Patent Publication Number: US-2011073840-A1

Title: Radial contact for nanowires

Description:
TECHNICAL FIELD 
     The presently disclosed embodiments are directed to the field of semiconductor devices, and more specifically, to nanowires. 
     BACKGROUND 
     Currently, there is great interest in growing nanowires of semiconducting materials on a growth substrate and then transferring them to a final substrate to form electronic devices. These nanowires generally have a high aspect ratio, e.g., 10-50 nm in radius and &gt;5 micron long. Patterning is typically accomplished by deposition of the nanowires in a random, network or by aligning the devices using liquid flow. These methods are limited due to the difficulty of errors in registration of the nanowires to electrode structures that are either previously defined or subsequently patterned by methods such as photolithography. 
     Single-crystal nanowires and carbon nanotubes have been demonstrated to be useful for high mobility transistors on a variety of substrates. Typically, circuits using these devices are made by spin coating blanket solutions of these nanowires onto a substrate and performing electron-beam lithography to pattern these circuits. These methods are needed because there are few methods to accurately place these wires in any pattern on a substrate. Micro-fluidic channels have been used to deposit these wires with some degree of patterning, but the demonstrations have not been shown to be able to fabricate arbitrary patterns or easily achieve registration. These techniques generally rely on depositing wires over larger areas than desired due relatively poor control of registration and the complexity of building fluidic systems that only contact the substrate in isolated locations. Since the cost of raw materials is important in large area devices, patterning methods that use as little material as possible are desirable. 
     In all reported work, nanowire devices have been fabricated with linear electrical contacts either in a single pair or in a set of electrodes. If the nanowire and a set of linear contact electrodes are misaligned, the channel length of the device will be affected. The range of angles where there is possible contact depends on the length of the nanowire itself and the length between the contacts. For a typical length of ˜20 micron and a channel length of ˜6 microns, approximately 30% of wires produce devices with no electrical continuity if a random method is used for deposition. If bundles of wires are used, the problem occurs that not all wires will have the same channel length due to their angular dispersion. 
     SUMMARY 
     One disclosed feature of the embodiments is a method and apparatus for radial contact using nanowires. An inner contact has a center. An outer contact circularly surrounds the inner contact around the center and is spaced from the inner contact by a channel length. A nanowire connects the center of the inner contact and the outer contact in a rotationally invariant geometry. 
     Another disclosed feature of the embodiments is a method and apparatus of a semiconductor device with bottom gate structure and having radial contact using nanowires. A gate electrode is deposited on a substrate. A dielectric layer is deposited on the substrate and the gate electrode. A source-drain assembly is deposited on the dielectric layer. The source-drain assembly has source and drain electrodes connected via a nanowire in a rotationally invariant geometry. 
     Another disclosed feature of the embodiments is a method and apparatus of a semiconductor device with top gate structure and having radial contact using nanowires. An isolation barrier layer is deposited on a substrate. A source-drain assembly is deposited on the substrate and within the isolation barrier layer. The source-drain assembly has source and drain electrodes connected via a nanowire in a rotationally invariant geometry. A dielectric layer is deposited on the source-drain assembly. A gate electrode is deposited on the dielectric layer. 
     Another disclosed feature of the embodiment is a method and apparatus of a semiconductor device having radial contact using nanowires of short lengths. Source and drain electrodes are fabricated having a contact structure with a rotationally invariant geometry. The contact structure has inner and outer contacts corresponding to the source and drain electrodes, respectively. The outer contact is spaced from the inner contact by a channel length. Wells are formed in vicinity of the contact structure. A suspension is placed in the wells. The suspension has single or multiple nanowires having a short length in a liquid. An alternating current (AC) source is applied to the contact structure to cause the single or multiple nanowires to align and connect the inner contact to the outer contact. The AC source has a first terminal connected to the inner contact and a second terminal not connected to the inner and outer contacts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
       Embodiments may best be understood by referring to the following description and accompanying drawings that are used to illustrate various embodiments. In the drawings. 
         FIG. 1  is a diagram illustrating a contact assembly according to one embodiment. 
         FIG. 2  is a diagram illustrating a misalignment error curve according to one embodiment. 
         FIG. 3  is a diagram illustrating a top view of patterned gate electrodes according to one embodiment. 
         FIG. 4  is a diagram illustrating a side view of patterned gate electrodes according to one embodiment. 
         FIG. 5  is a diagram illustrating a top view of liquid having nanowires on the patterned gate electrodes according to one embodiment. 
         FIG. 6  is a diagram illustrating a side view of liquid having nanowires on the patterned gate electrodes according to one embodiment. 
         FIG. 7  is a diagram illustrating a top view of liquid evaporated leaving nanowires on the patterned gate electrodes according to one embodiment. 
         FIG. 8  is a diagram illustrating a side view of liquid evaporated leaving nanowires on the patterned gate electrodes according to one embodiment. 
         FIG. 9  is a diagram illustrating a top view of source and drain electrodes deposited on the gate dielectric according to one embodiment. 
         FIG. 10  is a diagram illustrating a side view of source and drain electrodes deposited on the gate dielectric according to one embodiment. 
         FIG. 11  is a diagram illustrating gate electrodes patterned on a substrate according to one embodiment. 
         FIG. 12  is a diagram illustrating microwells formed on a flexographic plate according to one embodiment. 
         FIG. 13  is a diagram illustrating liquid deposited into the microwells according to one embodiment. 
         FIG. 14  is a diagram illustrating the flexographic plate being transferred onto the substrate according to one embodiment. 
         FIG. 15  is a diagram illustrating a side view of a device having a top gate electrode according to one embodiment. 
         FIG. 16  is a diagram illustrating a top view of a device having a top gate electrode according to one embodiment. 
         FIG. 17  is a flowchart illustrating a process to fabricate a device with a bottom gate structure according to one embodiment. 
         FIG. 18  is a flowchart illustrating a process to pattern source and drain electrodes according to one embodiment. 
         FIG. 19  is a flowchart illustrating a process to deposit liquid by printing according to one embodiment. 
         FIG. 20  is a flowchart illustrating a process to fabricate a device with a top gate structure according to one embodiment. 
         FIG. 21  is a diagram illustrating nanowires having short lengths in random orientation with respect to a pair of electrodes according to one embodiment. 
         FIG. 22  is a diagram illustrating alignment of nanowires having short lengths with respect to a pair of electrodes using AC source with only one terminal connected to electrodes according to one embodiment. 
         FIG. 23  is a diagram illustrating alignment of nanowires having short lengths with respect to multiple pairs of electrodes using a single AC source with only one terminal connected to electrodes according to one embodiment. 
         FIG. 24  is a diagram illustrating nanowires having short lengths in random orientation with respect to electrodes in rotationally invariant geometry according to one embodiment. 
         FIG. 25  is a diagram illustrating nanowires having short lengths in alignment with respect to electrodes in rotationally invariant geometry using an AC source with only one terminal connected to electrodes according to one embodiment. 
         FIG. 26  is a flowchart illustrating a process to align nanowires having short lengths according to one embodiment. 
         FIG. 27  is a diagram illustrating a top view of linear contacts in a prior art embodiment. 
         FIG. 28  is a diagram illustrating alignment of nanowires using an AC source with two terminals connected to electrodes in a prior art embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     One disclosed feature of the embodiments is a method and apparatus for radial contact using nanowires. An inner contact has a center. An outer contact circularly surrounds the inner contact around the center and is spaced from the inner contact by a channel length. A nanowire connects the center of the inner contact and the outer contact in a rotationally invariant geometry. 
     Another disclosed feature of the embodiments is a method and apparatus of a semiconductor device with bottom gate structure and having radial contact using nanowires. A gate electrode is deposited on a substrate. A dielectric layer is deposited on the substrate and the gate electrode. A source-drain assembly is deposited on the dielectric layer. The source-drain assembly has source and drain electrodes connected via a nanowire in a rotationally invariant geometry. 
     Another disclosed feature of the embodiments is a method and apparatus of a semiconductor device with top gate structure and having radial contact using nanowires. An isolation barrier layer is deposited on a substrate. A source-drain assembly is deposited on the substrate and within the isolation barrier layer. The source-drain assembly has source and drain electrodes connected via a nanowire in a rotationally invariant geometry. A dielectric layer is deposited on the source-drain assembly. A gate electrode is deposited on the dielectric layer. 
     Another disclosed feature of the embodiment is a method and apparatus of a semiconductor device having radial contact using nanowires of short lengths. Source and drain electrodes are fabricated having a contact structure with a rotationally invariant geometry. The contact structure has inner and outer contacts corresponding to the source and drain electrodes, respectively. The outer contact is spaced from the inner contact by a channel length. Wells are formed in vicinity of the contact structure. A suspension is placed in the wells. The suspension has single or multiple nanowires having a short length in a liquid. An alternating current (AC) source is applied to the contact structure to cause the single or multiple nanowires to align and connect the inner contact to the outer contact. The AC source has a first terminal connected to the inner contact and a second terminal not connected to the inner and outer contacts. 
     Aspects of the embodiments include a radial contact structure that may reduce the need to align nanowires during deposition using methods such as jet printing pr transfer printing. The use of rotationally invariant geometry may allow both rotational mis-alignment and mis-registration with smaller effects in the final device geometry. 
     One disclosed feature of the embodiments may be described as a process which is usually depicted as a flowchart, a flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed. A process may correspond to a method, a program, a procedure, a method of manufacturing or fabrication, etc. One embodiment may be described by a schematic drawing depicting a physical structure. It is understood that the schematic drawing illustrates the basic concept and may not be scaled or depict the structure in exact proportions. 
       FIG. 1  is a diagram illustrating a contact assembly  100  according to one embodiment. The contact assembly  100  includes an inner contact  110 , an outer contact  120 , and a nanowire  130 . It is noted that the contact assembly  100  may include more or less than the above components. 
     The inner contact  110  may be a contact having a high electrical conductivity. It may be formed by metal such as copper, or titanium and gold, or molybdenum/chromium, or aluminum, or by a doped semiconductor such as zinc oxide or amorphous silicon. It may correspond to a source or drain electrodes in a semiconductor device. It may include a center  115 . 
     The outer contact  120  may surround the inner contact  110  around the center  115 . The surrounding geometry may be circular or any suitable shape such that the entire outer contact  120  encircle or enclose the inner contact  110 . The outer contact  120  may enclose the inner contact  110  completely or partially, leaving some opening such as openings  122  and  123 . The outer contact  120  may be spaced from the inner contact  110  by a distance L. In one embodiment where the inner contact and the outer contact correspond to source and drain electrodes in a semiconductor device, the distance L may be referred to as a channel length. Depending on the contact geometry, the distance L may be uniform or non-uniform within a pre-defined tolerance. The outer contact  120  may have a largest diameter D L . The largest diameter D L  may be the length of the longest line that crosses the center of the outer contact  120  and touches the outer contact  120  at two points on the inner periphery of the outer contact  120 . When the outer contact  120  is circularly annular, the largest diameter D L  is the inner diameter of the circle. The nanowire  130  has a length and may connect the center  115  of the inner contact  110  and the outer contact  120  in a rotationally invariant geometry. A connection is rotationally invariant may be referred to as a connection uses a rotationally invariant geometry. A rotationally invariant geometry is a geometry in which a connection is maintained, or invariant, regardless of how the nanowire  130  may be rotated. For example, the nanowire  130  may be at a position  130   1  or  130   2 . The positions are relative to each other by a rotation of the nanowire  130  around the center  115 . In either position, a connection is made between the inner contact  110  and the outer contact  120 . Typically, the nanowire  130  may cross the center  115  of the inner contact  110  and connects to at least one point on the outer contact  120  on either side of the center  115 . Using this rotationally invariant geometry, the variation in channel length may be significantly less than the traditional linear contacts. In addition, when the radii or distances of the inner and outer contacts are optimized, the probability of an open connection is reduced significantly. In one embodiment, this probability may be less than 10%. The length of the nanowire  130  may be long or short. The definition of “long” or “short” is relative and not absolute. It may be defined with respect to the geometry of the contact structure, such as the largest diameter of the outer contact, and the channel length. In one embodiment, the length of the nanowire  130  may be long which is approximately greater than, or equal to, the largest diameter D L  of the outer contact  120 . In another embodiment, the length of the nanowire  130  may be short which is approximately less than, or equal to, half of the largest diameter D L  of the outer contact  120  and greater than the channel length. For nanowires with short lengths, a technique using AC source with a single terminal connected to the inner contact as illustrated in  FIGS. 22 ,  23 , and  25 , may be employed. 
       FIG. 2  is a diagram illustrating a misalignment error curve according to one embodiment. The horizontal axis corresponds to the distance from the edge of the center  115 . The vertical axis corresponds to the ratio p=D/D min  where D min  is the minimum distance. The r inner  is the radius of the center  115  and the r outer  is the radius of the outer contact  120  around the center  115 , assuming a circular geometry. 
     The contact structure shown in  FIG. 1  may be used to form connections between the source and drain electrodes of a semiconductor device. The process of fabricating a semiconductor device having nanowires as radial connections for the electrodes may be illustrated in  FIGS. 3  through  FIGS. 10 . 
       FIGS. 3 and 4  are diagrams illustrating a top view and a side view, respectively, of patterned gate electrodes  300  according to one embodiment. Gate electrodes  320  are patterned and formed on a substrate  305 . A gate dielectric layer  310  is deposited on the substrate  305  and the gate electrodes  320 . The regions  330  are directly above the gate electrodes  320  on the surface of the dielectric layer  310 . 
       FIGS. 5 and 6  are diagrams illustrating a top view and a side view, respectively, of liquid having nanowires on the patterned gate electrodes  500  according to one embodiment. Liquids or drops of liquid  520  are deposited on the regions  320  which are aligned or in registration with the gate electrodes  310 . The liquids  520  may be deposited using ink jet printing or flexographic printing from an elastomeric plate. The liquids  520  may contain a single or multiple nanowires  510 . 
       FIGS. 7 and 8  are diagrams illustrating a top view and a side view, respectively, of liquid evaporated leaving nanowires on the patterned gate electrodes  700  according to one embodiment. The liquids  510  are evaporated, leaving the nanowires  510  on the surface of the dielectric layer  310 , localized at the regions  320 . These nanowires  510  may be randomly arranged at the locations directly above the gate electrodes  310 . 
       FIGS. 9 and 10  are diagrams illustrating a top view and a side view, respectively, of source and drain electrodes deposited on the gate dielectric  900  according to one embodiment. The metals and bus lines and source electrodes  910  and drain electrodes  920  may be deposited on the dielectric layer  310  using standard photolithographic processes. The source electrodes  910  and drain electrodes  920  have contacts formed according to a geometry similar to the contact structure shown in  FIG. 1 . The nanowires  510  form connections to connect source electrodes  910  and drain electrodes  920  in a rotationally invariant geometry. In one embodiment, the length of the nanowire  520  may be approximately greater than, or equal to, the largest diameter D L  of the drain electrode  920 , or the outer contact. In another embodiment, the length of the nanowire  520  may be approximately less than, or equal to, half of the largest diameter D L  of the drain electrode  920 , or the outer contact, and greater than the channel length. 
     The nanowires  510  may be deposited on the dielectric layer  310  or the substrate  305  using a printing technique as illustrated in  FIGS. 11 to 14 . 
       FIG. 11  is a diagram illustrating gate electrodes patterned on a substrate  1100  according to one embodiment. Gate electrodes  1120  are patterned on a substrate  1110  using conventional techniques. 
       FIG. 12  is a diagram illustrating microwells formed on a flexographic plate  1200  according to one embodiment. Microwells  1220  may be formed on a flexographic plate  1210 . The flexographic plate  1210  may be made by a suitable polymeric compound such as Polydimethylsiloxane (PDMS). Each of the microwells  1220  may have a volume of less than 1 nL. The microwells  1220  may be formed to correspond to the gate electrodes  1120 . In other words, they may be aligned or registered to match in geometry with the gate electrodes  1120 . 
       FIG. 13  is a diagram illustrating liquid deposited into the microwells  1300  according to one embodiment. Liquids or drops of liquid  1310  containing nanowires  1320  are then deposited into the microwells  1220 . 
       FIG. 14  is a diagram illustrating the flexographic plate being transferred onto the substrate according to one embodiment. The plate  1300  including the flexographic plate  1210  and the liquids  1310  with nanowires  1320  in microwells  1120  is then transferred onto the substrate  1110  with the patterned gate electrodes  1120 . The transfer may be made by printing. 
     The process shown in  FIGS. 3 through 10  may be used to fabricate a semiconductor device with gate electrode at the bottom. A process to construct a semiconductor device with a top gate electrode structure may be performed as illustrated in  FIGS. 15 and 16 . A top gate electrode structure may allow the drain contact (e.g., n-channel device) to completely surround the source electrode. This structure may have interconnect lines separated from the source-drain region in order to allow a co-planar circular Field-Effect Transistor (FET) design. 
       FIGS. 15 and 16  are diagrams illustrating a side view and a top view, respectively, of a device  1500  having a top gate electrode according to one embodiment. 
     An isolation barrier layer  1520  may be deposited on a substrate  1510 . A source-drain assembly may be deposited on the substrate  1510  and within the isolation barrier layer  1520 . The source-drain assembly have source electrode  1530  and drain electrodes  1540  connected via a nanowire  1550  in a rotationally invariant geometry. In one embodiment, the length of the nanowire  1550  may be approximately greater than, or equal to, the largest diameter D L  of the drain electrode  1540 . In another embodiment, the length of the nanowire  1550  may be approximately less than, or equal to, half of the largest diameter D L  of the drain electrode  1540 , or the outer contact, and greater than the channel length. 
     A dielectric layer  1560  may be deposited on the source-drain assembly. A gate electrode  1530  may be deposited on the dielectric layer  1560 . 
     It is noted that that the structures shown in  FIGS. 9 ,  15 , and  16  may be patterned while the array of the source/drain contacts for the nanowire devices is biased with a voltage. The bias may create an electric field across the channel region that may provide a force that aligns the nanowires parallel to the electric field (in a normal direction to the metal contacts). In addition, any of the devices shown above may be repeated over a defined area to create an array of individually addressable devices, such as an array of transistors used in image pixel array. 
       FIG. 17  is a flowchart illustrating a process  1700  to fabricate a device with a bottom gate structure according to one embodiment. 
     Upon START, the process  1700  forms a gate electrode on a substrate (Block  1710 ). Next, the process  1700  deposits a gate dielectric layer on the gate electrode (Block  1720 ). Then, the process  1700  places a liquid suspension having a liquid containing a single or multiple nanowires on the gate dielectric layer in registration with the gate electrode (Block  1730 ). This may include evaporating the liquid to leave the single or multiple nanowires localized around a region aligned with the gate electrode. 
     Next, the process  1700  patterns source and drain electrodes connected via the single or multiple nanowires in a rotationally invariant geometry (Block  1740 ). The process  1700  is then terminated. 
       FIG. 18  is a flowchart illustrating a process  1740  to pattern source and drain electrodes according to one embodiment. 
     Upon START, the process  1740  patterns an inner contact corresponding to the source electrode having a center (Block  1810 ). Next, the process  1740  patterns an outer contact corresponding to the drain electrode such that the outer contact surrounds the inner contact around the center and is spaced from the inner contact by a channel length (Block  1820 ). The outer contact is connected to the inner contact via the single or multiple nanowires in the rotationally invariant geometry. The process  1740  is then terminated. The resulting contact structure is similar to that of  FIG. 1 . 
       FIG. 19  is a flowchart illustrating a process  1900  to deposit liquid by printing according to one embodiment. 
     Upon START, the process  1900  patterns gate electrodes on a substrate (Block  1910 ). Next, the process  1900  forms microwells in a flexographic plate in registration with the gate electrodes (Block  1920 ). Then, the process  1900  deposits liquid into the microwells (Block  1930 ). The liquid contains a single or multiple nanowires. This may be performed by printing the liquid using inkjet printing or flexographic printing. 
     Next, the process  1900  transfers the flexographic plate having the microwells filled with the liquid onto the substrate having the patterned gate electrodes (Block  1940 ). The process  1900  is then terminated. 
       FIG. 20  is a flowchart illustrating a process  2000  to fabricate a device with a top gate structure according to one embodiment. 
     Upon START, the process  2000  patterns source and drain interconnects and a bus line on a substrate (Block  2010 ). Next, the process  2000  deposits an isolation barrier on the patterned source and drain interconnects (Block  2020 ). Then, the process  2000  patterns and etches a via hole (Block  2030 ). Next, the process  2000  patterns source and drain electrodes on the patterned source and drain interconnects (Block  2040 ). The source and drain electrodes are connected to the bus line through the via hole. The patterning of the source and drain electrodes may be performed using a process operation similar to the process  1740  shown in  FIG. 18 . The source and drain electrodes have a contact structure similar to that of  FIG. 1 . 
     Then, the process  2000  deposits liquid containing a single or multiple nanowires onto the patterned source and drain electrodes such that the single or multiple nanowires connect the source and drain electrodes in a rotationally invariant geometry (Block  2050 ). Next, the process  2000  deposits a dielectric layer on the single or multiple nanowires and the isolation layer (Block  2060 ). Then, the process  2000  patterns a gate electrode on the dielectric layer (Block  2070 ). The process  2000  is then terminated. 
       FIG. 21  is a diagram illustrating a structure  2100  of nanowires having short lengths in random orientation with respect to a pair of electrodes according to one embodiment. The structure  2100  includes electrodes, or contacts,  2110   1  and  2120   1 , and nanowires  2130   1  and  2140   1 . 
     The electrodes, or contacts,  2110   1  and  2120   1  may correspond to source and drain electrodes in a semiconductor device. The nanowires  2130   1  and  2140   1  may have short lengths. As described above, for contact or electrode structures that do not have a rotationally invariant geometry, the distinction of short and long nanowires may not be relevant. The nanowires  2130   1  and  2140   1  are shown to be in random orientation with respect to the electrodes  2110   1  and  2120   1 . In this configuration, no reliable contacts may be formed to connect the electrodes or contacts together via the nanowires  2130   1  and  2140   1  whether or not the contact or electrode structure has a rotationally invariant geometry. The nanowires  2130   1  and  2140   1  may be immersed or embedded in a liquid or solution to form a suspension. When a drop of the suspension is placed between the source and drain electrodes or the contacts, the nanowires  2130   1  and  2140   1  may be dispersed randomly and may not be aligned so as to form a connection between the two electrodes. 
       FIG. 22  is a diagram illustrating a structure  2200  showing alignment of nanowires having short lengths with respect to a pair of electrodes using AC source with only one terminal connected to electrodes according to one embodiment. The structure  2200  is similar to the structure  2100  except that an alternating current (AC) source  2210  is applied to the contact or electrode structure. 
     The AC source  2210  may be any suitable AC source with appropriate voltage level or power or frequency. The AC source  2210  may create an electric field across the electrodes or contacts. This AC electric field may induce a dielectrophoretic force on the nanowires  2130   1  and  2140   1 . This dielectrophoretic force may position and align the between the source and drain electrodes such that the nanowires are oriented with one end at the source electrode or the inner contact if the geometry is rotationally invariant, and one end at the drain electrode or the outer contact if the geometry is rotationally invariant. 
     The AC source  2210  is applied to the contact or electrode structure such that only one terminal of the AC source  2210  is connected to the contact or electrode structure. The other terminal of the AC source  2210  is left floating. The floating terminal may become capacitively coupled to the driven terminal and may thus be able to act as a local ground resulting in aligned nanowires between the two contacts or the source and drain electrodes  2110   1  and  2120   1 . This approach is advantageous because it significantly reduces the complexity of interconnects needed to align nanowires in an array or a plurality of pairs of electrodes or contacts as illustrated in  FIG. 23 . 
       FIG. 23  is a diagram illustrating a structure  2300  showing alignment of nanowires having short lengths with respect to multiple pairs of electrodes using a single AC source with only one terminal connected to electrodes according to one embodiment. The structure  2300  includes a single AC source  2210  and L groups of electrode pairs  2110   k  and  2120   k  (k=1, . . . L) and nanowires  2130   k  and  2140   k  (k=1, . . . L) where L is a positive integer. The structure  2300  may be suitable for devices that have multiple electrode pairs such as an array of transistors (e.g., image pixel array). 
     The AC source  2210  may be applied to the L groups of electrode pairs  2110   k  and  2120   k  (k=1, . . . L) and nanowires  2130   k  and  2140   k  (k=1, . . . L) by connecting one terminal to all electrodes  2110   k  (k=1, . . . L). The other terminal of the AC source  2210  is left floating and/or connected to ground. The other electrodes  2120   k  (k=1, . . . L) are left unconnected to the AC source  2210 . In this construction, only one terminal of the devices in the array may need to be joined in order to align the nanowires, leading to efficient fabrication of an array of individual devices with a common source (or drain). 
       FIG. 24  is a diagram illustrating a structure  2400  showing nanowires having short lengths in random orientation with respect to electrodes in rotationally invariant geometry according to one embodiment. The structure  2400  includes an inner contact, or electrode (e.g., source electrode)  2410 , an outer contact, or electrode (e.g., drain electrode)  2420 , and nanowires  2430  and  2440 . The contact or electrode structure has a rotationally invariant geometry. For illustrative purposes, they are shown as circles or annular rings. The largest diameter of the outer contact or electrode  2420  is D L  and the channel length is L as shown. 
     If the length of the nanowires  2430  and  2440  is short, i.e., if it is approximately less than, or equal to, half of the largest diameter D L  of the outer contact and greater than the channel length L), placing the nanowires  2430  and  2440  in the vicinity, or near, or between the inner and outer contacts (or electrodes) may not form reliable connections. Since the length is short, it is possible that the nanowires  2430  and  2440  are oriented such that they do not connect the contacts or the electrodes as shown in  FIG. 24 . 
       FIG. 25  is a diagram illustrating a structure  2500  showing nanowires having short lengths in alignment with respect to electrodes in rotationally invariant geometry using an AC source with only one terminal connected to electrodes according to one embodiment. The structure  2500  includes the inner contact, or electrode (e.g., source electrode)  2410 , the outer contact, or electrode (e.g., drain electrode)  2420 , the nanowires  2430  and  2440 , and an AC voltage source  2450 . The contact or electrode structure has a rotationally invariant geometry as in  FIG. 24 . 
     The AC voltage source  2450  is applied to the contact structure to cause the single or multiple nanowires  2430  and  2440  to align and connect the inner contact  2410  to the outer contact  2420 . The AC source  2450  has a first terminal connected to the inner contact  2410  and a second terminal not connected to the inner and/or outer contacts. The second terminal may be left floating (open) or connected to ground. As discussed above, the AC voltage source  2450  creates an AC electric field that induces a dielectrophoretic force on the nanowires  2430  and  2440 . This dielectrophoretic force may position and align the between the inner contacts  2410  and  2420  (or the source and drain electrodes) such that the nanowires  2430  and  2440  are oriented with one end at the source electrode or the inner, and one end at the drain electrode or the outer contact. The alignment is radial, emanating from the center of the inner contact  2410 . 
     By applying the AC power source to a single terminal, it may be possible to easily fabricate a large array of devices in a rotationally invariant geometry. The rotationally invariant geometry is well suited for the dielectrophoretic alignment because it eliminates the need to consider the effects of fringe fields that may be present at sharp corners of the electrodes. Accordingly, the alignment yield may be higher than the traditional tecniques. 
       FIG. 26  is a flowchart illustrating a process  2600  to align nanowires having short lengths according to one embodiment. 
     Upon START, the process  2600  fabricates source and drain electrodes having a contact structure with a rotationally invariant geometry (Block  2610 ). The contact structure has inner and outer contacts corresponding to the source and drain electrodes, respectively. The outer contact is spaced from the inner contact by a channel length L. 
     Next, the process  2600  forms wells in vicinity of the contact structure (Block  2620 ). Then, the process  2600  places a suspension in the wells (Block  2630 ). The suspension has single or multiple nanowires having a short length in a liquid. 
     Next, the process  2600  applies an alternating current (AC) source to the contact structure to cause the single or multiple nanowires to align and connect the inner contact to the outer contact (Block  2640 ). The AC source has a first terminal connected to the inner contact and a second terminal not connected to the inner and/or outer contacts. Then, the process  2600  removes the liquid leaving the nanowires aligned and forming connections (Block  2650 ). The liquid may be removed by any suitable methods such as evaporation, suction, or forced air. The process  2600  is then terminated. 
       FIG. 27  is a diagram illustrating a top view of linear contacts in a prior art embodiment. In this prior art contact structure, the contacts  2710  and  2720  may be linear segments. A connecting wire  2730  may be used to connect the contacts  2710  and  2720 . The wire  2730  may have two positions  2730   1  and  2730   2 . Position  2730   1  may provide a good connection because it is orthogonal to both contacts  2710  and  2720 . However, if the wire  2730  is rotated, such as when it is move to the position  2730   2 , the connection may become marginal. Position  2730   2  is shown where it barely touches the contacts  2710  and  2720 . As the wire  2730  is rotated further, it may not touch one or both of the contacts  2710  and  2720 , resulting in an open circuit. The geometry of the device may also be changed significantly between position  2730   2  and position  2730   1 . The difference in the channel geometry for each position may vary by √2 for a square geometry (channel width, W, to channel length, L, ratio=1). The maximum variation increases as the ratio between W/L increases. 
       FIG. 28  is a diagram illustrating a structure  2800  alignment of nanowires using an AC source with two terminals connected to electrodes in a prior art embodiment. The structure  2800  includes electrodes, or contacts,  2110   1  and  2120   1 , and nanowires  2130   1  and  2140   1  and the AC source  2210  similar to the structure  2100 . The main difference is that the two terminals of the AC source  2210  are connected to the corresponding two electrodes, or contacts,  2110   1  and  2120   1 . This prior art embodiment is not very useful because for constructing an array of devices, it requires either all devices to be parallel or requires the application of an AC signal between each individual source and drain electrodes. This construction may not be practical or possible depending on the array design. 
     It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims.