Number 2475
Four-Probe Resistivity and Hall Voltage Measurements with the Model 4200-SCS
Application Note
Series
Introduction
Semiconductor material rearch and device testing often involve deter-mining the resistivity and Hall
mobility of a sample. The resistivity of miconductor material is primarily dependent on the bulk doping. In a device, the resistivity can affect the capacitance, the ries resistance, and the threshold voltage.
The resistivity of the miconductor is often determined using a four-point probe technique. With a four-probe, or Kelvin, technique, two of the probes are ud to source current and the other two probes are ud to measure voltage. Using four probes eliminates measurement errors due to the probe resistance, the spreading resistance under each probe, and the contact resistance between each metal probe and the miconductor material. Becau a high impedance voltmeter draws little current, the voltage drops across the probe resistance, spreading resis-tance, and contact resistance are very small.
Two common Kelvin techniques for determining the resistivity of a miconductor material are the four-point collinear probe method and the van der Pauw method. The Model 4200-SCS Semiconductor Characterization System can be ud for both. Becau of its high input impedance (>1016Ω) and accurate low current sourcing, the Model 4200-SCS with preamps is ideal for high resistance samples. This application note explains how to make resistivity measurements of miconductor materials using the Model 4200-SCS.
The Four-Point Collinear Probe Method
The most common way of measuring the resistivity of a miconduc-tor material is by using a four-point collinear probe. This technique
involves bringing four equally spaced probes in contact with a material of unknown resistance. The probe array is placed in the center of the mate-rial, as shown in Figure 1.
The two outer probes are ud for sourcing current and the two inner probes are ud for measuring the resulting voltage drop across the surface of the sample. The volume resistivity is calculated as follows: π V
ρ = ___ × __ × t × k
ln 2 I where: ρ = volume resistivity (Ω-cm) V = the measured voltage (volts) I = the source current (amperes) t = the sample thickness (cm)
k*
= a correction factor bad on the ratio of the probe to wafer diameter and on the ratio of wafer thickness to probe paration
* The correction factors can be found in standard four-point probe resistivity test proce-dures such as SEMI MF84-02—Test Method for Measuring Resistivity of Silicon Wafers With an In-Line Four-Point Probe.
大脚板Using the Model 4200-SCS to Make Four-Point Collinear Probe Measurements
The Model 4200-SCS can make four-point collinear probe measurements using either three or four SMUs (source-measure units). When using three SMUs, all three SMUs are t to Current Bias (voltmeter unit). However, one SMU will source current and the other two will be ud to measure the voltage difference between the two inner probes. An example of how this can be t up with the Model 4200-SCS is shown in Figure 2. One SMU (SMU1) and the GNDU (ground unit) are ud to source current between the outer two probes. Two other SMUs (SMU2 and SMU3) are ud to measure the voltage drop between the two inner probes.
This four-point probe measurement can be t up in the Model 4200-SCS’s Keithley Interactive Test Environment (KITE) by using the following steps: 1. Begin a new project. 2. Create a new sub-site plan.
3. Add a new device for a generic or custom-designed four-terminal device.
4. Add an ITM (Interactive Test Module) and t up the SMUs as shown in Figure 2. Make sure that the Current Measurement
option is checked for SMU1, which is t up as a Current Bias. This current source value will be ud to calculate the resistivity. Click the check boxes for the Voltage Measure options for SMU2 and SMU3. Set the source range for SMU2 and SMU3 to 1nA. In gen-eral, the current source range determines the input impedance of the SMU as a voltmeter. The lower the current range is, the higher the input impedance will be.
5. Change the mode to “Sampling.”
Figure 1. Four-Point Collinear Probe Resistivity Configuration
6. In the ITM Timing menu, choo the number of samples to take.
If the Timestamp Enabled option is lected, graphs of voltage vs.
time can be plotted and ud to determine the ttling time.
7. In the Formulator menu, type in the formula for the sheet resis-
tivity. First, calculate the voltage difference between SMU2 (BV)
and SMU3 (CV). This is VDIFF=BV-CV. For the sheet resistivity
(ohms/square), RESISTIVITY=4.532*(VDIFF/AI). To determine the volume resistivity, multiply the sheet resistivity by the thickness of
the sample in centimeters (cm).
8. After connecting the four-point probe to the wafer, run the pro-
gram by clicking on the green arrow key. The final resistivity value will be shown in the RESISTIVITY column of the data sheet. Example Application for Making
Four-Point Collinear Probe Measurements with the Model 4200-SCS
An example four-point probe resistivity application has already been cre-
ated for the Model 4200-SCS. This project was developed using the steps described previously. The name of the project is FourPtProbe. A screen capture of the project is shown in Figure 3. A custom-designed device structure is ud to illustrate the four-point measurement.
In this project, three SMUs and the GNDU (ground unit) are ud to measure the resistivity. For SMU1, enter an appropriate test current, depending on the resistivity of the sample. The green arrow key is ud to execute the project. Under the Sheet tab, the resistivity will appear.
A correction factor may be applied by using the Formulator menu or by entering a formula on the Calc sheet within the Sheet tab.
van der Pauw Resistivity
Measurement Method
痛苦的成语
The van der Pauw method involves applying a current and measuring voltage using four small contacts on the circumference of a flat, arbi-trarily shaped sample of uniform thickness. This method is particularly uful for measuring very small samples becau geometric spacing of the contacts is unimportant. Effects due to a sample’s size, which is the approximate probe spacing, are irrelevant.
Using this method, the resistivity can be derived from a total of eight measurements that are made around the periphery of the sample with the configurations shown in Figure 4.
Once all the voltage measurements are taken, two values of resistiv-ity, ρA and ρB, are derived as fo
llows:
π(V1 – V2 + V3 – V4)
ρA = ___f A t s_______________
ln 2 4I
π(V5 – V6 + V7 – V8)
ρB = ___f B t s_______________
ln 2 4I
where: ρA and ρB are volume resistivities in ohm-cm;国家安全手抄报
t s is the sample thickness in cm;
V1–V8 reprents the voltages measured by the
voltmeter;
I is the current through the sample in amperes;
f A and f B are geometrical factors bad on sample symmetry.
They are related to the two resistance ratios Q A and Q B as
Figure 2. SMU Designation for Four-Point Collinear Probe Measurement
Figure 3. Screen Capture of Model 4200-SCS with the Four-Point Probe Project
shown in the following equations (f A = f B = 1 for perfect sym-metry).
Q A and Q B are calculated using the measured voltages as follows: V 1 – V 2 Q A = ______ V 3 – V 4 V 5 – V 6 Q B = ______
V 7 – V 8
Also, Q and f are related as follows: Q – 1 f e 0.693/f _____
王莽岭景区简介= _____ arc cosh _____
Q + 1 0.693 ( 2 )
A plot of this function is shown in Figure 5. The value of f can be found from this plot once Q has been calculated.
Once ρA and ρB are known, the average resistivity (ρAVG ) can be determined as follows: ρA + ρB ρAVG = _______
2
Test Equipment
The electrical measurements for determining van der Pauw resistivity require a current source and a voltmeter. To automate measurements, one might typically u a programmable switch to switch the current source and the voltmeter to all sides of the sample. However, the Model 4200-SCS is more efficient than this.
老式月饼
The Model 4200-SCS with four SMUs and four preamps (for high resistance measurements) is an ideal solution for measuring van der Pauw resistivity, and should enable measurements of resistances greater than 1012Ω. Since each SMU can be configured as a current source or as a voltmeter, no external switching is required, thus eliminating leakage and offts errors caud by mechanical switches. This removes the need for additional instruments and programming.
For high resistance materials, a current source that can output very small current with a high output impedance is necessary. A differential
electrometer with high input impedance is required to minimize load-ing effects on the sample. On the lowest current source ranges (1pA and 10pA) of the Model 4200-SCS, the input resistance of the voltmeter is >1016Ω.
Using the Model 4200-SCS to Measure Resistivity with the van der Pauw Method
Each terminal of the sample is connected to one SMU, so a Model 4200-SCS with four SMUs is required. A test project with four ITMs (Interactive Test Modules) is written using a generic or custom-designed four-termi-nal device. Each ITM is a different measurement tup. An example of how the four SMUs are configured in the four ITMs is shown in Figure 6. For each ITM, three of the SMUs ar
e configured as a current bias and a voltmeter (VMU). One of the SMUs applies the test current and
悬针篆
Figure 4. van der Pauw Resistivity Conventions
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0.50.60.70.8
0.91.0Q
f
Figure 5. Plot of f vs. Q
the other two SMUs are ud as high impedance voltmeters with a test current of zero amps on a low current range (typically 1nA range). The fourth SMU is t to common. The voltage difference must be calculated between the two SMUs t up as high impedance voltmeters. This mea-surement tup is duplicated around the sample, with each of the four SMUs changing functions in each of the four ITMs.
Basic Procedure for Setting up a New Project for Measuring van der Pauw Resistivity:
1. Create a new project.
2. Create a new sub-site plan.
3. Add a new device plan. It must be either a generic or custom-
designed four-terminal device.
4. Four ITMs will need to be created. In each ITM, one SMU will
be configured as the current source using the current list sweep
function, two SMUs will be configured as voltmeters, and one will be configured as a common. Here is an example tup for a high
resistance sample:
Terminal A – SMU1: Set to a two-point Current List Sweep. Enter both the positive and negative values of the appropriate source
current. Enter the Compliance level and u the Best Fixed source range. Averaging voltage measurements (from SMU2 and SMU3)
taken at both a positive and negative test current will correct for
voltage offts in the circuit.
Terminal B – SMU2: Set to Current Bias (VMU) with a test cur-
rent of 0A. Set the appropriate compliance voltage, and check the
Measure Voltage box (VB). Even though 0A will be output, lect
an appropriate current source range. The input impedance of the
voltmeter is directly related to the current source range. The lower the current source range is, the higher the input impedance will
be. However, the lower the current source range, the slower the
measurement time will be. For most applications, the 1nA range
may be ud. However, for very high resistance measurements, u
a lower current range.
Terminal C – SMU3: Set up the same as Terminal B.
Terminal D – SMU4: Set the Forcing Function to Common.
In this example, the current will be sourced between Terminals
A and D (SMU1 to SMU4). SMU2 will measure the voltage from
Terminal B to Terminal D. SMU3 will measure the voltage from
Terminal C to Terminal D.
U the Formulator to calculate the voltage difference between
SMU2 and SMU3 for both the positive and negative test current.
This can be done using an equation such as V23DIFF=VB-VC. Take the absolute values of the numbers (from both the positive and
negative test current) using the ABS function with an equation
such as V23ABS=ABS(V23DIFF). Then average the two voltage
difference values using the AVG function with an equation, such as V23=AVG(ABSV23). In the Output Values window, check the average voltage (V23) so that it is nt to the sub-site data sheet, where it will be ud in the resistivity calculation. The magnitude of the current source must also be nt to the sub-site data sheet, so click that check box (I1) as well.
藕断丝连简谱
Using four ITMs, this same procedure will need to be repeated around all sides of the sample as shown previously in Figure 4.
The average voltages from each ITM are then ud to calculate the resistivity on the sub-site Calc sheet. A diagram showing how the
SMUs are tup in each ITM is shown in Figure 6.
Current Bias (+)Voltmeter Current Bias (–)Voltmeter
ITM NAME:
I1_V23
Voltmeter Voltmeter Voltmeter Voltmeter
ITM NAME:
I4_V12
Voltmeter Common Voltmeter Common
ITM NAME:
I3_V41
Common Current Bias (+)Common Current Bias (–)
ITM NAME:
I2_V34
Figure 6. SMU Configurations for van der Pauw Measurements
5. To calculate the resistivity in the sub-site level, open up the sub-site plan. In the Subsite Setup tab, lect Cycle Mode and enter “1” in the Number of Cycles field. The Output Values (voltage differ-ences and test current) will appear on the data sheet at the sub-site level. The resistivity is calculated on the Calc sheet from the cell references on the Data sheet. The thickness, coefficients, and correction factors are also input on the Calc sheet for the resistiv-ity equation.
Example van der Pauw Application Using the Model 4200-SCS
An example van der Pauw resistivity project, vdp_resistivity , has been created for KITE 5.0 or higher versions. This project follows the example listed previously. A window of this project is shown in Figure 7
.
Figure 7. Screen Capture of van der Pauw Resistivity Application on
Model 4200-SCS
This project has been written following the procedure previously described in this application note. Notice that a van der Pauw device structure is shown in the definition window. The ur will need to adjust the source current, the thickness of the material, and the ttling time of the measurement.
Adjusting the Source Current
The source current value will need to be modified according to the expected sample resistance. Adjust the current so that the voltage dif-ference will not exceed 25mV (approximately). In each of the four ITMs (I2_V34, I3_V41, I4_V12, I1_V23), enter both polarities of the test cur-rent. The same magnitude must be ud for each ITM.
Determining the Settling Time
For high resistance samples, it will be necessary to determine the ttling time of the measurement. This can be accomplished by sourcing current into two terminals of the sample and measuring the voltage difference between the other two terminals. The ttling time can be determined by graphing
the voltage difference versus the time of the measurement. Using the Model 4200-SCS, the voltage versus time graph can be easily created by modifying one of the ITMs described previously. In the
Timing menu, take a few hundred or so readings with a sweep time of one cond. Make sure that the Timestamp Enabled box is checked. After the readings are done, plot the voltage difference versus time on the graph. (You can choo the parameters to graph by right-clicking on the graph). The ttling time is determined from the graph. A timing graph of a very high resistance material is shown in Figure 8.
Determine the ttling time by visually inspecting the voltage dif-ference vs. time graph. Once the ttling time has been determined, u this time as the Sweep Delay (in the Timing menu) for the four resistivity measurement ITMs listed previously. This ttling time procedure will need to be repeated for different materials; however, it is not necessary
for low resistance materials since they have a short ttling time.
Figure 8. Voltage vs. Time Graph of Very High Resistance Sample
Inputting the Thickness of the Sample
The thickness of the material will also need to be entered into the Calc sheet in the sub-site level. Select the sub-site “vdp-test.” Go to the Subsite Data tab. It contains the output values of the voltage differences and the test current. From the Calc Sheet tab, the thickness can be adjusted. The default thickness is 1cm. If necessary, a correction factor can also be applied to the resistivity equation.
Running the Project
The “vdp_resistivity” project must be run at the “vdp-test” sub-site level. Make sure that all boxes in the Project/View are checked and highlight “vdp-test.” Execute the project by using the sub-site run button (circular arrow). Each time the test is run, the subsite data is updated. The voltage differences from each of the four ITMs (I2_V34, I3_V41, I4_V12, I1_V23) will appear in the Subsite Data “vdp-device” sheet. The resistivity will appear in the Subsite Data “Calc” sheet as shown in Figure 9.
Hall Voltage Measurements
Hall effect measurements are important to miconductor material char-acterization becau from the Hall voltage, the conductivity type, carrier density, and mobility can be derived. With an applied magnetic field, the Hall voltage can be measured using the configurations shown in Figure 10.
