Showing papers in "Semiconductor Science and Technology in 2001"

Surface passivation of silicon solar cells using plasma-enhanced chemical-vapour-deposited SiN films and thin thermal SiO2/plasma SiN stacks

Abstract: Two different techniques for the electronic surface passivation of silicon solar cells, the plasma-enhanced chemical vapour deposition of silicon nitride (SiN) and the fabrication of thin thermal silicon oxide/plasma SiN stack structures, are investigated. It is demonstrated that, despite their low thermal budget, both techniques are capable of giving an outstanding surface passivation quality on the low-resistivity (∼1 � cm) p-Si base as well as on n + -diffused solar cell emitters with the oxide/nitride stacks showing a much better thermal stability. Both techniques are then applied to fabricate frontand rear-passivated silicon solar cells. Open-circuit voltages in the vicinity of 670 mV are obtained with both passivation techniques on float-zone single-crystalline silicon wafers, demonstrating the outstanding surface passivation quality of the applied passivation schemes on real devices. All-SiN passivated multicrystalline silicon solar cells achieve an open-circuit voltage of 655 mV, which is amongst the highest open-circuit voltages attained on this kind of substrate material. The high open-circuit voltage of the multicrystalline silicon solar cells results not only from the excellent degree of surface passivation but also from the ability of the cell fabrication to maintain a relatively high bulk lifetime (>20 µs) due to the low thermal budget of the surface passivation process.

Spin interactions in diluted magnetic semiconductors and magnetic semiconductor structures

Abstract: The spin-dependent interactions in diluted magnetic semiconductors are reviewed. The non-trivial dependence of the p-d and the d-d exchange interactions, which rule the magnetic properties of these materials, on the electronic configuration of the magnetic ions is presented. Depending on the occupation numbers in the ionic d shell and the position of the d level with respect to the bands, both the kinetic exchange and the superexchange can lead to antiferromagnetic, ferromagnetic Kondo-like interactions or even orbital dependent, sensitive to Jahn-Teller distortion couplings. Finally, the interactions explaining the ferromagnetism in III-V and p-II-VI with Mn ions, the magnetic properties in semiconductor quantum wells and the interlayer spin correlations in magnetic/non-magnetic semiconductor superlattices are discussed.

Fabrication of conducting GeSi/Si micro- and nanotubes and helical microcoils

Abstract: Conducting micro- and nanotubes and free-standing flexible helical microcoils have been fabricated from strained GexSi1-x/Si heterolayers. The fabrication technique was based on self-rolling of a thin highly strained epitaxial GexSi1-x/Si bifilm detached from the substrate by selective etching of a sacrificial layer in a roll-shaped tube. The obtained tube diameters varied from 10 nm to 13 µm, depending on the thickness and lattice mismatch of the GeSi/Si bilayer. GeSi/Si tubes and helical coils, up to 70 nm in diameter, exhibit good conducting properties and high mechanical strength.

Raman microspectroscopy analysis of pressure-induced metallization in scratching of silicon

Abstract: A single-point diamond turning machine was used to make grooves on (111) p-type single-crystal silicon wafers at room temperature. Scratch tests have been performed with both sharp (Vickers and conical) diamond tools, and a spherical (Rockwell) diamond tool. Our results showed that material removal mechanisms differed between these tools. Pressure-induced metallization of Si allows the ductile regime mechanical micromachining of wafer surfaces. Raman microspectroscopy and electron microscopy were used to determine the machining parameters that do not introduce cracking or other types of damage. The surface of the groove, after machining, was covered by a mixture of metastable, high-pressure silicon phases and amorphous silicon. Further, these phases can be transformed into cubic silicon by annealing. The maximum depth of cut in the ductile regime has been determined for the given scratch test conditions and tools. The developed technique can be used to machine Ge, GaAs and other semiconductors. Applications drawing from this research are many. For example, channels for microfluidic devices can be engraved with a channel cross-section that is determined by the shape of the tool, which allows patterns that cannot be produced using etching. There are no limitations on the channel length or direction, and the channel width can vary from potentially a few nanometres to several micrometres.

Melting temperatures of semiconductor nanocrystals in the mesoscopic size range

Abstract: A model, free of any adjustable parameters, is extended to predict the size dependence of the melting temperature of semiconductor nanocrystals. The model predictions are consistent with the experimental results for Si, Bi and CdS semiconductor nanocrystals. In addition, the simplified model with fixed material constants is in agreement with the usual phenomenological relationship that the size dependence of the melting temperature is proportional to the reciprocal of the nanocrystal radius.

Device model for quantum dot infrared photodetectors and their dark-current characteristics

Abstract: We propose a device model for quantum dot infrared photodetectors (QDIPs) with relatively large lateral spacing between QDs as occurs in QDIPs fabricated and experimentally investigated recently. The developed model accounts for the self-consistent potential distribution and features of the electron capture and transport in realistic QDIPs in dark conditions. The model is used for the calculation of the dark current as a function of the structural parameters, applied voltage and temperature. It explains a rather sharp increase in the dark current with increasing applied voltage and its strong sensitivity to the density of QDs and the doping level of the active region. The calculated dependences are in good agreement with available experimental data. The obtained characteristics of QDIPs are compared to those of QWIPs with similar parameters.

Effect of O2 post-deposition anneals on the properties of ultra-thin SiOx/ZrO2 gate dielectric stacks

Abstract: The effect of post-deposition anneal in O2 at different temperatures (500-700 °C) on the microstructure and electrical properties of SiOx/ZrO2 gate dielectric stacks is investigated. It is shown that the as-deposited ZrO2 layers are partly amorphous and crystallize after post-deposition anneal. From the analysis of high-frequency capacitance-voltage (C-V) characteristics, positive (negative) fixed charge is found in the as-deposited layer when Al (Au) electrodes are used. Furthermore, positive charge is generated in the gate stack and the density of interface states is increased during post-deposition anneal in O2. Both positive charge and interface state density can be greatly reduced by an additional post-metallization anneal in H2 at low temperature (400 °C). The dielectric constant of the gate stack presents a large increase after O2 post-deposition anneal at 700 °C, which may be attributed to the partial transformation of the silicon oxide interfacial layer into a Zr silicate. The leakage current through the gate stack is reduced by several orders of magnitude after O2 annealing, consistent with the increase in SiOx layer thickness, as well as the reduction in bulk trap density revealed by the reduced hysteresis effect observed in the C-V characteristics. The temperature dependence of the current density through the gate stack is also reduced after the post-deposition anneal in O2, which is attributed to the reduction in the trap-assisted tunnelling contribution to the leakage current.

A comparative study of electrochemically formed and vacuum-deposited n-GaAs/Au Schottky barriers using ballistic electron emission microscopy (BEEM).

Abstract: A comparative study between n-GaAs/Au contacts, formed by electrochemical deposition or by vacuum evaporation, is presented. The main parameter, the barrier height ?B, was determined using three methods, i.e.?classical current-voltage and capacitance-voltage measurements as well as STM-based ballistic electron emission microscopy (BEEM). The latter method allowed us to determine the distribution of ?B over the contact area on a nanometre scale and showed that the electrochemically made contacts are inhomogeneous. The main result, confirmed by the three methods, was that ?B was higher for the electrochemically deposited contacts than for the evaporated ones. This higher value is attributed to O- groups, present at the interface during the electrochemical metallization, and forming interfacial dipoles with the Au, leading to an increase of the barrier.

Highly photoluminescent ZnSe/ZnS quantum dots

Abstract: ZnSe quantum dots have been synthesized using a simple aqueous route. Coating ZnSe quantum dots with a ZnS monolayer, yields a remarkable enhancement in the PL quantum efficiency at room temperature without affecting the spectral distribution. The results suggest that passivation of surface states, along with an increased localization of the hole in core ZnSe layer, gives rise to high luminescence quantum yield.

Optical properties of β-In2S3 and β-In2S3:Co2+ single crystals

Abstract: β-In2S3 and β-In2S3:Co2+ single crystals were grown by the chemical transport reaction method using In2S3, S, and ZnS as starting materials and (ZnCl2 + I2) as a transport agent. The single crystals crystallized into a tetragonal structure. The indirect optical energy band gaps of the single crystals at 298 K were found to be 2.240 eV and 1.814 eV for β-In2S3 and β-In2S3:Co2+, respectively. The direct optical energy band gaps were found to be 2.639 eV and 2.175 eV for β-In2S3 and β-In2S3:Co2+, respectively. Impurity optical absorption peaks were observed for the β-In2S3:Co2+ single crystal. These impurity absorption peaks were assigned, based on the crystal field theory, to the electron transitions between the energy levels of the Co2+ ion sited in Td symmetry.

Properties of InAs/InAlAs heterostructures

Abstract: InAs is the only binary III-V compound semiconductor that exhibits a natural surface accumulation due to the high density of donor surface states. The Fermi level is pinned at any surface of an InAs wafer, regardless of orientation. It is therefore very likely that an accumulation layer is present at both the top and bottom surface or interface of a thin InAs epilayer with an intermediate bulk-like region between them. Epitaxial layers of InAs sandwiched between two 30 nm thick layers of In0.8Al0.2As or In0.52Al0.48As were grown on InP substrates by solid-source molecular beam epitaxy. Their static and dynamic properties were determined by means of gated Hall, resistivity and C-V measurements using a three-layer model to account for interface accumulation as well as the residual bulk-like intermediate region. The InAs/In0.8Al0.2As heterojunction interface has a significantly lower density of interface states than that of the In0.52Al0.48As/InAs interface. It is possible to drive such a structure from accumulation through flat band into depletion by means of moderate negative gate voltages. Using similar measurements, the effect of the thickness of the InAs layer as well as the presence or absence of a step-graded buffer on the density of surface states was determined.

Thermodynamic balance in quantum dot lasers

Abstract: The spontaneous emission and optical gain spectra from an InGaAs quantum dot laser have been independently measured under the same operating conditions. Using these spectra a combined probability-distribution function describing the electron occupancy in the conduction and valence bands has been experimentally determined. Comparison of this function with theoretical curves based on Fermi-Dirac statistics shows that for temperatures down to 100 K the carrier occupancy statistics are accurately described by thermal distributions. Measurements at 70 K show a breakdown of thermodynamic equilibrium indicated by non-thermal carrier distributions.

Formation of conductive CdO layer on CdS thin films during air heating

Abstract: A thin layer of CdO is formed on a chemically deposited CdS thin film through reaction with atmospheric oxygen during heating in air for 5-240 min at 370-500 °C. The sheet resistance of the film drops from about 1013 Ω-3.5 kΩ (370 °C) and 470 Ω (500 °C). From optical transmittance and reflectance spectra, the thickness of the CdO layer was found to be about 10 nm; the crystalline grain size is 12-25 nm, depending on the temperature and duration of heating; and the estimated electrical resistivity is 10-4-10-3 Ω cm. The optical bandgap of the CdS-CdO layer is effectively that of the underlying CdS thin film, about 2.45 eV in the annealed film. The CdS, which remains under the conductive CdO top layer, is photosensitive, with a photo-to-dark current ratio of 103 and crystalline grain diameter of about 10 nm in the case of a film heated at 500 °C for 5 min. These results are discussed in the context of window layers in solar cells.

Gettering simulator: physical basis and algorithm

Abstract: The basic physical principles and mechanisms of gettering of metal impurities in silicon are well established. However, a predictive model of gettering that would enable one to determine what fraction of contaminants will be gettered in a particular process and how the existing process should be modified to optimize gettering is lacking. Predictive gettering of transition metals in silicon requires development of a robust algorithm to model diffusion and precipitation of transition metals in silicon, and material parameters to describe the kinetics of defect reactions and the stable equilibrium state of the formed complexes. This paper describes the algorithm of a gettering simulator, capable of modelling relaxation and segregation gettering of interstitially diffusing transition metal impurities in silicon wafers. The basic physical equations used to model gettering are differential equations for diffusion, precipitation and segregation. These equations are solved using the implicit finite-difference algorithm, based on the underlying physics of the problem. The material parameters required as input for the gettering simulator such as segregation coefficient, precipitation site density and precipitation radius, which need to be obtained experimentally, are briefly discussed.

Conductive copper sulfide thin films on polyimide foils

Abstract: Kapton polyimide is known for its high thermal stability, >400 °C Copper sulfide thin films of 75 and 100 nm thickness were coated on DuPont Kapton HN polyimide foils of 25 µm thickness by floating them on a chemical bath containing copper complexes and thiourea The coated foils were annealed at 150-400 °C in nitrogen, converting the coating from CuS to Cu18S The sheet resistance of the annealed coatings (100 nm) is 10-50 Ω/ and electrical conductivity, 2-10×103 Ω-1 cm-1, which remain nearly constant even after the foils are immersed in 01-1 M HCl for 30-120 min The coated polyimide has a transmittance (25-35%) peak located in the wavelength region 550-600 nm, with transmittance dropping to near zero below 450 nm and below 10% in the near-infrared spectral region These characteristics are relevant in solar radiation control applications The coated foils might also be used as conductive substrates for electrolytic deposition of metals and semiconductors and for optoelectronic device structures

Electrical properties of crystalline YSZ films on silicon as alternative gate dielectrics

Abstract: Crystalline yttria-stabilized zirconia oxide (YSZ) film was successfully deposited on a silicon wafer without an interfacial amorphous SiO2 layer. The film with equivalent oxide thickness teox down to 1.77 nm shows negligible hysteresis and low interface state density, less than 3×1011 cm-2 eV-1. The leakage current density for teox = 1.77 nm film, 1.5×10-5 A cm-2 at 1 V bias voltage, is five orders of magnitude lower than that for SiO2 with the same equivalent oxide thickness. The results demonstrate that an ultra-thin YSZ film has sufficient resistivity against the formation of an underlying amorphous layer, and can be a promising gate dielectric replacing SiO2 to reduce the feature size of devices.

Reversibility of the island shape, volume and density in Stranski-Krastanow growth

Abstract: We report on reversible and irreversible phenomena in size-limited InAs island growth (SLIG) on GaAs(001) surface. We found that, with increasing the substrate temperature, the island density of the SLIG islands decreases, the lateral size of the islands increases and the islands strongly flatten. The average volume is either decreased or weakly affected. The total amount of InAs accumulated in quantum dots (QDs) strongly decreases in favour of the gas of In adatoms on the surface. Both unidirectional and reversible tuning of the substrate temperature after formation of the islands causes reversible changes in the island shape and density. We show the possibility of dramatically increasing the volume and the density of QDs approaching the strategically important 1.3 µm wavelength range via adatom condensation with cooling of the substrate after the formation of QDs. We also demonstrate that the substrate temperature cycling procedure may remarkably reduce the defect density in QD structures.

Monte Carlo analysis of dynamic and noise performance of submicron MOSFETs at RF and microwave frequencies

Abstract: In this paper, an ensemble 2D bipolar Monte Carlo simulator is employed for the study of static characteristics, high-frequency response and noise behaviour in a 0.3 µm gate-length n-MOSFET in common source configuration. Short-channel effects, such as velocity overshoot in the pinch-off region, together with the appearance of hot electrons at the drain end of the channel are observed in the static characteristics. Admittance parameters and the small-signal equivalent circuit have been calculated in order to characterize the dynamic response of the device. The use of a bipolar simulator allows one to study the dynamics of both types of carriers simultaneously. While the static results are dominated by the electron transport, the contribution of holes mainly affects the drain-substrate capacitive coupling. The noise behaviour of the simulated MOSFET is also studied (up to 40 GHz) by means of different parameters, such as the spectral densities of the current fluctuations at the drain and gate terminals (and their cross-correlation), normalized α, β and C parameters and NFmin . In the saturation regime, due to the presence of hot carriers, an increase in drain and gate noise with respect to the long-channel prediction has been found. Moreover, a stronger correlation between drain and gate noise is observed, especially at low drain current. Induced gate noise is found to play a crucial role in the determination of NFmin at high drain currents.

Thermodynamic analysis of the MBE growth of GaInAsN

Abstract: A thermodynamic approach to analysis of the growth of InGaAsN compounds by molecular beam epitaxy (MBE) is proposed. The developed thermodynamic model allows estimation of the mole fraction of nitrogen in the obtained alloys as a function of external growth parameters: element fluxes and growth temperature. The model predicts that the nitrogen incorporation is temperature-independent below 500??C and markedly diminishes at higher growth temperatures. The incorporation of nitrogen is suppressed on raising the arsenic flux; the content of group?III elements in the alloy affects the nitrogen incorporation only slightly. The results of simulation are compared with experimental data on MBE-grown InGaAsN alloys with small nitrogen content (<3%).

Surface passivation of (100) InP by organic thiols and polyimide as characterized by steady-state photoluminescence

Abstract: A method for the passivation of indium phosphide, based on thiolated organic self-assembled monolayers (SAMs) that form highly ordered, close-packed structures on the semiconductor surface, is presented. It is shown that the intensity of steady-state photoluminescence (PL) of n-type InP wafers covered with the thiolated SAMs increases significantly (as much as 14-fold) upon their covering with the monolayers. The ease with which one can tailor the outer functional groups of the SAMs provides a way to connect this new class of passivators with standard encapsulators, such as polyimide. Indeed, the PL intensity of SAM-coated InP wafers was not altered upon their overcoating with polyimide, despite the high curing temperature of the polymer (200 °C).

Optical and structural properties of self-organized InGaAsN/GaAs nanostructures

Abstract: Structural and optical properties of thin InGaAsN insertions in GaAs, grown by molecular beam epitaxy using an RF nitrogen plasma source, have been investigated. Nitrogen incorporation into InGaAs results in a remarkable broadening of the luminescence spectrum as compared with that of InGaAs layer with the same indium content. Correspondingly, a pronounced corrugation of the upper interface and the formation of well defined nanodomains are revealed in cross-sectional and plan-view transmission electron microscope (TEM) images, respectively. Raising the indium concentration in InGaAsN (N<1 %) to 35 % results in the formation of well defined separated three-dimensional (3D) islands. The size of the nanodomains proves that the InGaAsN insertions in GaAs should be regarded as quantum dot structures even in the case of relatively small indium concentrations (25 %) and layer thicknesses (7 nm), which are below the values required for a 2D-3D transition to occur in InGaAs/GaAs growth. Dislocation loops have been found in TEM images of the structures emitting at 1.3 µm. They are expected to be responsible for the degradation of the luminescence intensity of such structures in agreement with the case of long-wavelength InGaAs-GaAs quantum dots.

GaN/AlGaN quantum wells for UV emission: heteroepitaxy versus homoepitaxy

Abstract: GaN/Al0.1Ga0.9N quantum wells (QWs) are grown by molecular beam epitaxy on (0001) sapphire and (0001) GaN single-crystal substrates. Their optical properties are investigated by temperature-dependent photoluminescence (PL). Ar room temperature, the integrated PL intensity of the homoepitaxial QW is 20 times higher than that of the heteroepitaxially grown QW. In the latter case, the PL intensity rapidly decreases even in the low-temperature range (10-100 K), This is ascribed to the non-radiative recombination of excitons on threading dislocations. In contrast, the PL intensity quenching of the homoepitaxial QW is purely governed by carrier thermal escape. These results demonstrate that GaN bulk substrates offer new opportunities for UV optoelectronics.

A novel Pd/oxide/GaAs metal-insulator-semiconductor field-effect transistor (MISFET) hydrogen sensor

Abstract: A novel and high-performance Pd/oxide/GaAs hydrogen sensor based on a metal-insulator-semiconductor field-effect transistor (MISFET) is fabricated and studied. In the presence of the interfacial oxide, high sensitivity and significant increase in output drain current are observed. In the presence of hydrogen, a 2×200 µm2 gate dimension device shows good dc characteristics including high turn-on voltage, an obvious variation of drain current and a short response time. In addition, under the applied voltage of -4 V and 537 ppm hydrogen in air, a very high sensitivity of 9473 is obtained. This performance shows that the device studied has a good potential for high-speed and high-sensitivity hydrogen sensor and MISFET integrated circuit applications.

Comparative study of 200-300 GHz microwave power generation in GaN TEDs by the Monte Carlo technique

Abstract: Electron transport and microwave power generation in the 200-300 GHz frequency range by n+-n--n-n+ zincblende GaN and n+-p-n-n--n+ wurtzite GaN structures have been studied by a Monte Carlo particle simulation which solves the Boltzmann transport and Poisson's equations along with equations governing the associated circuit elements and parasitic contact resistance. It is shown that at 300 K in the 230-250 GHz frequency range over 350 mW microwave power can be delivered by the n+-p-n-n--n+ wurtzite GaN structure in continuous wave operation mode and over 1.3 W in pulsed mode.

Ni/Ag metallization for SiGe HBTs using a Ni silicide contact

Abstract: We developed a self-aligned low-temperature process for the production of SiGe hetero bipolar transistors (HBTs) using a new metallization scheme with Ni/Ag taking advantage of the low specific resistivity of Ag and good contact resistance and low silicon consumption of the Ni silicide. Gummel plots of fabricated HBTs show sufficiently good behaviour. The formation of Ni silicide over temperature (325-500 °C) in a rapid thermal process system is studied. At temperatures above 425 °C a rather smooth film of monosilicide NiSi is formed. The resistivity of the thin (110 nm) NiSi was found to be excellent (11 µΩ cm) compared with bulk values. The contact resistance to n- and p-type silicon of 5×1019 cm-3 is determined. Formation of self-aligned Ni silicide/Ag contacts is investigated and compared to non-self-aligned contacts.

Interfacial charge trapping in extrinsic Y2O3/SiO2 bilayer gate dielectric based MIS devices on Si(100)

Abstract: Metal-insulator-semiconductor (MIS) structures based on an extrinsic Y2O3 dielectric film on Si show high leakage currents due to roughness-related highly localized fields. Oxygen annealing increases the dielectric constant and strength and reduces leakage currents by transforming Y2O3 (film)/Si(100) into a bilayer Y2O3 (film)/SiO2/Si(100) dielectric structure. Evolution of interfacial SiO2 causes generation of mid-gap interface states at Ev + 0.23 eV and Ev + 0.43 eV, which act as electron traps and are responsible for hysteresis effects in capacitance-voltage (C-V) and current-voltage (I-V) behaviour in the accumulation-inversion modes. The electron trapping reduces the cathodic field and causes lowering of the current and the shift in current to higher fields after successive ramps. The charge trapping effects cause varied and unstable C-V and I-V behaviour of MIS structures based on a Y2O3/SiO2 bilayer gate dielectric. Its origin has been attributed to microstructure and defect state modification at the Y2O3 film-Si interface. This limits its application in high-density dynamic random access memory and ultra-large-scale integration devices.

Antireflective porous-silicon coatings for multicrystalline solar cells: the effects of chemical etching and rapid thermal processing

Abstract: In this paper, the emitter of multicrystalline silicon solar cells has been chemically etched in order to form porous silicon (PS) layers, usually known as stain-etched PS, to be used at the same time as a selective emitter and as an efficient antireflective layer. The optical behaviour of the solar cells in the 250-850 nm wavelength range (5-1.45 eV range) was determined before and after PS formation, resulting in a notable reduction of reflectance after PS formation and a corresponding increase in cell efficiency. The different morphologies of the silicon emitter and metallic contacts, before and after PS formation, were analysed by scanning electron microscopy and atomic force microscopy. Furthermore, the electrical properties of both the emitter region and the contacts were investigated, as well as the most significant solar cell parameters before and after PS formation. Finally, the effect of rapid thermal processing in nitrogen and oxygen atmospheres on both the surface morphology and the optical behaviour of PS was studied.

High thin-film yield achieved at small substrate separation in chemical bath deposition of semiconductor thin films

Abstract: A technique to improve thin-film yield in chemical bath deposition of semiconductor thin films is presented. This involves the use of very small substrate separation, 0.1 mm, to eliminate the passive layer of the bath, which contributes solely to precipitation. At small substrate separation, a thin layer of the bath mixture is held by surface tension between pairs of substrates. The thin-film yield, which is the percentage of the metal ions in the bath utilized towards the film formation, obtained in this experimental set-up is considered to be near 100% for CuS, Cu2-xSe, CdS and CdSe thin films. The final thickness estimated for the films is about 40-50 nm. The optical and electrical properties of these films are presented to illustrate that at such film thickness they fulfil the requirements for certain applications.

SiGe HBTs for application in BiCMOS technology: I. Stability, reliability and material parameters

Abstract: Extensive work has been done on the SiGe HBTs for BiCMOS applications recently. The work on stability, reliability, simulation and material parameters is critically examined and reviewed in this part of the review. The work on the design, technology and performance of the HBTs will be discussed in part II of the review.

Energy relaxation of localized excitons at finite temperature

Abstract: Macro- and micro-photoluminescence (PL) spectroscopy has been applied to investigate the exciton localization in cubic CdS/ZnSe type-II superlattices (SL) in the temperature range 5-35 K. The non-monotonic shift of the macro-PL peak with increasing temperature reveals the kinetic contribution of acoustic-phonon-assisted exciton multi-hopping processes. The experimental data are described by means of computer simulation and calculations based on a kinetic theory generalized from zero to finite temperatures. The advantages of each theoretical approach are discussed.