Patent Publication Number: US-10790787-B2

Title: FET operational temperature determination by gate structure resistance thermometry

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This Application is a Continuation of U.S. application Ser. No. 16/212,585, filed Dec. 6, 2018, which is a Continuation of U.S. application Ser. No. 15/658,116, filed Jul. 24, 2017. The entire contents of these applications are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     Technical Field 
     The technology relates to field-effect transistors having internal temperature-sensing components. 
     Discussion of the Related Art 
     Among III-V semiconductor materials, gallium-nitride (GaN) has received appreciable attention in recent years because of its desirable electronic and electro-optical properties. Gallium nitride (GaN) has a wide, direct bandgap of about 3.4 eV, is more resistant to avalanche breakdown, and has a higher intrinsic field strength compared to more common semiconductor materials, such as silicon. In addition, GaN is able to maintain its electrical performance at higher temperatures as compared to other semiconductors, such as silicon or gallium arsenide. GaN also has a higher carrier saturation velocity compared to silicon. Additionally, GaN has a Wurtzite crystal structure, is a hard material, has a high thermal conductivity, and has a much higher melting point than other conventional semiconductors such as silicon, germanium, and gallium arsenide. 
     Because of its desirable properties, GaN is useful for high-speed, high-voltage, and high-power applications, as well as optoelectronic applications. For example, gallium-nitride materials are useful for active circuit components in semiconductor amplifiers (such as Doherty amplifiers) for radio-frequency (RF) communications, radar, and microwave applications. In high-power applications, GaN transistors may be driven near their performance limits and heat up to temperatures well over 120° C. Excessively high temperatures can lead to premature device degradation and/or failure in GaN transistors and in other semiconductor transistors as well. 
     SUMMARY 
     Structures and methods for sensing operational temperatures of transistors are described. Thermally-sensitive structures may be formed in a transistor and used to evaluate an operating temperature of the transistor by sensing changes in resistance of the thermally-sensitive structure, e.g., using metal resistance thermometry (MRT). In some embodiments, a source field plate and/or gate structure of a field-effect transistor (FET) may serve as the thermally-sensitive structure and be modified to apply a probe current, or currents, in a region of the source field plate and/or gate structure. A voltage may develop across the region(s) due to the applied current. The voltage may be monitored to sense temperature changes in a region of the FET that is adjacent to the thermally-sensitive structure(s). 
     Some embodiments relate to a field-effect transistor (FET) with temperature sensing comprising a gate, a floating gate plate adjacent to the gate and having an extended length, a source contact, a drain contact, and a first pair of contact tabs connected to the floating gate plate and separated by a first distance for applying a probe current through the floating gate plate. The FET may further comprise a second pair of contact tabs connected to the floating gate plate and separated by a second distance for sensing a voltage across a region of the floating gate plate through which the probe current flows. 
     In some aspects, the floating gate plate overlays at least a portion of the gate. The floating gate plate may exhibit a change in resistance with a change in temperature of the floating gate plate that is not less than 0.001 ohms/° C. 
     In some cases, the first pair of contact tabs comprises a first thin-film resistor and a second thin-film resistor. A resistance of the first thin-film resistor and of the second thin-film resistor may not be less than 300 ohms. In some implementations, the second pair of contact tabs comprises a third thin-film resistor and a fourth thin-film resistor. A resistance of the third thin-film resistor and of the fourth thin-film resistor may not be less than 300 ohms. 
     Some implementations of a FET may further comprise a source of the probe current connected to the first pair of contact tabs. The source of the probe current may be configured to provide alternating current. In some cases, the alternating current may have a frequency between 50 kilohertz and 5 megahertz. 
     According to some aspects, a FET may further comprise voltage-sensing circuitry connected to the second pair of contact tabs. The voltage-sensing circuit may provide an output signal to a feedback circuit that controls a power level of the field-effect transistor. 
     In some applications, a field-effect transistor may be incorporated in a power amplifier configured to amplify signals to a power level of not less than 0.25 Watt. A FET of the present embodiments may further comprise an active area controlled by the gate, wherein the active area comprises GaN, GaAs, or InP. A FET of the present embodiments may further comprise an active area controlled by the gate, wherein the active area comprises Si. In some implementations, a FET of the present embodiments may be an LDMOS FET, MOSFET, MISFET, or MODFET. In some cases, a FET of the present embodiments may be an HEMT, HFET, or pHEMT. 
     Some embodiments relate to a method of operating a field-effect transistor that uses a floating gate plate to sense transistor temperature. A method may comprise acts of applying a signal to a gate of the field-effect transistor; amplifying the signal with the field-effect transistor; applying a probe current along a region of a floating gate plate of the field-effect transistor, wherein the floating gate plate overlays at least a portion of the gate; and sensing a voltage produced by the probe current. 
     In some implementations, a method may further include evaluating from the sensed voltage a peak temperature of the field-effect transistor. The evaluating may comprise using calibration results relevant to the field-effect transistor. A method may also include acts of comparing the sensed voltage to a reference value and controlling a power level of the field-effect transistor based upon the comparison. 
     In some aspects, applying the probe current may comprise applying the probe current along a region of the floating gate plate that overlays at least a portion of the gate. In some cases, applying the probe current may comprise applying an alternating current to the region. Applying the alternating current may comprise applying the alternating current at a first frequency that is different from a carrier wave frequency of the signal amplified by the field-effect transistor by not less than a factor of 10. In some implementations, applying the probe current may comprise intermittently applying the probe current to the region, such that the probe current is driven for intervals of time that are spaced apart by other intervals of time in which no probe current is driven in the region of the floating gate plate. 
     Some embodiments relate to a field-effect transistor with temperature sensing comprising a gate metal having an extended length with a first end and an opposing second end, a source contact, a drain contact, a first contact tab connected to the gate metal near the first end for applying an alternating probe current to the gate metal, a capacitor and resistor connected in series between a reference potential and an end region of the gate metal that is remote from the first end, and a pair of contact tabs connected to separated regions of the gate metal for sensing a voltage drop along the gate metal in response to the alternating probe current. 
     In some implementations, the gate metal may exhibit a change in resistance with a change in temperature of the gate metal that is not less than 0.001 ohms/° C. 
     Some implementations may further comprise a source of the probe current connected to the first contact tab. The alternating probe current may have a frequency between 50 kilohertz and 5 megahertz. 
     In some cases, a FET may comprise voltage-sensing circuitry connected to the pair of contact tabs. The voltage-sensing circuit may provide an output signal to a feedback circuit that controls a power level of the field-effect transistor. 
     According to some aspects, a field-effect transistor of the present embodiments may be incorporated in a power amplifier configured to amplify signals to a power level of not less than 0.25 Watt. An FET of the present embodiments may further comprise an active area controlled by the gate metal, wherein the active area comprises GaN, GaAs, or InP. In some cases, an FET of the present embodiments may further comprise an active area controlled by the gate metal, wherein the active area comprises Si. According to some implementations, the field-effect transistor may be an LDMOS FET, MOSFET, MISFET, or MODFET. In some cases, the field-effect transistor may be an HEMT, HFET, or pHEMT. 
     Some embodiments relate to a method of operating a field-effect transistor that uses a gate metal for temperature sensing. A method may comprise acts of applying a signal to a gate metal of the field-effect transistor; amplifying the signal with the field-effect transistor; applying an alternating probe current to a first end region of the gate metal of the field-effect transistor, wherein a second end region of the gate metal is remote from the first end region and is terminated by a capacitor and resistor connected in series between a reference potential and the second end region; and sensing a voltage drop produced along a length of the gate metal by the alternating probe current. 
     According to some aspects, a method may further comprise evaluating from the sensed voltage a peak temperature of the field-effect transistor. A method may also include acts of comparing the sensed voltage to a reference value; and controlling a power level of the field-effect transistor based upon the comparison. 
     In some cases, applying the alternating probe current may comprise applying the alternating probe current at a first frequency that is different from a carrier wave frequency of the signal by not less than a factor of 10. According to some implementations, applying the alternating probe current may comprise intermittently applying the alternating probe current to the first end region, such that the alternating probe current is driven for intervals of time that are spaced apart by other intervals of time in which no alternating probe current is driven along the length of the gate metal. 
     Some embodiments relate to a field-effect transistor with temperature sensing comprising a gate metal having an extended length with a first end and a second end, a source, a drain, and a first contact tab connected to a first end region of the gate metal near the first end and configured for applying an alternating probe current to the gate metal, wherein no other contact tab is connected to the gate metal for conducting the probe current and wherein essentially all of the probe current, when applied, couples to a source of the field-effect transistor. 
     In some implementations, a FET may further comprise a pair of contact tabs connected to separated regions of the gate metal for sensing a voltage drop along the gate metal in response to the alternating probe current. In some cases, voltage-sensing circuitry may be connected to the pair of contact tabs. According to some aspects, the voltage-sensing circuit may provide an output signal to a feedback circuit that controls a power level of the field-effect transistor. 
     In some cases, the gate metal exhibits a change in resistance with a change in temperature of the gate metal that is not less than 0.001 ohms/° C. 
     According to some aspects, the alternating probe current may have a frequency between 50 kilohertz and 5 megahertz. In some cases, a FET of the present embodiments may be incorporated in a power amplifier configured to amplify signals to a power level of not less than 0.25 Watt. A FET of the present embodiments may further comprise an active area controlled by the gate metal, wherein the active area comprises GaN, GaAs, or InP. A FET of the present embodiments may further comprise an active area controlled by the gate metal, wherein the active area comprises Si. In some cases, the field-effect transistor may be an LDMOS FET, MOSFET, MISFET, or MODFET. In some aspects, the field-effect transistor may be an HEMT, HFET, or pHEMT. 
     Some embodiments relate to a method of operating a field-effect transistor that uses a gate metal for temperature sensing. A method may comprise acts of applying a signal to a gate metal of the field-effect transistor; amplifying the signal with the field-effect transistor; applying an alternating probe current to a region of the gate metal of the field-effect transistor, wherein essentially all of the alternating probe current couples to a source of the field-effect transistor; and sensing a voltage drop produced along a length of the gate metal by the alternating probe current. 
     In some aspects, a method may further comprise evaluating from the sensed voltage a peak temperature of the field-effect transistor. A method may also include acts of comparing the sensed voltage to a reference value; and controlling a power level of the field-effect transistor based upon the comparison. 
     In some cases, applying the alternating probe current may comprise applying the alternating probe current at a first frequency that is different from a carrier wave frequency of the signal by not less than a factor of 10. According to some implementations, applying the alternating probe current may comprise intermittently applying the alternating probe current to the region, such that the alternating probe current is driven for intervals of time that are spaced apart by other intervals of time in which no alternating probe current is driven in the region of the gate metal. 
     The foregoing apparatus and method embodiments may be implemented with any suitable combination of aspects, features, and acts described above or in further detail below. These and other aspects, embodiments, and features of the present teachings can be more fully understood from the following description in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The skilled artisan will understand that the figures, described herein, are for illustration purposes only. It is to be understood that in some instances various aspects of the embodiments may be shown exaggerated or enlarged to facilitate an understanding of the embodiments. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the teachings. In the drawings, like reference characters generally refer to like features, functionally similar and/or structurally similar elements throughout the various figures. Where the drawings relate to microfabricated circuits, only one device and/or circuit may be shown to simplify the drawings. In practice, a large number of devices or circuits may be fabricated in parallel across a large area of a substrate or entire substrate. Additionally, a depicted device or circuit may be integrated within a larger circuit. 
       When referring to the drawings in the following detailed description, spatial references “top,” “bottom,” “upper,” “lower,” “vertical,” “horizontal,” “above,” “below” and the like may be used. Such references are used for teaching purposes, and are not intended as absolute references for embodied devices. An embodied device may be oriented spatially in any suitable manner that may be different from the orientations shown in the drawings. The drawings are not intended to limit the scope of the present teachings in any way. 
         FIG. 1A  is an elevation view that depicts structure of a high-electron-mobility transistor (HEMT), according to some embodiments; 
         FIG. 1B  depicts a plan view of gate, source, and drain structure for a HEMT, according to some embodiments; 
         FIG. 1C  depicts a plan view of a linear array of HEMT gates, sources, and drains, according to some embodiments; 
         FIG. 2A  is an elevation view of a HEMT that includes a floating gate plate, according to some embodiments; 
         FIG. 2B  depicts a plan view of gate, source, and drain structure for a HEMT that includes a floating gate plate, according to some embodiments; 
         FIG. 2C  depicts a plan view of gate, source, and drain structure for a HEMT that includes a floating gate plate, according to some embodiments; 
         FIG. 3  depicts temperature-sensing circuitry that may be used with a floating gate plate, according to some embodiments; 
         FIG. 4  depicts temperature-sensing circuitry that may use a transistor&#39;s gate, according to some embodiments; 
         FIG. 5  depicts temperature-sensing circuitry that may use a transistor&#39;s gate, according to some embodiments; 
         FIG. 6A  is an elevation view of a HEMT having a source field plate that may be used for thermal sensing, according to some embodiments; 
         FIG. 6B  depicts a plan view of gate, source, and drain structure for a HEMT that includes a source field plate, according to some embodiments; 
         FIG. 6C  depicts a plan view of gate, source, and drain structure for a HEMT that includes a floating source field plate, according to some embodiments; 
         FIG. 7  plots measured resistance of a source field plate as a function of baseplate temperature, according to some embodiments; 
         FIG. 8  plots measured resistance of a source field plate as a function of amplifier operating power for different baseplate temperatures, according to some embodiments; 
         FIG. 9  plots inferred temperatures of a source field plate as a function of amplifier operating power at different baseplate temperatures based on the results of  FIG. 8 , according to some embodiments; and 
         FIG. 10  plots calculated thermal resistance of a source field plate as a function of baseplate temperature based on the results of  FIG. 9 , according to some embodiments. 
     
    
    
     Features and advantages of the illustrated embodiments will become more apparent from the detailed description set forth below when taken in conjunction with the drawings. 
     DETAILED DESCRIPTION 
     High-electron mobility transistors (HEMTs) are a type of semiconductor transistor that utilizes a two-dimensional electron gas (2DEG) for carrier transport. The 2DEG is formed at a heterojunction between two different semiconductor materials having different band gaps. The heterojunction results in the formation of a spatially thin potential well that collects a high-density electrons forming the 2DEG. Typically, the 2DEG forms in an undoped semiconductor. Because of the lack of dopants (which act as impurities) the free electrons can travel through the undoped semiconductor with greatly reduced scattering. Accordingly, HEMTs can be operated at very high frequencies, e.g., well into the terahertz frequency range, and are suitable for radar, microwave, and RF communication applications. HEMTs formed using gallium-nitride or gallium-arsenide materials can also be used for high power applications. In high-power operation, the transistor may heat to high temperatures (e.g., in excess of 120° C.), and it may be desirable to know a highest temperature the transistor attains and/or monitor the temperature of the transistor when placed in service for a particular application. 
     An example HEMT structure to which aspects of temperature sensing may be applied is depicted in  FIG. 1A , according to some embodiments, though the inventive aspects are not limited to HEMT transistors. A HEMT  100  may be formed as a lateral device, and include a source S, a drain D, and a gate G comprising a gate metal  140 . The gate metal  140  may have a length L g  and control the flow of current between the drain D and source S. The gate length L g  may be between approximately 0.1 micron and approximately 3.0 microns, according to some embodiments. The gate, source, and drain may be formed on a same side of a substrate  105  (e.g., on a process surface of the substrate). A lateral HEMT structure has the benefit of not needing through-substrate vias for connecting to a source or drain of the device, which can leave the entire backside of the device available for heat removal. Single-side electrical connections can also make integration of the HEMT into an integrated circuit (IC) an easier task. 
     In some embodiments, electrical isolation regions  115  may be formed around the source and drain to improve device isolation and reduce leakage currents. The isolation regions  115  may be formed by ion implantation that can damage the crystalline structure, and thereby increase its resistance to leakage current flow. 
     According to some implementations, a HEMT  100  may comprise a multi-layer structure that includes a substrate  105 , a buffer layer  112 , a conduction layer  114  in which the 2DEG  150  forms, a barrier layer  116 , and at least one electrically-insulating dielectric layer  120 . Some embodiments may, or may not, include a semiconductor cap layer  118 , which may be formed of a same material as the conduction layer  114 . A HEMT may further include a source contact  160  that connects to a source deposition  130  and a drain contact  162  that connects to a drain deposition  132 . 
     In some embodiments, a HEMT  100  may further include at least one gate-connected field plate  145  that is electrically connected to the gate metal  140  and extends beyond edges of the gate metal  140 . In some cases, the gate-connected field plate  145  and gate metal  140  may be formed from a same metal that is deposited in a same deposition step (e.g., a T-gate structure). According to some embodiments, the gate metal  140  may be located closer to the source  130  deposition than the drain  132  deposition, though the gate may be centered between the source deposition and drain deposition in some cases, or located nearer the drain in other embodiments. In some implementations, an insulating passivation layer (not shown) may be formed over the gate-connected field plate  145  and source and drain contacts  160 ,  162 . 
     One or more HEMTs  100  may be arranged on a die to operate together, as depicted in the plan views of  FIG. 1B  or  FIG. 1C . Other configurations are also possible, and there may be multiple transistors connected in a circuit that operate on separate signals. In some implementations, the source, gate, and drain of a transistor may have extended lengths in one direction (e.g., a width direction W g ) and run parallel to each other, as depicted in  FIG. 1B . In some embodiments, a HEMT may include conductive leads  170  (e.g., interconnects patterned during a metallization level) that extend between a gate or gate-connected field plate  145  and a gate contact pad  185 , between a source contact  160  or source field plate (not shown in  FIG. 1A - FIG. 1C ) and a source contact pad  180 , and between a drain contact  162  and a drain contact pad  182 . As depicted in  FIG. 1C , drain contacts  162  may be shared between two adjacent transistors and source contacts  160  may be shared between two adjacent transistors when the transistors are repeated many times across a substrate in an array, for example. In other configurations, there may be only one of a source contact  160  or drain contact  162  between two adjacent extended gates (sometimes referred to as gate fingers) in an array, and the source and drain contact may alternate along the array, so that each source contact  160  and drain contact  162  in the array is common to two adjacent gates in the array. 
     Although details of a HEMT are described in connection with various embodiments described herein, the invention is not limited to only HEMT devices. The embodiments may be used on other field-effect transistors such as, but not limited to, junction FETs (JFETs), metal-oxide-semiconductor FETs (MOSFETs), metal-insulator-semiconductor FETs (MISFETs), metal-semiconductor FETs (MESFETs), modulation-doped FETs (MODFETs), heterostructure FETs (HFETs), psuedomorphic HEMTs (pHEMTs), etc. Further, the invention is not limited to gallium-nitride materials. The above types of transistors may have active areas of semiconductor, controlled by the gate, that may be formed using any suitable semiconductor material or materials such as, but not limited to, silicon (Si), germanium (Ge), silicon-carbide (SiC), gallium-arsenide (GaAs), indium-phosphide (InP), cadmium-telluride (CdTe), etc. 
     As used herein, the phrase “gallium-nitride material” is used to refer to gallium nitride (GaN) and any of its alloys, such as aluminum gallium nitride (Al x Ga (1−x) N), indium gallium nitride (In y Ga (1−y) N), aluminum indium gallium nitride (Al x In y Ga (1−x−y) N), gallium arsenide phosphoride nitride (GaAs x P y  N (1−x−y) ), aluminum indium gallium arsenide phosphoride nitride (Al x In y Ga (1−x−y) As a P b N (1−a−b) ), amongst others. Typically, when present, arsenic and/or phosphorous are at low concentrations (i.e., less than 5 percent by weight). In certain preferred embodiments, the gallium-nitride material has a high concentration of gallium and includes little or no amounts of aluminum and/or indium. In high gallium concentration embodiments, the sum of (x+y) may be less than 0.4 in some implementations, less than 0.2 in some implementations, less than 0.1 in some implementations, or even less in other implementations. In some cases, it is preferable for at least one gallium-nitride material layer to have a composition of GaN (i.e., x=y=a=b=0). For example, an active layer in which a majority of current conduction occurs may have a composition of GaN. Gallium-nitride materials in a multi-layer stack may be doped n-type or p-type, or may be undoped. Suitable gallium-nitride materials are described in U.S. Pat. No. 6,649,287, which is incorporated herein by reference in its entirety. 
     The drawings of HEMTs in  FIG. 1A ,  FIG. 1B , and  FIG. 1C  are not to scale. The contact pads may be significantly larger than depicted in the drawings and may be significantly larger than the gate, source, and drain contacts, according to some embodiments. In some implementations, an extended gate metal  140  may be significantly narrower than source and/or drain contacts. Although  FIG. 1A ,  FIG. 1B , and  FIG. 1C  depict one or a few HEMT devices, many devices may be formed on a die or wafer in various embodiments. For example, linear arrays of HEMTs may be fabricated on a semiconductor die to form a power transistor. Because of their small size, there may be hundreds or thousands of HEMTs formed on a die and thousands or millions of HEMTs formed on a wafer. HEMTs or other types of transistors mentioned above may be connected in different types of integrated circuits on a die such as, but not limited to, amplifiers, current sources, signal switches, pulse-generation circuits, power converters, application-specific integrated circuits (ASICs), etc. 
     In applications such as radar, microwave, and RF communication, amplification or switching of signals at high power levels often occurs. For example, an amplifier may amplify signals to power levels of tens or hundreds of Watts for transmission over long distances. The high power levels can cause heating within the amplifying transistors which, if excessive, can lead to undesirable changes in device performance, premature aging, and/or device failure. The inventors have recognized and appreciated that the heating is non-uniform within a field-effect transistor, and that a hotspot  155  ( FIG. 1A ) near the drain side of the gate typically occurs. Temperatures in this region can exceed 160° C. during operation of a FET, in some implementations. Such elevated temperatures can accelerate aging of FETs and reduce the mean time to failure (MTTF). Accelerated aging is believed to be due, at least in part, to an increased rate of compound formation at material interfaces within the device. In some cases, prolonged excessive temperatures may lead to sudden device failure (by decreasing the device&#39;s resistance to high-voltage breakdown, for example). 
     To better understand heating in FETs, the inventors have conceived of and implemented structures and methods for monitoring temperature within a FET using metal resistance thermometry (MRT). In some implementations, thermally-sensitive structure near the gate metal  140 , and/or the gate metal itself, may be used to monitor FET temperature. In some embodiments, the thermally-sensitive structure may be coupled to the gate metal  140 . In other embodiments, the thermally-sensitive structure may connect or couple to the source contact  160 . In some cases, sensed temperature values may be used in a feedback paradigm to control operation of a FET, so as to reduce the operating temperature of the FET. 
     Referring now to the elevation view of  FIG. 2A , a HEMT is depicted in which a floating gate plate  147  has been formed adjacent to the gate metal  140  and gate-connected field plate  145 . The floating gate plate may serve as a thermally-sensitive structure in the transistor, according to some embodiments. The HEMT may otherwise be similar to the structure described for  FIG. 1A . The floating gate plate  147  may be isolated from the gate metal  140  and gate-connected field plate  145  by an insulating layer  122  (e.g., an oxide layer or other dielectric layer). The floating gate plate  147  may extend along and overlay a portion of the gate metal  140 , or may overlay all of the gate metal. In some cases, a floating gate plate  147  may be offset from the gate metal  140  toward the drain, and may not overlay the gate metal  140  nor overlay the gate-connected field plate  145 . Alternatively, a floating gate plate  147  may overlay a small portion of the gate metal  140  and/or a portion of the gate-connected field plate  145 . Offsetting the floating gate plate  147  may reduce capacitive coupling between it and the gate metal and/or gate-connected field plate and reduce an adverse effect on transistor speed. 
     When using the terms “on,” “adjacent,” or “over” to describe the locations of layers or structures, there may or may not be one or more layers of material between the described layer and an underlying layer that the layer is described as being on, adjacent to, or over. When a layer is described as being “directly” or “immediately” on, adjacent to, or over another layer, no intervening layer is present. When a layer is described as being “on” or “over” another layer or substrate, it may cover the entire layer or substrate, or a portion of the layer or substrate. The terms “on” and “over” are used for ease of explanation relative to the illustrations, and are not intended as absolute directional references. A device may be manufactured and/or implemented in other orientations than shown in the drawing (for example, rotated about a horizontal axis by more than 90 degrees. 
     Plan views of different embodiments of a floating gate plate  147  are illustrated in  FIG. 2B  and  FIG. 2C . Other configurations of the floating gate plate  147  are also possible, and the invention is not limited to only the layout patterns shown. When FETs are formed in arrays, such as depicted in  FIG. 1C , a floating gate plate  147  may be formed on each transistor, so that each transistor&#39;s temperature can be monitored independently. Alternatively, a floating gate plate  147  may be formed on one (e.g., one at or near the center of the array) or a few transistors distributed along an array to sample one or more representative temperatures in the array. 
     According to some embodiments, a floating gate plate  147  (or floating gate) may be configured for four-point probing, so that four-terminal Kelvin resistance measurements may be made, for example. In some cases, there may be two pairs of conductive contact tabs  210   a ,  210   b ,  212   a ,  212   b  providing electrical connection to the floating gate plate  147 . The contacts in a pair of contact tabs may be spaced apart (e.g., located in distant or opposite end regions of the thermally-sensitive structure) according to some embodiments. In some implementations, the contact tabs of a pair may not be located at the ends of the floating gate plate, and may be located at different points along the floating gate plate  147 . In preferred cases, at least two of the contact tabs ( 212   a ,  212   b ) are spaced apart on the floating gate plate  147  by a distance D that is large enough to measure changes in a voltage drop along the floating gate plate when a current is forced along the floating gate plate  147 . 
     The contact tabs  210   a ,  210   b ,  212   a ,  212   b  may be electrically isolated from interconnects  161  that provide electrical connections to the gate metal  140 , source contact  160 , and drain contact  162 . According to some embodiments, the contact tabs  210   a ,  210   b ,  212   a ,  212   b  may be formed from the same material as the floating gate plate  147  and patterned at the same time. In other embodiments, the contact tabs may be formed from a different material than the floating gate plate  147  and deposited in electrical contact with the floating gate plate during a separate processing step. In some cases, the contact tabs may be formed as conductive interconnects. 
     In some implementations, a gate plate  147  may not be floating, and instead be driven at one or more desired voltage values. Instead, the gate metal  140  and gate-connected field plate  145  (if present) may be floating. In such implementations, four-point probes may be connected to the floating gate metal  140  and/or floating gate-connected field plate  145 , either or both of which may serve as thermally-sensitive structure in the transistor. 
     In operation and referring to  FIG. 2B , a probe current I P  may be applied through a first pair of contact tabs  210   a ,  210   b  on a thermally-sensitive structure. The applied current may be a DC current or an AC current. The probe current I P  may be applied in a region of the floating gate plate  147  running adjacent to the gate metal  140  (not visible in  FIG. 2B ), which may lie under a gate-connected field plate  145  if the gate-connected field plate is present. While the probe current I P  is applied, a voltage V S  may be monitored across at least a portion of the region in which the current flows using a second pair of contact tabs ( 212   a ,  212   b ). From the measured voltage V S  and known value of applied current I P , a resistance value R S  can be determined for the probed region of the thermally-sensitive structure. The amount of applied probe current may be between 200 microamps and 10 milliamps, according to some embodiments. 
     Many metals or materials that are used for gate metals, gate field plates (connected or coupled), source contacts, source field plates (connected or coupled), and drain contacts have a resistance that is temperature sensitive R S (T). Such metals or materials may be used for thermally-sensitive structure in a transistor, according to some embodiments. The temperature-dependent resistivity will be reflected in the measured voltage V S (T). Accordingly, monitoring the voltage V S (T) of a microscale thermally-sensitive structure within a FET can provide an indication of the operational temperature of the FET in a region near the gate and close to a highest temperature region of the device. 
     Materials that may be used for the floating gate plate  147  or other thermally-sensitive structures described herein are numerous. A single metal or material layer may be used in some cases, or multilayer metal stacks may be used in other cases. In some implementations, non-metal materials such as polysilicon may be used. Example metal stacks that may be used include, but are not limited to, Ni/Au, Ni/Au/Ti, Ti/Pt/Au, Ti/Au, Ti/Pt/Au/Ti, Ni/Pd/Au/Ti, Ni/Pt/Au/Ti, Ni/Ti/Al/W, Ni/W/Al/W, Ni/Ta/Al/Ta, Ni/Ta/Al/W, Ni/NiO/Al/W, Ni/NiO/Ta/Al/Ta, Ni/NiO/Ta/Al/W, W/Al/W, Ni/WN/Al/W, Ni/NiO/W/Al/W, Ni/NiO/WN/Al/W, WN/Al/W, Pt/Au/Ti, Ti/Pt/Au, Al/Cu, Ni/Cr, or TiN/Cu. Single metal layers may be formed from any one of the metals in these multilayer stacks. 
     In practice, a gate  140  metal may be driven at RF frequencies (e.g., frequencies over 500 MHz and as high as 7 GHz) for communications applications. Higher frequencies may be used in other embodiments. In high-frequency applications, it may be desirable to reduce adverse coupling of the RF signal to circuitry connected to the floating gate plate  147  or thermally-sensitive structure (circuitry not shown in  FIG. 2B  or  FIG. 2C ). According to some embodiments, coupling of the RF signal to thermally-sensitive structure and/or its circuitry may be reduced by adding a high-impedance elements  220  between the floating gate plate/thermally-sensitive structure and the connected circuitry. According to some embodiments, an inductance or resistance, or combination thereof, may be used as a high-impedance element, though a capacitor may be used alternatively or additionally in embodiments in which an applied probe current I P  is an AC current. 
     In some implementations, a high-impedance element  220  (four shown in  FIG. 2B ) comprises a resistor, e.g., a thin-film resistor. A thin-film resistor may be formed from TaN, for example, polysilicon, or any other suitable material. A resistive high-impedance element  220  may have a resistance value between 300 ohms and 2000 ohms. According to some embodiments, the resistance value may be between 500 ohms and 1500 ohms. In some cases, thin-film resistors or high-impedance elements  220  may be formed on a same die as the transistor for which temperature sensing is implemented. In some cases, high-impedance elements may be formed on a separate die (packaged with the transistor, for example) or located on a circuit board (on which the transistor is mounted, for example) and electrically connect to contact tabs of the floating gate plate  147 , for example. In some cases, a high-impedance element  220  may comprise a discrete resistor that can be mounted external to a packaged transistor that includes thermally-sensitive structure. The package may include pins for connecting resistors for the high-impedance elements  220 . Thin-film resistive elements formed on a same die as the transistor may allow for a more compact assembly than having external discrete resistors. Alternatively, external resistors may allow for more design flexibility by a customer. 
     According to some implementations, contact tabs  211   a ,  211   b ,  213   a ,  213   b  may be formed from thin-film resistors, as depicted in  FIG. 2C . The thin-film resistors may be deposited and patterned before or after the floating gate plate  147 . The resulting contact tabs  211   a ,  211   b ,  213   a ,  213   b  may form ohmic contacts at one end to the floating gate plate  147 , and connect, or provide connection points, at opposing ends to additional temperature-sensing circuitry. 
     One example of temperature-sensing circuitry  300  that includes a floating gate plate  147  formed on a transistor (not shown) is depicted in  FIG. 3 , according to some embodiments. Temperature-sensing circuitry  300  may comprise a source of current  310  and a differential amplifier  320 , for example. Temperature-sensing circuitry may also include high-impedance elements  220  described above and shown in  FIG. 3  as resistors R 1 -R 4 . In some implementations, the source of current  310  may comprise an integrated current source formed from one or more transistors, for example. The source of current  310  may be formed on a same die as the transistor and floating gate plate  147 , or may be formed on a separate die in some cases. The source of current  310  may be configured to provide DC current, for the embodiment depicted in  FIG. 3 , or may be configured to provide AC current in other embodiments. 
     A differential amplifier  320  may comprise an integrated circuit having several transistors (e.g., two transistors in parallel circuit branches with their emitters or sources connected to a common current source). The differential amplifier may be configured to sense a difference in electric potential between two regions of the floating gate plate  147 , as depicted in  FIG. 3 . According to some embodiments, the differential amplifier  320  may comprise operational amplifier circuitry that provides finite differential gain for voltage sensed between the two regions of the floating gate plate  147 . The differential amplifier  320  may be formed on a same die as the transistor and floating gate plate  147 , or may be formed on a separate die. 
     An output V M  from the differential amplifier  320  may be used to monitor changes in a voltage drop across a region of the floating gate plate  147  during operation of the transistor. As described above, the monitored voltage V S (T) is temperature-dependent, and can provide an indication of the peak operating temperature of the transistor. In some implementations, the output voltage V M  may be processed to estimate and/or track an operating temperature of the FET. For example, V M  may be converted to a temperature value as described herein, and the temperature value may be output as digital data and/or visually displayed on test equipment. In some cases, FET temperature may be monitored during device testing to assess how well a FET may operate when placed in service and/or to estimate a MTTF of the FET when placed in service. In some implementations, FET temperature may be monitored during quality control procedures at a time of manufacture. 
     In other embodiments, the output voltage V M  may be provided to a comparator  330  to determine whether or not a FET is operating within a predetermined temperature limit. For example, the output voltage V M  may be compared against a preset reference voltage V ref  to produce a control signal C S . The control signal may be fed back to control operation of the transistor. For example, the control signal may be used to change transistor biasing, voltage supply values, and/or change a variable attenuator on an input RF signal, so that the operating power of the transistor is changed to reduce temperature or allow for a temperature increase. Other methods may be used to process V M  and generate a control signal C S  in other embodiments. 
     Components other than a floating gate plate  147  may be used as a thermally-sensitive structure in a FET and other temperature-sensing circuits may be used in other embodiments. Further embodiments are depicted in  FIG. 4 - FIG. 6B . In some implementations, the gate metal or material  140  of a FET may be used to sense FET temperature, as depicted in  FIG. 4 . The inventors have recognized and appreciated that application of a DC current to the gate may adversely affect transistor bias, since it will introduce a gradient in bias along the gate. Accordingly, an AC probe current I P,AC  from an AC current source  410  may be applied to the transistor&#39;s gate  140  in addition to the gate bias V gs . An AC current source  410  may comprise an integrated oscillator and current amplifier, according to some embodiments. The AC current source  410  may be integrated on a same die as the transistor for which temperature sensing is implemented, or integrated on a separate die. 
     An RC shunt comprising a capacitor C 1  and resistor R 2  may connect to the gate  140  to provide a path for the AC probe current. The RC shunt may attach to the gate at a region that is remote from a location at which the current source  410  connects to the gate. To avoid interfering with the RF signal, the frequency of the probing AC current may be significantly less than a frequency of the RF signal. A characteristic frequency of the RF signal may be the frequency of a carrier wave used to transmit data in RF communications, for example, or may be the carrier frequency of a radar pulse for radar applications. 
     In some implementations, the frequency of the probing AC current may differ from the frequency of the RF signal by not less than a factor of 25. In some cases, the frequency of the probing AC current may differ from the frequency of the RF signal by not less than a factor of 10. Various probing AC frequencies may be used. For example, the frequency of the probe current I P  may be approximately 1 MHz in some embodiments. In some cases, the probing AC frequency may be a value between 50 kHz and 5 MHz. Other embodiments may use a probing AC frequency having a value not less than 10 Hz. Other embodiments may use a probing AC frequency having a value up to 10&#39;s or hundreds of MHz. The RC shunt may comprise a low-pass filter that provides a path for the probe current but blocks high frequencies. In some implementations, the value of C 1  and R 2  may be selected to provide a cut-off frequency for the RC shunt that is approximately equal to or up to 20% higher than a frequency of the probe current I P . When an AC probe current is used, AC voltage-sensing circuitry  420  may be employed. In some implementations, AC voltage-sensing circuitry may comprise an averaging peak-voltage detector. The AC voltage-sensing circuitry  420  may be integrated on a same die as the transistor for which temperature sensing is implemented, or integrated on a separate die. 
     In some embodiments (such as a testing facility), one or both of the source of current  310 ,  410  and voltage-sensing circuit  320 ,  420  may be embodied as a commercial instrument or stand-alone test equipment. In such cases, probes may be used to connect to contact tabs or connected probe pads (not shown) on a die containing one or more transistors under test. Such embodiments may be used when testing or qualifying devices at manufacture, for example, and allow a more compact transistor die. 
       FIG. 5  depicts another embodiment of temperature-sensing circuitry for a FET in which an AC probe current is applied to a gate metal  140  of the FET. In such embodiments, an RC shunt may not be used, and there may not be a contact tab at a distal end of the gate metal for the probe current to flow through. Instead, essentially all of the AC current I P,AC  may couple to a source  130  (shown in this example) of the transistor, source contact  160 , and/or source field plate through parasitic resistance and/or parasitic capacitance (not depicted in the drawing). The probe current frequency may be selected to increase or maximize flow of the probing AC current to the source, source contact, and/or source field plate. The embodiment depicted in  FIG. 5  may result in a more compact transistor die or overall assembly than the embodiment shown in  FIG. 4 . 
       FIG. 6A  depicts an embodiment in which a source field plate  660  may be used as a thermally-sensitive structure for sensing temperature during operation of a FET. In this example, a HEMT is depicted though other types of FETs may be used. A plan view of the device is illustrated in  FIG. 6B , according to one example. According to some embodiments, a source field plate  660  may be patterned to overlie at least a portion of the gate  140  and/or gate-connected field plate  145 . The source field plate  660  may be insulated from the gate and/or gate-connected field plate by an insulating layer  122  and connected to the source contact  160  by a conductive interconnect  665 . In some embodiments, the conductive interconnect  665 , source contact  160 , and source field plate  660  may be formed at a same time from a same layer of material (e.g., during a same deposition process). In some embodiments, the conductive interconnect  665  may comprise a thin-film resistor, as described above, that is patterned and deposited in a separate processing step from the source field plate. A resistive interconnect  665  may provide a slight DC potential to the source field plate, so that an AC probe current applied to the source field plate  660  rides above a ground voltage, for example. 
     The conductive interconnect  665  may be located near or at an end of the source field plate, in some cases, so that an applied probe current flows over a majority of the length of the source field plate  660 , rather than being shunted near the middle of the source field plate. In some embodiments, a contact tab (e.g., tab  210   b  in  FIG. 6B ) may be omitted, and the applied probe current may flow along a majority of the length of the source field plate  660  via the conductive interconnect  665  to a reference potential that is connected to the transistor&#39;s source contact  160 . In some cases, the conductive interconnect  665  may comprise a thin-film resistor, as described above, that reduces RF coupling to the source contact  160 . 
     According to some implementations, a source field plate  660  may be electrically floating. For example, there may not be a direct-current path between the source field plate  660  and the source contact  160 . In some cases, there may be one or more capacitive couplers  667  that capacitively couple the source field plate  660  to the source contact  160 , as depicted in  FIG. 6C . The capacitive couplers  667  may be formed from a conductive film that is separated from the source contact  160  by an insulating layer, e.g., an oxide layer or other dielectric. To improve thermal-sensing accuracy of the transistor&#39;s hot spot  155  (depicted in  FIG. 6A ) by the floating source field plate, there may be narrow conductive interconnects  665  connecting the capacitive couplers  667  to the source field plate  660 . 
     In other embodiments, a source field plate  660  may extend all the way to and overlay the source contact  160  to provide capacitive coupling to the source contact. In such embodiments, separate capacitive couplers  667  may not be present. Instead the source field plate  660  may appear as a single rectangular-shaped conductive film that overlays at least a portion of the source contact  160  and at least a portion of the gate  140  and/or gate-connected field plate  145 . 
     There can be several benefits to using a source field plate  660  for thermal sensing of a FET rather than a gate  140  or gate-connected field plate  145 . A first benefit is that a source field plate  660  may have a portion located near the FET&#39;s hottest region  155 . In some implementations, the source field plate  660  may be limited in shape to a region near the transistor&#39;s hot spot, as depicted in  FIG. 6A . For example, the source field plate  660  may be limited to a region that overlaps none or a portion of the gate metal  140  and extends no more than one-quarter of the distance to the drain contact  162  from the gate. An additional benefit is that the source field plate  660  can be electrically connected to the source with RF/DC isolation, resulting in little or no perturbation to transistor performance. Such perturbation might otherwise occur when current and voltages for sensing temperature are imposed on the transistor&#39;s gate metal  140  or gate-connected field plate  145 . 
     Another benefit, for certain FET types, of using a source field plate  660  for temperature sensing is that problems associated with leakage of the probe current applied to the transistor&#39;s gate may be avoided. In some FETs, a probe current applied to the transistor&#39;s gate metal may leak to alternate current paths (to the transistor&#39;s source, for example). Such leaking may be temperature dependent and result in an inaccurate evaluation of device temperature over a range of temperatures. In contrast, a source field plate  660  may have better isolation than a gate and can reduce leakage of probe current I P  during temperature sensing. 
     Although use of a source field plate may be preferred in some cases, some implementations may use a gate metal  140  and/or gate-connected field plate  145  for thermal sensing. In yet other embodiments, independent temperature sensing circuits in a same transistor may use both a gate metal or gate field plate and a source field plate. Two temperature-sensing circuits with two thermally-sensitive structures may be employed for redundancy and/or measurement confirmation. In some implementations, two temperature-sensing circuits may be used to evaluate a thermal gradient in a FET and to better estimate a peak temperature of the device based on the thermal gradient. 
     There is also a benefit to using the thermally-sensitive structures described above. For example, existing FET structure and materials (with only slight modification) may be used to sense FET temperature. Additionally, the thermally-sensitive structure may be microscale and located adjacent to the FET&#39;s hot spot  155 , so that an improved, localized estimate of the FET&#39;s peak temperature can be obtained. In some implementations, the thermally-sensitive structure may have a length, in the direction of the gate length, that is any value between 0.2 microns and 5 microns. A width of the thermally-sensitive structure may be approximately equal to a width of the FET&#39;s gate and may be between 1 micron and 1 millimeter. A thickness of a thermally-sensitive structure may be between 50 nanometers and 2 microns. Other sizes may be used for a thermally-sensitive structure in other embodiments. 
     According to some embodiments, the temperature sensitivity of a thermally-sensitive structure (gate metal, gate-connected field plate, source field plate) in a FET may be calibrated using one or more FETs on a die or wafer. For example, a die or wafer may be placed on a thermal plate and heated over a range of temperatures while the FET&#39;s source, gate, and drain contacts are left floating. The wafer or die may be allowed to reach thermal equilibrium at each temperature before resistance measurements are made. The resistance measurements may comprise applying a probe current I P  and sensing a voltage drop V S (T) across a region of the thermally-sensitive structure in which the probe current flows. Results for such a calibration may appear as shown in  FIG. 7 . 
     The data for  FIG. 7  was obtained for an example HEMT device using a metal source field plate as the thermally-sensitive structure. The graph shows resistance values (calculated from the applied current and measured voltage drops) plotted as a function of baseplate temperature. In this example device, the change in resistance of the thermally-sensitive structure with respect to change in temperature of the structure is about 0.006 ohm/° C. Other embodiments with different materials may have different thermal sensitivity. In some cases, the thermal sensitivity may be between 0.001 ohm/° C. and 0.05 ohm/° C. In other cases the thermal sensitivity of the thermally-sensitive structure may have a lower or higher value than this range. 
     The graph of  FIG. 7  may be used to evaluate temperatures of identical FET devices (or similar FET devices that include identical thermally-sensitive structures) that are probed during device operation. As an example, a calibration equation (e.g., an equation for a line that fits the data in points in  FIG. 7 ) or look-up table may be determined from the measured data and used to convert subsequently-measured resistance values to temperatures. 
     Although resistance is plotted in  FIG. 7 , other embodiments may use other values. In some cases, voltage may not be converted to resistance. Instead, measured voltage may be plotted as a function of baseplate temperature and voltage values may be used directly to evaluate temperatures of identical FET devices that are probed during device operation. In other cases, sheet resistance (Ohm/square) may be determined for the thermally-sensitive structure and plotted as a function of temperature, so that the results may be used to evaluate temperatures in FETs having a thermally-sensitive structure of a different shape and/or size, though having a same sheet resistance. 
     An example of using calibration values, such as those obtained for the example of  FIG. 7 , is described further in connection with  FIG. 8  and  FIG. 9 . To produce the graph of  FIG. 8 , a HEMT was operated at different power levels (from  0  to approximately 8 W/mm) while a baseplate supporting the HEMT was sequentially set at five different temperatures. The plotted resistance values for each measurement shown in  FIG. 8  were determined from measured voltage drops V S (T) across a region of the source field plate and the applied probe current I P . 
     After finding the resistance values (plotted in  FIG. 8 ) under the different operating conditions, the calibration values of  FIG. 7  (or a resulting calibration equation or look-up table) may be used to convert the measured resistances of  FIG. 8  to temperature values. The corresponding temperature values are plotted in  FIG. 9 , as an example of data conversion using the calibration data. 
     The slope of each line in  FIG. 9  represents the thermal resistance of the thermally-sensitive structure (source field plate) at a different baseplate operating temperature. Thermal resistance for the example device is plotted as a function of temperature in  FIG. 10 . 
     In a packaged power transistor, a thermal sink (e.g., thermally-conductive plate) may be included to improve thermal conduction of heat away from the transistor. In some cases, there may be more than one thermal sink. A thermal sink may be included in a power transistor package, in some cases. In some embodiments, there may be additionally or alternatively a thermal sink external to the power transistor package to which the transistor package may be mounted. Some implementations may include a temperature sensor (e.g., a thermistor) on a thermal sink, so that a temperature of the thermal sink can be monitored during operation of the power transistor. Accordingly, data like that shown in  FIG. 8  and  FIG. 9  may be used to estimate operating temperature of a power transistor using a measured resistance value and a measured temperature of a thermal sink that is in thermal contact with the power transistor. 
     It will be appreciated that the values plotted in  FIG. 7 - FIG. 10  are for an example device and for explanation purposes only. Different values and calibration curves may be obtained for devices different from the sample device. The invention is not limited to the values and calibration data shown in these figures. 
     Methods of operating FETs in accordance with the present embodiments provide techniques for sensing and evaluating operating temperatures of FETs. In some cases, values of sensed temperatures may be used for feedback control of a FET. According to some embodiments, a method of operating a field-effect transistor may comprise acts of applying a signal to a gate of the field-effect transistor, amplifying the signal with the FET, and applying a probe current in a region of a thermally-sensitive structure (e.g., a source field plate) of the FET. The source field plate may be coupled to a source contact of the FET. A method may further comprise sensing a voltage produced by the applied probe current. In some cases, the probe current may be applied to a gate, floating gate, gate field plate, or floating gate plate of a FET. In other cases, the probe current may be applied to at least two components from among the FET&#39;s gate, floating, gate field plate, floating gate plate, and source field plate. 
     A method of operating a FET may include evaluating, from the sensed voltage, a temperature of the field-effect transistor that is representative of a localized peak temperature near the gate of the transistor. The evaluation of temperature may comprise using calibration results for the field-effect transistor&#39;s thermally-sensitive structure. In some embodiments, sensed voltages may not be converted to temperature. Instead, the sensed voltages may be used as indicators of FET temperature. For example, in some implementations, a method of operating a FET may comprise acts of comparing a sensed voltage to a reference value. In some cases, a power level of the field-effect transistor may be controlled based upon the comparison. 
     In some aspects of temperature sensing, a method may comprise applying the probe current along a region of a thermally-sensitive structure (e.g., source field plate or floating gate plate) that overlays at least a portion of the FET&#39;s gate. In some cases, applying the probe current comprises applying an alternating current in the region. For some embodiments, applying the alternating current may comprise applying the alternating current at a first frequency that is different from a characteristic frequency amplified by the field-effect transistor by not less than a factor of 25. 
     In some implementations, applying the probe current may comprise intermittently applying the current in the region, such that the current is driven for intervals of time that are spaced apart by other intervals of time in which no probe current is applied in the region of the thermally-sensitive structure. Intermittent applying of probe current may reduce power consumption and interference with FET operation. According to some embodiments, the probe current may be applied only at times during and/or immediately after an input signal rises above a predetermined power or voltage level. For example, a comparator may be connected to sense an input level applied to a gate  140  of a FET, and activate a current source  310 ,  410  in response to the input level exceeding or falling below a reference value. In this manner, temperature sensing may be executed only during and/or immediately after the transistor handles large input signals (e.g., during and/or after peak power intervals). 
     Methods of operating FETs that include temperature sensing may further include acts of amplifying signals (for communication systems, medical imaging equipment, or microwave applications, for example) or switching voltages and/or currents (for power conversion applications, power generation, snubber circuits, or overvoltage/overcurrent protection, for example). In power applications, a FET with thermal sensing may be used in power amplifiers (such as Doherty amplifiers) that amplify signals to power levels of not less than 0.25 Watts. In some implementations, thermal sensing may be used in power amplifiers that amplify signals to power levels in a range of not less than 0.5 Watts and as high as 150 Watts. It will be appreciated that FETs with temperature sensing may be used for various different FET applications, and that temperature sensing techniques that use existing gate and/or source structures, as described herein, can have little or no impact on normal operation of the FET. 
     CONCLUSION 
     The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. 
     The technology described herein may be embodied as a method, of which at least some acts have been described. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than described, which may include performing some acts simultaneously, even though described as sequential acts in illustrative embodiments. Additionally, a method may include more acts than those described, in some embodiments, and fewer acts than those described in other embodiments. 
     Having thus described at least one illustrative embodiment of the invention, various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description is by way of example only and is not intended as limiting. The invention is limited only as defined in the following claims and the equivalents thereto.