Impurity Content of a Semiconductor Crystal Experiment F1/3
Contents Impurity Content of a Semiconductor Crystal... 2 1 Aims... 2 Background... 3 Doping... 3 Crystal Growth... 4 The 4-point probe... 6 The P-N Tester... 7 Results... 8 Silicon Slice Resistivity... 8 Silicon Slice p-n type... 8 Silicon Crystal Resistivity... 8 Silicon Crystal Mass Ratio... 9 Data Analysis... 10
Impurity Content of a Semiconductor Crystal Aims 1. To become familiar with the production of single crystals of Silicon from the melt. 2 2. To study the relationship between the conductivity of a semiconductor and the dopant concentration. 3. To learn the theory and use of the 4 point probe and p-n tester. 4. Determine the resistivity of a sample of Silicon. 5. Determine the p-n characteristics of a Silicon sample. The object of this experiment is to demonstrate just how pure a silicon crystal must be in order for it to be suitable for device production. The concentration of impurities is so low that conventional chemical analysis is impractical and it is only the electrical properties of the crystal that can tell us anything of it quality. [1]
Background Doping Valence electrons in Silicon are held to the atom by a strong attractive force. At room temperature, only several electrons in an entire Silicon crystal would have enough energy in order to break free from their corresponding atoms to become free electrons. This is why silicon is not a good conductor of electricity. 3 In a Silicon crystal, each Silicon atom is bonded to 4 others, using the 4 valence electrons in its outer shell. However, there will always be a small number of free electrons, as the lattice is broken down by heat energy. Only at absolute zero (0K) would there be no free electrons. Semiconductors are known to conduct electrical current in two ways. Electrons that have sufficient thermal energy to break from their atom (free electrons) are known as conduction electrons. As they are free, the easily move through the semiconductor when a potential difference is applied to it. This process in itself is responsible for the second method of electron movement. In the covalent structure, every time an electron escapes to the conduction band, a hole is left in the valence band where it used to be. Electrons in neighbouring covalent bonds can move to nearby holes using a relatively tiny amount of energy. This means that in practise, the holes in the covalent lattice are seen to move in the opposite direction to electron flow. This is known as the hole current. Pure semiconductors are known to be poor conductors. However, their conductivity can be drastically improved by the addition of impurities into the crystal lattice. This controlled addition is known as doping, and increases the number of current carriers available inside the lattice. P-Type doping involves doping the pure semiconductor with atoms that have a valence number of 3. This means that the doping atoms only have 3 electrons in their outer shell, so when bonded in the covalent lattice to 4 Silicon (or Germanium) atoms, a hole results, as it does not have enough electrons to complete the bonds. Atoms of this type are called acceptor atoms. These holes do not have a matching free electron in the crystal, therefore this process, in a controlled manor, can be used to increase the number of holes and therefore the conductivity of the semiconductor due to increasing hole current. In N-type doping the semiconductor is doped with atoms that have a valence number of 5. When these doping atoms are introduced to the semiconductor lattice, they form covalent bonds with 4 adjacent Silicon (or Germanium) atoms. As each bond uses 1 of the valence electrons, there is 1 extra electron. This electron is not involved in the bonding and therefore enters the conduction band. The number of conduction electrons added can be carefully controlled in the doping process. A conduction electron created from the doping process does not have a matching electron hole, as it is provided by the donor atom. [2] Please see Diode Characteristics for more information on P-N doping.
Crystal Growth The Silicon crystal used in this experiment was pre-prepared using the following process: 4 A mass of Silicon was melted in a suitable crucible. A single crystal seed was dipped into the molten mass and slowly withdrawn. As it is withdrawn a much larger crystal grows. The crystal was allowed to cool down and was prepared for the experiment by marking the testing points along it. It is known that the crystal will not have uniform conductivity (and therefore resistivity) along its entire length because the impurities that produce the conductivity in the semiconductor will have a higher solubility in molten Silicon than in the solid crystal. Understanding this, the prepared crystal will have a higher conductivity at the lower regions because as it grows, more and more impurities are concentrated in the molten melt. The way in which an impurity is distributed along the length of the crystal is governed by the ratio of the impurity in the solid phase to that in the molten phase. It can be shown that there is a relationship between k (the segregation coefficient) and the impurity content at any point along the crystal. (1) Where M is the mass of the grown crystal N 0 is the initial impurity concentration in M 0 N I is the concentration of impurity in crystal region grown at any time t It can be safely assumed for experimental purposes, that there are only 2 impurities in the melt, one p-type impurity and one n-type impurity. Equation 1 applies to both concentration of donors and acceptors in the silicon crystal. It is also known that the conductivity of a semiconductor device can be written as (2) Where N Di is the concentration of the donor (n-type) N Ai is the concentration of the acceptor (p-type) is the electron mobility
q is the electronic charge. If equations 1 and 2 are combined and written in terms of a straight line graph: 5 (3) Where And As can be seen above, the expressions only involve resistivity of the sample and the volume ratio. All other terms are constants.
The 4-point probe It is important when measuring the resistivity of a sample that ever step is taken to eliminate surface resistance between the sample and the measurement equipment. A four point probe can be used to measure resistivity accurately. The two outer pins passes a small current though the sample. This current, sets up a potential difference across the pins. The two inner probes are then connected to a voltmeter of extremely high resistance and voltage can be measured. The DC current supply means that the magnitude of the current is independent of any contact resistance. 6 To convert the measured current and voltage into a resistivity value it is required to know some information about the sample. In this experiment we have two samples: Silicon Slice Were the thickness of the slice is less than the distance between the pins. (4) Where is the resistivity V is the voltage in volts I is the current in Amperes T is the thickness of the slice in cm Silicon Crystal A different approach is required when the sample thickness is much greater than the distance between the pins. (5) Where S is 0.162 cm All other values are the same as equation 4
The P-N Tester This is a very simple piece of equipment designed to determine if a semiconductor sample is predominantly p or n type. 7 It consists of 2 probes, one of which is heated to a high temperature. Once sufficiently hot, both probes are placed on the sample about 1cm apart. The free charge carriers near the hot probe diffuse away towards the cold probe. It there is an excess of electrons in the semiconductor (it is n-type) then the potential of the cold probe will be negative with respects to the hot. The opposite is true for p-type, as there are excess holes.
Resistivity/ohmcm Impurity Content of a Semiconductor Crystal Results Silicon Slice Resistivity Inital V/mV I/uA Voltage/mV Voltage Difference/mV (V/I)/ohms T/cm Resistivity/ohmcm 2.15 2400 0.20 2.35 0.98 0.12 0.53 8 Were V and I were measured using a voltmeter and ammeter. Initial voltage was the measured voltage across the sample when no current was flowing. Resistivity was calculated using equation (4). Silicon Slice p-n type This experiment was carried out on 12/03/12, and the sample was found to be clearly p type by the p-n tester as described in the P-N Tester section above. Silicon Crystal Resistivity Number V/mV I/uA Inital Voltage/mV Voltage Difference/mV (V/I)/ohms 2pi S/cm Resistivity/cmohms 1 1.80 120.00 0.20 2.00 16.67 6.28 0.13 13.93 2 2.60 150.00 0.20 2.80 18.67 6.28 0.13 15.60 3 2.50 133.00 0.20 2.70 20.30 6.28 0.13 16.97 4 5.00 250.00 0.20 5.20 20.80 6.28 0.13 17.38 5 2.80 135.00 0.20 3.00 22.22 6.28 0.13 18.57 6 1.90 89.00 0.20 2.10 23.60 6.28 0.13 19.72 7 1.80 80.00 0.20 2.00 25.00 6.28 0.13 20.89 Were V and I were measured using a voltmeter and ammeter. Initial voltage was the measured voltage across the sample when no current was flowing. Resistivity was calculated using equation (5). 30 20 10 0 Resistivity 0 2 4 6 8 Point on Crystal (1 is bottom) Resistivity Figure 1 This graph shows the measured resistivity at each point along the Silicon Crystal. It is worth noting that point 1 is at the bottom. Notice that as the readings move to the top of the crystal, resistivity increases linearly.
Mass Ratio % Impurity Content of a Semiconductor Crystal Silicon Crystal Mass Ratio Number V0/ml V/ml Mass Ratio 1 15.00 4.00 73.33 2 15.00 5.00 66.67 3 15.00 7.00 53.33 4 15.00 8.00 46.67 5 15.00 9.00 40.00 6 15.00 10.00 33.33 7 15.00 12.50 16.67 Were V0 is the volume of the crystal, V is the volume of the crystal up to the point numbered and the Mass Ratio is defined as 9 (6) Mass Ratio 80 60 40 20 Mass Ratio 0 0 2 4 6 8 Point on Crystal (1 is bottom) Figure 2 Clearly showing that there is a decrease in Mass Ratio as the points move up the crystal.
Yσ/10^14 Impurity Content of a Semiconductor Crystal Data Analysis Number V0/ml V/ml Mass Ratio X Y x10^16 ρ/ohmcm σ(1/ρ) Yσ/10^14 1 15.00 4.00 73.33 0.767 0.4647 13.93 0.07179 3.3360 2 15.00 5.00 66.67 0.691 0.4789 15.60 0.06410 3.0699 3 15.00 7.00 53.33 0.575 0.5050 16.97 0.05893 2.9758 4 15.00 8.00 46.67 0.540 0.5141 17.38 0.05754 2.9580 5 15.00 9.00 40.00 0.506 0.5238 18.57 0.05385 2.8207 6 15.00 10.00 33.33 0.478 0.5328 19.72 0.05071 2.7018 7 15.00 12.50 16.67 0.428 0.5501 20.89 0.04787 2.6333 This table is a summary of the key results from the tables above, as well as the values referenced from the table in the red book for X and Y values. Plotting Yσ against X gives the following graph 10 Impurity Analysis 8 7 6 5 4 3 2 1 0 X -2-1 -1 0 1 2 3-2 Yσ/10^14 Linear (Yσ/10^14) Figure 3 Will be used to calculate the impurities in the sample. As you can see, the result values only cover a very small sample therefore a best fit line has been drawn to allow readings to be taken. Using equation (3): The n-type concentration is the gradient of this graph The p-type concentration is the y-intercept of this graph Figure 3 has a gradient of 1.9105 and a y-intercept of 1.84. However, the graph has a scale factor applied to the Y-axis meaning the gradient must be multiplied by 10^14 to get the true value.