Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UK Essays.
At the start of every growth campaign, the MBE growth chamber undergoes a bakeout of about a week’s duration to remove any unwanted residues (e.g. organics, oxygen, and water vapor) that may have accumulated on the chamber components due to opening of the chamber for servicing and re-charging of cells. Bakeout is achieved by building an ‘oven’ equipped with heating elements over the whole chamber and heating the enclosure to ≈ 130 ◦C while the chamber is cryogenically pumped. After the bakeout, the chamber should have a pressure in the low 10−9 Torr range. Note that after the first growth of a campaign, the total pressure in the MBE growth chamber will generally be greater than this pressure due to residual Hg being present. As in most MBE laboratories, HgCdTe growth generally employs the use of a binary CdTe source, elemental Te and Hg. Hg and Cd evaporate as single monomers while Te evaporates as Te2 dimers. Using CdTe instead of elemental Cd allows for better compositional control because CdTe evaporates congruently as Cd and Te2 species while HgTe evaporates incongruently due to the weak Hg-Te bonding. The growth rate and composition x of Hg1−xCdxTe is primarily controlled by the Te and CdTe fluxes.
In contrast, HgCdSe growth was conducted using elemental Hg, Cd, and Se sources. The Se and Hg sources are valved sources while the Cd source is a standard Knudsen effusion cell. Nominal flux values were measured by a nude ion gauge located at the substrate growth position. For this study, the growth fluxes were kept constant while the growth temperature was varied. The goal was to identify the appropriate growth temperature for HgCdSe and study the surface morphology, crystallinity, electrical transport properties, and defect structure of the epilayers.
Epilayers of HgCdTe and superlattice HgTe/CdTe materials in this thesis were grown on Cd0.96Zn0.04Te (211)B substrates with dimensions 1 cm×1 cm. The substrates are specified to have etch pit densities (EPD) of ≤ 105 cm−2 and an X-ray rocking curve full-width-half-maximum (FWHM) of ≤ 50 arcsecs. Before loading into the MBE system, each substrate undergoes a chemical cleaning procedure to remove any residual contaminants and polishing damage. This involves a warm trichloroethylene (TCE) clean, followed by acetone, methanol, a light etch in Br/Methanol (0.1%Bromine) solution for 60 secs to reveal a freshly etched surface, and finally a thorough methanol wash. The wafer is then rinsed under running DI water for 5-10 mins before it is dried under a jet of ultra-pure N2 gas. Note that before the DI wash, there must not be any traces of bromine left on the wafer as this can result in the formation of a yellow-brown stain that is difficult to remove. This preparation of the substrate is very important as the quality of the surface will determine the quality of the subsequently-grown HgCdTe epilayers.
For studying HgCdTe epilayers growth on alternative substrates, epi-ready GaAs and GaSb (211)B substrates were used. This removed the need for chemical cleaning and organic washing, since received substrates were directly loaded into the MBE. Thick CdTe buffer layers (5-6 μm) were grown to overcome the lattice mismatch between HgCdTe and alternative substrates. However, HgCdSe material was grown on GaSb (211)B substrates, because of its near perfect lattice match. Although we are capable of growing on 3-in wafers, we used smaller substrates initially. This was done to minimize costs associated with substrate consumption as we fully expected to conduct numerous growth experiments.
The substrate is first mounted using liquid graphite, held in place on the Mo block by surface tension and stored in a glove box under nitrogen atmosphere. The wafer is then transferred into the loading chamber where it is heated under vacuum for several minutes to remove any water that may be present on the surface. The substrate is then moved into the growth chamber through the analysis chamber, and the temperature set to above 300°C for 10 mins to 15 mins. The high temperature thermally cleans the substrate of any native oxide and excess Te on CdZnTe substrates, which are always present after the Br/Methanol etch due to bromine preferentially etching the Cd and leaving the surface Te rich. This process can be viewed on the RHEED screen where spots indicate the presence of oxides and excess Te on the substrate surface when initially loaded into the growth chamber. As the substrate undergoes further heating, a streaky pattern can be observed to slowly appear until all the spots are no longer present and bright long streaks become apparent. The thermal preparation typically takes about 10mins to 15mins before the substrate is ramped back down to the growth temperature.
When the substrate temperature stabilizes around the optimum growth temperature and the cell temperatures are all stabilized, the shutters are opened and nucleation can begin. The RHEED pattern of the growing crystal is monitored closely during nucleation for the first few minutes. An indication of Hg deficiency during nucleation can be identified by spots observed on the RHEED screen. Any Hg deficiency can be compensated by either increasing the Hg flux by increasing the Hg cell temperature or by reducing the substrate temperature . Optimum growth conditions, and hence two dimensional growth of epilayers, are then maintained by continual in-situ control by RHEED and monitoring the cell/substrate temperatures in real time. It has been postulated in the literature that RHEED may be quite destructive to the sample due to the high energy of the electron beam . As such, for the growths in this thesis, RHEED electrons are focused onto the sample only during nucleation to ensure that growth occurs close to optimum conditions, and at 30 min intervals for a few seconds each time to ensure that growth is proceeding normally.
Epitaxial films with a desired x value are achieved by choosing appropriate cell temperatures to control the intensities (fluxes) of the molecular beams in the correct proportion, and by choosing the appropriate substrate temperature. Note that a few hours prior to every growth, the cells are firstly outgassed at higher than growth temperatures for 10 mins, before being lowered down to growth temperatures where flux measurements are taken. The beam equivalent pressure of each cell is obtained by the pressure difference measured when the shutter is open and the background pressure when the shutter is closed. This is done prior to heating the Hg cell or carrying out any other growths, since once the Hg cell is operational, flux measurements are not possible due to the high Hg overpressure.
During growth, the substrate and cell temperatures are continually monitored and controlled to within ± 0.1°C to ensure minimal deviation from optimum growth conditions. An in-situ Hg flux measurement is achieved by continually monitoring the pressure reading from an ion gauge mounted in direct view of the Hg cell behind the manipulator. When the required approximate epilayer thickness has been achieved, all shutters are closed with the exception of the Hg shutter, while the sample is slowly cooled to around 80°C under Hg flux. This is to prevent preferential desorption of Hg from the grown surface layer at high temperatures, thereby avoiding a Hg deficient surface. Alternatively, after HgCdTe growth, a thin CdTe capping/passivation layer of ≈ 100 nm can also be grown to prevent Hg desorption. Once all required growths have been completed within a given growth campaign, the chamber undergoes another bakeout procedure similar to the one described at the beginning of this section, to remove all Hg and other unwanted residues in the chamber.
3.2. Critical Characterization Techniques
- Photoconductive Decay Measurements:
The principle of the experiment is to shine a pulse of light with energy greater than the bandgap energy of the sample so as to generate excess carrier densities Δn and Δp. Generation in semiconductors refers to the process by which electron-hole pairs are created. The energy required for the excitation of an electron from valence band to conduction band can come from thermal processes or through the absorption of photons. Recombination refers to the inverse processes by which electron-hole pairs are lost due to the spontaneous transition of an excited electron from the conduction band to an unoccupied state in the valence band. The excess energy and the change in the momentum are either released as photons or phonons or transferred to other carriers, which ensure energy and momentum conservation for the individual processes of electron-hole recombination.
In thermal equilibrium, generation rate G0 is counterbalanced by recombination rate R0, leading to a constant electron-hole product, n0p0 = ni2. If the system is exposed to an external optical excitation, both the new generation rate and recombination rate, will be greater than the thermal generation and recombination rates, which will lead to increased non-equilibrium electron-hole densities n and p with np>ni2. As thermal equilibrium cannot be reached instantaneously after switching off the external generation source, the excess carrier densities, Δn = n – n0 and Δp = p – p0 decay with a net recombination rate, U = R – R0, which is a characteristic of the individual recombination mechanism, and vanishes in thermal equilibrium. Assuming charge neutrality, i.e, Δn = Δp, the time dependent decay of the excess carrier density is defined by the following rate equation .
δΔ(t)δt = -U(Δnt, n0, p0)
According to Eq. (3.3), the time dependent decay of Δn follows an exponential law. The time constant of this exponential decay represents the recombination lifetime – often also referred to as the minority carrier lifetime or simply lifetime – which is thus generally defined via the following equation .
τΔn, n0, p0= ΔnU(Δnt, n0, p0)
The recombination lifetime is a property of the carriers within the semiconductor, rather than a property of the semiconductor itself. As such, it is a weighted average across all the carriers, whose individual behaviors may be influenced by different factors, including surfaces, bulk defects and the density of carriers, besides the fundamental properties of the semiconductor material. Interpreting the recombination lifetime can, therefore, be difficult as it represents a number of specific recombination mechanisms occurring simultaneously within the bulk and at the surfaces. For this reason, the recombination lifetime is often referred to as an effective lifetime.
Lifetime measurements were carried out using the photoconductive decay method on full samples (dimensions=1×1 cm). There was no post-growth annealing and passivation applied to the samples. Ohmic contacts were made on these n-type layers by pressing indium on the corners. A block diagram of the lifetime measurement technique is shown in Fig. 3.3(a), using a pulsed laser beam to generate excess carriers in the samples. The laser pulse width was 300 ns and the power output was controlled by the voltage supply. By using the already derived expression for laser power, beam spot area, sample layer thickness, and delay time, the calculated excess carrier concentrations were always less than 5×1014 cm-3 . The injection level as per calculations was below the thermal equilibrium carrier concentration and hence it did not affect the lifetime measurement. A cryostat with cold finger was used for mounting the samples to allow cooling under vacuum to 70 K. To avoid sweep-out effects, the biasing was kept low, and the decay curves were fitted exponentially to obtain the minority carrier lifetimes (as shown in Fig. 3.3(b)).
t1 = lifetime
Figure 3.3. (a) Illustration for photoconductive decay measurement setup, (b) representation of the transient photovoltage of the HgCdTe, fitted by exponential decay curve by using equation shown.
- Recombination Mechanisms and Carrier Lifetime
Once electron-hole pairs are generated by absorption in the semiconductor, they are exposed to several recombination mechanisms. These processes occur in parallel and the not recombination rate is the sum of those for individual processes. Different recombination mechanisms and the lifetime associated with each of them are discussed below.
- Radiative Recombination
Radiative recombination is simply the direct annihilation of an electron-hole pair. It is the inverse process to optical generation, with the excess energy being released mainly as a photon with energy close to that of the bandgap. It involves a conduction band electron falling from an allowed conduction band state into a vacant valence band state (a hole). The radiative recombination rate, Urad, therefore, depends on the concentration of free electrons, n, and free holes, p :
Urad = B(np- ni2)
where B is the coefficient of radiative recombination. The coefficient B directly reflects the quantum-mechanical probability of a radiative transition, which strongly depends on the band structure of the semiconductor.
Inserting the non-equilibrium concentration n = n0+Δn and p = p0+Δp in Eq. (3.5), and assuming charge neutrality (Δn=Δp) in Eq. (3.3), the following general expression for radiative recombination lifetime, τrad yields :
Urad = Bn0+ p0 Δn+BΔn2
τrad = 1Bn0+ np+BΔn
From Eq. (3.7), the common relationships for the radiative lifetime in n-type and p-type material under low-level injection (τrad.li) and high injection conditions (τrad.hi) can be determined
τrad.li = 1B Ndop
τrad.hi = 1BΔn
From Fig. 3.4, it can be seen that the radiative lifetime depends on the inverse of the carrier density. Therefore, τrad is constant at low injection, but then decreases and continues to decrease as the injection level increases.
- Band-To-Band Auger Recombination
As discussed previously, band-to-band radiative recombination is the inverse process of fundamental optical absorption in a semiconductor. In a similar manner, the Auger recombination is the inverse process of impact ionization. The band-to-band Auger recombination is a three-particle process, which involves either electron-electron collisions in the conduction band followed by recombination with holes in the valence band, or hole-hole collisions in the valence band followed by recombination with electrons in the conduction band.
For narrow band gap semiconductors such as HgCdTe and HgCdSe, the minority carrier lifetime is usually controlled by band-to-band Auger recombination, and energy loss occurs either by electron-electron collisions or hole-hole collisions and subsequent Auger recombination. To derive the band-to-band Auger recombination lifetime, the rate of Auger recombination under equilibrium conditions can be written as
Ra = G0 = Cnn02p0 + Cpp02n0
Under nonequilibrium conditions, the Auger recombination rate is given by
rA = Cnn2p + Cpp2n
Therefore, the net Auger recombination rate under steady-state conditions can be obtained from Eqs. (3.9) and (3.10), which yields
UA = rA – G0 = Cnn2p- n02p0+ Cp(p2n+ p02n0)
where Cn and Cp are the capture probability coefficients when the third carrier is either an electron or a hole, respectively. Both Cn and Cp can be calculated from their inverse process, namely, impact ionization. In thermal equilibrium, the rate at which carriers are annihilated via Auger recombination is equal to the generation rate averaged over the Boltzmann distribution function in which the electron-hole pairs are generated by impact ionization. Thus, one obtains
C0n02p0 = ∫0∞PEdndEdE
where P(E) is the probability per unit time that an electron with energy E makes an ionizing collision, and can be described by
PE= mq42h3G (EEt-1)S
where G < 1 is a parameter, which is a complicated function of the band structure of the semiconductor. The exponent s is an integer, which is determined by the symmetry of the crystal in momentum space at a threshold energy Et. The value of Et for impact ionization is roughly equal to 1.5Eg, where Eg is the energy band gap of the semiconductor. By substituting Eq. (3.13) into Eq. (3.12), one obtains
ni2Cn = Sπmq4h3 G kBTEt(s-12)e-EtkBT
Equation (3.14) shows that the Auger capture coefficient Cn for electrons depends exponentially on both the temperature and energy band gap of the semiconductor. The Auger lifetime may be derived from Eq. (3.11), and the result yields
τA = ΔnUA = 1n2Cn+2ni2(Cn+ Cp) p2Cp
If one assumes that Cn= Cp and n = p = ni, then Eq. (3.15) shows that τA has a maximum value of τi = 1/6ni2Cn for an intrinsic semiconductor. For an extrinsic semiconductor, τA is inversely proportional to the square of the majority carrier density. For the intrinsic case, the Auger lifetime can be obtained from Eqs. (3.14) and (3.15) with s = 2 and Cn ≠ Cp, which yields
τAi = 13ni2(Cn+ Cp) = 3.6 X 10-17 (EtkBT)3/2 eEt/kBT
which shows that the intrinsic Auger lifetime is an exponential function of temperature and energy band gap. Note that the temperature dependence of the Auger lifetime in an extrinsic semiconductor is not as strong as in an intrinsic semiconductor. However, due to the strong temperature dependence of the Auger lifetime, it is possible to identify the Auger recombination process by analyzing the measured lifetime as a function of temperature. For a heavily doped semiconductor, Eq. (3.15) predicts that the Auger lifetime is inversely proportional to the square of the majority carrier density. The Auger recombination has been found to be the dominant recombination process for degenerate semiconductors and narrow band gap semiconductors.
Under high injection conditions (i.e., no, po « Δn = Δp), Auger recombination becomes the predominant recombination process. In this case, the Auger lifetime is given by
τAh = 1Δn2(Cn+ Cp) =3ni2Δn2τAi
where τAi is the intrinsic Auger lifetime given by Eq. (3.16).
- Shockley-Read-Hall Recombination
In nonradiative recombination processes, the recombination of electron-hole pairs may take place at localized trap states in the forbidden gap of a semiconductor. This process involves the capture of electrons (or holes) by the trap states, followed by the recombination with holes in the valence band (or electrons in the conduction band). When electron-hole pairs recombine, energy is released via phonon emission. The localized trap states may be associated with deep-level impurities (e.g., metals such as Fe, Ni, Co, W, Au, etc.), or by radiation- and process-induced defects such as vacancies, interstitials, antisite defects and their complexes, dislocations, and grain boundaries. The nonradiative recombination process in a semiconductor can be best described by the Shockley-Read-Hall (SRH) model. A localized deep-level trap state may be in one of two charge states differing by one electronic charge. Therefore, the trap could be in either a neutral or a negatively charged state, or in a neutral or a positively charged state. If the trap state is neutral, then it can capture an electron from the conduction band. The capture of electrons by an empty neutral trap state is accomplished through the simultaneous emission of phonons during the capture process.
The rate equations, which describe the SRH model, can be derived from the four emission and capture processes. In deriving the SRH model, it is assumed that the semiconductor is nondegenerate and that the density of trap states is small compared to the majority carrier density. When the specimen is in thermal equilibrium, ft denotes the probability that a trap state located at Et in the forbidden gap is occupied by an electron. Using Fermi-Dirac (F-D) statistics, the distribution function ft of a carrier at the trap state is given by
ft = 1(1+eEt- EfkBT)
The physical parameters used in the SRH model are defined as follows:
Ucn is the electron capture probability per unit time per unit volume (cm–3 · sec–1).
Uen is the electron emission probability per unit time per unit volume.
Ucp is the hole capture probability per unit time per unit volume.
Uep is the hole emission probability per unit time per unit volume.
cn and cp are the electron and hole capture coefficients (cm3/sec).
en and ep are the electron and hole emission rates (sec–1).
Nt is the trap density (cm–3).
In general, the rate of electron capture probability is a function of the density of electrons in the conduction band, capture cross section, and density of the empty traps. However, the rate of electron emission probability depends only upon the electron emission rate and the density of traps being filled by the electrons. Thus, the expressions for Ucn and Uen can be written as
Ucn = CnnNt(1- ft)
Uen = enNtft
Similarly, Ucp, the rate of hole capture probability, and Uep, the rate of hole emission probability are given by
Ucp = CppNtft
Uep = epNt (1- ft)
According to the principle of detailed balance, the rates of emission and capture at a trap level are equal in thermal equilibrium. Thus, one can write
Ucn = Uen
for electrons 3.23
Ucp = Uep
for holes 3.24
Solving Eqs. (3.19) through (3.24) yields
en = Cnn0(1- ft)/ft
ep = Cpp0ft/(1-ft)
From Eqs. (3.25) and (3.26) one obtains
enep = cncpn0p0 = cncpni2
From Eq. (3.18) one can write
1- ftft= eEt- Ef/kBT
Now solving Eqs. (3.25), (3.26), and (3.28), one obtains
en = cnn1
ep = cpp1
where n1 and p1 denote the electron and hole densities, respectively, when the Fermi level Ef is coincided with the trap level, Et. Expressions for n1 and p1 are given respectively by
n1 = n0e(Et- Ef)/kBT
p1 = p0e(Ef- Et)/kBT
Solving Eqs. (3.31) and (3.32) yields
n1 = np = ni2
Under the steady-state condition, the net rate of electron capture per unit volume may be found by solving Eqs. (3.19) through (3.33), which yields
Un = Ucn- Uen = cnNt[n1- ft- n1ft]
Similarly, the net rate of hole capture per unit volume may be written as
Up = Ucp- Uep = cpNt[pft- p11- ft]
The excess carrier lifetimes under steady-state conditions are defined by the ratio of the excess carrier density and the net capture rate for electrons and holes, and are given respectively by
τn = ΔnUn
for electrons 3.36
τp = ΔpUp
for holes 3.37
For the low level injection case (i.e., Δn « no and Δp « po), the charge-neutrality condition requires that
Δn = Δp
Under steady-state conditions, if one assumes that the net rates of electron and hole capture via a recombination center are equal, then one can write
U = Un = Up
Substituting Eqs.(3.38) and (3.39) into Eqs. (3.36) and (3.37) one finds that the electron and hole lifetimes are equal (i.e., τn = τp) for the low level injection case. The electron distribution function at the trap level can be expressed in terms of the electron and hole capture coefficients as well as the electron and hole densities. Now solving Eqs. (3.34), (3.35), and (3.38), one obtains
ft = cnp+ cpp1cnn+ n1+ cp(p+ p1)
A general expression for the net recombination rate can be obtained by substituting Eq.(3.40) into Eq.(3.34) or (3.35), and the result yields
U = Un = Up = np- ni2τp0n+n1+τn0(p+ p1)
where τpo and τno are given, respectively, by
τp0 = 1cpNt
τn0 = 1cnNt
where cp = σp<υth> and cn = σn<υth> denote the hole- and electron- capture coefficients; σp and σn are the hole- and electron- capture cross sections, respectively, and <υth> = (3kBT/m*)1/2 is the average thermal velocity of electrons or holes; τpo is the minority hole lifetime for an n-type semiconductor, and τno is the minority electron lifetime for a p-type semiconductor. Now solving Eqs. (3.34) through (3.43), one obtains a general expression for the excess carrier lifetime, which is given by
τ0 = ΔnUn = ΔpUp= τp0n0+ n1+ Δnn0+ np+ Δn+τn0p0+ p1+ Δpn0+ p0+ Δp
where n = no + Δn and p = po + Δp denote the nonequilibrium electron and hole densities, no and po are the equilibrium electron and hole densities, and Δn and Δp denote the excess electron and hole densities, respectively.
For the low level injection case (i.e., Δn « no and Δp « po), the excess carrier lifetime given by Eq. (3.44) reduces to
τ0 = τp0n0+ n1n0+ np + τn0p0+ p1n0+ p0
Figure 3.4. The calculated minority carrier lifetime of τAug, τRad, and the lifetime considering the radiative and Auger recombination processes only versus composition for p-type HgCdTe at different doping concentration (a) 4.96 × 1015cm−3, (b) 8 × 1015cm−3, (c) 9 × 1015cm−3.
- Surface Recombination
The surfaces and/or interfaces of HgCdTe represent severe discontinuities in crystalline structure. The large numbers of partially bonded atoms give rise to many dangling bonds and, therefore, a large density of defect levels are found within the bandgap near the semiconductor surface. Even if the surface is not bare and is covered by oxides, the presence of Te-oxygen bonds can stress the crystal structure at the surface, which again introduces many defect states. The SRH analysis still applies, although it has to be reformulated in terms of recombination events per unit surface area, rather than per unit volume.
For a single defect at the surface, the rate of surface recombination, US is given by :
Us = nsps- ni2ns+ n1Sp0+ ps+ p1Sn0
where ns and ps are the concentrations of electrons and holes at the surface, and Sp0 and Sn0 are related to the density of surface states per unit area, Nts, and the capture cross-sections, δn and δp, for the specific defect :
Sn0 = δnvthNts
Sp0 = δpvthNts
In reality, defect levels are so numerous that they can be considered to be continuously distributed throughout the bandgap, and both their density and capture cross-sections will be dependent on their energy level.
Similar to the definition of the recombination lifetime, the surface recombination velocity, S is defined as
Us = SΔns
and so the surface recombination velocity can be related to the fundamental properties of the surface defects through Eq. (3.48). It is the surface recombination velocity, S, that is typically used for quantifying surface recombination processes. Surface recombination lifetime is given as :
τsurface = [2SW+ 1DnWπ2]-1
- Effective Lifetime
The four recombination mechanisms discussed so far may occur simultaneously in a given sample. For an independent process the overall recombination rate is just the sum of the individual recombination rates, resulting in an effective lifetime τeff given by :
1τeff = 1τSRH+ 1τAuger+ 1τrad+ 1τsurface
1τeff = 1τbulk+ 1τsurface
Based on these models, the minority carrier lifetime is an important physical parameter, which is directly related to the recombination mechanisms in a semiconductor. A high-quality semiconductor with few defects generally has long minority carrier lifetime, while a poor-quality semiconductor usually has short minority carrier lifetime and high defect density. The minority carrier lifetime plays an important role in the performance of semiconductor optoelectronic devices, because it directly affects the minority carrier diffusion length and, hence, the quantum efficiency.
- X-ray Diffraction
X-ray diffraction is arguably the most important tool for the crystal grower, as it allows for a thorough structural analysis of the grown crystal. Technological advances in this field over the last decade have allowed for a deeper understanding of the crystal structure and associated defects. As x-ray wavelengths are comparable to the crystal lattice spacing, the interaction between the two is strong, and data from the scattering process reveals information on the crystal structure. The most fundamental characteristic that can be extracted is the lattice spacing itself which, for ternary materials, can then be used to determine the composition provided the lattice constants of the constituent binaries follow Vegard’s law. From a crystal quality perspective, the most important measurable characteristic is the spread in the lattice spacing. This is quantified from the full width at half maximum (FWHM) of the diffraction peak of the associated crystal layer. This FWHM is a frequently quoted metric of crystal quality, however the measurement conditions vary so greatly that it can often be misinterpreted.
In this thesis two types of x-ray diffraction measurements have been carried out to characterize the HgCdTe structures. Rocking curve measurements, whereby the sample is ‘rocked’ over a small range of angles about a diffraction peak, is the most common measurement on single crystal samples, and can be performed quickly and routinely to find out fundamental structural properties. Reciprocal space mapping is a powerful high-resolution x-ray diffraction technique that is used to effectively reveal the reciprocal lattice of the crystal within the diffraction plane. This graphical representation allows for a detailed analysis of the distortions present in the crystal. Strain, lattice mismatch, and the spread of lattice spacing and tilts are investigated for (211) orientated materials. A study of the variation of these properties across the surface of a number of samples is presented, and is shown to be an excellent technique to simultaneously investigate the uniformity of both the grown layer and underlying substrate.
- Experimental Configuration
All x-ray measurements were performed on a Panalytical XPert Pro diffractometer at Center for Microscopy, Characterization, and Analysis (CMCA), at The University of Western Australia. The configuration was set for the investigation of single crystal samples. Figure 3.5 shows a schematic of the x-ray setup, which is composed of four main parts: the x-ray tube, the incident optics, the sample stage, and the diffraction optics. A copper x-ray tube provides the source of x-rays, which are produced by accelerating 40 kV electrons into a copper target. The associated emission current is 40 mA. This interaction excites the Kα1 line of copper, which corresponds to an x-ray photon with a wavelength peaked at λx = 1.544 Ǻ. The tube can be operated in two modes: line or point focus. As the name suggests, this describes the divergence of the beam from the tube. Point focus provides a less intense but much narrower beam, and is used for reciprocal space mapping, while the line focus, which has a wider beam spread but higher intensity, is used for rocking curve measurements.
The incident optics are used to align, collimate and monochromate the beam. The x-ray mirror reduces the divergence of the output beam of the tube, as shown in Fig. 3.5(a), and focuses the beam toward the four bounce monochromator. This monochromator contains four high-purity germanium crystals arranged so that the incident beam is diffracted about the (440) reflection of Ge. After the first reflection the beam consists of a range of wavelengths and angles that simultaneously meet the diffraction conditions. The angular divergences are reduced by the subsequent reflections from the remaining Ge crystals.
Figure 3.5. (a) A schematic diagram of the main components of the Panalytical XPert PRO diffractometer used for high resolution x-ray diffraction. (b) The orientation of sample stage of the XPert PRO can be manipulated by the three translational axes (x, y, z) and three rotational axes (φ, ψ, ω/2θ). The ω/2θ axis is used during measurement, while the others are used to facilitate alignment of the sample to the plane of the incident x-ray beam.
The last section of the incident optics are the vertical and horizontal crossed slits, which are used to adjust the lateral size of the output beam anywhere between 0.1 − 10 mm. The 20 cm circular sample stage has six degrees of freedom, as shown in Fig. 3.5(b). Movement in the three Cartesian directions (x, y, z) is controlled to ensure the x-ray beam is incident on the sample region of interest. The other three movements adjust the tilt (ψ), rotation (φ), and incident angle (ω), which sets the angle between the sample and the x-ray beam. All three angular displacements are required for correct orientation since the crystal planes are rarely aligned with the sample stage. The incident angle, ω can be adjusted with a precision of 0.0001°. This alignment becomes crucial for high resolution measurements, where the acceptance angle associated with the diffracted beam is very narrow.
- X-ray Rocking Curve Measurements
Rocking curves are primarily used to study defects such as dislocation density, mosaic spread, curvature, misorientation, and inhomogeneity. In lattice matched thin films, rocking curves can also be used to study layer thickness, superlattice period, strain and composition profile, lattice mismatch, ternary composition, and relaxation. A rocking curve is recorded by moving the diffractometer into a reflecting position and then scanning the shape of the reflected curve. The diffractometer motion sequence is similar to the Theta Scan. Additionally a special collimator, e.g. a double crystal, is placed in the primary beam path to reduce the influence of the divergence and spectral width of the beam. In a perfect crystal, the width of the rocking curve is determined by the beam geometry and the spectral width of the source. Crystal imperfections cause a broadening of the rocking curve. Usually the half-width of the measured rocking curve is compared with that calculated for a perfect crystal. With our instruments we can reach a minimum half-width of 0.002° (7 seconds).
X-ray diffraction is based on Bragg’s law, which defines a condition of constructive interference between the incident x-ray radiation with wavelength λx and a set of crystal planes (hkl):
λx = 2dhklsinӨ
where the spacing between these diffracting planes, dhkl is a function of the lattice spacing, a:
dhkl = ah2+k2+ l2
The following are the definitions of the angles in the software:
ω – angle between incident x-rays and sample surface
2θ – angle between incident x-rays and detector
ψ – azimuthal sample tilt
φ – in-plane sample rotation
x,y – horizontal and vertical position of sample, respectively
z – sample height
Figure 3.6. Illustration of angles and axis in a triple-axis x-ray diffraction equipment.
Rocking curve measurements probe the crystal lattice by scanning a diffraction peak about an angle θ associated with a particular (hkl) reflection (as defined by Eqn. 4.9). The two main types of rocking curve measurement that are usually performed are:
- ω scan: The ω-axis is scanned about the reflection of interest while the 2θ remains fixed at 2θ = ω. The analyzer is removed from the diffracted optics arm, and the intensity is measured as a function of ω. This is used for smaller scans as the measurement is restricted by the acceptance angle of the detector. The peak measured will be influenced by both the spread of d-spacing in the sample along with any spread in tilt of the measured layer.
- ω-2θ scan: When larger scans are required, which is often the case when studying large-area samples, the 2θ axis is scanned proportionally to the ω. For each step of the scan, every ∆ω increment of the ω axis, the 2θ axis moves by ∆2θ = 2∆ω. When the analyzer is used, and because the acceptance angle is comparable or less than ∆ω, the diffracted beam is scattered from layers oriented at the same tilt. Therefore, it contains information entirely on the d-spacing spread.
All epitaxial growths were subjected to rocking curve measurements immediately after growth. A primary symmetric reflection is chosen and a quick scan about the approximate angle is undertaken. The omega axis is ‘rocked’ about this angle until the peak is found, then a longer ω-2θ scan is taken, typically of 1 arcsecond resolution and 1 second step duration at two values of ψ, separated by 180°. The only symmetric reflection of interest for (211) orientations is (422). As discussed before, the x-ray rocking curve full-width at half-maximum (FWHM) has long been a widely quoted metric of crystal quality. The routine nature of the measurement, usually performed immediately after growth, enables the crystal grower to gauge the variation of lattice spacings present in the layer and provides a fast method in determining the quality of the growth.
- Reciprocal Space Mapping
In addition to the double and triple axis rocking curves, high resolution x-ray diffraction can be used to map the reciprocal lattice. The Bragg equation implies an inverse relationship between lattice spacing and the sine of the primary diffraction angle, and as the reciprocal lattice represents the inverse of the interplanar spacing, scanning the diffractometer axis is a direct probe of a slice of reciprocal space. Accordingly, rocking curves provide a one dimensional slice of this reciprocal space, but the measurement is often a convolution of both lattice spacing and tilt. By scanning both primary axes of the diffractometer, these can be resolved separately, and a two dimensional image of the reciprocal lattice can be generated.
Two-dimensional X-ray diffraction is a well-established technique in the field of X-ray diffraction . The main complication of data analysis in two dimensional XRD compared to one dimension XRD is the remapping of detector pixel coordinates into momentum transfer or scattering vector coordinates. The geometry of a two-dimensional X-ray diffraction system consists of three reference systems: laboratory, detector, and sample. The laboratory coordinate system is the reference or global three dimensional coordinate system. The sample coordinate system shares the same origin with the laboratory system but its basis can be oriented in a different way. The detector coordinates system is two-dimensional. The three reference systems are represented by orthogonal Cartesian bases [23-27].
In this work we employed a ‘3D+1S’ diffractometer, where three diffractometer circles (3D) are used for moving the 3D detector across the Ewald sphere, and one circle is used for orienting the sample. The simplest detector orientation corresponds to the situation in which the normal to the detector is coincident to the X-ray incident beam or, equivalently, points towards the origin of the laboratory coordinate system, where the sample is placed (detector circle angles are zero). The simplest sample orientation corresponds to the grazing case in which the sample surface is parallel to the direct beam (sample circle angle is zero). Assuming that the sample is a single crystal with lattice defects and considering a diffracting plane, then the diffracting plane would project a line of rays onto the detector. Since the detector is perpendicular to incident beam and the sample is parallel to the incident beam, the projection of the diffracting line onto the detector would be a perfect circle. In this case, converting the detector pixel coordinates into scattering vector coordinates is non-trivial. However, one might want to move the detector to non-zero azimuth and elevation to visualize extra features like strain, and defects. This complicates the procedure and introduces distortions in the diffraction pattern. In this case, the conversion between pixels and scattering vector coordinates is more complicated.
Thus, a number of ω − 2θ scans are taken at successive values of ω, much like taking a set of rocking curves at different values of crystal tilt. The ω axis is scanned with the 2θ axis, with steps of ∆2θ=2∆ω, with ω being offset for each new scan. In order to generate a reciprocal space map from the set of ω − 2θ scans, the following transformation needs to be used:
Qx = cosω-cos(2Ө- ω)
Qz = sinω-sin(2Ө- ω)
where Qx and Qz are in reciprocal space lattice units (rlu), and 1 rlu = 1/λx.
Ewald Sphere Construction
A Ewald sphere reconstruction for a (211) orientated surface is shown in Fig. 3.9. It shows all possible reflections in the slice of reciprocal spacing along the  azimuth, with black and white dots signifying allowed and disallowed reflections, respectively. In the case of the zincblende structure, reflections from the (hkl) plane are allowed if the indices are all odd or all even . The main reflections of interest in this thesis are the primary symmetric reflection (422) and the asymmetric reflections (333) and (511), the three of which are common to the plane of reciprocal space depicted in Fig. 3.9. The plot also illustrates the relationship between the θ and ω axes and reciprocal space.
Figure 3.7. Illustration of Ewald sphere containing the  azimuth, relevant for growth on (211) substrates. Black and white dots indicate allowed and forbidden reflections, respectively, while the grey areas indicate inaccessible reflections due to wavelength and instrument limitations. The θ and ω axes indicate the points of reciprocal space sampled during a scan. The three main reflections of interest studied in this thesis: (333), (422), and (511) are shown in the dashed box.
The alignment procedure for reciprocal spacing mapping is more involved than for rocking curve measurements. For (211)-oriented samples, the (311) reflection is used since it is a unique reflection for the  azimuth (no other exists at the same values of ω and θ) so it provides a useful peak to ensure the plane of diffraction is aligned with the (110) crystallographic planes. This is done by first setting the ω and 2θ axes according to the (311) reflection, then rotating φ to the correct angle and then slowly rocking this axis to maximize the peak intensity. The same is done for the tilt axis ψ to ensure the azimuth normal to  is also perpendicular to the plane of diffraction. In the case of (100)-oriented samples, only the (400) symmetric reflection was examined, so the alignment procedure did not require identification of each azimuth.
Once the alignment is complete, the scan parameters are set. A step size of 0.005° was used for all measurements for both the ω and θ axes, while the integration time per step was chosen depending on the reflection of interest. For the bright symmetric reflections an integration time of 0.5 seconds was sufficient, while for the (333) and (511) reflections (on (211)-oriented samples) times of up to 3 seconds were used. As a result, measurements could take up to 14 hours per scan. The range of angles were sample specific, larger for those with greater separation between epilayer and substrate peaks.
Prior to applying the transformation to convert the real space data into reciprocal space as described in the previous section, the layer tilt must be accounted for by aligning the surface-symmetric planes to ω = 0°. This can be performed prior to the measurement, but it is easier to simply add an offset ω° to all values of ω such that the (422) superlattice peak is rotated in reciprocal space to align with the Qx = 0 axis (i.e. 2 × ω = θ). The same offset is added to the (311), (422) and (511) space maps, so that they are all effectively rotated about the origin together in reciprocal space. This alignment is especially important as it ensures the strains can be correctly interpreted, as discussed in the following section.
Determination of Mosaic Spread Dimensions
A mosaic block is a discrete diffracting entity similar to a crystallite discussed above, except that its relationship to the matrix of the sample is different in that it is connected via small-angle grain boundaries. This link leaves no voids but a series of dislocations that accommodate the misorientation between neighboring blocks. The analysis of the mosaic structure, dimensions and orientation distribution, is often what is relevant when referring to the crystal quality [28, 29]. The analysis method applicable can be defined by the size and the instrument resolution. Generally, since the misorientation angles are small, double-crystal diffractometers or triple-crystal diffractometers are often required. The presence of mosaic blocks in some systems simplifies the analysis if their dimensions are less than the extinction distance, since the kinematical diffraction model can be applied. The presence of mosaic blocks in ideally imperfect crystals allows the determination of molecular structures without the complications of dynamical theory.
Basically, a mosaic crystal will consist of finite dimensions or correlation lengths perpendicular and parallel to the surface, and each mosaic block will have a different scattering vector direction to its neighbor. Also, in general, the relative lattice parameter between mosaic blocks is small and so the scattering angle will be essentially unchanged but the angle of incidence at which each will diffract will differ according to their relative misorientation. Clearly, isolating an individual block with a very small probe will imply that the probe is smaller than the block, otherwise the interference of other blocks will influence the observation. Hence, either the diffracted response has to be modelled or special experimental techniques need to be employed.
With the development of high resolution multiple crystal multiple-reflection diffractometers, it has been possible to obtain diffraction space maps with minimal artifacts, and therefore diffuse scattering can be observed, which was the configuration used by Holy´ et al for their studies . The shape of the diffraction peaks are sensitive to microscopic tilts and lateral correlation lengths and these can be separated using a very pragmatic approach, and hence the mosaic-block dimensions are accessible almost directly from these maps . If the block sizes approach a few microns then an imaging method can be used . Because of the very high angular resolution of the instrument, individual mosaic blocks can be isolated in diffraction space and imaged.
Lateral correlation length and microscopic tilt (Mosaicity) were calculated as :
Lateral Correlation Length = 1L1
Microscopic Tilt =L2qx2+ qz2
L1L2 = -cosξcos(φ+ ξ)
L3L2 = -sinφcosξ
L3 = Δqx2+ Δqz2
φ = 1tanqxqz
The dislocation density Ddis of HgCdTe epilayers was estimated by the following equation :
ρ = β9b2
where b is the Burgers vector length, and β is the breadth of the peaks.
Lattice Mismatch and Strain Determination
Mismatch between the lattice constants of the substrate and epilayer material to be grown leads to distortion of the crystal structure. Lattice mismatch is defined as the ratio of the two lattice spacings:
m = al- asas
where al is the lattice constant of the free-standing grown layer, and as is the substrate lattice constant. Generally, substrates are chosen so that the mismatch is minimized. The Cd1−xZnxTe substrates used for growths studied in this thesis are nominally 4% zinc, lattice-matched for the growth of Hg0.7Cd0.3Te alloy material. However, HgCdTe grown on GaSb and GaAs substrates, were grown with a sandwiched CdTe buffer layer to accommodate the lattice mismatch between HgCdTe and the substrate. For superlattices, the average lattice spacing varies depending on the individual layer thicknesses, so it becomes impractical (and expensive) to use different substrates for each new sample. The strain in a grown layer is proportional to the unrelaxed lattice mismatch, and it is this strain that has a large bearing on the nature of the distortions present in the layer. The biaxial in-plane strain (εǁ) and out-of-plane strain (ε﬩) are defined as :
ϵǁ = aǁ- a0a0
ϵ┴ = a┴- a0a0
where a0 is the free-standing lattice parameter of the layer. Initially, the strain is accommodated elastically by the epitaxial layer and the in-plane lattice spacing of the grown material will be equal to the substrate lattice spacing, as = a∥. Fully-strained layers are sometimes referred to as pseudomorphic, and the biaxial in-plane compressive (tensile) strain is related to the tensile (compressive) out-of-plane strain as defined by Poisson’s ratio . Fig. 3.8 illustrates the influence of pseudomorphic and relaxed strain states on the lattice parameters and tilts in the epilayers. As the thickness of the epitaxial layer is increased, the stain energy increases accordingly. Eventually, a critical thickness is reached, above which it becomes energetically favorable for the epitaxial layer to accommodate a portion of the misfit strain by introducing a network of misfit dislocations at the epitaxial interface, thereby inducing plastic deformation throughout the layer, a process known as relaxation. Partially relaxed layers are characterized by a lattice spacing which approaches that of the free standing lattice constant, and fully relaxed layers are completely unstrained (a∥ = a⊥ = a0).
Relaxed layer lattice mismatch : Δaarel = al- asas
Compressive strain: Δaarel>0
Tensile Strain: Δaarel<0
Figure 3.8. Illustration of strain in epilayers grown on lattice mismatched substrates.
Fully strained epitaxial layers grown on lattice mismatched substrates can be seen in reciprocal space as depicted in Fig. 3.9.
Figure 3.9. Illustration of a Pseudomorphic (fully strained) layer in reciprocal space.
Figure 3.10. Illustration of fully relaxed layer in reciprocal space.
The reflection of a fully strained layer is located on a perpendicular line. A reflection of a fully relaxed layer is on a line through the substrate reflection and (000). Reflections of partly relaxed layers are on the relaxation line, as shown in Fig. 3.11. And the tilt angle is given by:
tanα = -tanτD
Figure 3.11. Illustration of partially relaxed epitaxial layer in reciprocal space.
- Secondary Ion Mass Spectrometry
Also known as an ion microprobe, secondary ion mass spectrometry (SIMS) is a high sensitivity surface analysis technique within a high vacuum chamber, and is used to extract the composition/concentration of atoms in a sample. During an analysis, a focused beam of primary ions is directed toward the sample where they interact with surface layer atoms down to a few tens of angstroms (see Figure 3.12). Through a series of collisions with the target atoms, some of the surface atoms are ejected or sputtered as neutral species or charged secondary ions. The charged species are then collected and analyzed through a mass spectrometer to provide quantitative data such as the elemental, isotopic, or molecular composition of the surface. Current SIMS instruments have excellent concentration detection range, and are capable of resolving major constituents as well as trace species at a sensitivity of parts per billion .
Figure 3.12. Schematic for basic SIMS operation.
Known primarily as dynamic SIMS, depth information can be obtained by having the primary beam on an area of the sample for some time, simultaneously etching and analyzing the sputtered particles. With calibration of the sputtering rate and a depth measurement of the resultant crater bore with a stylus profilometer, an approximate depth profile of constituents can be built up. This is particularly useful in the study of multi-layered samples. While the technique is obviously destructive, the major advantage of a SIMS measurement is that no sample preparation is required. The SIMS measurements for the majority of samples grown in this work were performed at the University of New South Wales (UNSW), utilizing a number of HgCdTe samples analyzed by Evans Analytical Group (EAG) as reference standards.
EAG is a specialized micro-analytical laboratory located in Sunnyvale, CA, USA with extensive experience in analyzing HgCdTe materials. SIMS experiments at EAG were performed using a CAMECA IMS 4f double focusing magnetic sector instrument equipped with oxygen and cesium primary ion beam sources. Compared with using noble gas ions, oxygen and cesium primary ion beams enhance the intensities of both the positive and negative secondary ions by about two to three orders of magnitude. EAG uses high ion beam currents and claim to be able to determine accurate volume concentrations [36, 37].
The SIMS equipment used at UNSW is a Time of Flight Secondary Ion Mass Spectrometer (TOFSIMS) magnetic sector instrument equipped with dual sources, a duoplasmatron (O2+ , Ar+, or O−) gas source and a Cesium (Cs+) source. Primary beam energies ranging from 5 keV to 15 keV are typically utilized and rastered over a square area of 250×250 μm2. The instrument also allows for up to 10 species to be acquired concurrently during analysis. A depth resolution capability of 2 nm to 5 nm with sputter rates down to 0.1 nm s−1 allows the characterization of crucial interfaces. In any SIMS analysis, the most abundant isotopes are typically monitored in order to maximize the intensity of the secondary ion yield for the elements of interest.
A SIMS spectrum (using the UNSW facility) showing the major constituents (Hg, Cd) for an MBE grown iodine doped nBn HgCdTe heterostructure, sample CMCT-038, is illustrated in Figure 3.13. After SIMS analysis, the depth of the resultant crater is measured using an Alpha-Step IQ surface profiler. An SEM image of a SIMS crater on sample CMCT-046 (x = 0.27, d = 2.5 μm) is shown in Fig. 3.14.
Figure 3.13. SIMS depth profile of CMCT-038, showing variations in composition of Hg and Cd in an nBn heterostructure.
Figure 3.14. SEM image of a crater left behind after a SIMS measurement on sample
CMCT-046 (x = 0.27, d = 2.5 μm).
The cadmium composition (x value) can be found from SIMS analysis by monitoring the 106Cd and 123Te isotope ion counts as a function of depth throughout the HgCdTe epilayer and the substrate. A simple relationship between the composition of the material and the ion yield (counts) is based on the following equation,
x = ϓsubsCs133Cd+106Cs133Te+123
ϓsubs = xsubsCs133Cdsubs+106Cs133Tesubs+123
where xsubs used here is 0.9. This value of 0.9 assumes that the Cd+ and Te+ ion yields in the substrate are equivalent to the yield that would be obtained from an Hg0.1Cd0.9Te layer . This method enables SIMS to be a viable technique for molar ratio determination from a single measurement without requiring a reference standard.
- Magneto-Transport Hall Measurements
- Hall Effect in Semiconductors
The Hall Effect is traditionally used to characterize carrier transport in semiconductors by allowing determination of electrical parameters such as the carrier type, concentration, and mobility, thus providing an immediate indication of material quality and eventual device performance . The basic principle behind the Hall Effect is best explained by considering a slab of conducting material through which a uniform current density flows under the presence of an applied magnetic field directed perpendicular to the current flow. Under an applied electric field Ex along the x-axis, charge carriers will flow along the same axis with an average drift velocity vx, proportional to the electric field. The proportionality constant, μ, is the carrier mobility and is independent of electric field for small field intensities. When a uniform magnetic field, Bz is applied along the z-axis, a force termed the Lorentz force, FB, which is perpendicular to the applied magnetic field and drift velocity, acts to deflect moving charge carriers to one side of the sample. An electrostatic force, FE is then set up in such a way as to oppose the deflection by the Lorentz force creating a measurable electric field, Ey along the y-axis. This field, also known as the Hall field, is proportional to the current density, Jx and the magnetic field, Bz. The proportionality constant is known as the Hall coefficient, RH where
Ey = -RHJxBz
Assuming hole carriers with density, p, the resulting current density, Jx can be expressed as
Jx = qvxp
The Lorentz force, FB exerted on the carriers is given by
FB = qBzvx
Under steady state conditions, the Lorentz and electrostatic forces balance resulting in zero current in the y direction and a constant Hall voltage (Vy), such that
-qEy = qBzvx
Substituting Equation 3.67 into 3.70, the Hall coefficient is found to be directly related to the carrier density by
RH = -EyJxBz = vxJx = 1qp
where the sign of RH denotes whether the carriers are electrons (negative) or holes (positive). Equation 3.71 implies that the larger the carrier density, the smaller the Hall coefficient due to a smaller Hall voltage being measured. Resistivity, r of the sample can be defined from the above equations using the following expression for conductivity, σ, where
σ = qpμ = 1ρ= JxEx
Since the Hall coefficient and resistivity at zero magnetic field are directly measurable, the carrier type, density, and mobility can easily be calculated from the above expressions. More specifically, experimental data on Hall Effect and resistivity over a wide temperature range (e.g. 4 K to 300 K) can be analyzed to give information concerning impurities, dopant activation energies, material imperfections and uniformity, and carrier scattering mechanisms .
- Structure Configuration for Hall Measurements
For all the samples used in this work, Van der Pauw (VDP) structures  were utilized for Hall measurements. To use the Van der Pauw technique, any arbitrary shape may be used, but must satisfy the two following conditions:
- Sample material must be laterally uniform, which means that it should be free from extended defects, holes, gaps, lateral composition gradients, areas in the plane of localized stress, and non-uniform thickness. When this condition is not satisfied, erroneous resistivity and Hall voltages are encountered.
- Contact dimensions must be small and positioned at the edge (or circumference) of the sample. Contacts not at an edge allow current to flow from contact to the edge compromising van der Pauw’s derived resistivity expression for a uniform sample with arbitrary shape.
- Sample Preparation and Experimental Setup
For this thesis, all samples for Hall measurements were washed by organic solvents in the cleanroom nanofabrication facility at UWA, prior to measurements. Regarding the contacts, it is imperative that they remain Ohmic at high magnetic fields and low temperatures. Non-Ohmic contacts have built-in barrier voltages which will be added to the Hall and resistivity voltages, leading to erroneous results. Ohmic contacts for n-type samples are established when the work function of the contact metal is less than that of the semiconductor, and vice versa for p-type material. For all n-type samples studied in this thesis, indium was used for contacts, using pressed indium, and gold was deposited as a contact for p-type materials.
The magnets used for Hall characterization at UWA are a 2 Tesla (2 T) electromagnet and a 12 Tesla (12 T) superconducting magnet. Samples measured on the 2 T system were placed on a carrier which is connected to a cold finger inside a cryostat. On the 12 T system, samples are placed in a cryostat with continuous helium flow. In both systems, the sample holder is positioned perpendicular to the applied magnetic field. Sample mounting involves hand bonding of thin gold wires from the sample onto a suitable insulating carrier.
Ohmic contacts are verified using current-voltage measurements on a HP4156A semiconductor parameter analyzer. An initial measurement of the Hall coefficient and resistivity with two values for current must be run to check that there is no dependence on the current magnitude. The lowest possible current that gives good signal-to-noise ratio and a low power dissipation to prevent sample/contact heating is utilized. A fully automated system with in-house developed software is then used to run the measurement for a given temperature. To reduce contact alignment errors and any thermoelectric field effects, voltages over both current directions and magnetic field polarities are taken and averaged. The magnetic fields utilized are logarithmically spaced and measurements taken as the magnet is ramped from a high positive magnetic field to zero magnetic field, and then repeated from a negative high magnetic field to zero magnetic field. With the 2 T magnet, variable magnetic field Hall measurements may be taken at 90 K and 300 K, and for the 15 T magnet, temperatures between 10 K and 300 K are utilized. A Matlab program was written that takes the measured Hall and resistivity voltages at each magnetic field point and converts them to the required Hall coefficients, RH and resistivity, r.
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