Aug 12, 2009 - This project focuses on the use of the Van der Pauw technique to measure the resistivity of ... be discussed. Chap. 4 will examine calibration testing of the system as well ... erative algorithm written in Python. Once the final ...
Electrical Characterization of Thin Solid Films Sebastian Requena August 12, 2009
Abstract The goal of this project is to characterize the electrical properties of thin solid films for the development of nano and microelectronics. The Van der Pauw technique is used for the measurement of the resistivity of bulk material samples of arbitrary shapes. This system utilizes multiple voltage and current measurements in rapid succession to determine the resistivity of a sample. By understanding these fundamental material properties we are able to better understand how these materials behave on a micro and nano scale.
Contents 1 Introduction 1.1 Context and motivation . . . . . . . . . . . . . . . . . . . . . 1.2 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2 2
2 Measurements and Equations 2.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 3 4 4
3 Experimental Procedure 3.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . 3.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 5 6 7
4 Data and Results 4.1 Calibration Testing 4.2 Porous Silicon . . . 4.3 Results . . . . . . . 4.4 Future Work . . . 4.5 Acknowledgements
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
Acknowledgements
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
8 8 8 10 10 10 10
1
Chapter 1
Introduction This project focuses on the use of the Van der Pauw technique to measure the resistivity of arbitrarily shaped thin films. The typical four point probe technique is unable to measure non-rectangular thin film geometry and is destructive to the sample. The Van der Pauw technique addresses these issues as well as increasing sensitiviy and reliability of measurements.
1.1
Context and motivation
Electrical characterization is a critical area in all technology development. The use of electrical characterization is ubiquitous in all major research institutions. It is used in all stages of development including manufacturing, process monitoring, and fabrication. The Van der Pauw technique allows for the measurement of non-rectangular geometries. The technique is mostly non-destructive in that the probes placed on the sample will scratch the sample surface and deposit small amounts of metal. This makes the sample unsuitable for fabrication, but allows it to be used in a variety of other characterization techniques. It increases accuracy by only requiring the thickness of the sample to be known. The technique is effective for high resistivity measurement up to 109 Ω-cm.
1.2
Contents
The main body of this report is divided as follows. Chap. 2 will discuss the measurements and equations used for the Van der Pauw technique. Chap. 3 will explain the setup and experimental procedure used. Additionally, difficulties in the low level measurements will be discussed. Chap. 4 will examine calibration testing of the system as well as the characterization of porous silicon. Chap 4. will end with a discussion of the data results, Future work, and plans for the system.
2
Chapter 2
Measurements and Equations This chapter will outline the measurements used in the Van der Pauw technique. The Van der Pauw equation and related equations will be shown, with explanations of their use. The technique uses a basic application of voltage and current measurements to solve for resistance. As these resistances are found the sheet resistance is solved for through the use of the Van der Pauw equation
2.1
Measurements
Eight sequential voltage and current measurements are required in the Van der Pauw technique. These measurements are best understood with a diagram.
Figure 2.1: This is an example sample measurement. The probes are placed on the edge of the sample at equal distances apart if possible. Current is pushed from probe 1 to probe 2. Voltage is then measured 3
from probes 3 and 4. Resistance is solved for using Ohm’s Law. This value would then be called R12 . The current is then reversed and pushed throught 2 to 1. The voltage measurement then repeated. This value of resistance would be called R21 . This process is then repeated for each edge of the sample. The reversal of the current polarity is an important part of eliminating thermally generated EMFs. Since the probes used are gold plated tungsten and the wires are copper, a temperature difference in the metals creates a voltage potential. When the voltages are averaged the thermally generated EMFs cancel each other out.
2.2
Equations
Once data acquisition is completed, Ohm’s Law is used to find the resistance of each measurement R = V /I. The Van der Pauw equation is based on Reciprocity Theorem which requires: R12 + R21 = R34 + R43
(2.1)
R13 + R31 = R24 + R42
(2.2)
If these aren’t true within 3% then the measurements must be repeated. Once these conditions have been met we may solve for two sheet resistances given by: R12 + R21 + R34 + R43 Ra = (2.3) 4 R13 + R31 + R24 + R42 Rb = (2.4) 4 These two values of sheet resistance are then placed in the Van der Pauw equation which is then solved for Rs which will be the final sheet resistance. 1 = exp(−π
Rb Ra ) + exp(−π ) Rs Rs
(2.5)
This equation is solved using Newton Raphson root finding via an iterative algorithm written in Python. Once the final sheet resistance Rs is found the resistivity is solved for using ρ = Rs d where d is the thickness of the sample in centimeters. This will give the resisitivity in units of Ω-cm.
2.3
Summary
While the equations are simple in application. Many precaution must be taken in the data acquisition. The reciprocity theorem requires symmetric values for resistance. There are many aspects of low level electrical measurements that must be observed, as in the case of thermally generated EMFs. The next section will deal with the experimental procedure of the Van der Pauw technique. 4
Chapter 3
Experimental Procedure The procedure used for the Van der Pauw system will be outlined in the chapter. This will deal with the sample cleaning and preparation as well as the probe preparation steps. The main focus of this area is to minimize the uncertainty due to the non-ideal nature of the probes and sample, and how to minimize various sources of error in the electrical measurements. Here we deal firstly with the sample preparation and cleaning, as well as the probe preaparation and cleaning. Then we will examine the effects of the assumptions of the Van der Pauw equation, and how uncertainty is minimized. Finally, the procedure and use of the VAN DER PAUW.vi file.
3.1
Sample Preparation
This procedure will remain widely the same for most thin films being prepared for the Van der Pauw system. If the sample thickness is unknown then it is measured using micrometers. Multiple measurements are taken and then averaged. This is usually the largest source of uncertainty. If it is necessary, the probes should be cleaned. The probes are cleaned by wiping them with acetone and then methanol. The probes are then dipped in dilute HCl and allowed to drip dry with the points facing down. This will preserve the points of the tips. The Van der Pauw equation assumes infinitely small points from the probes which is why it is necessary to use 10 micron tipped probes. Cleaning the sample will remove any dirt or particles from the surface of the sample which will alter the surface resistivity. The sample must be handled only using gloves so as not to cause any skin oils to come in contact with the sample. The sample is cleaned by placing a drop of acetone on the surface of the sample and wiping it of with an optical lens wipe. A drop of the methanol is then placed on the sample and it is wiped off with an optical lens wipe. This is repeated until there are no blemish or marks from dirt or grease on the sample. 5
Small contacts must be prepared on the sample. This is to eliminate the creation of metal-oxide-metal diodes, or Schottky diodes. Small amounts of silver paste are placed where the probes will make contact with the sample. As little paste as possible is used and then allowed to dry.
Figure 3.2: An example probe orientation that still had good reciprocal readings even though the probes were not equal distances apart.
Figure 3.1: A sample prepared on the probe stage.
The sample is then mounted to the micrometer stage. The sample is placed on a glass slide and then on the brass stage so as not to allow the brass stage to alter the voltage and current readings as seen in Fig. 3.1. Using the stereo microscope, the probes are placed on the edge of the sample surface. The probes are carefully placed on the sample so as not to scratch the sample surface. The probes are placed equal distances apart from each other if possible. This minimizes problems with the reciprocal readings, but isn’t neccessary to achieve good reciprocal readings as noted in Fig.3.2.
3.2
Procedure
Once the sample is properly prepared the file VAN DER PAUW.vi is run one trial at a low current source, (usually around 100µA.) Once this is done, the values Ra and Rb are recorded. The highest resistance of these two values is used in the equation P = I 2 R setting P as .001W. Using the previous value for R, the current I is solved for. This value for I is the highest current source setting that can be used without exceeding 1mW power dissapation and thus increasing the temperature of the sample. The current source is set as near to this value as possible and the number of trials in the Van der Pauw .vi is set to 10. The values for resistivity as well as uncertainty are recorded in the lab notebook.
6
3.3
Summary
The Van der Pauw procedure minimizes sources of error and uncertainty by using a variety of careful lab procedures and techniques. These must be followed carefully in order for good data acquisition. Calibration testing and sample data using this procedure will be discussed in the next chapter.
7
Chapter 4
Data and Results Sample calibration data as well as the characterization of porous silicon will be examined in the chapter. The data will follow with a complete discussion of the results as well as future work for the system.
4.1
Calibration Testing
To test the system, doped crystalline silicon wafers with known values of resistivity were used. Preparation and procedures were followed as in the previous section. The below table is a collection of the data that was collected. Sample 1 2 3 4
Type n p n n
Dopant Arsenic Boron Phos Phos
Accepted 15-17 Ω-cm .014-.022 Ω-cm 1-10 Ω-cm 250-330 Ω-cm
Measured 16.7 Ω-cm .019 Ω-cm 4.8 Ω-cm 242 Ω-cm
Table 4.1: Sample calibration data. This data shows reasonable values of resistivity with the exception of sample 4. The sample was re-tested with different probe orientations and still gave unusually low values for resistivity. The measured values is within 6% of the acceptable range. However, further testing of higher resistivities is required.
4.2
Porous Silicon
The object of this experiment is to measure the resistivity of porous silicon. Since porous silicon contain an increased number of voids within the material there should be fewer electrical pathways for electrons to travel. This
8
should lead to an increase in electrical resistivity. An unprocessed sample was first characterized. The sample was SiO2 of the (111) orientation. It is n-type Antimony doped. The sample’s resistivity was measured to be .0061 Ω-cm. The manufacturer gave values of resistivity to be .006-.008 Ωcm. This measured value fell within the acceptable range. The sample was then preprocessed with KOH. This is to rough up the sample surface so it will better react with HF. While this does increase surface roughness, the electrical properties of the sample should not change. The resistivity was re-measured to be .0062 Ω-cm. The sample was then processed with HF and KIO3 . A visible porous film developed as visible in Fig. 4.1. The sample’s
Figure 4.1: Sample processed with KIO3 measured resistivity was .0077 Ω-cm. A second sample was processed with F eCl3 . This sample has a different pore distribution as visible in Fig. 4.2. The measured resistivity was .0084 Ω-cm.
4.3
Results
A small increase in resistivity was apparent in both processed samples. However, an increase on the order of two to three magnitudes was expected. The reason for the lower than expected resistivity is apparent after conducting ellipsometric characterization. The measured thickness for the porous film is only 320˚ A. Current will briefly pass through the porous upper film and then travel through the much lower resistivity of the substrate. Characterization suggests a gradient of decreasing porosity as the substrate is approached. While an increase of resistivity is evident, no quantitative measurement may be taken at this time due to the non-uniform pore distribution and influence from the substrate.
9
Figure 4.2: Sample processed with F eCl3
4.4
Future Work
Plans to measure the bulk carrier density of materials have begun. By using a similar four point measurement it is possible to measure the sheet carrier density of thin films. This measurement is complementary to resistivity because it allows for the Hall Mobility of materials to be solved for. A process to either manufacture porous silicon on a glass substrate or to seperate the porous film from the substrate are also being investigated. Samples of porous silicon will continue to be characterized through various means. The processing techniques are also being refined. The use of a cryostat will allow for temperature dependence studies of materials. Resistivity is a temperature dependent value and creating temperature vs. resistivity graphs would allows for a more complete understanding of the fundamental properties of materials.
4.5
Acknowledgements
I would like to thank Dr. Sauncy for the time she has invested in me and this project. As well as the ASU Physics department and the ASU Research Enhancement program. I would also like to thank the National Science Foundation for their generous contributions to this project.
10
