Electronic Properties of Semiconductors - Lab Report Example

Lab report on electronic properties of semiconductors Name Subject Institution Instructor Date Abstract Semiconductors such as germanium would have voltage across them when the temperature rises from about 150 to 383K. The mechanism of conduction is affected by various factors such as the magnetoresistance and Hall Effect. Moreover, the effects of the impurities, magnetic fields and temperature also have an impact in the conduction of semiconductors. The properties of the semiconductors are dependent on the Hall Effect  and the resistivity. This paper elucidates the mobility of the charge carriers and the discrimination of the power law in the intrinsic and extrinsic region as well as, the power law in the magnetoresistance (B). The electronic property of semiconductors is analyzed in this lab report with the focus on germanium crystal. Introduction The knowledge of quantum physics explains the phenomenon in which current tends to flow in a unique direction from the expected norm. These studies have led to the development of solid state physics that, further explains these happenings. Hall noted that, whenever there is a current and a magnetic field in the crystal, there would be voltage across it. The knowledge about resistivity, of a given semiconductor has developed the knowledge of Hall Effect that describes the properties such as extrinsic and intrinsic conduction of mechanism and the mobility of the charge carriers. The mystery behind the conduction of materials was discovered way back in 1879 (Harker, 2010). He asserted that, voltage would appear across the crystals when they are subjected to a magnetic field and current. The aspect of semi conductivity and the resistivity has led to the development quantum physics on particulate matter. On the other hand, the effect of magnetoresistance relies on the effect of Lorentz force. If the modulus of the speed is kept at voltage say vd, it aids in calculating the relative distance travelled The application of Ohms law governs the conduction of materials when there is an application of electric field. It is governed by the equation  Where J is the current density is the conductivity. Essentially, semiconductors have an energy gap of 1 eV. When the temperatures are low, they are poor conductors. However, when the temperatures rise gradually, they start conducting charges. This is because there is a population of electrons in the conduction band. Semiconductors posses both the positive and negative charge carriers. The conduction is by aid of holes which are the positively charged electrons brought about by deficiency in the electron deficient site. Pure crystals have equal number of positively and negatively charged electrons. This leads to intrinsic conduction. This type of conduction has a high energy approximation of approximately E>> This is further explained in the Boltzmann distribution. Whereby n Inherently, the conduction of extrinsic semiconductors is due to the doping that exists. There exists a donor impurity that lies below the conduction band and plays the role of donating electrons (Kasap, 2001). This type of semiconductor would be known as an n type semiconductor. When the acceptor atoms are added to a particular crystal, the semiconductor is termed as p type semiconductor. Due to these impurities, the symmetry of the charge carriers is lost. Germanium has a separation of approximately, 0.01eV having a smaller value of KBT. For a doped semiconductor, the temperature dependence of electron concentration can be seen in graph 1. At very low temperatures (large 1/T), negligible intrinsic electron-hole-pairs (EHPs) exist (ni is very small), and the donor electrons are bound to the donor atoms. This is termed as the ionization process or the freeze-out) region. An increase in temperature causes increased ionization to occur (Varpula, 2009). At about 100K, all of the donor atoms are ionized, at which point the carrier concentration is determined by doping. The region where every available dopant has been ionized is called the extrinsic (or saturation) region. In this region, an increase in temperature produces no increase in carrier concentration. This is the region where, , and . At high temperatures, the thermally generated intrinsic carriers outnumber the dopants (ni>). In this intrinsic region, carrier concentration increases when temperature increases. Apparatus: Ge Slab Cryostat Liquid Nitrogen Resistance Heater Stainless steel rod Exchange Gas (Ar) Specimen Dipstick Procedures 1. The setting is mounted on the cryostat while its temperature is adjusted from 80K to 430K 2. Heat the setting using a heat sink 3. When the pressure drops to about 20 millitorr, pure N2 at 500 psi is passed to purge the system for about 10 minutes. 4. Connect the two leads at one end of Ge sample are connected to terminals 1 & 4 of the terminal box, the other two leads at the other end of the sample to terminals 2 & 3. 5. Measure the resistance of the sample connect 1 & 4 to high input terminals of the resistance meter with 2 & 3 connected to the low input terminals of the meter. 6. Increase the, N2 pressure is increased to 1800 psi when the pressure in the system is close to 20 millitorr. 7. Leave the rotary pump connected to the exchange-gas space and continue the measurements at intervals of 10oC or so up to 160oC Temperature is again set to 100K and resistance recorded. 8. Gas flow is stopped(Main valve of N2 cylinder is also closed) Fig 1 Fig 1 Experiment set up Results TC is the thermocouple temperature T = -155° C, TC = -4.77 (mV) Reversed B (-) Forward B (+) VH = -18.37 (mV) -99.24 (mV) IH = 0.040 (A) 0.0034 (A) VX =3.006 (V) 3.006 (V) T = -125° C, TC = -4.05 (mV) Reversed B (-) Forward B (+) VH = -21.64 (mV) -78.55 (mV) IH = 0.024 (A) 0.022 (A) VX =3.006 (V) 3.006 (V) T = -120° C, TC = -3.84 (mV) Reversed B (-) Forward B (+) VH = -21.75 (mV) -76.63 (mV) IH = 0.023 (A) 0.021 (A) VX =3.006 (V) 3.006 (V) T = -110° C, TC = -3.62 (mV) Reversed B (-) Forward B (+) VH = -21.98 (mV) -72.25 (mV) IH = 0.021 (A) 0.019 (A) VX =3.006 (V) 3.006 (V) T = -100° C, TC = -3.35 (mV) Reversed B (-) Forward B (+) VH = -22.12 (mV) -68.67 (mV) IH = 0.019 (A) 0.018 (A) VX =3.006 (V) 3.006 (V) T = -90° C, TC = -3.06 (mV) Reversed B (-) Forward B (+) VH = -22.19 (mV) -66.06 (mV) IH = 0.017 (A) 0.015 (A) VX =3.006 (V) 3.006 (V) T = -80° C, TC = -2.77 (mV) Reversed B (-) Forward B (+) VH = -22.26 (mV) -63.23 (mV) IH = 0.015 (A) 0.014 (A) VX =3.006 (V) 3.006 (V) T = -70° C, TC = -2.46 (mV) Reversed B (-) Forward B (+) VH = -22.27 (mV) -60.42 (mV) IH = 0.014 (A) 0.013 (A) VX =3.006 (V) 3.006 (V) T = -60° C, TC = -2.14 (mV) Reversed B (-) Forward B (+) VH = -22.23 (mV) -58.30 (mV) IH = 0.012 (A) 0.012 (A) VX =3.006 (V) 3.006 (V) T = -50° C, TC = -1.81 (mV) Reversed B (-) Forward B (+) VH = -22.20 (mV) -56.48 (mV) IH = 0.012 (A) 0.011 (A) VX =3.006 (V) 3.006 (V) T = -40° C, TC = -1.47 (mV) Reversed B (-) Forward B (+) VH = -21.92(mV) -54.05 (mV) IH = 0.010 (A) 0.009 (A) VX =3.006 (V) 3.006 (V) T = -30° C, TC = -1.11 (mV) Reversed B (-) Forward B (+) VH = -21.93 (mV) -51.94 (mV) IH = 0.009 (A) 0.009 (A) VX =3.006 (V) 3.006 (V) T = -20° C, TC = -0.75 (mV) Reversed B (-) Forward B (+) VH = -18.23 (mV) -50.86 (mV) IH = 0.010 (A) 0.009 (A) VX =3.006 (V) 3.006 (V) T = -10° C, TC = -0.38 (mV) Reversed B (-) Forward B (+) VH = -16.35 (mV) -46.82 (mV) IH = 0.009 (A) 0.008 (A) VX =3.006 (V) 3.006 (V) T = 0° C, TC = 0 (mV) Reversed B (-) Forward B (+) VH = -15.34 (mV) -44.55 (mV) IH = 0.008 (A) 0.008 (A) VX =3.006 (V) 3.006 (V) T = 10° C, TC = 0.39 (mV) Reversed B (-) Forward B (+) VH = -13.52 (mV) -41.25 (mV) IH = 0.008 (A) 0.008 (A) VX =3.006 (V) 3.006 (V) T = 20° C, TC = 0.79 (mV) Reversed B (-) Forward B (+) VH = -13.22 (mV) -39.42 (mV) IH = 0.008 (A) 0.008 (A) VX =3.006 (V) 3.006 (V) T = 30° C, TC = 1.19 (mV) Reversed B (-) Forward B (+) VH = -12.34 (mV) -37.15 (mV) IH = 0.007 (A) 0.007 (A) VX =3.006 (V) 3.006 (V) T = 40° C, TC = 1.61 (mV) Reversed B (-) Forward B (+) VH = -11.30 (mV) 35.21 (mV) IH = 0.007 (A) 0.006 (A) VX =3.006 (V) 3.006 (V) T = 50° C, TC = 2.03 (mV) Reversed B (-) Forward B (+) VH = -10.62 (mV) -32.88.42 (mV) IH = 0.006 (A) 0.006 (A) VX =3.006 (V) 3.006 (V) T = 60° C, TC = 2.47 (mV) Reversed B (-) Forward B (+) VH = -10.09 (mV) -30.43 (mV) IH = 0.006 (A) 0.005 (A) VX =3.006 (V) 3.006 (V) T = 70° C, TC = 2.91 (mV) Reversed B (-) Forward B (+) VH = -9.44 (mV) -26.87 (mV) IH = 0.006 (A) 0.005 (A) VX =3.006 (V) 3.006 (V) T = 80° C, TC = 3.36 (mV) Reversed B (-) Forward B (+) VH = -10.82 (mV) -22.39 (mV) IH = 0.006 (A) 0.006 (A) VX =3.006 (V) 3.006 (V) T = 90° C, TC =3.81 (mV) Reversed B (-) Forward B (+) VH = -11.76 (mV) -19.72 (mV) IH = 0.007 (A) 0.007 (A) VX =3.006 (V) 3.006 (V) T = 100° C, TC = -4.28 (mV) Reversed B (-) Forward B (+) VH = -28.39 (mV) -31.88 (mV) IH = 0.009 (A) 0.010 (A) VX =3.006 (V) 3.006 (V) T = 110° C, TC = 4.75 (mV) Reversed B (-) Forward B (+) VH = -29.78 (mV) -29.03 (mV) IH = 0.013 (A) 0.013 (A) VX =3.006 (V) 3.006 (V) T = 120° C, TC = 5.23 (mV) Reversed B (-) Forward B (+) VH = -30.07 (mV) -26.44 (mV) IH = 0.018 (A) 0.018 (A) VX =3.006 (V) 3.006 (V) Graph 1 Graph of log hall resistance vs. Log 1/T Graph 1of Hall voltage vs temp Graph 2 Discussion Hall Effect This effect is used to investigate the various types of the carriers, impurity concentration, and the nature of a given dopant. Apparently, current would flow along the x axis whereas; the magnetic field would presume the Z axis. A potential difference is created when the charges are deflected on one side thereby creating a lateral difference. When the semiconductor acts as an n type semiconductor, its equilibrium magnetic forces are compensated by the charges which have accumulated. Assuming the y direction, the hall effect is governed by this equation This is a clear indication that, the nature of the charge carrier is invariant with the simultaneous sign of the velocity and charge. On the other hand considering p type carriers, the Hall Effect presumes a different sign as compared with its electric field. The Hall Effect function presumes the following equation Where  and  are their respective charge nobilities of the electrons and the holes. This surmises that the hall coefficient inversion is applicable in the p type semiconductors. Moreover, the halls coefficient is dependent on temperature. In the experiment, the hall mobility was estimated to be 0.495T from the gradient of the curve. The random error that occurred was minimal and could not be indicated in the graph. Magnetoresistance The effect of magnetic field may also have an impact on the trajectory of the moving charges. This is due to the effect of Lorentz force. If the modulus of the speed is kept at vd, it will aid in calculating the relative distance travelled. This deviation has a minimal impact on the current along the x axis which causes an increase in current. The resistivity by the magnetic field is governed by  The value of Hall coefficient is approximately constant from the graph in the extrinsic conduction zone. This is evident in temperatures that are above 120oC. The halls constant is approximately 1.48104cm3/C. The Hall Effect also experienced a sharp effect in the phase transition. An increase in temperature from about 160K could have led to the evaporation of Nitrogen, which tends to use the ambient thermal energy that inhibits rapid increase in temperature. Error analysis During the experiment there were errors which were either systematic or random errors. Systematic errors were more pronounced that led to deviation from the expected results. The errors could have emanated from the statistical data due to, poor calibration of the equipments, parallax reading or the environmental conditions. Conclusion This experiment has indicated the effect of temperature, magnetic field and impurities in the conduction processes of semiconductors. The measurement of temperature is dependent on the Hall Effect and the resistivity. The experiment had various errors that emanated from the discrepancies of the theoretical models. It is evident that, temperatures that are above absolute values would cause the conduction of semiconductors. This is because; there would be a migration of valence electrons from the adjacent bonds.This gives a clear indication of solid state physics among the crystals. Answers to questions TI. Show that d

=q  Hence J= Taking {(J/E)/nq2}-1=f F=mq/τ T3 Under steady state conditions, and, show that the drift velocity in the i-direction is  and  And from , It follows that T4. The current density of the species in the i-direction is Where is the number per unit volume of the species and is the component of its drift velocity. By solving the differential equations for and under steady state conditions, show that = E=  = p Hence T5. By setting , show that = nqE And  But = Hence i.e. independent of the magnetic field, so there is no transverse magnetoresistance (transverse because is transverse to , defined as T6 With again, show that the Hall constant is = (i) And vd=│ (ii) J=envd (iii) Therefore Hence halls constant T7. With this assumption show that and Note that conductivity is positive so is positive for any species . Setting as before, show that Note that is conventionally written as. Now for a semiconductor lightly doped with acceptor impurities in concentration , in the intrinsic range when in the extrinsic range when T8. Show that the conductivity is where . In the extrinsic range,. Show also that when and Finally, show that In the intrinsic range , the intrinsic carrier density, so and Now in the intrinsic range. Assuming that vary slowly, T9. Given that you will measure conductivity as a function of temperature, what kind of graph Should you plot to obtain the value of , the band gap, for ? You should plot the log of mobility vs. the log of 1/ temp so as to get the values of Eg . E1. Why does this "four probe" method give a more accurate answer than simply using an ohm-meter? This is because this method separates the sample resistance from the given contact resistance. It does so by separating the current contact and the voltage contacts thereby giving accurate results. E2. Given that the distance between the -contacts is known, derive a formula for an equivalent cross-sectional area (based on the known resistivity of at one temperature) which will allow you to convert resistance to conductivity at all temperatures. o exp-( E3. Given that you will measure with forward and reversed, and forward and reversed, how would you combine these data to extract the true Hall voltage, ? Can you suggest a reason for measurements with forward and reversed leading to different magnitudes of ? To obtain the final hall voltage; the difference has to be deduced from the forward biased values, together with the reverse biased values. The difference in these values arises due to the magnitude of resistivity offered. Reverse biased values have sharp knee values as compared to forward biased values. E4. Explain the principle of the thermocouple and how it is used to find an unknown temperature Principle of operation of a thermocouple The basis of thermocouples operates on the fact that, a voltage would be generated when a conductor is subjected to a temperature gradient. Another dissimilar material is required so as to generate a different voltage under the same temperature. The difference in voltage between the materials is compared with the temperature gradient, This would give the temperature of a given substance that is being measured. References Harker, H. (2010). Semiconductor Physics. London: University College, U.K Kasap, O (2001). Hall Effect in Semiconductors. Canada: University of Saskatchewan. Varpula, A. (2009) “Modelling of electrical properties of granular semiconductors,” Licentiate’s thesis, Helsinki University of Technology. Read More

An increase in temperature causes increased ionization to occur (Varpula, 2009). At about 100K, all of the donor atoms are ionized, at which point the carrier concentration is determined by doping. The region where every available dopant has been ionized is called the extrinsic (or saturation) region. In this region, an increase in temperature produces no increase in carrier concentration. This is the region where, , and . At high temperatures, the thermally generated intrinsic carriers outnumber the dopants (ni>).

In this intrinsic region, carrier concentration increases when temperature increases. Apparatus: Ge Slab Cryostat Liquid Nitrogen Resistance Heater Stainless steel rod Exchange Gas (Ar) Specimen Dipstick Procedures 1. The setting is mounted on the cryostat while its temperature is adjusted from 80K to 430K 2. Heat the setting using a heat sink 3. When the pressure drops to about 20 millitorr, pure N2 at 500 psi is passed to purge the system for about 10 minutes. 4. Connect the two leads at one end of Ge sample are connected to terminals 1 & 4 of the terminal box, the other two leads at the other end of the sample to terminals 2 & 3. 5. Measure the resistance of the sample connect 1 & 4 to high input terminals of the resistance meter with 2 & 3 connected to the low input terminals of the meter. 6. Increase the, N2 pressure is increased to 1800 psi when the pressure in the system is close to 20 millitorr. 7. Leave the rotary pump connected to the exchange-gas space and continue the measurements at intervals of 10oC or so up to 160oC Temperature is again set to 100K and resistance recorded. 8. Gas flow is stopped(Main valve of N2 cylinder is also closed) Fig 1 Fig 1 Experiment set up Results TC is the thermocouple temperature T = -155° C, TC = -4.77 (mV) Reversed B (-) Forward B (+) VH = -18.37 (mV) -99.

24 (mV) IH = 0.040 (A) 0.0034 (A) VX =3.006 (V) 3.006 (V) T = -125° C, TC = -4.05 (mV) Reversed B (-) Forward B (+) VH = -21.64 (mV) -78.55 (mV) IH = 0.024 (A) 0.022 (A) VX =3.006 (V) 3.006 (V) T = -120° C, TC = -3.84 (mV) Reversed B (-) Forward B (+) VH = -21.75 (mV) -76.63 (mV) IH = 0.023 (A) 0.021 (A) VX =3.006 (V) 3.006 (V) T = -110° C, TC = -3.62 (mV) Reversed B (-) Forward B (+) VH = -21.98 (mV) -72.

25 (mV) IH = 0.021 (A) 0.019 (A) VX =3.006 (V) 3.006 (V) T = -100° C, TC = -3.35 (mV) Reversed B (-) Forward B (+) VH = -22.12 (mV) -68.67 (mV) IH = 0.019 (A) 0.018 (A) VX =3.006 (V) 3.006 (V) T = -90° C, TC = -3.06 (mV) Reversed B (-) Forward B (+) VH = -22.19 (mV) -66.06 (mV) IH = 0.017 (A) 0.015 (A) VX =3.006 (V) 3.006 (V) T = -80° C, TC = -2.77 (mV) Reversed B (-) Forward B (+) VH = -22.26 (mV) -63.

23 (mV) IH = 0.015 (A) 0.014 (A) VX =3.006 (V) 3.006 (V) T = -70° C, TC = -2.46 (mV) Reversed B (-) Forward B (+) VH = -22.27 (mV) -60.42 (mV) IH = 0.014 (A) 0.013 (A) VX =3.006 (V) 3.006 (V) T = -60° C, TC = -2.14 (mV) Reversed B (-) Forward B (+) VH = -22.23 (mV) -58.30 (mV) IH = 0.012 (A) 0.012 (A) VX =3.006 (V) 3.006 (V) T = -50° C, TC = -1.81 (mV) Reversed B (-) Forward B (+) VH = -22.20 (mV) -56.48 (mV) IH = 0.

012 (A) 0.011 (A) VX =3.006 (V) 3.006 (V) T = -40° C, TC = -1.47 (mV) Reversed B (-) Forward B (+) VH = -21.92(mV) -54.05 (mV) IH = 0.010 (A) 0.009 (A) VX =3.006 (V) 3.006 (V) T = -30° C, TC = -1.11 (mV) Reversed B (-) Forward B (+) VH = -21.93 (mV) -51.94 (mV) IH = 0.009 (A) 0.

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