of applying a predetermined set of nanosheet widths and nanosheet spacings in Tables (a) and (b). 
     In Table (a), the first row and the first column list nanosheet widths W 1 , W 2 , W 3 , W 4  in a predetermined set of nanosheet widths. Each of the nanosheet widths W 11 , W 12 , W 21  and W 22  in  FIG. 3A  is configured to have one of the predetermined nanosheet widths W 1 , W 2 , W 3 , W 4 . In this example, W 11 =W 12  and W 21 =W 22 , and W 11  and W 21  are listed in Table (a). A formula for ΔW=2*(|W 11 −W 21 |) is listed in various cells of Table (a). For example, the cell at the column corresponding to W 3  and the row corresponding to W 1  has a formula 2*(|W 1 −W 3 |). 
     In Table (b), the first row and the first column list nanosheet spacings S 1 , S 2 , S 3 , S 4 , S 5  in a predetermined set of nanosheet spacings. Each of the nanosheet spacings S 11 , S 21  in  FIG. 3A  is configured to have one of the predetermined nanosheet spacings S 1 , S 2 , S 3 , S 4 , S 5 . A formula for ΔS=|S 11 −S 21 | is listed in various cells of Table (b). For example, the cell at the column corresponding to S 3  and the row corresponding to S 1  has a formula |S 1 −S 3 |. 
     As discussed herein, in the example configuration in  FIG. 3A , to achieve the same cell height CH 1  in various cells, the flexibility width T 1  is configured to be the same in such cells, i.e., T 1 =S 11 +W 11 +W 12 =S 21 +W 21 +W 22 . When ΔS=ΔW, this relationship for T 1  is satisfied. In some embodiments, Tables (a) and (b) are used to calculate various values for ΔS and ΔW. A cell in Table (a) having the same value (other than zero) as a cell in Table (b) indicates ΔS=ΔW and corresponding combinations of nanosheet widths and nanosheet spacings that will result in cells having the same T 1  and the same cell height. 
     Tables (c) and (d) show specific numeric examples for Tables (a) and (b). The first row and the first column of Table (c) list exemplary nanosheet widths selected from a predetermined set of nanosheet widths in the unit of nanometer, while the first row and the first column of Table (d) list exemplary nanosheet spacings selected from a predetermined set of nanosheet spacings in the unit of nanometer. Any nanosheet width or nanosheet spacing values not included in the predetermined set of nanosheet widths or nanosheet spacings may not pass the design rule check in an initial layout design stage or a layout revision stage. A value in a cell (x, y) of Table (c) represents a width difference ΔW calculated as described with respect to Table (a) for the nanosheet widths in the x-th row and the y-th column. Similarly, a value in a cell (x, y) of Table (d) represents a spacing difference ΔS calculated as described with respect to Table (b) for the nanosheet spacings in the x-th row and the y-th column. A cell in Table (c) and a cell in Table (d) that have the same value are indicated by the same label, e.g., one of L_a1, L_a2, L_a3, L_b1, L_b2 and L_c1. 
     The nanosheet widths W 11 , W 12 , W 21  and W 22 , and corresponding nanosheet spacings S 11 , S 21  selected for generating the standard cells  300 A and  300 B can be obtained from Tables (c) and (d). For example, in Table (c), the set of selected values of the widths W 11 =W 12  and W 21 =W 22  are provided as 15, 22, 35 and 41 (nm), while, in Table (d), the set of selected values of the spacings S 11  and S 21  are provided as 28, 34, 36, 40, 66 and 80 (nm, the unit is omitted for brevity hereinafter). Given the finite numbers of the selected widths and spacings, there is a finite number of combinations of nanosheet widths and nanosheet spacings that satisfy the same flexibility width T 1  across the standard cells  300 A and  300 B. 
     An exemplary fulfilling condition is given with reference to the entries in Tables (c) and (d) with labels L_a1 which indicate that the flexibility width T 1  is kept as  110  with W 11 =W 12 =15 and S 11 =80 in standard cell  300 A, and W 21 =W 22 =22 and S 21 =66 in standard cell  300 B. Similarly, another fulfilling condition is given with reference to the entries in Tables (c) and (d) with labels L_a2, which indicate that the flexibility width T 1  is kept as  110  with W 11 =W 12 =15 and S 11 =80 in standard cell  300 A, and W 21 =W 22 =35 and S 21 =40 in standard cell  300 B. A further fulfilling condition is given with reference to the entries in Tables (c) and (d) with labels L_a3, which indicate that the flexibility width T 1  is kept as  110  with W 11 =W 12 =15 and S 11 =80 in standard cell  300 A, and W 21 =W 22 =41, and S 21 =28 in standard cell  300 B. 
     Given the above, the standard cell  300 A or  300 B can be generated sharing an equal flexibility width T 1 =110 with four different combinations of selected nanosheet widths and nanosheet spacings. The cell heights CH 1  of different standard cells can be kept unchanged given that the marginal distances M 1  and M 2  are set equal in the standard cells  300 A and  300 B, while the nanosheet dimensions, e.g., nanosheet width and/or nanosheet spacing, can be made various, i.e., selected from a predetermined set of nanosheet widths and nanosheet spacings, in the standard cells  300 A and  300 B. 
     As shown in  FIG. 3C , six entries of Tables (c) and (d) in  FIG. 3C  are marked with labels (e.g., L_a1, L_a2, L_a3, L_b1, L_b2 and L_c1) to indicate the compliant combinations of nanosheet widths and nanosheet spacings to achieve equal flexibility widths T 1 , thereby attaining the purpose of equal cell heights of the standard cells  300 A and  300 B. In some embodiments, some entries of Tables (c) and (d) are left without any label, which indicates no compliant combinations exist with respect to these nanosheet widths and nanosheet spacings to achieve equal flexibility widths T 1 , and thus these combinations are discarded from consideration during the generation of standard cells for a standard cell library. 
     The marginal distance M 1  or M 2  is selected in a manner similar to that for selecting compliant nanosheet widths and nanosheet spacings with reference to  FIG. 3C . Referring to  FIG. 2  and  FIG. 3A , the marginal distance M 1  or M 2  may be set as one half of a spacing between two adjacent active regions of two abutting standard cells, e.g., a spacing Sx between the active regions NOD 3  and NOD 42 , i.e., M1=Sx/2. For example, the marginal distance M 1  or M 2  is selected from the set formed of numbers {14, 17, 18, 20, 33, 40} being half of the corresponding values {28, 34, 36, 40, 66, 80} in Table (d) of  FIG. 3C . In this way, when two standard cells abut in the column direction, the adjacent marginal distance M 1  or M 2  of each standard cell contributes one half of the spacing between the cell boundary and a closest nanosheet, and thus the total spacing between two adjacent nanosheets of the abutting standard cells fulfill the requirement as provide in the set of the spacings shown in Table (d). 
     In some embodiments, the grouped active regions OD 11  and OD 12  (or the grouped active regions OD 21  and OD 22 ) have equal nanosheet widths to maintain comparable electrical performance for the grouped active regions OD 11  and OD 12  (or the grouped active regions OD 21  and OD 22 ). Under this assumption, the above formula can be further simplified as follows. 
         T 1= S 11+2* W 11= S 21+2* W 21. 
     According to the above formulas, the nanosheet width W 11  can be different from the nanosheet width W 21  by an amount of D=|S 11 −S 21 |/2 to provide design flexibility between the standard cells  300 A and  300 B under the constraint of equal cell heights CH 1  for the standard cells  300 A and  300 B. In some embodiments, the difference between the widths W 11  and W 21  is greater than a tolerance level due to process variations during manufacturing of the nanosheets OD 11  and OD 21 . In some embodiments, the nanosheet width W 11  is different from the nanosheet width W 21  by at least 2.5% of the nanosheet width W 11 , by at least 5% of the nanosheet width W 11  or by at least 10% of the nanosheet width W 11 . Accordingly, the width S 11  is different from the width S 21  by an amount greater than a tolerance level due to process variations during manufacturing of the nanosheets OD 11  and OD 21 . In some embodiments, the spacing width S 11  is different from the spacing width S 21  by at least 5%, 10% or 20%, of the nanosheet width W 11 . 
     In some embodiments, the nanosheet width W 11  or W 12  in the standard cell  300 A is a multiple of the nanosheet width W 21  or W 22 , respectively, in the standard cell  300 B. 
     In some embodiments, the flexibility widths T 1  in the standard cells  300 A and  300 B are kept equal but may not be flush with each other along the lines K 1  and K 2 . In other words, the marginal distances M 1  and M 2  in the standard cell  300 A may not be equal to the corresponding marginal distances M 1  and M 2  in the standard cell  300 B. In some embodiments, to ensure equal cell height CH 1  across the standard cells  300 A and  300 B, the sum of marginal distances M 1 +M 2  in the standard cell  300 A is set to be equal to the sum of marginal distances M 1 +M 2  in the standard cell  300 B, in which the individual marginal distances M 1  and M 2  for the standard cells  300 A and  300 B are selected to be one half of any of the spacings in Table (d). In this way, the requirement of equal cell height CH 1  can still be maintained and greater design flexibility of the standard cells can be obtained. 
     As discussed previously, the planar areas of the nanosheet, determined by the nanosheet length and width, are closely related to the electrical performance of the nanosheet FET. The nanosheet widths and nanosheet spacings may be selected from a predetermined set of specific numbers of nanosheet widths and nanosheet spacings due to some manufacturing constraints. Therefore, the proposed framework of standard cell generation provides as many compliant combinations of nanosheet widths and nanosheet spacings as possible for a same type of standard cell, e.g., standard cells having the same functionality, with equal cell heights. For example, a standard cell library is provided or generated to include a plurality of inverter cells having the same cell height but with different nanosheet widths and/or nanosheet spacings. These inverter cells can replace each other in the circuit design stage. This will provide benefits when revisions to the placed cell layouts are required to meet the design requirements in the circuit design stage. For example, a placed cell that fails the circuit simulation may not need to be redesigned from scratch. Rather, the failed cell, e.g., an inverter cell, can be efficiently replaced with a similar standard cell, e.g., another inverter cell, which has the same cell height but with different nanosheet widths without revising other portions of the already placed layout or alteration of the cell height. As a result, a better tradeoff between performance, area and power is achieved while the design cycles can be improved. 
       FIG. 3B  is a schematic diagram of design layouts for standard cells  300 C and  300 D, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  300 C and  300 D are similar to those of the standard cells  300 A and  300 B, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIG. 3A  and  FIG. 3B , new lines K 3  and K 4  are used to define a flexibility width T 2 , in which the line K 3  is aligned with the upper cell sides of the standard cells  300 C and  300 D, and the lower sides of the active regions OD 11  and OD 21  are aligned with each other at the line K 4 . Lines K 4  and K 2  are used to define a flexibility width T 4 . As a result, the nanosheet widths W 11 , W 12 , W 21  and W 22  are tunable according to the following formulas: 
         T 2= S 21+ W 11= S 22+ W 21. 
         T 3= S 31+ W 12= S 32+ W 22. 
     The determination of the flexibility width T 2  and the selection of compliant nanosheet widths W 11 , W 21  and nanosheet spacings S 21 , S 22  are performed with help of Tables (a) and (b), or Tables (c) and (d), shown in  FIG. 3C , in a manner similar to that discussed for determining the flexibility width T 1  shown in  FIG. 3A . Similarly, the determination of the flexibility width T 3  and the selection of compliant nanosheet widths W 12 , W 22  and nanosheet spacings S 31 , S 32  are performed with help of Tables (a) and (b), or Tables (c) and (d), shown in  FIG. 3C , in a manner similar to that discussed for determining the flexibility width T 1  shown in  FIG. 3A . With the above arrangement, the active region OD 12  can be designed to have the nanosheet width W 12  independent of the nanosheet width W 11  of the active region OD 11  under the constraint of the flexibility width T 2 . Similarly, the active region OD 22  can be designed to have the nanosheet width W 22  independent of the nanosheet width W 21  of the active region OD 21  under the constraint of the flexibility width T 3 . 
     According to the above formula, the nanosheet width W 12  can be different from the nanosheet width W 22  by an amount of D=|S 31 −S 32 | to provide design flexibility between the standard cells  300 A and  300 B under the constraint of the flexibility width T 3  for the standard cells  300 A and  300 B. In some embodiments, the difference between the widths W 12  and W 22  is greater than a tolerance level due to process variations during manufacturing of the nanosheets OD 12  and OD 22 . In some embodiments, the nanosheet width W 12  is different from the nanosheet width W 22  by at least 2.5%, 5% or 10% of the nanosheet width W 12 . Accordingly, the spacing width S 31  is different from the spacing width S 32  by an amount greater than a tolerance level due to process variations during the manufacturing of the nanosheets OD 21  and OD 22 . In some embodiments, the spacing width S 21  is different from the spacing width S 21  by at least 2.5%, 5% or 10% of the nanosheet width W 21 . 
       FIG. 4A  shows schematic diagrams of design layouts for standard cells  400 A and  400 B, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  400 A and  400 B are similar to those of the standard cells  300 A and  300 B, and description of similar aspects are not repeated herein for brevity. Referring to  FIG. 3A  and  FIG. 4A , the active regions OD 11 , OD 12 , OD 21 , OD 22  and lines K 1 , K 2  in the standard cells  400 A and  400 B are similar to those in the standard cells  300 A and  300 B. The standard cells  400 A and  400 B each further includes a third active region OD 13  and OD 23  with respective nanosheet widths W 13  and W 23  measured in the column direction. In some embodiments, the active region OD 13  or OD 23  is configured to be paired with another active region of another standard cell for forming a nanosheet FET, in which the standard cells of these paired active regions will be arranged in adjacent rows in a cell placement operation. 
     The nanosheet widths W 11 , W 12 , W 21 , W 22  of the grouped active regions OD 11 , OD 12 , OD 21 , OD 22  are defined by lines K 1  and K 2  and the flexibility width T 1 . A third line K 3  is defined as a line extending in the row direction parallel to the upper or lower cell side of the standard cells  300 A,  300 B, in which the line K 3  is distant from the lower cell side of the standard cells  300 A,  300 B by a marginal distance M 2  while the line K 2  is distant from the line K 3  by a flexibility width T 2 . In some embodiments, the marginal distances M 1  and M 2  and the flexibility widths T 1  and T 2  are predetermined cell parameters and obey the constraint of the cell height CH 1  as follows: 
       CH1= M 1+ T 1+ T 2+ M 2. 
     The upper sides of the active regions OD 11  and OD 21  are aligned with each other at the line K 1 , while the lower sides of the active regions OD 12  and OD  22  are aligned with each other at the line K 2 , in which the following formula holds: 
         T 1= S 11+ W 11+ W 12= S 21+ W 21+ W 22. 
     Similarly, the lower side of the active regions OD 13  and OD  23  are aligned with each other at the line K 3 , and a spacing width S 12  or S 22  exists between the active regions OD 12  and OD 13  or between the active region OD 22  and OD 23 , in which the following formula holds: 
         T 2= S 12+ W 13= S 22+ W 23. 
     In some embodiments, the nanosheet width W 11 , W 12  or W 13  in the standard cell  400 A is a multiple of the nanosheet width W 21 , W 22  or W 23  associated with the same flexibility width T 1  or T 2  of the standard cell  400 B. 
     The different flexibility widths T 1  and T 2  can be different from each other and the spacing widths S 11 , S 12 , S 21  and S 22  can be different from each other. As a result, the active region OD 13  can be designed to have the tunable nanosheet width W 13  independent of the tunable nanosheet width W 11  or W 12  under the constraint of the flexibility width T 1 . Similarly, the active region OD 23  can be designed to have the tunable nanosheet width W 23  independent of the tunable nanosheet width W 21  or W 22  under the constraint of the flexibility width T 2 . 
       FIG. 4B  shows schematic diagrams of design layouts for standard cells  400 C and  400 D, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  400 C and  400 D are similar to those of the standard cells  400 A and  400 B, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIG. 4A  and  FIG. 4B , the standard cells  400 C and  400 D further include new lines K 4  and K 5  defining a flexibility width T 3 , for the active regions OD 13  and OD 23 , instead of the flexibility width T 2  in  FIG. 4A . The upper sides of the active regions OD 13  and OD 23  are aligned with each other at the line K 4  while the line K 5  is aligned with the lower cell sides of the standard cells  400 C and  400 D. The line K 2  is distant from the line K 4  by a marginal distance M 3  instead of the marginal distance M 2  in  FIG. 4A . As a result, the following formulas hold: 
         T 3= S 13+ W 13= S 23+ W 23. 
       CH1= M 1+ T 1+ M 3+ T 3. 
       FIG. 4C  shows schematic diagrams of design layouts for standard cells  400 E and  400 F, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  400 E and  400 F are similar to those of the standard cells  400 A and  400 B, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIG. 4A  and  FIG. 4C , the standard cells  400 E and  400 F further include new lines K 6  and K 7  defining a flexibility width T 4 , for the active regions OD 11  and OD 21 , instead of the flexibility width T 1  in  FIG. 4A . The line K 7  further defines a flexibility width T 5  with the line K 2 , for the active regions OD 12  and OD 22 , instead of the flexibility width T 1  in  FIG. 4A . The line K 6  is aligned with the upper cell sides of the standard cells  400 E and  400 F while the lower sides of the active regions OD 11  and OD 21  are aligned with each other at the line K 7 . A spacing width S 14  or S 24  is defined as a distance between the line K 6  and the upper side of the active region OD 11  or OD 21 . A spacing width S 15  or S 25  is defined as a distance between the line K 7  and the upper side of the active region OD 12  or OD 22 . As a result, the following formulas hold: 
         T 4= S 14+ W 11= S 24+ W 21. 
         T 5= S 15+ W 12= S 25+ W 22. 
       CH1= T 4+ T 5+ T 2+ M 2. 
       FIG. 4D  shows schematic diagrams of design layouts for standard cells  400 G and  400 H, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  400 G and  400 H are similar to those of the standard cells  400 C,  400 D,  400 E and  400 F, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIGS. 4B, 4C and 4D , the standard cells  400 G and  400 H can be seen as a combination of  FIG. 4B  with  FIG. 4C  by adopting the lines K 6 , K 7 , K 2 , K 4  and K 5  for defining the flexibility widths T 4 , T 5  and T 3 , as discussed above. As a result, the following formula holds: 
       CH1= T 4+ T 5+ M 3+ T 3. 
       FIG. 5A  is a schematic diagram of design layouts for standard cells  500 A and  500 B, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  500 A and  500 B are similar to those of the standard cells  400 A and  400 B, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIG. 4A  and  FIG. 5A , the active regions OD 11 , OD 12 , OD 21 , OD 22  and lines K 1 , K 2  in the standard cells  500 A and  500 B are similar to those in the standard cells  400 A and  400 B, in which the grouped active regions OD 11  and OD 12  (or OD 21  and OD 22 ) are configured to form a first nanosheet FET of the standard cell  500 A (or  500 B). The standard cells  400 A and  400 B each further includes a fourth active region OD 14  and OD 24  with respective nanosheet widths W 14  and W 24  measured in the column direction. In some embodiments, the active region OD 13  or OD  23  is grouped with the active region OD 14  or OD 24  and the grouped active regions OD 13 /OD 23  and OD 14 /OD 24  are configured to form a second nanosheet FET. 
     The nanosheet widths of the aforesaid active regions OD 11  through OD 14  and OD 21  through OD  24  and their related parameters are defined in a way similar to those discussed in previous embodiments. For example, nanosheet widths W 11 , W 12 , W 21 , W 22  of the grouped active regions OD 11 , OD 12 , OD 21 , OD 22  are defined by lines K 1  and K 2  and a flexibility width T 1  along with spacing widths S 11  and S 21 . Nanosheet widths W 13 , W 14 , W 23 , W 24  of the grouped active regions OD 13 , OD 14 , OD 23 , OD 24  are defined by lines K 3  and K 4  and a flexibility width T 2  along with spacing widths S 21  and S 22 . The lines K 1  through K 4  are defined as lines extending in the row direction parallel to the upper or lower cell side of the standard cells  500 A,  500 B. The lines K 1  and K 4  are distant from the upper and lower cell sides, respectively, of the standard cells  500 A and  500 B by marginal distances M 1  and M 2 , respectively. The line K 2  is distant from the line K 3  by a marginal distance M 3 . In some embodiments, the marginal distances M 1 , M 2  and M 3  and the flexibility widths T 1  and T 2  are predetermined cell parameters and obey the constraint of the cell height CH 1  as follows: 
       CH1= M 1+ T 1+ M 3+ T 2+ M 2. 
     The upper sides of the active regions OD 11  and OD 21  are aligned with each other at the line K 1 , while the lower sides of the active regions OD 12  and OD  22  are aligned with each other at the line K 2 , in which the following formula holds: 
         T 1= S 11+ W 11+ W 12= S 21+ W 21+ W 22. 
     The upper sides of the active regions OD 13  and OD 23  are aligned with each other at the line K 3 , while the lower sides of the active regions OD 14  and OD  24  are aligned with each other at the line K 4 , in which the following formula holds: 
         T 2= S 12+ W 13+ W 14= S 22+ W 23+ W 24. 
     In some embodiments, the grouped active regions, such as the active regions OD 11  and OD 12 , OD 21  and OD 22 , OD 13  and OD 23 , and OD 14  and OD 24 , have equal nanosheet widths to maintain comparable electrical performance between the grouped active regions. Under this assumption, the above formula can be further simplified as follows: 
         T 1= S 11+2* W 11= S 21+2* W 21. 
         T 2= S 12+2* W 13= S 22+2* W 23. 
     In some embodiments, the nanosheet width W 11 , W 12 , W 13  or W 14  in the standard cell  500 A is a multiple of the nanosheet width W 21 , W 22 , W 23  or W 24  associated with the same flexibility width T 1 , T 2  in the standard cell  500 B. 
       FIG. 5B  shows schematic diagrams of design layouts for standard cells  500 C and  500 D, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  500 C and  500 D are similar to those of the standard cells  500 A and  500 B, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIG. 5A  and  FIG. 5B , the standard cells  500 C and  500 D further include new lines K 5 , K 6 , K 7 , K 8 , K 9  and K 10  defining flexibility widths T 3 , T 4  and T 5 , along with respective spacing widths S 13 , S 23 , S 14 , S 24 , S 15  and S 25 , instead of the flexibility widths T 1  and T 2  in  FIG. 4A . The lines K 5  and K 10  are aligned with the upper and lower cell sides, respectively, of the standard cells  500 A,  500 B. The lower sides of the active regions OD 11  and OD 21  are aligned with each other at the line K 6 . The upper sides of the active regions OD 12  and OD 22  are aligned with each other at the line K 7  while the lower sides of the active regions OD 13  and OD 23  are aligned with each other at the line K 8 . The upper sides of the active regions OD 14  and OD 24  are aligned with each other at the line K 9 . 
     The line K 6  is distant from the line K 7  by a marginal distance M 4  and the line K 8  is distant from the line K 9  by a marginal distance M 5 . As a result, the following formulas hold: 
         T 3= S 13+ W 11= S 23+ W 21. 
         T 4= S 14+ W 12+ W 13= S 24+ W 22+ W 23. 
         T 5= S 15+ W 14= S 25+ W 24. 
       CH1= T 3+ M 4+ T 4+ M 5+ T 5. 
       FIG. 5C  shows schematic diagrams of design layouts for standard cells  500 E and  500 F, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  500 E and  500 F are similar to those of the standard cells  500 A,  500 B,  500 C and  500 D, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIGS. 5A, 5B and 5C , the standard cells  500 E and  500 F can be seen as a combination of  FIG. 5A  with  FIG. 5B , in which new flexibility widths T 6  and T 7  are defined by the lines K 7 , K 3  and K 9  along with respective spacing widths S 16 , S 26 , S 17  and S 27  for replacing the flexibility width T 4 . As a result, the following formulas hold: 
       CH1= T 3+ M 4+ T 6+ T 7+ T 5. 
     In this way, the active region OD 12  or OD 22  can be designed to have the nanosheet width W 12  or W 22  independent of the nanosheet width W 13  or W 23  of the active region OD 13  or OD 23  under the constraint of the flexibility width T 6 . Similarly, the active region OD 13  or OD  23  can be designed to have the nanosheet width W 13  or W 23  independent of the nanosheet width W 12  or W 22  of the active region OD 12  or OD 22  under the constraint of the flexibility width T 7 . 
       FIG. 5D  shows schematic diagrams of design layouts for standard cells  500 G and  500 H, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  500 G and  500 H are similar to those of the standard cells  500 A,  500 B,  500 C and  500 D, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIGS. 5A, 5B and 5D , the standard cells  500 G and  500 H can be seen as a combination of  FIG. 5A  with  FIG. 5B , in which new flexibility widths T 8  and T 9  are defined by the lines K 6 , K 2  and K 8  along with respective spacing widths S 18 , S 28 , S 19  and S 29  for replacing the flexibility width T 4 . As a result, the following formulas hold: 
       CH1= T 3+ T 8+ T 9+ M 5+ T 5. 
       FIG. 5E  shows schematic diagrams of design layouts for standard cells  500 I and  500 J, in accordance with various embodiments of the present disclosure. The arrangements of the standard cells  500 I and  500 J are similar to those of the standard cells  500 A,  500 B,  500 C and  500 D, and descriptions of similar aspects are not repeated herein for brevity. Referring to  FIGS. 5A, 5B and 5E , the standard cells  500 I and  500 J can be seen as a combination of  FIG. 5A  with  FIG. 5B , in which the flexibility widths T 7  and T 8  are defined instead of the flexibility width T 4 . As a result, the following formula holds: 
       CH1= T 3+ T 8+ M 3+ T 7+ T 5. 
       FIG. 6A  is a flowchart of a layout method  600 A, in accordance with some embodiments. It should be understood that additional steps can be provided before, during, and after the steps shown in these figures, and some of the steps described below can be replaced or eliminated in other embodiments of the method  600 A. The order of the steps may be interchangeable. 
     At step  602 , design data of a semiconductor device are generated or received. The design data may be represented as a netlist, a schematic diagram, a circuit diagram or the like. In some embodiments, the semiconductor device includes at least one electronic circuit, which can be a logic gate device in various types, such as a NAND gate, an inverter gate, an XOR gate, an AND gate, a NOR gate, an AOI gate, or another suitable logic gate device. In some embodiments, the design data in step  602  are generated during a synthesis stage of a design flow for manufacturing the semiconductor device. 
     At step  604 , a design rule deck is received. In some embodiments, the design rule deck includes design rules, such as a predetermined set of specified values of widths and spacings associated with active regions. In some embodiments, the active regions are implemented by nanosheets, and the predetermined set includes specified values of nanosheet widths and nanosheet spacings. In some embodiments, the specified widths and spacings are provided by a semiconductor manufacturer or circuit designer. In some embodiments, the specified values of the widths and spacings are unrelated to each other and are unpredictable through an equation or formula. In some embodiments, the specified values of the widths and spacings are elements of an irregular data sequence. 
     At step  606 , a standard cell library is provided according to the design data, and includes a first cell and a second cell, e.g., standard cells  300 A and  300 B. The first cell comprises a first active region having a first width, and the second cell comprises a second active region having a second width different from the first width. In some embodiments, each of the first cell and the second cell includes a nanosheet FET having a respective nanosheet stack, in which a first nanosheet stack of the first cell overlaps a second nanosheet stack of the second cell in the row direction. The first cell and the second cell have equal cell heights. In some embodiments, the first nanosheet stack and the second nanosheet stack have different nanosheet widths and nanosheet spacings, which are selected from the predetermined set of widths and spacings of the design rule deck. The first cell and the second cell are discussed above and are not repeated for brevity. 
     At step  608 , a design layout is generated by placing the first cell and the second cell, e.g., in a same row, according to the design data. The step  608  may be performed during a placement and routing stage of a design flow for manufacturing a semiconductor device. 
     At step  610 , a lithography mask is manufactured according to the design layout. At step  611 , a semiconductor device is fabricated in which a layer of the semiconductor device is formed according to the lithography mask. In some embodiments, the semiconductor device is fabricated according to the design layout. 
       FIG. 6B  is a flowchart of a layout method  600 B, in accordance with some embodiments. It should be understood that additional steps can be provided before, during, and after the steps shown in these figures, and some of the steps described below can be replaced or eliminated in other embodiments of the method  600 B. The order of the steps may be interchangeable. 
     The steps  602 ,  604 ,  606 ,  610  and  611  of the method  600 B are similar to those of method  600 A, and thus descriptions of these steps are simplified. At step  602 , design data of a semiconductor device are generated or received. At step  604 , a design rule deck is received including a predetermined set of specified values for widths and spacings for active regions, e.g., nanosheet widths and nanosheet spacings. At step  606 , a standard cell library is provided which includes a first cell and a second cell according to the design data. In some embodiments, the first cell and the second cell have equal cell heights, and corresponding first and second active regions with different first and second widths. In some embodiments, the first and second active regions comprise first and second nanosheet stacks with different nanosheet widths and nanosheet spacings. In some embodiments, the different nanosheet widths and nanosheet spacings are selected from the predetermined set of nanosheet widths and nanosheet spacings of the design rule deck. 
     At step  612 , a design layout is generated by placing the first cell in a row. The step  612  may be performed during a placement and routing stage of a design flow for manufacturing a semiconductor device. 
     At step  614 , a circuit simulation is performed to examine the physical characteristics and the electrical performance of the design layout. In some embodiments, the circuit simulation includes a post-layout simulation. In some embodiments, additional steps, such as parasitic parameter extraction and timing analysis, may be performed to provide layout-related information to support the circuit simulation. At step  616 , it is determined whether the design layout meets the design requirement according to the circuit simulation result. 
     If affirmative, at step  610 , a lithography mask is manufactured according to the design layout. At step  611 , a semiconductor device fabricated in which a layer of the semiconductor device is formed according to the lithography mask. In some embodiments, the semiconductor device is fabricated according to the design layout. 
     If it is determined that the first cell fails the circuit simulation, that means a circuit revision is required. At step  618 , the first cell is replaced with the second cell of the same cell height, and the method  600 B loops back to step  616  for performing another circuit simulation. In some embodiments, the second cell has a nanosheet width greater than that of the first cell and thus is capable of providing greater circuit performance than the first cell given the same cell height. In some embodiments, since the second cell resembles the first cell in most portions of the cell layout except for the nanosheet width, the difference between the original design layout incorporating the first cell and the revised design layout incorporating the second cell is minimized. In this way, the likelihood of revising the remaining portions of the revised design layout is reduced or minimized accordingly, and the cycle time of revising the design layout can be greatly shortened. 
       FIG. 7A  is a schematic diagram  700  showing an integrated circuit (IC) manufacturing system, in accordance with some embodiments. The IC manufacturing system  700  is configured to manufacture an IC device  780  through a plurality of entities, such as a design subsystem  710 , a mask subsystem  720 , and a fabrication subsystem  730 . The entities in the IC manufacturing system  700  may be linked by a communication channel, e.g., a wired or wireless channel, and interact with one another through a network, e.g., an intranet or the internet. In an embodiment, the design subsystem  710 , the mask subsystem  720  and the fabrication subsystem  730  belong to a single entity, or are operated by independent parties. 
     The design subsystem  710 , which may be provided by a design house or a layout design provider, generates a design layout  750 , e.g., the design layout  200 , in a design phase for the IC devices  780  to be fabricated. The design subsystem  710  may perform the layout methods discussed in the present disclosure to generate the design layout  750 , e.g., the design layouts shown with reference to the figures of the present disclosure. In an embodiment, the design subsystem  710  operates a circuit design procedure to generate the design layout  750 . The design subsystem  710  may include further one or more steps, such as logic design, physical design, pre-layout simulation, placement and routing, timing analysis, parameter extraction, design rule check and post-layout simulation, to generate the design layout  750 . The design layout  750  may be converted from description texts into their visual equivalents to show a physical layout of the depicted patterns, such as the dimensions, shapes and locations thereof. In an embodiment, the design layout  750  can be expressed in a suitable file format such as GDSII, DFII, OASIS, or the like. 
     The mask subsystem  720  receives the design layout  750  from the design subsystem  710  and manufactures one or more masks (photomask, lithography masks or reticles) according to the design layout  750 . In an embodiment, the mask subsystem  720  includes a mask data preparation block  722 , a mask fabrication block  724  and a mask inspection block  726 . The mask data preparation block  722  modifies the design layout  750  so that a revised design layout  760  can allow a mask writer to transfer the design layout  750  to a writer-readable format. 
     The mask fabrication block  724  is configured to fabricate the one or more masks by preparing a substrate based on the design layout  760  provided by the mask data preparation block  722 . A mask substrate is exposed to a radiation beam based on the pattern of the design layout  760  in a writing operation, which may be followed by an etching operation to leave behind the patterns corresponding to the design layout  760 . In an embodiment, the mask fabrication block  724  includes a checking procedure to ensure that the layout data  760  complies with requirements of a mask writer and/or a mask manufacturer to generate the mask as desired. An electron-beam (e-beam), multiple e-beams, an ion beam, a laser beam or other suitable writer source may be used to transfer the patterns. 
     After the one or more masks are fabricated, the mask inspection block  726  inspects the fabricated masks to determine if any defects, such as full-height and non-full-height defects, exist in the fabricated mask. If any defects are detected, the mask may be cleaned or the design layout in the mask may be modified. 
     The fabrication subsystem  730  is an IC manufacturing entity that includes multiple manufacturing facilities or tools for the fabrication of a variety of the IC devices  780 . The fabrication subsystem  730  uses the mask fabricated by the mask subsystem  720  to fabricate a wafer  770  having a plurality of IC devices  780  thereon. The wafer  770  includes a semiconductor substrate and optionally various layers formed thereon. The operations provided by the manufacturing facilities or tools may include, but are not limited to, photolithography, deposition, sputtering, etching, diffusion, ion implantation and annealing. In some embodiments, test structures may be formed on the wafer  770  to generate test data indicative of the quality of the fabricated wafer  770 . In an embodiment, the fabrication subsystem  730  includes a wafer testing block  732  configured to ensure that the wafer  770  conforms to physical manufacturing specifications and mechanical and/or electrical performance specifications. After the wafer  770  passes the testing procedure performed by the wafer testing block  732 , the wafer  770  may be diced (or sliced) along the scribe line regions to form separate IC devices  780 . The dicing process can be accomplished by scribing and breaking, by mechanical sawing (e.g., with a dicing saw) or by laser cutting. 
       FIG. 7B  is a schematic diagram of a system  700  for implementing or storing the design layouts discussed above, in accordance with some embodiments. The system  700  includes a processor  701 , a network interface  703 , an input and output (I/O) device  705 , a storage device  707 , a memory  709 , and a bus  708 . The bus  708  couples the network interface  703 , the I/O device  705 , the storage device  707 , the memory  709  and the processor  701  to each other. 
     The processor  701  is configured to execute program instructions that include a tool configured to generate the design layouts as described and illustrated with reference to figures of the present disclosure. 
     The network interface  703  is configured to access program instructions and data accessed by the program instructions stored remotely through a network (not shown). 
     The I/O device  705  includes an input device and an output device configured for enabling user interaction with the system  700 . In some embodiments, the input device includes, for example, a keyboard, a mouse, and other devices. Moreover, the output device includes, for example, a display, a printer, and other devices. 
     The storage device  707  is configured for storing the design layouts, one or more cell libraries including the configurations and settings of the standard cells as discussed previously, program instructions and data accessed by the program instructions. In some embodiments, the storage device  707  includes a non-transitory computer-readable storage medium, for example, a magnetic disk and an optical disk. 
     The memory  709  is configured to store program instructions to be executed by the processor  701  and data accessed by the program instructions. In some embodiments, the memory  709  includes any combination of a random access memory (RAM), some other volatile storage device, a read-only memory (ROM), and some other non-volatile storage device. 
     According to an embodiment, a method includes: receiving a design rule deck including a predetermined set of widths and spacings associated with active regions. The method also includes providing a cell library including cells having respective active regions, wherein widths and spacings of the active regions are selected from the predetermined set of the design rule deck. The method includes placing a first cell and a second cell from the cell library in a design layout. The first cell has a cell height in a first direction, and the first cell comprises a first active region having a first width in the first direction. The second cell has the cell height, and the second cell comprises a second active region having a second width in the first direction. The second width is different from the first width. The method further comprises manufacturing a semiconductor device according to the design layout. 
     According to an embodiment, a method comprises placing a first cell and a second cell in a first row of a design layout. The first cell comprises a first active region and a second active region. The first active region is separated from the second active region by a first distance in a first direction. The second cell comprises a third active region and a fourth active region. The third active region is separated from the fourth active region by a second distance in the first direction. The second distance is different from the first distance. The method further comprises manufacturing a semiconductor device according to the design layout. 
     According to an embodiment, a non-transitory computer readable storage medium comprises instructions which, when executed by a processor, cause the processor to perform a circuit simulation of an operation of a design layout comprising a first cell. The first cell has a cell height in a first direction, and the first cell comprises a plurality of first nanosheets having a first width in the first direction. In response to the circuit simulation failing to meet a design requirement, the processor is caused to replace the first cell in the design layout with a second cell to obtain a revised design layout. The second cell has the cell height, and the second cell comprises a plurality of second nanosheets having a second width in the first direction. The second width is greater than the first width. The processor is further caused to control manufacturing of a semiconductor device according to the revised design layout. 
     The foregoing outlines features of several embodiments so that those skilled in the art may better understand the aspects of the present disclosure. Those skilled in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the embodiments introduced herein. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions, and alterations herein without departing from the spirit and scope of the present disclosure.