The implementations of the disclosure relate generally to electronic devices and, more specifically, to crossbar circuits including resistive random-access memory (RRAM or ReRAM) devices and schemes for minimizing write disturbances for the crossbar circuits.
A crossbar circuit may refer to a circuit structure with interconnecting electrically conductive lines sandwiching a memory element, such as a resistive switching material, at their intersections. The resistive switching material may include, for example, a memristor (also referred to as resistive random-access memory (RRAM or ReRAM)). Crossbar circuits may be used to implement in-memory computing applications, non-volatile solid-state memory, image processing applications, neural networks, etc.
The following is a simplified summary of the disclosure to provide a basic understanding of some aspects of the disclosure. This summary is not an extensive overview of the disclosure. It is intended to neither identify key or critical elements of the disclosure, nor delineate any scope of the particular implementations of the disclosure or any scope of the claims. Its sole purpose is to present some concepts of the disclosure in a simplified form as a prelude to the more detailed description that is presented later.
According to one or more aspects of the present disclosure, an apparatus is provided. The apparatus includes a plurality of bit lines intersecting with a plurality of word lines, a plurality of cross-point devices, and one or more first capacitors operatively connected to the plurality of bit lines. Each of the plurality of cross-point devices is connected to at least one of the plurality of word lines and at least one of the plurality of bit lines.
In some embodiments, the apparatus further includes a first plurality of switches, wherein the one or more first capacitors are operatively connected to the plurality of bit lines via the first plurality of switches.
In some embodiments the one or more first capacitors are operatively connected to each of the plurality of bit lines via a respective switch of the first plurality of switches.
In some embodiments, the apparatus further includes one or more second capacitors operatively connected to the plurality of word lines.
In some embodiments, the apparatus further includes a second plurality of switches, wherein the one or more second capacitors are operatively connected to the plurality of word lines via the second plurality of switches.
In some embodiments, the plurality of cross-point devices includes at least one of a memristor, a phase-change memory (PCM) device, a floating gate device, a spintronic device, a ferroelectric device, or a resistive random-access memory (RRAM) device.
In some embodiments, the apparatus further includes a plurality of select lines connected to the plurality of cross-point devices.
In some embodiments, the plurality of cross-point devices includes at least one transistor that connects to at least one select line of the plurality of select lines.
In some embodiments, the apparatus further includes one or more third capacitors operatively connected to the plurality of select lines.
In some embodiments, the apparatus further includes a third plurality of switches. The one or more third capacitors are operatively connected to each of the plurality of select lines via a respective switch of the third plurality of switches
In some embodiments, the plurality of select lines is parallel to the plurality of word lines.
In some embodiments, the plurality of select lines is parallel to the plurality of bit lines.
According to one or more aspects of the present disclosure, a method for programming a crossbar circuit is provided. The method includes connecting one or more first capacitors of the crossbar circuit to a first bit line of a plurality of bit lines and applying a programming voltage to a first word line of a plurality of word lines or the first bit line. The plurality of bit lines intersects with the plurality of word lines. The crossbar circuit includes a plurality of cross-point devices, wherein each of the plurality of cross-point devices is connected to at least one of the word lines and at least one of the bit lines. A first cross-point device of the plurality of cross-point devices is connected to the first word line and the first bit line.
In some embodiments, the method further includes resetting the one or more first capacitors of the crossbar circuit to ground before connecting the one or more first capacitors to the first bit line of the crossbar circuit.
In some embodiments, the method further includes connecting one or more second capacitors of the crossbar circuit to a first word line of the crossbar circuit prior to the application of the programming voltage to the first word line or the first bit line.
In some embodiments, the method further includes resetting the one or more second capacitors of the crossbar circuit to ground before connecting the one or more second capacitors to the first word line of the crossbar circuit.
In some embodiments, the method further includes connecting one or more third capacitors of the crossbar circuit to a select line of the crossbar circuit prior to the application of the programming voltage to the first word line or the first bit line.
In some embodiments, the method further includes resetting the one or more third capacitors of the crossbar circuit to ground before connecting the one or more third capacitors to the first select line of the crossbar circuit.
In some embodiments, the method further includes applying a select voltage to a first select line connected to the first cross-point device.
In some embodiments, the programming voltage is applied to the first word line, wherein the first bit line is grounded, wherein a second bit line of the crossbar circuit is set to float, and wherein a second cross-point device of the crossbar circuit is connected to the first word line, the second bit line, and the first select line.
In some embodiments, the programming voltage is applied to the first bit line, wherein the first word line is grounded, wherein a second word line is set to float, and wherein a third cross-point device of the crossbar circuit is connected to the second word line, the first bit line, and a second select line.
The disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various embodiments of the disclosure. The drawings, however, should not be taken to limit the disclosure to the specific embodiments, but are for explanation and understanding.
Aspects of the disclosure provide crossbar circuits with minimized write disturbances. A crossbar circuit may include intersecting electrically conductive wires (e.g., row lines, column lines, etc.) and cross-point devices arranged in one or more arrays. Each of the cross-point devices may be connected to a word line, a bit line, and a select line. The cross-point devices may include, for example, a phase-change memory (PCM) device, a floating gate device, a spintronic device, a ferroelectric device, a resistive random-access memory (RRAM) device, etc.
Write disturbances may occur in a crossbar circuit when the programming of a selected cross-point device inadvertently affects the resistance state of another unselected cross-point device. After achieving and maintaining the target conductance within an acceptable limit for several cycles in certain RRAM devices in the crossbar circuit, unexpected conductance shifts can occur due to the programming of other memristors in the same array. Such disturbance of the originally programmed RRAM devices may necessitate a restart of a programming process, consequently extending the overall programming time required to program the crossbar circuit. In some cases, it may be impossible to program each of the RRAM devices in the array to its target conductance, thereby undermining the overall efficiency and functionality of the crossbar circuit. The write disturbance is primarily caused by the parasitic capacitance of the crossbar circuit. The parasitic capacitance can affect the voltage difference across RRAM devices that are not selected for programming, causing these unselected RRAM devices to change their resistance state unintentionally.
The present disclosure provides mechanisms for minimizing write disturbance in crossbar circuits. In accordance with one or more aspects of the present disclosure, a crossbar circuit may include one or more first capacitors operatively connected to the bit lines, one or more second capacitors operatively connected to the word lines of the crossbar circuit, and/or one or more third capacitors operatively connected to the select lines. The capacitance of the first capacitor(s), the capacitance of the second capacitor(s), and the capacitance of the third capacitor(s) may be significantly greater (e.g., 100 times greater) than the parasitic capacitance of the crossbar circuit. Prior to programming the conductance of a target cross-point device to a target conductance value, the first capacitors, the second capacitors, and the third capacitors may be reset to ground. The first capacitors, the second capacitors, and the third capacitors may then be connected to a bit line, a word line, and a select line connected to the target cross-point device, respectively. A suitable programming voltage may then be applied to the word line and the bit line, respectively. The word line and the bit line may be brought down to ground at the end of the programming cycle. When the crossbar circuit is performing in-memory computing, the first capacitors are disconnected from the bit lines, and the second capacitors are disconnected from the word lines.
Connecting additional capacitors to the bit lines, the word line, and/or the select line may slow down the voltage changes on the bit line, the word line, and/or the select line connected to the target cross-point device to be programmed, thereby allowing the voltage on the parasitic capacitors to synchronize with the bit line and word line voltage alterations. As a result, the voltage difference across the unselected RRAM devices may be maintained at a sufficiently low level to prevent unintentional programming of unselected RRAM devices.
Row wires 111a-n may include a first row wire 111a, a second row wire 111b, . . . , 111i, . . . , and an n-th row wire 111n. Each of row wires 111a, . . . , 111n may be and/or include any suitable electrically conductive material. In some embodiments, each row wire 111a-n may be a metal wire.
Column wires 113a-m may include a first column wire 113a, a second column wire 113b, . . . , and an m-th column wire 113m. Each column wire 113a-m may be and/or include any suitable electrically conductive material. In some embodiments, each column wire 113a-m may be a metal wire.
Each cross-point device 120a-z may be and/or include any suitable device with tunable resistance, such as a PCM (phase change memory) device, a floating gate device, a spintronic device, a ferroelectric device, resistive random-access memory (RRAM), static random-access memory (SRAM), etc. In some embodiments, one or more of cross-point devices 120 may include a cross-point device as described in connection with
Crossbar circuit 100 may perform parallel weighted voltage multiplication and current summation. For example, an input voltage signal may be applied to one or more rows of crossbar circuit 100 (e.g., one or more selected rows). The input signal may flow through the cross-point devices of the rows of the crossbar circuit 100. The conductance of the cross-point device may be programmed to a specific value (also referred to as a “weight”). By Ohm's law, the input voltage multiplies the cross-point conductance and generates a current from the cross-point device. By Kirchhoff's law, the summation of the current passing the devices on each column generates the current as the output signal, which may be read from the columns (e.g., outputs of the ADCs). According to Ohm's law and Kirchhoff's current law, the input-output relationship of the crossbar array can be represented as I=VG, wherein I represents the output signal matrix as current; V represents the input signal matrix as voltage; and G represents the conductance matrix of the cross-point devices. As such, the input signal is weighted at each of the cross-point devices by its conductance according to Ohm's law. The weighted current is output via each column wire and may be accumulated according to Kirchhoff's current law. This may enable in-memory computing (IMC) via parallel multiplications and summations performed in the crossbar arrays.
As shown in
As shown in
Transistor 1203 may function as a selector as well as a current controller and may set the current compliance to RRAM device 1201 during programming. The gate voltage on transistor 1203 can set current compliances to cross-point device 1220a-b during programming and can thus control the conductance and analog behavior of cross-point device 1220a-b. For example, when cross-point device 1220a-b is set from a high-resistance state to a low-resistance state, a set signal (e.g., a voltage signal, a current signal) may be provided via bit line (BL) 1211 or word line (WL) 1215. Another voltage, also referred to as a select voltage or gate voltage, may be applied via select line (SEL) 1213 to the transistor gate to open the gate and set the current compliance, while word line (WL) 1215 or bit line (BL) 1211 may be grounded. When cross-point device 1220a-b is reset from the low-resistance state to the high-resistance state, a gate voltage may be applied to the gate of transistor 1203 via select line 1213 to open the transistor gate. Meanwhile, a reset signal may be sent to RRAM device 1201 via word line 1215 or bit line 1211, while bit line 1211 or word line 1215 may be grounded.
During a form operation or a set operation that programs a cross-point device 310a and/or RRAM device 311a, the word line WLn may be grounded. A programming voltage may be applied to the bit line BL0. A select voltage may be applied to the select line SEL0. The select lines that are not connected to the cross-point device 310a (e.g., SELn) may be grounded. The bit lines and the word lines that are not connected to the cross-point device 310a (e.g., BLm, WL0, etc.) may be set to float. A disturbance may occur during the form operation or the set operation if the voltage across an unselected RRAM device exceeds a predefined amount within a certain time duration. For example, even though the word line WL0 is set to float, the RRAM device 311c may still be charged by BL0, because the RRAM device 311c shares the same bit line with the RRAM device 311a. If the bit line junction capacitance or other parasitic capacitance (e.g., C1 and C2 as shown in
Write disturbance may also occur during a deform or reset process if the voltage across an unselected RRAM device exceeds a predefined amount of voltage during a certain time duration. For example, performing a deform operation or reset operation on the cross-point device 310a and/or the RRAM device 311a may involve applying a programming voltage to the word line WLn connected to the cross-point device 310a. The select voltage is applied to the select line SEL0 to enable the programming of the RRAM device 311a. The bit line BL0 is grounded. The word lines and the bit lines that are not connected to the cross-point device 310a may be set to float. However, an unselected RRAM device, such as the RRAM device 311b, may still be programmed and/or disturbed. Even though the bit line BLm connected to the unselected RRAM device is set to float, it may still be charged by the programming voltage applied to the word line WLn, because the RRAM devices 311a and 311b share the same word line WLn. If the bit line junction capacitance or other parasitic capacitance (e.g., C3 as shown in
During a form operation or a set operation that programs a cross-point device 320a and/or RRAM device 321a, the word line WLn may be grounded. A programming voltage may be applied to the bit line BL0. A select voltage may be applied to the select line SEL0. The select lines that are not connected to the cross-point device 320a (e.g., SELm) may be grounded. The bit lines and the word lines that are not connected to the cross-point device 320a (e.g., BLm, WL0, etc.) may be set to float. A disturbance may occur during the form operation or the set operation if the voltage across an unselected RRAM device exceeds a predefined amount within a certain time duration. Even though the word line WL0 is floated, the RRAM device 321c may still be charged by BL0 or SEL0, because the RRAM device 321c shares the same bit line and select line with the RRAM device 321a. If the bit line parasitic capacitor or other parasitic capacitors (e.g., C4, C5, and C6 as shown in
A disturbance may also occur during a deform or reset process if the voltage across an unselected RRAM device exceeds a predefined amount of voltage during a certain time duration. For example, performing a deform operation or reset operation on the cross-point device 320a and/or the RRAM device 321a may involve applying a programming voltage to the word line WLn connected to the cross-point device 320a. The select voltage is applied to the select line SEL0 to enable the programming of the RRAM device 321a. The bit line BL0 is grounded. The word lines and the bit lines that are not connected to the cross-point device 320a may be set to float. However, an unselected RRAM device, such as the RRAM device 321c, may still be programmed and/or disturbed, because the RRAM devices 321a and 321c share the same select line SEL0. If the parasitic capacitor is large enough, the unselected RRAM device 321c may be unintendedly programmed and thus disturbed by the voltage buildup across it.
Crossbar circuit 400a and crossbar circuit 400b may include word lines 411a, . . . , 411n, bit lines 413a, . . . , 413m, cross-point devices 420a, 420b, 420c, . . . , 420z, and select lines 415a, . . . , 415n. Word lines 411a-n and bit lines 413a-m may be the same as row lines 111a-n and column lines 113a-m of
As shown, each cross-point device 420a, 420b, . . . , 420z may be connected to a bit line 413a-m, a select line 415a-n, and a word line 411a-n. In some embodiments, each cross-point device 420a-z may include a transistor and an RRAM device (e.g., RRAM devices 421a, 421b, 421c, . . . , 421z) connected in series (e.g., a 1T1R configuration described in connection with
The crossbar circuit 400a may further include one or more capacitors 430a (also referred to as the “first capacitors”) that may be operatively connected to bit lines 413a-m. For example, each bit line 413a, . . . , 413m may be connected to the capacitor 430a via a switch (e.g., a switch 440a, . . . , 440m). The capacitance of the capacitor(s) 430a may be significantly greater than (e.g., at least 100 times greater) the parasitic capacitance of the crossbar circuit 400a (e.g., parasitic capacitance 401a, 401b, 401c, etc.).
The crossbar circuit 400a may further include one or more capacitors 430b (also referred to as the “second capacitors”) that may be operatively connected to word lines 411a-n. For example, each word line 411a-n may be connected to the capacitor(s) 430b via a respective switch 450a, . . . , 450n. The capacitance of the capacitor(s) 430b may be significantly greater than the parasitic capacitance of the crossbar circuit 400a.
In some embodiments, as shown in
While one capacitor 430a, one capacitor 430b, and one capacitor 430c are shown in
Prior to a programming operation (e.g., a set operation, a form operation, a reset operation, a deform operation), the capacitors 430a, 430b and 430c may be reset to ground. To initiate a programming operation and/or program a target cross-point device to a target conductance value, the capacitors 430a, 430b, and 430c may be connected to a bit line connected to the target cross-point device (also referred to as the “selected bit line”) and a word line connected to the target cross-point device (also referred to as the “selected word line”), and a select line connected to the target cross-point device, respectively. A first programming voltage and a second programming voltage may then be applied to the selected word line and the selected bit line, respectively. The selected word line and the selected bit line may be brought down to ground at the end of the programming cycle. When the crossbar circuit 400a-b is performing in-memory computing (e.g., performing a VMM operation), the capacitors 430a are disconnected from the bit lines 413a-m, and the capacitors 430b are disconnected from the word lines 411a-n. The capacitors 430c are also disconnected from the select lines 415a-n during in-memory computing operations.
Connecting additional capacitors 430a-c to the bit line, the word line, and the select line may thus slow down the voltage changes on the selected bit line and the selected word line, thereby allowing the voltage on the parasitic capacitors to synchronize with the bit line and word line voltage alterations. As a result, the voltage difference across the unselected RRAM devices may be maintained at a sufficiently low level to prevent unintentional programming of unselected RRAM devices.
For example, the capacitors 430a, 430b, and 430c may be reset to ground prior to performing a programming operation on the cross-point device 420a and/or the RRAM device 421a. The capacitor 430a may then be connected to the bit line 413a via the switch 440a. The capacitor 430b may be connected to the word line 411n via the switch 450n. The capacitor 430c may be connected to the select line 415n via the switch 460n. A select voltage may be applied to the select line 415a to select the cross-point device 420a and/or the RRAM device 421a for programming. The select lines that are not connected to the cross-point device 420a (e.g., select line 415n) may be grounded. During a form operation or a set operation, the word line 411n may be grounded. A programming voltage may be applied to the bit line 413a. The bit lines and the word lines that are not connected to the cross-point device 420a (e.g., the bit line 413m, the word line 411a, etc.) may be set to float. During a deform operation or reset operation on the cross-point device 420a and/or the RRAM device 421a, a programming voltage may be applied to the word line 411n connected to the cross-point device 420a. The bit line 413a is grounded. The word lines and the bit lines that are not connected to the cross-point device 420a may be set to float.
The capacitor 430a may slow down the ramping speed of the bit line voltage. The capacitor 430b may slow down the ramping speed of the word line voltage. The capacitor 430c may slow down the ramping speed of the select line voltage. As a result, the voltage difference across the unselected RRAM devices (e.g., RRAM device 421b, 421c, etc.) during the programming of the RRAM device 421a may not trigger the programming of the unselected RRAM devices.
Crossbar circuit 500a-b may include word lines 511a, . . . , 511n, bit lines 513a, . . . , 513m, cross-point devices 520a, 520b, 520c, . . . , 520z, and select lines 515a, . . . , 515m. Word lines 511a-n and bit lines 513a-m may be the same as row lines 111a-n and column lines 113a-m of
As shown, each cross-point device 520a, 520b, . . . , 520z may be connected to a bit line 513a-m, a select line 515a-n, and a word line 511a-n. In some embodiments, each cross-point device 520a-z may include a transistor and an RRAM device (e.g., RRAM devices 521a, 521b, 521c, . . . , 521z) connected in series (e.g., a 1T1R configuration described in connection with
The crossbar circuit 500a may further include one or more capacitors 530a that are operatively connected to bit lines 513a-m. For example, each bit line 513a, . . . , 513m may be connected to the capacitor 530a via a switch (e.g., a switch 540a, . . . 540m). The capacitance of the capacitor(s) 530a may be significantly greater than the parasitic capacitance of the crossbar circuit 500a-b (e.g., the capacitance of parasitic capacitors 501a, 501b, 501c, etc.).
In some embodiments, as shown in
Prior to a programming operation (e.g., a set operation, a form operation, a reset operation, a deform operation), the capacitor(s) 530a-b may be reset to ground. To initiate a programming operation and/or program a target cross-point device to a target conductance value, the capacitor(s) 530a-b may be connected to a bit line connected to the target cross-point device (also referred to as the “selected bit line”) and a select line connected to the target cross-point device, respectively. A first programming voltage and a second programming voltage may then be applied to the selected word line and the selected bit line, respectively. The selected word line and the selected bit line may be brought down to the ground at the end of the programming cycle. When the crossbar circuit 500a-b is performing in-memory computing (e.g., performing a VMM operation), the capacitor 530a is disconnected from the bit lines 513a-m. The capacitor 530b is also disconnected from the select lines 515a-m when the crossbar circuit 500b is performing in-memory computing.
Connecting additional capacitors 530a-b to the bit lines and the select lines may slow down the voltage changes on the selected bit line and the selected word line, thereby allowing the voltage on the parasitic capacitors to synchronize with the bit line and word line voltage alterations. As a result, the voltage difference across the unselected RRAM devices may be maintained at a sufficiently low level to prevent unintentional programming of unselected RRAM devices.
As an example, the capacitor(s) 530a-b may be reset to ground prior to performing a programming operation on the cross-point device 520a and/or the RRAM device 521a. The capacitor(s) 530a may then be connected to the bit line 513a via the switch 540a. The capacitor(s) 530b may also be connected to the select line 515a via the switch 545a. A select voltage may be applied to the select line 515a to select the cross-point device 520a and/or the RRAM device 521a for programming. The select lines that are not connected to the cross-point device 520a may be grounded. During a form operation or a set operation, the word line 511n may be grounded. A programming voltage may be applied to the bit line 513a. The bit lines and the word lines that are not connected to the cross-point device 520a (e.g., 513m, 511a, etc.) may be set to float. During a deform operation or reset operation on the cross-point device 520a and/or the RRAM device 521a, a programming voltage may be applied to the word line 511n connected to the cross-point device 520a. The bit line 513a is grounded. The word lines and the bit lines that are not connected to the cross-point device 520a may be set to float. The capacitor(s) 530a-b may slow down the ramping speed of the bit line voltage. As a result, a programming process that programs the cross-point device 520a and/or the RRAM device 521a to a target value does not involve unintentional programming and/or disturbance of unselected RRAM devices (e.g., RRAM device 521c).
At 610, a current conductance value of a current cross-point device in the cross-point device may be read using suitable circuitry.
At 620, the current conductance value may be compared to a target conductance value to determine if the current conductance value matches the target conductance value. The current conductance value may be regarded as matching the target conductance value when a difference between the current conductance value and the target conductance value is not greater than a predetermined threshold.
In some embodiments in which the current conductance value does not match the target conductance value (“NO” at 620), the current cross-point device may be programmed based on the comparison result at 630. For example, in some embodiments in which the current conductance value is higher than the target conductance value, a reset operation may be performed on the current cross-point device. As another example, in some embodiments in which the current conductance value is lower than the target conductance value, a set operation may be performed on the current cross-point device. Programming the current cross-point device may involve performing one or more operations as described in
In some embodiments in which the current conductance value matches the target conductance value, method 600 may proceed to 640 and may determine if a next cross-point device of the crossbar circuit is to be programmed. If one or more cross-point devices in the crossbar circuit are to be programmed, the next cross-point device may be selected for programming until the conductance of each of the cross-point devices to be programmed reaches its corresponding target value. If the conductance of each of the cross-point devices to be programmed reaches its respective target value, method 600 may conclude.
Method 700 may start at 710, when one or more first capacitors of the crossbar circuit may be reset to ground. The first capacitor(s) may be operatively connected to each of a plurality of bit lines of the crossbar circuit. The first capacitor(s) may be the capacitor(s) 430a of
At 720, one or more second capacitors of the crossbar circuit may be reset to ground. The second capacitor(s) may be operatively connected to each of a plurality of word lines of the crossbar circuit. The second capacitor(s) may be, for example, the capacitor(s) 430b of
At 730, one or more third capacitors of the crossbar circuit may be reset to ground. The third capacitor(s) may be operatively connected to each of a plurality of select lines of the crossbar circuit. The third capacitor(s) may be, for example, the capacitor(s) 430c of
At 740, the one or more first capacitors may be connected to the first bit line. For example, the first capacitor(s) may be connected to the first bit line via a switch (e.g., switch 440a-m of
At 750, the one or more second capacitors may be connected to the first word line. For example, the second capacitor(s) may be connected to the first word line via a switch (e.g., switch 450a-n of
At 760, the one or more third capacitors may be connected to the first select line. For example, the third capacitor(s) may be connected to the first select line via a switch (e.g., switch 460a-n of
At 770, a programming voltage may be applied to the first word line and/or the first bit line to program the first cross-point device to a target conductance. For example, during a form operation or a set operation, the programming voltage is applied to the first bit line. The first word line is grounded. One or more other word lines (e.g., a second word line) that are not connected to the first cross-point device may be set to float. The conductance values of the cross-point devices that are not selected for programming are not disturbed. For example, the conductance of a second cross-point device connected to the second word line and the first bit line is not disturbed even though the second cross-point device and the first cross-point device share the same bit line.
As another example, during a deform operation or a reset operation, the programming voltage may be applied to the first word line. The first bit line may be grounded. One or more other bit lines that are not connected to the first cross-point device are set to float. The conductance values of the cross-point devices that are not selected for programming are not disturbed. For example, the conductance of a third cross-point device connected to the first word line and the second bit line is not disturbed.
The terms “approximately,” “about,” and “substantially” as used herein may mean within a range of normal tolerance in the art, such as within 2 standard deviations of the mean, within ±20% of a target dimension in some embodiments, within ±10% of a target dimension in some embodiments, within ±5% of a target dimension in some embodiments, within ±2% of a target dimension in some embodiments, within ±1% of a target dimension in some embodiments, and yet within ±0.1% of a target dimension in some embodiments. The terms “approximately” and “about” may include the target dimension. Unless specifically stated or obvious from context, all numerical values described herein are modified by the term “about.”
As used herein, a range includes all the values within the range. For example, a range of 1 to 10 may include any number, combination of numbers, sub-range from the numbers of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 and fractions thereof.
In the foregoing description, numerous details are set forth. It will be apparent, however, that the disclosure may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form, rather than in detail, in order to avoid obscuring the disclosure.
The terms “first,” “second,” “third,” “fourth,” etc. as used herein are meant as labels to distinguish among different elements and may not necessarily have an ordinal meaning according to their numerical designation.
The words “example” or “exemplary” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example” or “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the words “example” or “exemplary” is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, “X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then “X includes A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form. Reference throughout this specification to “an implementation” or “one implementation” means that a particular feature, structure, or characteristic described in connection with the implementation is included in at least one implementation. Thus, the appearances of the phrase “an implementation” or “one implementation” in various places throughout this specification are not necessarily all referring to the same implementation.
As used herein, when an element or layer is referred to as being “on” another element or layer, the element or layer may be directly on the other element or layer, or intervening elements or layers may be present. In contrast, when an element or layer is referred to as being “directly on” another element or layer, there are no intervening elements or layers present.
Whereas many alterations and modifications of the disclosure will no doubt become apparent to a person of ordinary skill in the art after having read the foregoing description, it is to be understood that any particular embodiment shown and described by way of illustration is in no way intended to be considered limiting. Therefore, references to details of various embodiments are not intended to limit the scope of the claims, which in themselves recite only those features regarded as the disclosure.