Session A41: Semiconductors: Thermodynamics and Transport

Heat Capacity and Isotopic Masses of Semiconductors

The heat capacity of semiconductors has been investigated both theoretically and experimentally since the early 20$^{th}$ century. Its dependence on the isotopic masses of its constituents, however, has only received attention during the past few years [1]. The quantity usually investigated vs. temperature$ T $is D( $T$ )= d ln $C_{v} T^{-3}$ / d ln $M. $For monatomic diamond, Si, and Ge, D($T)$ exhibits a peak at a temperature 0.1 times that of TA phonons at the X-point of the BZ. In binary tetrahedral semiconductors (GaN, ZnO) D($T)$ differs for the heavier and lighter mass, peaking at 0.15 times the TA temperature of the former and at 0.25 times the TO temperature of the latter. The ratio 0.15 can also can also be estimated with a one-oscillator Einstein model. Here we present similar measurements for a binary compound with rock salt structure: PbS (galena). The phonon density of states (DOS) of this material is shown to peak at 80K for the Pb-like phonons. For the S-like phonons a broad band between 150 and 350K is found, in \textit{ab initio} calculations, to dominate the DOS. The corresponding D($T)$ peaks in both cases at 0.14 times the temperature of the corresponding phonons ( 80K and 240K, respectively). The D($T)$ will be compared with \textit{ab initio} calculations, performed with the ABINIT code. [1] J.Serrano, Phys. Rev. B 73, 094303 (2006) and references therein.   

Magnetic and electrical transport properties of Fe$_{1-x}$Cr$_{x}$Sb$_{2}$

We have investigated magnetic, thermodynamic and electrical transport properties of Fe$_{1-}$xCr$_{x}$Sb$_{2}$ (0$\le $x$\le $1) single crystals. Ground state of the system evolves from nonmagnetic semiconductor for x = 0 to antiferromagnetic semiconductor for x = 1. In contrast to Co substitution, Cr doping in FeSb$_{2}$ does not result in metallic state and magnetoresistance is negligible. Magnetic phase diagram and conduction mechanism will be discussed.   

High Temperature thermoelectric properties of Ba$_{x}$Yb$_{y}$Co$_{4}$Sb$_{12}$ composites

In materials where the mean free path of charge carriers is smaller than that of phonons, enhancing boundary scattering in the matrix may improve the thermoelectric figure of merit$^{1}$. We have applied this idea to n-type skutterudites that have large effective mass and consequently small carrier mean free path. We prepared double-filled Ba$_{x}$Yb$_{y}$Co$_{4}$Sb$_{12}$ skutterudite composites with a wide range of the filling fractions $x$ and $y$. The experimental filling fraction limits are in a good agreement with the values predicted theoretically. In cases where we intentionally exceeded the filling limit, the excess filler atoms form fine oxide particles that are distributed mainly on the grain boundaries. While the composites maintain good electrical transport properties due to weak charge carrier scattering from the oxide particles, the lattice thermal conductivity is reduced significantly. The highest ZT in these composite skutterudites reaches 1.3 at 800K.   

Reciprocal capacitance transients?

When the reverse bias across a semiconductor diode is changed, charge carriers move to accommodate the appropriate depletion thickness, producing a simultaneous change in the device capacitance. Transient capacitance measurements can reveal inhibited carrier motion due to trapping, where the depth of the trap can be evaluated using the temperature-dependent escape rate. However, when we employ this technique on a GaAs$_{0.72}$P$_{0.28}$ n+/p diode (which is a candidate for incorporation in multi-junction solar cells), we observe a highly non-exponential response under a broad range of experimental conditions. Double exponential functions give good fits, but lead to non-physical results. The deduced rates depend on the observation time window and fast and slow rates, which presumably correspond to deep and shallow levels, have identical activation energies. Meanwhile, we have discovered a universal linear relationship between the inverse of the capacitance and time. An Arrhenius plot of the slope of the reciprocal of the transient yields an activation energy of approximately 0.4 eV, independent of the observation window and other experimental conditions. The reciprocal behavior leads us to hypothesize that hopping, rather than escape into high-mobility bands, may govern the transport of trapped holes in this system.   

First principles calculation of bulk semiconductor mobilities for radiation detection application

The development of high energy resolution, room temperature semiconductor radiation detectors requires the development of materials with both an increased carrier mobility-lifetime product ($\mu\tau$) and a band gap in the 1.6-2.5 eV range. An adequate $\mu\tau$ is required for efficient collection of generated carriers from large devices, maximizing S/N ratio and resolution. We use density functional theory to study the microscopic mechanisms of mobility degradation from point defects and to calculate the intrinsic limits of mobility for a given bulk material. Scattering rates obtained from the Born approximation allow us to calculate the contributions of different point defects on mobility degradation, within Boltzmann transport theory. Both native defects and impurities were considered. Formation energies for the various defects were calculated to determine their equilibrium concentrations. Combined with calculations of the defect chemical potentials, we make predictions on the feasibility of improving mobility by thermal annealing to remove the most detrimental defects. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

Two-contact and four-contact magnetoresistance in InSb / Au hybrid structures.

We present magnetoresistance measurements on hybrid InSb-Au structures in two-contact and four-contact configurations. Large geometrical magnetoresistances in InSb-Au structures are enabled by the high electron mobility, and hence large Hall angle, in InSb and by the difference in conductivity between semiconductors and metals. InSb / metal hybrid magnetoresistors have attracted attention for applications in data storage and sensing, where a two-contact geometry is appealing. Our geometries consist of mm-sized thin-film InSb bar mesas paralleled by Au shunts, fabricated by lithographic techniques. The four-contact magnetoresistances are experimentally observed to be substantially higher (up to 8000 perc. at a magnetic field of 1 T, at 6 K and at an InSb mobility 40,000 cm2/Vs) than the two-contact magnetoresistances (average 80 perc.) over the temperature range studied. The two-contact magnetoresistances further stay short of the Corbino limit. Effects of the hybrid structure are evident however: for two-contact magnetoresistances at 1 T, an absence of Au shunts in otherwise equivalent geometries leads to magnetoresistances of about 15 perc., one-sided shunts result in about 70 perc., and two-sided shunts in about 140 perc. (NSF DMR-0618235).   

Nonadiabatic electron heat pump

We investigate a mechanism for extracting heat from metallic conductors based on the energy-selective transmission of electrons through a spatially asymmetric resonant structure subject to ac driving. This quantum refrigerator can operate at zero net electronic current as it replaces hot by cold electrons through two energetically symmetric inelastic channels. We present numerical results for a specific heterostructure and discuss general trends. We also explore the conditions under which the cooling rate may approach the ultimate limit given by the quantum of cooling power.   

Scanned-gate and Kelvin-probe microscopy to investigate surface-acoustic-wave-driven transport through a depleted GaAs channel

Electron transport driven by a surface acoustic wave (SAW) through a depleted GaAs channel is the basis for a proposed device capable of quantum information transfer or processing. Device fabrication benefits from a detailed understanding of the capture process at the channel entrance and the dynamics in the channel. We report two experiments to obtain spatial information uniquely provided by low-temperature scanning-probe microscopy. Scanned-gate microscopy, which generates images of SAW-induced current, shows features near the channel entrance that evolve from spots to crescents. Comparison with simulations confirms that the SAW current increases when the maximum potential gradient along the channel is reduced. Kelvin-probe microscopy is adapted to make images of SAW-induced charge, revealing a build-up of negative charge at the channel entrance when no SAW current flows, and a broken line of negative charge, and occasionally positive charge or dipole behavior, with a SAW current.   

Can we use scanned probe microscopy to measure local carrier mobility?

A local measurement of charge carrier mobility in pi conjugate systems would provide much new insight into charge injection, trapping and transport. We have demonstrated recently that low-spring-constant cantilevers can be used to observe minute electric field fluctuations arising from thermal dielectric fluctuations in polymers [S. Kuehn et al., PRL, \textbf{96, }156103 (2006); S. Kuehn et al., JPCB 110, 14525 (2006)]. Here we show how ultra-sensitive cantilevers can also be used to measure the local charge diffusion constant via the effect of the associated electric field fluctuations on cantilever frequency and ringdown time. Analytical scaling laws and numerical simulations of the electric field power spectrum resulting from the thermal motion of holes in a N,N'-diphenyl-N-N'-bis(3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD) / polystyrene field effect transistor suggest that the local hole diffusion constant can be inferred from measurements of cantilever frequency and ringdown time as a function of tip height and charge density. We suggest a route to directly testing the Einstein relation by comparing the locally measured charge diffusion constant to the bulk field effect transistor mobility.   

Charge Transfer Statistics in Quantum Point Contact

We present the results of the experimental study of the Charge Transfer Statistics for a Quantum Point Contact up to the third cumulant. QPC creates a variable transmission probability barrier, and therefore allows to check the CTS predictions [1] beyond the Poissonian limit. It has been recently understood that the intrinsic CTS is strongly affected by the measurement circuit, see [2] and references therein. We calculated the effect of the measurement circuit for a simple and realistic model of a capacitively shunted resistive load. We found the experimental results to be consistent with the calculations. We believe the results to be the first measurements of the third cumulant in a system different from the low transmission tunneling junction. \newline \newline [1] L.\,S. Levitov, G.\,B. Lesovik, JETP Lett. {\bf 58}, 230 (1993). \newline [2] B.~Reulet, J. Senzier and D. E. Prober, Phys. Rev. Let. {\bf 91}, 196601 (2003).   

Thermopower of a Quantum Dot in a Coherent Region

Thermoelectric power can provide useful information on electron transmission processes. Recently, thermoelectric power of quantum dots made in two-dimensional electron gases and carbon nanotubes has been measured by several groups, and compared with the theory based on sequential-tunneling and co-tunneling. It, however, remains an unsolved problem to study how electron coherency during transmission affects the thermoelectric power. In this presentation, thermoelectric power due to coherent electron transmission through a quantum dot is theoretically discussed. In addition to the known features related to resonant peaks, we show that a novel significant structure appears between the peaks. This structure arises from the so-called transmission zero, which is characteristic of coherent transmission through several quantum levels. It has also been shown that these structures are sensitively suppressed by weak phase-breaking, and that the calculated thermoelectric power coincides with the co-tunneling theory for sufficiently large phase-breaking. It has been proposed that, due to sensitivity to phase breaking, thermoelectric power can be used to measure electron coherency in a quantum dot. We also present the improved Mott formula, which can reproduce correct results for arbitrary transmission probabilities. (Reference: T. Nakanishi and T. Kato: cond-mat/0611538.)   

Green Kubo calculations of thermal conductivity for skutterudites

The thermal conductivity of skutterudites have been studied experimentally for several years and the results clearly show a strong dependence on whether or not the skutterudite is filled. This result has been explained, and indeed predicted, by the presence of a rattling ion in the filled materials. On the other hand, it has been shown that the potential of the rattling ion is not dramatically anharmonic as expected within a simple rattling ion concept. In this work we will discuss the thermal conductivity of a realistic model of the skutterudites through a Green-Kubo calculation using molecular dynamics. We represent the interatomic potentials as Taylor series in displacements from equilibrium with up to quartic anharmonic terms. In this initial study we explore different central force parameters from empirical models and first principles calculations in the literature.   

Lattice thermal conductivity of porous silicon : Molecular dynamics study

Thermoelectric (TE) materials, which are important for power-generation and solid-state refrigeration devices, have received revived interest due to the discovery of a high figure of merit, $ZT$, in materials with reduced dimensions such as BiTe/SbTe superlattices or BiTe nanocomposites. Recently, nanowires and nano-porous materials have also been considered experimentally as good candidates for increasing $ZT$ beyond 3, considered a minimum for practical applications of TE materials. Although such materials are very promising, it is important to understand the underlying principles of how charge and heat transport occur at the nanoscale in order to predict the dependence of $ZT$ on, e.g., structure, surface chemistry, and defects. In this work, we perform theoretical studies of lattice thermal conductivities, $\kappa_{L}$, of nano-porous silicon with a range of configurations. Specifically, $\kappa_{L}$ is calculated using classical molecular dynamics with varying hole diameter, hole-hole distance, and hole passivation chemistry. These results are compared both with bulk calculations as well as the inverted case of nanowires, and $\kappa_{L}$ is discussed in terms of specific phonon scattering at surface boundaries.