Patent Publication Number: US-2023152355-A1

Title: Nanoseconds-pulse based current/voltage measurement for testing vertical-cavity surface-emitting laser

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     This invention relates to measurement and data acquisition systems, including a system and method for testing a vertical-cavity surface-emitting laser (VCSEL) with a nanoseconds electric pulse. 
     Description of the Related Art 
     Measurement systems are oftentimes used to perform a variety of functions, including measurement of physical phenomena, measurement of certain characteristics or operating parameters of a unit under test (UUT) or device under test (DUT), testing and analysis of physical phenomena, process monitoring and control, control of mechanical or electrical machinery, data logging, laboratory research, and analytical chemistry, to name a few examples. 
     An example of a device that may be tested by a measurement system is a vertical-cavity surface-emitting laser (VCSEL), a semiconductor-base laser diode used in computer mice, fiber optics, laser printers, and more recently, facial recognition applications. The operating characteristics of a VCSEL are commonly tested using a Light Intensity-Current-Voltage (LIV) sweep test. In an LIV test, current applied to the VCSEL is swept and the intensity of the resulting emitted light is measured using a photo detector. Traditional current sweeping and LIV measurement technologies are limited by bandwidth and proximity (e.g. cabling length) considerations. Therefore, improvements in the field are desired. 
     Other corresponding issues related to the prior art will become apparent to one skilled in the art after comparing such prior art with the present invention as described herein. 
     SUMMARY OF THE INVENTION 
     Embodiments are presented herein of a system and method to test vertical-cavity surface-emitting lasers (VCSELs). In contrast to prior closed-loop test configurations, various embodiments of a VCSEL test system disclosed herein feature an open-loop configuration and a compensation algorithm. In some aspects, a high-speed pulse generator may be used to produce nanosecond pulses and provide the nanosecond pulses to a VCSEL device under test (DUT). An appropriate measurement device, e.g. a high-speed scope may then be used to measure voltage pulses (or voltage) developed across the VCSEL DUT in response to the nanosecond pulses. The pulse current may be obtained by comparing pulse voltages under different load conditions. In some aspects, a compensation algorithm may be used to scale the pulse voltage at the pulse generator to the desired corresponding pulse current at the VCSEL device, and may be further used to compensate for the loss of signal caused by high-speed signals being transmitted over long cables. The compensation algorithm may further be used to correct system measurement errors by characterizing various system components and equipment, for example the pulse generator, the measurement device (e.g. high-speed oscilloscope), cables and other system elements. 
     Pursuant to the above, a system for testing a VCSEL device may include a high-speed pulse generator to produce a nanosecond pulse generated based at least on first compensation data derived from the system, and to provide the nanosecond pulse to the VCSEL device. The system may further include a high-speed measurement instrument to obtain a measured VCSEL device voltage-pulse generated by the VCSEL device responsive to the nanosecond pulse, and further to obtain a measured VCSEL device current-pulse based at least on the measured VCSEL device voltage-pulse and second compensation data derived from the system. In this manner, compensation data derived from the system may be used to adjust/set at least the amplitude of the nanosecond pulse generated by the pulse generator, and may further be used to obtain (or derive) a corresponding measured VCSEL DUT current-pulse from a measured voltage-pulse effected across the VCSEL DUT responsive to the stimulus nanosecond pulses. 
     In some aspects, a pre-test compensation procedure may be performed on the system to obtain various parameters corresponding to the compensation data. The compensation data is representative of various elements and/or components of the system, and may be used to adjust input signals and measured outputs of the system to obtain an accurate characterization or test result of the tested VCSEL device or DUT. The pre-test compensation procedure may include a system compensation procedure and a pulse compensation procedure. The system compensation procedure may include performing a series of operational steps to obtain representative characteristics of each system component. For example, the system compensation procedure may be used to obtain parameters of systems components including, but not limited to, output impedance of the pulse generator, pulse output cable loss, scope measurement cable loss, pulse output cable impedance, scope measurement cable impedance, scope measurement error correction factor, and/or scope input impedance. 
     The pulse compensation procedure may include capturing specified pulse trains under different load conditions and determining/obtaining a scaling relationship between the voltage-setting for a voltage used in the pulse generation, e.g. the voltage-setting of an SMU used to provide the input voltage based on which the current pulses are generated, and the current-setting of the VCSEL device (or DUT). Once the scaling relationship has been established/obtained, appropriate scaling coefficients may be used to set up the pulse generation, e.g. to set up the SMU, and generate high-speed current pulses proportional to the SMU voltage. Additionally, the pulse waveform may be acquired under various different loading conditions (e.g. open and shorted conditions) to enable obtaining accurate VCSEL device current and VCSEL device voltage. Under the open condition, the waveform may be used to derive the current-pulse VCSEL DUT waveform. Under the shorted condition, the voltage amplitude may be used to derive fixture leading resistance, which in turn may be used to correct the VCSEL DUT voltage value. 
     This Summary is intended to provide a brief overview of some of the subject matter described in this document. Accordingly, it will be appreciated that the above-described features are merely examples and should not be construed to narrow the scope or spirit of the subject matter described herein in any way. Other features, aspects, and advantages of the subject matter described herein will become apparent from the following Detailed Description, Figures, and Claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing, as well as other objects, features, and advantages of this invention may be more completely understood by reference to the following detailed description when read together with the accompanying drawings in which: 
         FIG.  1    shows an exemplary instrumentation control system with instruments networked together, according to some embodiments; 
         FIG.  2    shows an example of a traditional Vertical-Cavity Surface-Emitting Laser, VCSEL, test measurement system; 
         FIG.  3    shows a simplified system diagram of an exemplary VCSEL test measurement system, according to some embodiments; 
         FIG.  4    shows a more detailed simplified system diagram of an exemplary VCSEL test measurement system, according to some embodiments; 
         FIG.  5    shows a simplified equivalent circuit of an exemplary pulse generator in a VCSEL test measurement system with first configuration settings applied during a system compensation procedure, according to some embodiments; 
         FIG.  6    shows a simplified equivalent circuit of an exemplary pulse generator in a VCSEL test measurement system with second configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  7    shows a simplified equivalent circuit of an exemplary pulse generator in a VCSEL test measurement system with third configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  8    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with fourth configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  9    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with fifth configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  10    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with sixth configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  11    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with seventh configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  12    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with eighth configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  13    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with ninth configuration settings applied during the system compensation procedure, according to some embodiments; 
         FIG.  14    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with first configuration settings applied during a pulse compensation procedure, according to some embodiments; 
         FIG.  15    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with second configuration settings applied during the pulse compensation procedure, according to some embodiments; and 
         FIG.  16    shows a simplified equivalent circuit of an exemplary VCSEL test measurement system with third configuration settings applied during the pulse compensation procedure, according to some embodiments. 
     
    
    
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. Note, the headings are for organizational purposes only and are not meant to be used to limit or interpret the description or claims. Furthermore, note that the word “may” is used throughout this application in a permissive sense (i.e., having the potential to, being able to), not a mandatory sense (i.e., must).” The term “include”, and derivations thereof, mean “including, but not limited to”. The term “coupled” means “directly or indirectly connected”. 
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Terms 
     The following is a glossary of terms that may appear in the present disclosure: 
     Memory Medium—Any of various types of non-transitory memory devices or storage devices. The term “memory medium” is intended to include an installation medium, e.g., a CD-ROM, floppy disks, or tape device; a computer system memory or random access memory such as DRAM, DDR RAM, SRAM, EDO RAM, Rambus RAM, etc.; a non-volatile memory such as a Flash, magnetic media, e.g., a hard drive, or optical storage; registers, or other similar types of memory elements, etc. The memory medium may comprise other types of non-transitory memory as well or combinations thereof. In addition, the memory medium may be located in a first computer system in which the programs are executed, or may be located in a second different computer system which connects to the first computer system over a network, such as the Internet. In the latter instance, the second computer system may provide program instructions to the first computer system for execution. The term “memory medium” may include two or more memory mediums which may reside in different locations, e.g., in different computer systems that are connected over a network. The memory medium may store program instructions (e.g., embodied as computer programs) that may be executed by one or more processors. 
     Computer System (or Computer)—any of various types of computing or processing systems, including a personal computer system (PC), mainframe computer system, workstation, network appliance, Internet appliance, personal digital assistant (PDA), television system, grid computing system, or other device or combinations of devices. In general, the term “computer system” may be broadly defined to encompass any device (or combination of devices) having at least one processor that executes instructions from a memory medium. 
     Processing Element (or Processor)—refers to various elements or combinations of elements that are capable of performing a function in a device, e.g., in a user equipment device or in a cellular network device. Processing elements may include, for example: processors and associated memory, portions or circuits of individual processor cores, entire processor cores, processor arrays, circuits such as an ASIC (Application Specific Integrated Circuit), programmable hardware elements such as a field programmable gate array (FPGA), as well any of various combinations of the above. 
     Configured to—Various components may be described as “configured to” perform a task or tasks. In such contexts, “configured to” is a broad recitation generally meaning “having structure that” performs the task or tasks during operation. As such, the component can be configured to perform the task even when the component is not currently performing that task (e.g., a set of electrical conductors may be configured to electrically connect a module to another module, even when the two modules are not connected). In some contexts, “configured to” may be a broad recitation of structure generally meaning “having circuitry that” performs the task or tasks during operation. As such, the component can be configured to perform the task even when the component is not currently on. In general, the circuitry that forms the structure corresponding to “configured to” may include hardware circuits. 
     VCSEL—Vertical-Cavity Surface-Emitting Laser—a type of semiconductor laser diode with laser beam emission perpendicular from the top surface, contrary to conventional edge-emitting semiconductor lasers which emit from surfaces formed by cleaving the individual chip out of a wafer. 
     LIV Sweep Test—Light-Intensity-Current-Voltage Sweep Test—a measurement to determine operating characteristics of a laser diode. In the LIV test, current applied to the laser diode is swept and the intensity of the resulting emitted light is measured using a photo detector. 
     In some aspects, the LIV test involves sweeping the current through the VCSEL device and measuring the current (I), forward voltage (V) and resulting light output (L). 
     SMU—Source Measurement Unit—an instrument that combines a sourcing function and a measurement function on the same pin or connector. An SMU may source voltage and/or current and may simultaneously measure voltage and/or current. 
     LiDAR—Light Detection and Ranging—a remote sensing method for measuring distances by illuminating a target with laser light and measuring the reflection with a sensor. In one sense, LiDAR involves the use of a pulsed laser to measure ranges, or distances. 
     TOF sensing—Time of Flight sensing—the measurement of the time taken by an object, particle or wave to travel a distance. 
     DUT—Device Under Test 
     Various components may be described as performing a task or tasks, for convenience in the description. Such descriptions should be interpreted as including the phrase “configured to.” Reciting a component that is configured to perform one or more tasks is expressly intended not to invoke 35 U.S.C. § 112, paragraph six, interpretation for that component. 
     Example Measurement/Storage System 
       FIG.  1    illustrates an exemplary instrumentation control system  100  which may include a VCSEL device test system configured according to various embodiments disclosed herein. System  100  comprises a host computer  82  which may couple to one or more instruments configured to perform a variety of functions using system level health monitoring implemented according to various embodiments of the present invention. Host computer  82  may comprise a CPU, a display screen, memory, and one or more input devices such as a mouse or keyboard as shown. Computer  82  may operate with one or more instruments to analyze, measure, or control a unit under test (UUT) or process  150 . The one or more instruments may include a GPIB instrument  112  and associated GPIB interface card  122 , a data acquisition board  114  inserted into or otherwise coupled with chassis  124  with associated signal conditioning circuitry  126 , a VXI instrument  116 , a PXI instrument  118 , a video device or camera  132  and associated image acquisition (or machine vision) card  134 , a motion control device  136  and associated motion control interface card  138 , and/or one or more computer based instrument cards  142 , among other types of devices. The computer system may couple to and operate with one or more of these instruments. In some embodiments, the computer system may be coupled to one or more of these instruments via a network connection, such as an Ethernet connection, for example, which may facilitate running a high-level synchronization protocol between the computer system and the coupled instruments. The instruments may be coupled to the unit under test (UUT) or process  150 , or may be coupled to receive field signals, typically generated by transducers. System  100  may be used in a data acquisition and control applications, in a test and measurement application, an image processing or machine vision application, a process control application, a man-machine interface application, a simulation application, or a hardware-in-the-loop validation application, among others. In some embodiments, at least some components of system  100 , for example, PXI instrument  118 , may be configured to perform VCSEL (device) testing as disclosed herein. For example, PXI instrument  118  may include some or all components of a VCSEL test system as disclosed herein to perform testing of VCSEL devices autonomously or under partial or full control of host computer  82 . 
     FIG.  2 —Contemporary Light Intensity-Current-Voltage (LIV) Sweep Testing 
     As previously mentioned, Light-Intensity-current-Voltage (LIV) sweeping is a common production test performed on VCSEL devices to determine pass or fail by checking the operation characteristics of the device. The LIV test typically involves sweeping the current through the VCSEL (device) and measuring the current (I), forward voltage (V) and resulting light output (L). 
       FIG.  2    illustrates an exemplary contemporary VCSEL test system  200 . As seen in  FIG.  2   , the test system  200  features a closed loop configuration including a Source Measure Unit (SMU)  202  which sources the test pulses to VCSEL DUT  206 , and also measures the resulting signal developed across VCSEL DUT  206 .  FIG.  2    also illustrates a simplified system diagram  204  of the SMU  202 . As shown in  FIG.  2   , SMU  202  includes four terminals, two output terminals for sourcing a signal, and two sense terminals for sensing a signal. The test system (or setup) shown in  FIG.  2    represents a traditional current sweeping and IV (current/voltage) measurement solution which utilizes a closed loop control equipment (in this case SMU  202 ) to generate a current pulse, then measure the pulsed current amount and voltage amplitude across DUT  206 . However, the signal generation and measurement capabilities of SMU  202  are limited by its bandwidth and cabling length. 
     As the demand of distance and velocity measurement grows, VCSELs used in TOF (time of flight) sensing and LiDAR require pulse widths on the order of a couple nanoseconds. However, the relatively low sample rate and low bandwidth of SMU limit the pulse width to the microseconds range. The phase margin of the control loop also limits the capacity of the SMU when it comes to generating high-speed current pulses over long cables. When the SMU is set to generate a current pulse, it is expected to be located close to DUT in order to minimize inductance loading. However, in real-life production test systems the test instrument is typically at least a couple of meters away from the DUT. Cables of that length (at least 2 meters) may heavily reduce the phase margin and may thereby cause system instability. In addition to the phase margin limitation, the inductance of a long cable may also degrade the pulse-current ramping rate in a closed-loop control configuration. In order to address the application challenges faced by traditional IV test solutions mentioned above, an open-loop control system and a set of compensation algorithms may be implemented to more accurately and efficiently test VCSEL devices. 
     FIG.  3 —Exemplary VCSEL IV Nanoseconds Pulse Test System 
       FIG.  3    shows a simplified system diagram of an exemplary VSCEL test system  300 . The system  300  incorporates a high-speed pulse generator  302  to produce a nanoseconds pulse (i.e. a pulse having a pulse width in the nanosecond range) having an amplitude based at least on some portion of compensation data  308 , and further incorporates a high-speed measurement device  304  (e.g. a high-speed oscilloscope or scope, for short) to measure the voltage pulse developed across the VCSEL DUT  306  responsive to the generated nanosecond pulse. The measured DUT voltage pulse  310  may then be used to obtain the VCSEL DUT voltage and the corresponding VCSEL device current pulse  312  according to compensation information obtained based at least on some portion of compensation data  308  as will be further detailed below. The system  300  may implement measuring pulse current by comparing pulse voltages under different load conditions as part of a compensation algorithm used to scale the pulse voltage at the pulse generator  302  to the desired pulse current at the VCSEL DUT  306 . The compensation algorithm may further be used to correct system measurement errors by characterizing various system components and equipment, for example the pulse generator  302 , the measurement device  304 , cables interconnecting pulse generator  302 , measurement device  304 , and VCSEL DUT  306 , and other system elements, and to compensate for signal loss resulting from transmission of a high-speed signal over a long cable. 
     FIG.  4 —More Detailed Exemplary VCSEL IV Nanoseconds Pulse Test System 
       FIG.  4    shows a more detailed simplified system diagram of an exemplary VCSEL test measurement system  400 . The system  400  includes a high speed pulse generator  402  and a high speed measurement device  410 . In some embodiments, pulse generator  402  may include a pulse module  404  that receives a voltage from an SMU  420  and generates high-speed current pulses proportional to the received voltage. In some aspects, a minimum pulse width output by pulse module  404  may be 5 ns. More generally, the minimum (i.e. the narrowest) pulse width may be limited by the switching speed of pulse module  404 . In some embodiments, high speed measurement device  410  may include a high-speed oscilloscope (scope, for short)  422 , which may have a specified input bandwidth, e.g. a 1.5 GHz input bandwidth. Accordingly, a sample rate of up to 5 Gsps (Giga-samples per second) may be used to measure the nanoseconds pulses. An attenuator  430  may be used as required to attenuate the signal to a specified input amplitude range of the scope  422 . As shown in  FIG.  4   , the SMU  420  and scope  422  may be coupled to an interconnecting bus  406  and may be controlled via the interconnecting bus  406  through a controller, or control circuit  432 . In some aspects, controller  432  may receive data/information from pulse module  404 , and may use the received data/information in controlling the voltage that SMU  420  provides to pulse module  404 . DUT  408  may be configured on a load board  412  for the purposes of testing, using BNC input connectors on load board  412  to couple to the output ports of pulse generator  402 , and using a BNC output connector on load board  412  to couple to the input of measurement device  410 . In some embodiments, controller  432  may be a control circuit or a controller included in an instrument such as PXI instrument  118 , or it may be a host such as computer  82 , or it may be a combination of components that includes computer  82  or it may be an autonomous external controller. In some aspects controller  432  may include various elements (e.g. circuits) or combinations of elements that are capable of controlling at least pulse generator  402  and measurement device  410 . Controller  432  may include, for example: general purpose processors and associated memory, portions or circuits of individual processor cores, entire processor cores or processing circuit cores, processing circuit arrays or processor arrays, circuits such as ASICs (Application Specific Integrated Circuits), programmable hardware elements such as a field programmable gate array (FPGA), as well as any of various combinations of the above. 
     System Operation 
     According to some aspects, the operation of system  400  may include three main stages. A pre-test compensation stage, a VCSEL voltage derivation stage, and a VCSEL current derivation stage. 
     Pre-Test Compensation 
     First, a pre-test compensation procedure may be performed in order to correctly set the pulse amplitude for the nanoseconds pulse(s) and accurately perform the IV (current/voltage) measurement. More specifically, the pre-test compensation procedure may be used to characterize the system  400  and the pulse (output by pulse generator  402 ) prior to performing the IV measurements. The pre-test compensation procedure may be split into a system compensation procedure and a pulse compensation procedure. 
     System Compensation Procedure 
     The system compensation procedure may include performing a series of operational steps to obtain the characteristics of each system component, including the scope  422 , pulse module  404 , attenuator  430 , and the interconnecting cables between load board  412  and pulse generator  402  and measurement device  410 , respectively. The following chart illustrates exemplary parameters that may be obtained through the system compensation procedure. 
     
       
         
           
               
               
             
               
                   
               
               
                 System Components 
                 Parameters of System Components 
               
               
                   
               
             
            
               
                 Pulse Generator 
                 Output Impedance 
               
               
                 Cables 
                 Pulse Output Cable Loss 
               
               
                   
                 Scope Measurement Cable Loss 
               
               
                   
                 Pulse Output Cable Impedance 
               
               
                   
                 Scope Measurement Cable Impedance 
               
               
                 Scope 
                 Scope Measurement Error Correction Factor 
               
               
                   
                 Scope Input Impedance 
               
               
                   
               
            
           
         
       
     
     An exemplary system compensation procedure is described below with respect to  FIGS.  5 - 13   . As indicated in the chart above, there are several unknown system parameters that may be obtained through the system compensation procedure. A more detailed list of parameter values that may be obtained through the system compensation procedure is provided below. The parameters, or values of the parameters, in bold underlined print may be used for compensating the pulse waveform and for calculating the voltage and current. The remaining parameters represent intermediate parameters obtained throughout the procedure. The intermediate parameters may also be saved and reused for repeating parts or all of the compensation procedure.
         ACF 50  Scope measurement error correction factor @ 50Ω input   ACF 1M  Scope measurement error correction factor @ 1MΩ input      Scope measurement error correction factor @ 50Ω input with 50Ω xdB attenuator (note: “x” refers to a selected positive value, e.g. 30, selected as required in the specific system implementation or set of embodiments)   R SF0  Pulse generator Port 0 output resistance   R SF0_atten  Pulse generator Port 0 internal attenuator resistance   R SF1  Pulse generator Port 1 output resistance   R scope50  Scope input resistance @ 50Ω input impedance   R scope1M  Scope input resistance @ 1MΩ input impedance      Scope input resistance @50Ω input with 50Ω xdB attenuator   Loss SF0  Pulse generator Port 0 cable loss (Resistive Loss and Dielectric Loss)   Loss SF1  Pulse generator Port 1 cable loss (Resistive Loss and Dielectric Loss)      Scope cable loss (Resistive Loss and Dielectric Loss)      Pulse generator Port 0 cable impedance      Pulse generator Port 1 cable impedance      Scope cable impedance       

     First setting: Port 0 of the pulse generator is shorted while Port 1 of the pulse generator is left open. 
     Step 1—Measure the resistance of Port 0 of the pulse generator. Set pulse generator in DC calibration mode. SMU output=1 VDC. See circuit diagram in  FIG.  5   . 
     
       
         
           
             
               R 
               
                 SF 
                 ⁢ 
                 0 
               
             
             = 
             
               
                 V 
                 SMU 
               
               
                 I 
                 SMU 
               
             
           
         
       
     
     Second setting: Port 0 and Port 1 of pulse generator remain open. 
     Step 2—Measure the internal attenuator resistance of Port 0 of the pulse generator. Set pulse generator in DC calibration mode. SMU output=1 VDC. See circuit diagram in  FIG.  6   . 
     
       
         
           
             
               R 
               
                 SF 
                 ⁢ 
                 0 
                 ⁢ 
                 
                   _ 
                   ⁢ 
                   atten 
                 
               
             
             = 
             
               
                 
                   V 
                   SMU 
                 
                 
                   I 
                   SMU 
                 
               
               - 
               
                 R 
                 
                   SF 
                   ⁢ 
                   0 
                 
               
             
           
         
       
     
     Third setting: Port 0 of the pulse generator is left open while Port 1 of the pulse generator is shorted. 
     Step 3—Measure the output resistance of Port 1 of the pulse generator. Set pulse generator in DC calibration mode. SMU output=1 VDC. See circuit diagram in  FIG.  7   . 
     
       
         
           
             
               R 
               
                 SF 
                 ⁢ 
                 1 
               
             
             = 
             
               
                 V 
                 SMU 
               
               
                 
                   I 
                   SMU 
                 
                 - 
                 
                   
                     V 
                     SMU 
                   
                   
                     
                       R 
                       SF 
                     
                     + 
                     
                       R 
                       
                         SF 
                         ⁢ 
                         0 
                         ⁢ 
                         
                           _ 
                           ⁢ 
                           atten 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     This completes the pulse generator characterization, and the following measured module parameters may be saved:
         R SF0  Pulse generator Port 0 output resistance   R SF0_atten  Pulse generator Port 0 internal attenuator resistance   R SF1  Pulse generator Port 1 output resistance       

     Fourth setting: One BNC terminal of the cable is connected to Port 0 of the pulse generator and the other BNC terminal of the cable is shorted. 
     Step 4—Measure BNC Cable DC Resistance. Set pulse generator in DC calibration mode. SMU output=1 VDC. See circuit diagram in  FIG.  8   . 
     
       
         
           
             
               R 
               cable 
             
             = 
             
               
                 
                   
                     R 
                     
                       SF 
                       ⁢ 
                       0 
                       ⁢ 
                       
                         _ 
                         ⁢ 
                         atten 
                       
                     
                   
                   · 
                   
                     V 
                     SMU 
                   
                 
                 - 
                 
                   
                     I 
                     SMU 
                   
                   · 
                   
                     R 
                     
                       SF 
                       ⁢ 
                       0 
                     
                   
                   · 
                   
                     R 
                     
                       SF 
                       ⁢ 
                       0 
                       ⁢ 
                       
                         _ 
                         ⁢ 
                         atten 
                       
                     
                   
                 
               
               
                 
                   
                     I 
                     SMU 
                   
                   · 
                   
                     R 
                     
                       SF 
                       ⁢ 
                       0 
                     
                   
                 
                 - 
                 
                   V 
                   SMU 
                 
                 + 
                 
                   
                     I 
                     SMU 
                   
                   · 
                   
                     R 
                     
                       SF 
                       ⁢ 
                       0 
                       ⁢ 
                       
                         _ 
                         ⁢ 
                         atten 
                       
                     
                   
                 
               
             
           
         
       
     
     Fifth setting: The short is removed from previously shorted BNC terminal and is connected to the measurement instrument/scope. See circuit diagram in  FIG.  9   . 
     Step 5—Measure Scope Input Resistance @ 1 MΩ input impedance. 
     
       
         
           
             
               R 
               
                 scope 
                 ⁢ 
                 1 
                 ⁢ 
                 M 
               
             
             = 
             
               - 
               
                 1 
                 · 
                 
                   ( 
                   
                     
                       
                         R 
                         cable 
                       
                       + 
                       
                         
                           
                             ( 
                             
                               
                                 R 
                                 cable 
                               
                               + 
                               
                                 R 
                                 
                                   SF 
                                   ⁢ 
                                   0 
                                   ⁢ 
                                   
                                     _ 
                                     ⁢ 
                                     atten 
                                   
                                 
                               
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               
                                 R 
                                 
                                   SF 
                                   ⁢ 
                                   0 
                                 
                               
                               - 
                               
                                 
                                   V 
                                   SMU 
                                 
                                 
                                   I 
                                   SMU 
                                 
                               
                             
                             ) 
                           
                         
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                             ⁢ 
                             
                               _ 
                               ⁢ 
                               atten 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             R 
                             
                               SF 
                               ⁢ 
                               0 
                             
                           
                           - 
                           
                             
                               V 
                               SMU 
                             
                             
                               I 
                               SMU 
                             
                           
                         
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                             ⁢ 
                             
                               _ 
                               ⁢ 
                               atten 
                             
                           
                         
                       
                       + 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Step 6—Correct Scope DC error @ 1MΩ input impedance. Set pulse generator in DC calibration mode. SMU output=1 VDC. 
     
       
         
           
             
               V 
               
                 scope 
                 ⁢ 
                 1 
                 ⁢ 
                 
                   M 
                   ⁢ 
                   _ 
                   ⁢ 
                   expected 
                 
               
             
             = 
             
               
                 
                   I 
                   SMU 
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     1 
                     ⁢ 
                     M 
                   
                 
                 · 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0 
                     ⁢ 
                     
                       _ 
                       ⁢ 
                       atten 
                     
                   
                 
               
               
                 
                   R 
                   cable 
                 
                 + 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     1 
                     ⁢ 
                     M 
                   
                 
                 + 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0 
                     ⁢ 
                     
                       _ 
                       ⁢ 
                       atten 
                     
                   
                 
               
             
           
         
       
     
     The uncorrected scope measurement is: V scope1M_raw . A correction factor for the scope measurement may be calculated as: 
     
       
         
           
             
               ACF 
               
                 1 
                 ⁢ 
                 M 
               
             
             = 
             
               
                 V 
                 
                   scope 
                   ⁢ 
                   1 
                   ⁢ 
                   
                     M 
                     ⁢ 
                     _ 
                     ⁢ 
                     expected 
                   
                 
               
               
                 V 
                 
                   scope 
                   ⁢ 
                   1 
                   ⁢ 
                   
                     M 
                     ⁢ 
                     _ 
                     ⁢ 
                     raw 
                   
                 
               
             
           
         
       
     
     Step 7—Measure scope input resistance @ 50Ω input impedance. Set scope input impedance to be 50Ω. Set pulse generator in DC calibration mode. SMU output=1 VDC. See circuit diagram in  FIG.  10   . 
     
       
         
           
             
               R 
               
                 scope 
                 ⁢ 
                 50 
               
             
             = 
             
               - 
               
                 1 
                 · 
                 
                   ( 
                   
                     
                       
                         R 
                         cable 
                       
                       + 
                       
                         
                           
                             ( 
                             
                               
                                 R 
                                 cable 
                               
                               + 
                               
                                 R 
                                 
                                   SF 
                                   ⁢ 
                                   0 
                                   ⁢ 
                                   
                                     _ 
                                     ⁢ 
                                     atten 
                                   
                                 
                               
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               
                                 R 
                                 
                                   SF 
                                   ⁢ 
                                   0 
                                 
                               
                               - 
                               
                                 
                                   V 
                                   SMU 
                                 
                                 
                                   I 
                                   SMU 
                                 
                               
                             
                             ) 
                           
                         
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                             ⁢ 
                             
                               _ 
                               ⁢ 
                               atten 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             R 
                             
                               SF 
                               ⁢ 
                               0 
                             
                           
                           - 
                           
                             
                               V 
                               SMU 
                             
                             
                               I 
                               SMU 
                             
                           
                         
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                             ⁢ 
                             
                               _ 
                               ⁢ 
                               atten 
                             
                           
                         
                       
                       + 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Step 8—Correct scope DC error @ 50Ω input impedance. 
     
       
         
           
             
               V 
               
                 scope 
                 ⁢ 
                 50 
                 ⁢ 
                 
                   _ 
                   ⁢ 
                   expected 
                 
               
             
             = 
             
               
                 
                   I 
                   SMU 
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     50 
                   
                 
                 · 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0 
                     ⁢ 
                     
                       _ 
                       ⁢ 
                       atten 
                     
                   
                 
               
               
                 
                   R 
                   cable 
                 
                 + 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     50 
                   
                 
                 + 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0 
                     ⁢ 
                     
                       _ 
                       ⁢ 
                       atten 
                     
                   
                 
               
             
           
         
       
     
     The uncorrected scope measurement is: V scope50_raw . A correction factor for the scope measurement may be calculated as: 
     
       
         
           
             
               ACF 
               50 
             
             = 
             
               
                 V 
                 
                   scope 
                   ⁢ 
                   50 
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     expected 
                   
                 
               
               
                 V 
                 
                   scope 
                   ⁢ 
                   50 
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     raw 
                   
                 
               
             
           
         
       
     
     The corrected scope measurements may then be used to characterize the scope cable, also referred to herein as the 1 st  cable. The scope cable (1 st  cable) may be characterized using Steps 9 and 10 below. 
     Step 9—Measure pulse with scope set at 50Ω input. Set scope input impedance to be 50Ω. Set pulse generator in pulse mode to generate a 4V pulse to obtain V scope50 . See circuit diagram in  FIG.  11   . 
     Step 10—Measure pulse with scope set at 1MΩ input. Set scope input impedance to be 1MΩ. Set pulse generator in pulse mode and generate a 4V pulse to obtain V scope1M . See circuit diagram in  FIG.  12   . 
     The cable impedance may then be derived by: 
     
       
         
           
             
               Z 
               cable 
             
             = 
             
               
                 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       50 
                     
                   
                   · 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       50 
                     
                   
                   · 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       1 
                       ⁢ 
                       M 
                     
                   
                 
                 - 
                 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       50 
                     
                   
                   · 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       1 
                       ⁢ 
                       M 
                     
                   
                   · 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       1 
                       ⁢ 
                       M 
                     
                   
                 
               
               
                 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       50 
                     
                   
                   · 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       1 
                       ⁢ 
                       M 
                     
                   
                 
                 - 
                 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       50 
                     
                   
                   · 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       1 
                       ⁢ 
                       M 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               Loss 
               cable 
             
             = 
             
               
                 
                   V 
                   
                     scope 
                     ⁢ 
                     50 
                   
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       para 
                       ( 
                       
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                             ⁢ 
                             
                               _ 
                               ⁢ 
                               atten 
                             
                           
                         
                         · 
                         
                           Z 
                           cable 
                         
                       
                       ) 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       cable 
                     
                     + 
                     
                       R 
                       
                         scope 
                         ⁢ 
                         50 
                       
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   V 
                   SMU 
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     50 
                   
                 
                 · 
                 
                   para 
                   ( 
                   
                     
                       R 
                       
                         SF 
                         ⁢ 
                         0 
                         ⁢ 
                         
                           _ 
                           ⁢ 
                           atten 
                         
                       
                     
                     · 
                     
                       Z 
                       cable 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Step 11 and Step 12—Repeat Step 9 and Step 10 to characterize the pulse generator Port 0 cable, also referred to herein as the 2 nd  cable, e.g. to obtain cable loss and cable impedance for the 2 nd  cable.
 
Sixth setting: Replace the BNC cable with the 3 rd  cable.
 
Step 13 and Step 14—Repeat Step 9 and Step 10 to characterize the pulse generator Port 1 cable, also referred to herein as the 3 rd  cable, e.g. obtain cable loss and cable impedance for the 3 rd  cable.
 
This completes the scope and cable characterization, and the following measured parameters may be saved:
         ACF 50  Scope measurement error correction factor @ 50Ω input   ACF 1M  Scope measurement accuracy correction factor @ 1MΩ input   R scope50  Scope input resistance @50Ω input impedance   R scope1M  Scope input resistance @ 1MΩ input impedance   Loss SF0  Pulse generator Port 0 cable loss (Resistive Loss and Dielectric Loss)   Loss SF1  Pulse generator Port 1 cable loss (Resistive Loss and Dielectric Loss)   Loss scope  Scope cable loss (Resistive Loss and Dielectric Loss)   Z SF0  Pulse generator Port 0 cable impedance   Z SF1  Pulse generator Port 1 cable impedance   Z Scope  Scope cable impedance   R cable  1 st  cable resistance, i.e. scope cable resistance
 
Seventh setting: Replace BNC cable with 1 st  BNC cable. Attach xdB BNC attenuator to the input of scope. See circuit diagram of  FIG.  13   .
 
Step 15—Measure scope input resistance @ 50Ω with xdB BNC attenuator. Set scope input impedance to be 50Ω. Set pulse generator in DC calibration mode. SMU output=1 VDC.
       

     
       
         
           
             
               R 
               
                 scope 
                 ⁢ 
                 _ 
                 ⁢ 
                 atten 
               
             
             = 
             
               
                 - 
                 1 
               
               · 
               
                 ( 
                 
                   
                     
                       R 
                       cable 
                     
                     + 
                     
                       
                         
                           ( 
                           
                             
                               R 
                               cable 
                             
                             + 
                             
                               R 
                               
                                 SF 
                                 ⁢ 
                                 0_ 
                                 ⁢ 
                                 atten 
                               
                             
                           
                           ) 
                         
                         · 
                         
                           ( 
                           
                             
                               R 
                               
                                 SF 
                                 ⁢ 
                                 0 
                               
                             
                             - 
                             
                               
                                 V 
                                 SMU 
                               
                               
                                 I 
                                 SMU 
                               
                             
                           
                           ) 
                         
                       
                       
                         R 
                         
                           SF 
                           ⁢ 
                           0_ 
                           ⁢ 
                           atten 
                         
                       
                     
                   
                   
                     
                       
                         
                           R 
                           
                             SF 
                             ⁢ 
                             0 
                           
                         
                         - 
                         
                           
                             V 
                             SMU 
                           
                           
                             I 
                             SMU 
                           
                         
                       
                       
                         R 
                         
                           SF 
                           ⁢ 
                           0_ 
                           ⁢ 
                           atten 
                         
                       
                     
                     + 
                     1 
                   
                 
                 ) 
               
             
           
         
       
     
     Step 16—Correct Scope DC error @ 50Ω with xdB BNC attenuator. 
     
       
         
           
             
               V 
               
                 
                   scope 
                   ⁢ 
                   _ 
                   ⁢ 
                   atten 
                 
                 ⁢ 
                 
                   _ 
                   ⁢ 
                   expected 
                 
               
             
             = 
             
               
                 
                   I 
                   SMU 
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0_ 
                     ⁢ 
                     atten 
                   
                 
               
               
                 
                   R 
                   cable 
                 
                 + 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 + 
                 
                   R 
                   
                     SF 
                     ⁢ 
                     0_ 
                     ⁢ 
                     atten 
                   
                 
               
             
           
         
       
     
     The uncorrected scope measurement is: V scope_atten_raw . A correction factor for the scope measurement may be calculated as: 
     
       
         
           
             
               ACF 
               atten 
             
             = 
             
               
                 V 
                 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     expected 
                   
                 
               
               
                 V 
                 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                   ⁢ 
                   
                     _ 
                     ⁢ 
                     raw 
                   
                 
               
             
           
         
       
     
     This completes the scope input characterization, and the following measured module parameters may be saved:
         ACF atten  Scope measurement error correction factor @ 50Ω input with 50Ω xdB attenuator   R scope_atten  Scope input resistance @ 50Ω input with 50Ω xdB attenuator
 
This completes the system compensation procedure, and the following parameters may be used for pulse correction and DUT test:
   ACF atten  Scope measurement error correction factor @ 50Ω input impedance with 50Ω xdB attenuator   R scope_atten  Scope input resistance @ 50Ω input impedance with 50Ω xdB attenuator   Loss scope  Scope cable loss (Resistive Loss and Dielectric Loss)   Z SF0  Pulse generator Port 0 cable impedance   Z SF1  Pulse generator Port 1 cable impedance   Z Scope  Scope cable impedance
 
The following system compensation data may be saved for further re-compensation, pulse compensation, or pulse measurement:
   R SF0  Pulse generator Port 0 output resistance   R SF0_atten  Pulse generator Port 0 internal attenuator resistance   R SF1  Pulse generator Port 1 output resistance   ACF 50  Scope measurement error correction factor @ 50Ω input impedance   ACF 1M  Scope measurement error correction factor @ 1 MΩ input impedance   R scope50  Scope input resistance @ 50Ω input impedance   R scope1M  Scope input resistance @1 MΩ input impedance   Loss SF0  Pulse generator Port 0 cable loss (Resistive Loss and Dielectric Loss)   Loss SF1  Pulse generator Port 1 cable loss (Resistive Loss and Dielectric Loss)   Loss scope  Scope cable loss (Resistive Loss and Dielectric Loss)   Z SF0  Pulse generator Port 0 cable impedance   Z SF1  Pulse generator Port 1 cable impedance   Z Scope  Scope cable impedance   R cable  1 st  Cable resistance (i.e. scope cable resistance)   ACF atten  Scope measurement error correction factor @ 50 ohm input with 50 ohm xdB attenuator   R scope_atten  Scope input resistance @50 ohm input with 50 ohm xdB attenuator       

     Pulse Compensation Procedure 
     The pulse compensation procedure may be used to capture or measure the generated nanosecond pulse under different load conditions of the pulse generator, including open loading, short loading, and “known-good” DUT loading. A “known-good” DUT is representative of typical operational characteristics of a DUT, e.g. voltage drop and impedance of the DUT. In one sense a “known-good” DUT may therefore be considered a known device or DUT used for the pulse compensation procedure as a representative of DUT devices expected to be tested in the future. The pulse compensation may be primarily used to obtain a scaling relationship between the SMU voltage-setting, or SMU voltage, and DUT current-setting, or DUT current. Following the pulse compensation, appropriate scaling coefficients may be used to set up the SMU and generate high-speed current pulses proportional to the SMU voltage. The waveform acquired under open loading conditions may later be used to derive the VCSEL current pulse waveform during actual VCSEL DUT measurements. The voltage amplitude acquired under shorted loading conditions may be used to derive fixture leading resistance which may be later used to correct the VCSEL voltage amount during actual VCSEL DUT measurements. 
     An exemplary pulse compensation procedure is described below with respect to  FIGS.  14 - 16   . This procedure may be used to characterize the scaling relation between SMU settings to DUT current by performing OPEN/DUT measurements. It may also include performing OPEN/SHORT measurements to obtain fixture series resistance which may be subsequently used to compensate the DUT voltage. The pulse width may thus be compensated to match the desired pulse-on time (or pulse width). 
     Pulse Amplitude Correction and Fixture Resistance Measurement: 
     The following formulas may be used to calculate the DUT voltage and current using scope measurements.
 
For single-port pulse generation:
 
     
       
         
           
             
               
                 Current 
                 DUT 
               
               ( 
               
                 V 
                 SMU 
               
               ) 
             
             = 
             
               
                 
                   ( 
                   
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         OPEN 
                       
                     
                     - 
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         DUT 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     For two-port pulse generation: 
     
       
         
           
             
               Current 
               DUT 
             
             = 
             
               
                 
                   ( 
                   
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         OPEN 
                       
                     
                     - 
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         DUT 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           0 
                         
                       
                       · 
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     1 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     The following formula may be used to calculate the DUT voltage, with scope measurement: 
     
       
         
           
             
               Voltage 
               DUT 
             
             = 
             
               
                 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       _ 
                       ⁢ 
                       DUT 
                     
                   
                   · 
                   
                     ( 
                     
                       
                         R 
                         
                           scope 
                           ⁢ 
                           50 
                         
                       
                       + 
                       
                         Z 
                         scope 
                       
                     
                     ) 
                   
                 
                 
                   2 
                   · 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       _ 
                       ⁢ 
                       atten 
                     
                   
                   · 
                   
                     Loss 
                     scope 
                   
                 
               
               - 
               
                 
                   Current 
                   DUT 
                 
                 · 
                 
                   R 
                   Fixture 
                 
               
             
           
         
       
     
     As noted above, the following system parameters may have been obtained by performing system compensation:
         ACF atten  Scope measurement error correction factor @ 50Ω input impedance with 50Ω xdB attenuator (again, “x” refers to a positive number, specified as required by the given system implementation/embodiments)   R scope_atten  Scope input resistance @ 50Ω input impedance with 50Ω xdB attenuator   Loss scope  Scope cable loss (Resistive Loss and Dielectric Loss)   Z SF0  Pulse generator Port 0 cable impedance   Z SF1  Pulse generator Port 1 cable impedance   Z Scope  Scope cable impedance
 
The remaining unknowns to be obtained in order to derive the DUT voltage and current from scope measurements are:
   Current DUT (V SMU ) SMU voltage-settings vs DUT current-setting   R Fixture  The fixture resistance between the DUT and remote sense
 
The relation between the SMU voltage and the DUT current-setting may be expressed as:
       

     
       
         
           
             
               V 
               SMU 
             
             = 
             
               
                 
                   Current 
                   DUT 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       SF 
                     
                     + 
                     
                       Z 
                       SF 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       
                         Z 
                         SF 
                       
                       · 
                       
                         R 
                         DUT 
                       
                     
                     + 
                     
                       
                         Z 
                         SF 
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                     + 
                     
                       
                         R 
                         DUT 
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   SF 
                 
                 · 
                 
                   Z 
                   SF 
                 
               
             
           
         
       
     
     Below are three methods to set the SMU voltage per current-setting, considering DUT resistance is unknown. An exemplary procedure designed according to the 2 nd  method will be further presented below.
 
1. Assuming the DUT resistance is 0.3Ω (0.3Ω is the nominal resistance obtained from a typical sample), the SMU voltage may be calculated per current-settings. This method may still enable plotting the IV curve but it may not allow the pulse generator to provide pulses that accurately represent the desired current.
 
2. The relationship between the SMU settings and the DUT current may be characterized using a “known-good” DUT. In such case it is not necessary to know the resistance of the known-good DUT, but the known-good DUT may need to provide an adequate representation of the typical resistance of used/expected DUTs, and the distribution of DUT resistance is tight.
 
3. The SMU output may be dynamically tweaked to regulate DUT current in a real test by comparing measured DUT current over different settings, which essentially represents closed loop control. It may provide the best current-setting accuracy, but the test times may be longer.
 
First setting: Set the load condition to OPEN, and connect the pulse generator cable and oscilloscope cable to the load. Configure the pulse generator to work in pulse mode. Step the SMU voltage from low to high, to obtain V scope_OPEN  (V SMU ). See the circuit diagram of  FIG.  14   .
 
Second setting: Set the load condition to SHORTED, and connect the pulse generator cable and oscilloscope cable to the load. Configure the pulse generator to work in pulse mode. Step the SMU voltage from low to high, to obtain V scope_SHORT  (V SMU ). See the circuit diagram of  FIG.  15   .
 
The single-port current output under short condition is expressed by:
 
     
       
         
           
             
               
                 Current 
                 SHORT 
               
               ( 
               
                 V 
                 SMU 
               
               ) 
             
             = 
             
               
                 
                   ( 
                   
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           OPEN 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                     - 
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           SHORT 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     The two-port current output under short condition is expressed by: 
     
       
         
           
             
               
                 Current 
                 SHORT 
               
               ( 
               
                 V 
                 SMU 
               
               ) 
             
             = 
             
               
                 
                   ( 
                   
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           OPEN 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                     - 
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           SHORT 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           0 
                         
                       
                       · 
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     1 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     The fixture resistance may then be calculated as: 
     
       
         
           
             
               R 
               Fixture 
             
             = 
             
               
                 V 
                 
                   scope 
                   ⁢ 
                   _ 
                   ⁢ 
                   SHORT 
                 
               
               
                 Current 
                 SHORT 
               
             
           
         
       
     
     The fixture series resistance may be used to calculate the DUT Voltage.
 
Third setting: Set the load condition to “known-good” DUT, and connect the pulse generator cable and oscilloscope cable to the load. Sweep all pulse generator pulse voltages from low to high with the same steps of open pulse, to obtain V scope_DUT  (V SMU ). See the circuit diagram of  FIG.  16   . The DUT current for each pulse step may be calculated.
 
The DUT Current sourced by a single pulse generator port may be obtained according to:
 
     
       
         
           
             
               
                 Current 
                 DUT 
               
               ( 
               
                 V 
                 SMU 
               
               ) 
             
             = 
             
               
                 
                   ( 
                   
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           OPEN 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                     - 
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           DUT 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     The DUT current sourced by two pulse-generator ports may be obtained according to: 
     
       
         
           
             
               
                 Current 
                 DUT 
               
               ( 
               
                 V 
                 SMU 
               
               ) 
             
             = 
             
               
                 
                   ( 
                   
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           OPEN 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                     - 
                     
                       
                         V 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           DUT 
                         
                       
                       ( 
                       
                         V 
                         SMU 
                       
                       ) 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           0 
                         
                       
                       · 
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     1 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     In order to obtain the relationship between the DUT current and the SMU voltage, a function of the DUT current vs. SMU voltage may be plotted. The SMU voltage may be interpolated and calculated for desired current-settings.
 
This completes the pulse amplitude correction and fixture series resistance measurement, and the plot of the measured current vs SMU voltage-setting [Current DUT (V SMU )], and the fixture series resistance [R Fixture ] may both be saved.
 
The following data may thus be obtained for pulse measurement:
         V scope_OPEN (V SMU ) The measured pulse waveform under open load condition   V scope_SHORT (V SMU ) The measured pulse waveform under short load condition   V scope_DUT (V SMU ) The measured pulse waveform with DUT   R Fixture  Fixture impedance   Current DUT (SMU) The relation between SMU settings and measured current       

     VCSEL Voltage Derivation 
     In some embodiments, the following algorithm may be used to derive the actual VCSEL device voltage by using the acquired VCSEL waveform (i.e. the measured VCSEL device voltage) and compensation data (or information) obtained from the system compensation. 
     
       
         
           
             
               Voltage 
               DUT 
             
             = 
             
               
                 
                   
                     V 
                     
                       scope 
                       ⁢ 
                       _ 
                       ⁢ 
                       DUT 
                     
                   
                   · 
                   
                     ( 
                     
                       
                         R 
                         
                           scope 
                           ⁢ 
                           _ 
                           ⁢ 
                           atten 
                         
                       
                       + 
                       
                         Z 
                         scope 
                       
                     
                     ) 
                   
                 
                 
                   2 
                   · 
                   
                     R 
                     
                       scope 
                       ⁢ 
                       _ 
                       ⁢ 
                       atten 
                     
                   
                   · 
                   
                     Loss 
                     scope 
                   
                 
               
               - 
               
                 
                   Current 
                   DUT 
                 
                 · 
                 
                   R 
                   Fixture 
                 
               
             
           
         
       
     
     where
         V scope_DUT  VCSEL voltage waveform acquired by scope   R scope_atten  Scope input impedance   Z scope  The impedance of scope measurement cable   Loss scope  Signal loss caused by scope measurement cable   Current DUT  Current waveform through DUT   R Fixture  Fixture leading resistance       

     VCSEL Current Derivation 
     In some embodiments, the following algorithm may be used to derive the actual VCSEL device current by using the acquired VCSEL waveform (i.e. the measured VCSEL device voltage) and compensation data (or information) obtained from the system compensation. 
     Single-Port Pulse Generation: 
     
       
         
           
             
               Current 
               DUT 
             
             = 
             
               
                 
                   ( 
                   
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         OPEN 
                       
                     
                     - 
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         DUT 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     Two-Port Pulse Generation: 
     
       
         
           
             
               Current 
               DUT 
             
             = 
             
               
                 
                   ( 
                   
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         OPEN 
                       
                     
                     - 
                     
                       V 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         DUT 
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       Z 
                       
                         SF 
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                       · 
                       
                         Z 
                         scope 
                       
                     
                     + 
                     
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           0 
                         
                       
                       · 
                       
                         Z 
                         
                           SF 
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       R 
                       
                         scope 
                         ⁢ 
                         _ 
                         ⁢ 
                         atten 
                       
                     
                     + 
                     
                       Z 
                       scope 
                     
                   
                   ) 
                 
               
               
                 2 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     0 
                   
                 
                 · 
                 
                   Z 
                   
                     SF 
                     ⁢ 
                     1 
                   
                 
                 · 
                 
                   R 
                   
                     scope 
                     ⁢ 
                     _ 
                     ⁢ 
                     atten 
                   
                 
                 · 
                 
                   Z 
                   scope 
                 
                 · 
                 
                   Loss 
                   scope 
                 
               
             
           
         
       
     
     where
         V scope_DUT  VCSEL voltage waveform acquired by scope   V scope_OPEN  Voltage waveform acquired by scope under OPEN loading condition   Z SF0  The impedance of the primary output cable   Z SF1  The impedance of the secondary output cable   Z scope  The impedance of the scope measurement cable   Loss scope  Signal loss caused by the scope measurement cable   R scope_atten  Scope input impedance       

     VCSEL Current-Setting 
     As previously described above, a scaling relationship between the DUT current-setting and the SMU voltage-setting may be obtained through the pulse compensation procedure. To drive the desired amount of current, the SMU voltage value(s) may be interpolated from the known scaling relationship between the DUT current and the SMU voltage, and the pulse generator may be set to produce high-speed current pulses proportional to SMU voltage by using the interpolated voltage values for the SMU voltage. 
     Although the embodiments above have been described in considerable detail, other versions are possible. Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications. Note the section headings used herein are for organizational purposes only and are not meant to limit the description provided herein or the claims attached hereto.