Capacitance spectroscopy in hydrogenated amorphous silicon Schottky diodes and high efficiency silicon heterojunction solar cells

In this thesis, research on a-Si:H Schottky diodes and a-Si:H/c-Si heterojunctions is presented with the focus on the capacitance spectroscopy and information on electronic properties that can be derived from this technique. Last years a-Si:H/c-Si heterojunctions (HJ) have received growing attention as an approach which combines wafer and thin film technologies due to their low material consumption and low temperature processing. Compared to conventional crystalline silicon (c-Si) technologies, HJ solar cells benefit from lower fabrication temperatures (around 200°C) thus reduced costs, possibilities of large-scale deposition, better temperature coefficient and lower silicon consumption (thinner wafers can be used due to excellent passivation quality). In this area impressive results were achieved by Sanyo Electric with the so called a-Si/c-Si Heterojunction with Intrinsic Thin layer (HIT) solar cell. This technology showed excellent surface passivation and the highest power conversion efficiency. The most recent record efficiency belongs to Panasonic with 24.7% for a cell of practical size (100 cm2 and above) : was obtained. There are several key properties of a-Si:H/c-Si heterojunctions that should be addressed when fabricating a high efficiency device. Firstly, the density of states (DOS) in the bandgap of a-Si:H is of particular importance since bandgap defects determine the band bending and space charge in aSi:H, favor the trapping and recombination of free carriers and thus also have an impact on transport of the carriers and their collection on the contacts. Secondly, determination of band offsets between a-Si:H and c-Si is of crucial importance since they govern the carrier transport across the junction and determine the band bending in c-Si. The aim of this thesis is to provide a critical study of the capacitance spectroscopy as a technique that can provide information on both subjects: DOS in a-Si:H and band offset values in a-Si:H/c-Si heterojunctions. In Chapter 1 a description of hydrogenated amorphous silicon is presented with the focus on its application in photovoltaic devices. Chapter 2 recalls the basics of p-n junctions and the fundamental principles of the capacitance vs voltage (C-V) technique. Possibilities and limitations of C-V measurements and admittance spectroscopy are addressed as well. The depletion approximation is recalled since it plays a very important role in the description of a junction and may be a reason of erroneous interpretations of the capacitance measurements. In Chapter 3, capacitance spectroscopy in a-Si:H Schottky diodes is investigated. Our interest is concentrated on the simplified treatment of the temperature and frequency dependence of the capacitance that allows one to extract the density of states at the Fermi level in a-Si:H Schottky diodes. To our knowledge no critical assessment of this treatment has been carried out. We focus on the study of the reliability and validity of this approach applied to a-Si:H Schottky barriers with various magnitudes and shapes of the DOS. Several structures representing n-type and undoped hydrogenated amorphous silicon Schottky diodes are modeled with the help of numerical simulation softwares. We show that the reliability of the studied treatment drastically depends on the approximations used to obtain the explicit analytical expression of the capacitance in such an amorphous semiconductor. te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 In the second part of the chapter, we study the possibility of fitting experimental capacitance data by numerical calculations with the input a-Si:H parameters obtained from other experimental techniques. With slight corrections of parameters describing the DOS distributions a very good reproduction of experimental capacitance data is obtained. We conclude that the simplified treatment of the experimentally obtained capacitance data together with numerical modeling is a valuable tool to assess some important parameters of the material with no need in any additional knowledge on the DOS of a studied sample. In chapter 4, we study the capacitance spectroscopy of a-Si:H/c-Si heterojunctions with special emphasis on the influence of a strong inversion layer in c-Si at the interface. Firstly, we focus on the study of the frequency dependent low temperature range of capacitance-temperature dependencies of a-Si:H/c-Si heterojunctions. The theoretical analysis of the capacitance steps in calculated capacitance-temperature dependencies is presented by means of numerical modeling. It is shown that two steps can occur in the low temperature range, one being attributed to the activation of the response of the gap states in a-Si:H to the small signal modulation, the other one being related to the response of holes in the strong inversion layer in c-Si at the interface. The experimental behavior of C-T curves is discussed. In the second part of Chapter 4, the quasi-static regime of the capacitance is studied. We show that the depletion approximation fails to reproduce the experimental data obtained for (p) a-Si:H/(n) c-Si heterojunctions. Due to the existence of the strong inversion layer, the depletion approximation overestimates the potential drop in the depleted region in crystalline silicon and thus underestimates the capacitance and its increase with temperature. A complete analytical calculation of the heterojunction capacitance taking into account the hole inversion layer is developed. It is shown that within the complete analytical approach the inversion layer brings significant changes to the capacitance for large values of the valence band offset. The experimentally obtained C-T curves show a good agreement with the complete analytical calculation and the presence of the inversion layer in the studied samples is thus confirmed. The application of capacitance measurements in the derivation of the band-offsets is discussed by comparing experimentally and analytically obtained C-V dependencies at different temperatures. The discussion of the influence of the c-Si surface inversion layer on the C-V profiles is provided as well. We demonstrate that due to the existence of the strong inversion layer, the derivation of the band offsets from C-V measurements leads to erroneous results. te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 Résumé Les travaux développés dans cette thèse sont dédiés à l’étude des propriétés électroniques de diodes Schottky de silicium amorphe hydrogéné (a-Si:H) et d'hétérojonctions entre silicium amorphe hydrogéné et silicium cristallin, a-Si:H/c-Si au moyen de spectroscopies de capacité de jonctions. Parmi les technologies photovoltaïques à base de silicium, les cellules solaires à hétérojonction a-Si:H/c-Si ont reçu un intérêt croissant car cette nouvelle technologie a un fort potentiel d’amélioration du rendement photovoltaïque et de réduction de coûts. Par rapport aux cellules photovoltaïques classiques à homojonctions, les cellules à hétérojonctions bénéficient des avantages de dépôt des couches amorphes à grande échelle et à des températures faibles, autour de 200°C (procédés de dépôt par décomposition assistée par plasma de gaz précurseurs), d’un meilleur coefficient de température, et d’une consommation plus faible de silicium (des plaques plus minces peuvent être utilisées en raison de l’excellente qualité de passivation de surface par le a-Si:H). A partir de cette technologie à hétérojonctions, la société japonaise Panasonic a réalisé en 2013 une cellule de grande surface (>100 cm2) possédant un rendement de conversion record de 24,7%. Lors de la fabrication des cellules solaires à haut rendement plusieurs paramètres d’une hétérojonction a-Si:H/c-Si doivent être considérés. Premièrement, la densité d’états (DOS, Density Of States) dans le gap du a-Si:H est d’une grande importance car il s’agit de défauts qui : • déterminent la courbure des bandes et la charge d’espace dans le a-Si:H ; • favorisent le piégeage et la recombinaison de porteurs libres ; • influencent le transport des porteurs libres jusqu'aux contacts et leur collecte. Deuxièmement, la détermination des désaccords des bandes entre la couche amorphe et la couche cristalline est indispensable puisque ceux-ci contrôlent le transport à travers la jonction et déterminent la courbure des bandes dans c-Si, ce qui va notamment influencer la recombinaison des porteurs sous lumière, donc la tension de circuit ouvert des cellules. Cette thèse a pour but d’étudier la spectroscopie de capacité comme technique d'analyse de paramètres clés pour les dispositifs à hétérojonctions de silicium : la densité d’états dans le a-Si:H et les désaccords des bandes entre aSi:H et c-Si. Dans le premier chapitre de ce manuscrit, nous présentons une description du silicium amorphe axée sur son application dans le domaine du photovoltaïque. Dans le deuxième chapitre nous rappelons les éléments de base de la théorie sur la jonction p-n te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 ainsi que les principes de la technique couramment désignée C-V (capacité-en fonction de la tension). Nous abordons aussi les potentiels et les limitations des mesures C-V et de la spectroscopie d’admittance. A ce stade, un rappel est effectué sur l’approximation courante consistant à déterminer l'extension de la zone de charge d'espace de la jonction et sa capacité en négligeant les contributions des deux types de porteurs libres (dénommée quelquefois approximation de déplétion, par transposition de sa désignation anglo-saxonne), car elle joue un rôle important dans la description d’une jonction et elle peut être à l’origine de fausses interprétations des mesures de capacité. Le troisième chapitre est dédié à l’étude de la capacité de diodes Schottky. Nous nous concentrons sur un traitement simplifié de la capacité en fonction de la température et de la fréquence reposant sur une expression analytique obtenue par une résolution approchée de l'équation de Poisson. Ce traitement permet en principe d’extraire la densité d’états au niveau de Fermi dans le a-Si:H et la fréquence de saut des électrons depuis un état localisé au niveau de Fermi vers la bande de conduction, mais il n'a jamais été critiqué sur la base d'une comparaison avec un calcul numérique complet. En appliquant ce traitement simplifié à la capacité calculée sans approximation à l'aide de deux logiciels de simulation numérique, nous montrons que sa fiabilité et sa validité dépendent fortement de la distribution des états localisés dans la bande interdite du aSi:H et de la position du niveau de Fermi. Globalement, le traitement permet toujours d'obtenir l'ordre de grandeur de la densité d'états au niveau de Fermi, mais la fréquence de saut peut être surestimée de plusieurs ordres de grandeur Nous montrons également que le calcul numérique de la capacité, à partir de paramètres du matériau obtenus par d'autres techniques de caractérisation, permet, moyennant de légers ajustements de ces paramètres, de bien reproduire les données mesurées expérimentalement, en particulier la dépendance de la capacité en fonction de la température et de la fréquence.. Dans le chapitre 4 nous abordons l’étude de la capacité des hétérojonctions entre a-Si:H de type p et c-Si de type n, et nous mettons particulièrement en avant l’existence d'une couche d’inversion forte à l’interface dans le c-Si, formant un gaz bidimensionnel de trous. Dans une première partie, nous présentons une étude par simulation numérique de la dépendance de la capacité en fonction de la température, pour laquelle un ou deux échelons peuvent être mis en évidence à basse température. Leur analyse montre qu’un des ces échelons est attribué à l’activation de la réponse de la charge dans le a-Si:H, qui peut dépendre à la fois du transport et du piégeage/dépiégeage d'électrons au niveau de Fermi, alors que l’autre, présentant une énergie d'activation plus grande, est lié à la modulation de la concentration des trous dans la couche d’inversion forte, lorsque celle-ci existe (i.e. pour des valeurs suffisamment élevées du désaccord de bande de valence). On présente ensuite une discussion de résultats expérimentaux. Si un échelon de capacité peut quelquefois être détecté, son énergie d'activation reste toujours plus faible que celle observée dans les simulations pour la modulation du gaz de trous. Une interprétation basée sur des mécanismes de transport par effet tunnel et par saut dans le a-Si:H est proposée pour expliquer ce désaccord entre résultats expérimentaux et simulation numérique, celle-ci n'intégrant pas ce type de mécanismes. Nous mettons par ailleurs en évidence un comportement quasi statique de la capacité montrant une augmentation significative avec la température. te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 Ce régime quasi-statique de la capacité fait l’objet d’une discussion dans la deuxième partie du chapitre 4. Nous mettons en relief le fait que l’approximation de la zone de déplétion ne permet pas de reproduire cette augmentation de la capacité en fonction de la température. Du fait de l’existence de la couche d’inversion forte, la chute de potentiel dans la zone de déplétion du c-Si est plus faible que la valeur déterminée par le calcul attribuant toute la chute de potentiel à la zone de déplétion. Par conséquent, cette approximation conduit à sous-estimer la capacité ainsi que son augmentation avec la température. Nous présentons alors un calcul analytique complet qui tient compte à la fois de la distribution particulière du potentiel dans le a-Si:H, et des trous dans le c-Si dont la contribution à la concentration totale de charges n'est pas négligeable dans la couche d’inversion forte. Le calcul analytique complet permet de bien reproduire les résultats expérimentaux de capacité en fonction de la température; ceci confirme la présence de la couche d’inversion forte dans les échantillons étudiés. On présente enfin une discussion sur l’application de la technique C-V pour la détermination des désaccords des bandes, ainsi que la comparaison des courbes capacitétension obtenues expérimentalement et analytiquement à différentes températures. Nous précisons ainsi aussi l’influence et l'importance de la prise en compte de la couche d’inversion forte dans l'analyse des mesures C-V. te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 Table of contents 1 a-Si:H and its applications...........................................................................................................10 1.1 Description of the a-Si material..............................................................................................10 1.1.1 Atomic structure..............................................................................................................11 1.1.2 Electronic structure and properties..................................................................................12 1.1.3 Density of states in the band gap.....................................................................................14 1.1.3.1 Dangling bonds........................................................................................................16 1.2 Growth of a-Si:H....................................................................................................................18 1.3 Photovoltaic applications of hydrogenated amorphous silicon .............................................22 1.3.1 Amorphous silicon solar cells.........................................................................................22 1.3.2 Amorphous silicon / crystalline silicon heterojunction solar cells..................................25 1.4 Aim of this work.....................................................................................................................29 1.5 References...............................................................................................................................31 2 Application of capacitance spectroscopy in semiconductors....................................................36 2.1 Basic concepts of a p-n junction.............................................................................................36 2.2 Two types of capacitance: differential and depletion capacitance..........................................39 2.2.1 Diffusion capacitance......................................................................................................40 2.2.2 Depletion Capacitance....................................................................................................41 2.3 Capacitance –voltage technique..............................................................................................42 2.3.1 Doping concentration......................................................................................................42 2.3.2 Barrier height..................................................................................................................47 2.4 DOS in the band gap from capacitance measurements...........................................................49 2.4.1 The influence of deep defects on C-V profiles................................................................49 2.4.2 Admittance spectroscopy................................................................................................50 2.4.3 Transient measurements..................................................................................................54 2.5 Conclusions.............................................................................................................................56 2.6 References...............................................................................................................................58 3 Capacitance spectroscopy of a-Si:H Schottky diodes................................................................61 3.1 Theoretical development.........................................................................................................61 3.1.1 Dynamics of capture and emission processes.................................................................61 3.1.2 Band diagram and capacitance of a Schottky diode........................................................65 3.1.3 The simple treatment K-T of the C-T data.......................................................................70 3.2 Modeling of a-Si:H Schottky diodes......................................................................................74 3.2.1 Determination of the DOS at the Fermi level, N(EF), the activation energy, Ea, and the attempt-to-escape frequency, νn.................................................................................................76 3.2.1.1 Constant DOS..........................................................................................................76 3.2.1.1.a n-type a-Si:H: EC–EF=0.2 eV, N(EF)=1×10cmeV.....................................76 3.2.1.1.b n-type a-Si:H: EC–EF=0.2 eV, N(EF)=1×10cmeV.....................................79 3.2.1.1.c Undoped a-Si:H: EC–EF=0.7 eV, N(EF)=1×10cmeV.................................84 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 3.2.1.2 Non constant DOS distributions..............................................................................90 3.2.1.2.a Exponential conduction band tail DOS............................................................90 3.2.1.2.b Gaussian DOS distribution..............................................................................94 3.2.2 Capture cross section and mobility influence on capacitance-temperature dependencies ...................................................................................................................................................97 3.3 Experimental results. Comparison with modeling................................................................101 3.3.1 The simplified K-T treatment of the experimental C-T data.........................................101 3.3.2 Fitting of the experimental C-T data with the DOS distribution obtained from other techniques................................................................................................................................105 3.3.3 The comparison of pm-Si:H and a-Si:H by the K-T treatment of the experimental capacitance data.......................................................................................................................110 3.4 Conclusions...........................................................................................................................113 3.5 References.............................................................................................................................116 4 Capacitance spectroscopy of a-Si:H/c-Si heterojunctions.......................................................118 4.1 Theory on a-Si:H/c-Si heterojunctions.................................................................................118 4.1.1 Band diagram and band offsets in a-Si:H/c-Si heterojunctions....................................118 4.1.2 Inversion layer in c-Si at a-Si:H/c-Si interface.............................................................122 4.1.2.1 (p) a-Si:H/ (n) c-Si case.........................................................................................122 4.1.2.2 (n) a-Si:H/ (p) c-Si case.........................................................................................124 4.1.3 Capacitance measurements of a-Si:H/c-Si heterojunctions..........................................125 4.2 Frequency dependent behavior of C-T dependencies: capacitance steps.............................131 4.2.1 Numerical modeling of C-T dependencies....................................................................132 4.2.2 Experimental results. Comparison with modeling........................................................145 4.2.3 Conclusions...................................................................................................................152 4.3 Quasi-static behavior of C-T dependencies: band offsets and the inversion layer...............154 4.3.1 Calculation of the junction’s capacitance: depletion approximation............................154 4.3.1.1 Failure of the depletion approximation to reproduce experimental C-T data......156 4.3.2 Calculation of the junction capacitance: complete analytical calculation....................161 4.3.2.1 C-T dependencies at zero polarization..................................................................166 4.3.3 Conclusions...................................................................................................................170 4.3.3.1 C-V dependencies..................................................................................................171 4.3.3.1.a Experimental 1/C2 vs Va curves and intercept voltage Vint............................171 4.3.3.1.b Intercept voltage derived from analytically calculated 1/C2 vs Va curves......174 4.3.4 Conclusions...................................................................................................................177 4.4 Influence of the buffer (i) a-Si:H layer and interface defects on C-T dependencies............178 4.4.1 Buffer (i) a-Si:H layer and its influence on C-T curves................................................178 4.4.2 Influence of interface defects on capacitance-temperature behavior............................180 4.5 References.............................................................................................................................182 5 Conclusions and perspectives....................................................................................................186 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 Appendix A....................................................................................................................................192 Appendix B....................................................................................................................................196 Appendix C....................................................................................................................................202 List of symbols and abbreviations...............................................................................................205 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications 1 a-Si:H and its applications 1.1 Description of the a-Si material Silicon in its amorphous state (a-Si) was first obtained by Bertzelius at the beginning of the 19 century [1], but until the 1960s it was not used as a semiconductor. Amorphous silicon without hydrogen was prepared in those days by thermal evaporation or sputtering [2]. This unhydrogenated material was highly defective, which inhibited its use as a useful semiconductor. In 1965 it was discovered that deposition of amorphous silicon employing glow discharge as the deposition technique yielded a material with much more useful electronic properties [3,4]. Some years later, Fritsche and co-workers in Chicago confirmed that a-Si produced from a glow discharge of SiH4 contains hydrogen [5,6]. In 1975 a boost in research activities occurred when it was shown that hydrogenated amorphous silicon (a-Si:H) could be nor ptype doped by introducing phosphine (PH3) or diborane (B2H6) in the plasma [7]: a variation of resistivity of more than 10 orders of magnitude could be reached by adding small amounts of these dopants. This discovery immediately initiated the research on practical amorphous silicon devices. Carlson and Wronski at RCA Laboratories started in 1976 with the development of photovoltaic devices [8]. The first p-i-n junction type solar cell was reported by the group of Hamakawa [9,10]. In 1980, Sanyo was the first to fabricate market devices: solar cells for hand-held calculators [11]. Application of a-Si:H in field effect transistors [12-14] is based on the capability to deposit and process a-Si:H over large areas. Combining the photoconductive properties and the switching capabilities of a-Si:H has yielded many applications in the field of linear sensor arrays, e.g. 2D image sensors, position-sensitive detectors of charged particles, X-rays, gamma rays, and neutrons [15-18]. The photovoltaic applications of a-Si:H will be discussed in details in Section 1.3. 10 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications 1.1.1 Atomic structure The disorder of the atomic structure is the main feature which distinguishes amorphous from crystalline materials. Hydrogenated amorphous silicon is a disordered semiconductor whose optoelectronic properties are governed by the large number of defects present in its atomic structure. The amorphous nature arises from the absence of long-range order in the lattice of the material. The first few nearest neighbor distances are separately distinguished, but the correlation between atom pairs disappears after a few interatomic spacings [19]. One can describe the disorder by the atom pair distribution function, which is the probability of finding an atom at a distance r from another atom. A perfect crystal is completely ordered to large pair distances, while an amorphous material only shows short-range order. Because of the short-range order, material properties of amorphous semiconductors are similar to their crystalline counterparts. The covalent bonds between the silicon atoms in a-Si:H are similar to the bonds in crystalline silicon. Amorphous semiconductors are often described as a continuous random network (CRN) [20,21], that is shown in Fig.1.1. The periodic crystalline structure is replaced by a random network in which each atom has a specific number of bonds to its closest neighbors (the coordination). The random network easily incorporates atoms of different coordination, even in small concentration. This is in marked contrast to the crystalline lattice in which impurities are generally constrained to have the coordination of the host because of the long range ordering of the lattice. This difference is most distinctly reflected in the doping and defect properties of a-Si:H. In the ideal CRN model for amorphous silicon, each atom is fourfold coordinated, with bond lengths similar (within 1 % [22]) to that in the crystal. In this respect, the short range order (< 2 nm) of the amorphous phase is similar to that of the crystalline phase. Amorphous silicon lacks long-range order because the bond-angles deviate from the tetrahedral value. 11 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications Fig.1.1. An example of a continuous random network containing atoms of different bonding coordination (from [19]). The continuous random network may contain defects, but the concepts of interstitials or vacancies applicable for crystalline materials are not valid here. Instead, in the CRN one uses the coordination defect when an atom has too few or too many bonds. In a-Si:H, dangling bonds arise when a silicon atom has too few bonds to satisfy its outer sp3 orbital. It is the common view that the dominant defect in amorphous silicon is a threefold-coordinated silicon atom. This structural defect has an unpaired electron in a non-bonding orbital, called a dangling bond. Pure amorphous silicon has a high defect density of the order of 10 cm, which prevents photoconductance and doping. The special role of hydrogen with regard to amorphous silicon is its ability to passivate defects by providing for electrons to the dangling bonds. Hydrogenation to a level of ~ 10 at.% reduces the defect density by four to five orders of magnitude. 1.1.2 Electronic structure and properties The structural disorder influences the electronic properties in several different ways. The similarity of the covalent silicon bonds in crystalline and amorphous silicon leads to a similar overall electronic structure amorphous and crystalline phases of the same material tend to have comparable band gaps. The disorder represented by deviations in the bond lengths and bond angles broadens the electron distribution of states and causes electron and hole localization as well as strong scattering of the carriers. Structural defects such as broken 12 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications bonds have corresponding electronic states which lie in the band gap. There are also phenomena which follow from the emphasis on the local chemical bonds rather than the long range translational symmetry. The possibility of alternative bonding configurations of each atom leads to a strong interaction between the electronic and structural states and causes the phenomenon of metastability. One of the fundamental properties of a semiconductor or insulator is the presence of a band gap separating the occupied valence band from the empty conduction band states. Since according to the free electron theory, the band gap is a consequence of the periodicity of the crystalline lattice, in the past there were considerable debates over the reason that amorphous semiconductors had a band gap at all. It was stated by Weaire and Thorpe [23] that the bands are most strongly influenced by the short range order, which is the same in amorphous and crystalline silicon and the absence of periodicity is a small perturbation. The preservation of the short-range order results in a similar electronic structure of the amorphous material compared to the crystalline one: bands of extended mobile states are formed (defined by the conduction and valence band edges, EC and EV) separated by the energy gap, Eg, more appropriately termed "mobility gap". The long-range atomic disorder broadens the densities of energy states, resulting in band tails of localized states that may extend deep into the band gap. Coordination defects (dangling bonds) result in electronic states deep in the band gap, around mid-gap. As electronic transport mostly occurs at the band edges, the band tails greatly determine the electronic transport properties. The deep defect states determine electronic properties by controlling trapping and recombination. In crystalline semiconductors the energy bands are described by energy-momentum (E-k) dispersion relations that arise from Bloch solution for the wavefunction of the electronic states. This solution to Schrödinger's equation does not apply to an amorphous semiconductor because the potential energy of an atomic structure is no longer periodic. A weak disorder potential results in only a small perturbation of the wavefunction and has the effect of scattering the electron from one Bloch state to another. The strong scattering causes a large uncertainty in the electron momentum, so that it is not a good quantum number and is not conserved in electronic transitions. The loss of k-conservation is one of the most important results of disorder and changes much of the basic description of the electronic states. Some consequences of the loss of kconservation are:  The energy bands are no longer described by the E-k dispersion relations, but instead by a density-of-states distribution N(E). Also the electron and hole effective masses must be redefined as they are usually expressed from the curvature of E(k).  The conservation of momentum selection rules does not apply to optical transitions in amorphous semiconductors. Consequently, the distinction is lost between a direct and an indirect band gap, in which transitions from the highest-energy state in the valence 13 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications band to the lowest-energy state in the conduction band are forbidden by momentum conservation. Instead transitions occur between states which overlap in real space. This distinction is most obvious in silicon which has an indirect band gap in its crystalline phase but not in the amorphous phase.  The disorder reduces the carrier mobility because of the frequent scattering and causes the much more profound effect of the wavefunction localization. 1.1.3 Density of states in the band gap The loss of momentum conservation in the electronic transitions results in the replacement of the energy-momentum band structure of a crystalline semiconductor by an energy-dependent density of states (DOS) distribution, N(E). It is convenient to divide N(E) into three different energy ranges: the main conduction and valence bands, the band tail regions close to the band edges, and the defect states in the forbidden gap. Our interest is concentrated on the two latter since electronic defects reduce the photosensitivity, suppress doping and impair the device performance of a-Si:H. They control many electronic properties and are centrally involved in the substitutional doping process. Defects are described by three general properties. First is the set of electronic energy levels of different charge states. Those defects with states within the band gap are naturally of the greatest interest in understanding the electronic properties because of their role as traps and recombination centers. Second is the atomic structure and bonding of the defect, which determine the electronic states. Finally, the defect reactions describe how the defect density depends on the growth and on the treatment after growth. The first arising question is the definition of a defect in an amorphous material. In a crystalline material any deviation from an ideal lattice would be considered as a defect, naming a vacancy or an interstitial atom. By analogy with the crystal one can define a defect in an amorphous material as a deviation from the ideal amorphous network where all the bonds are satisfied. This approach gives an idea of a coordination defect in which an atom has a distinctly different bonding state from the ideal. In ideal a-Si: H all the silicon atoms are four-fold coordinated and all the hydrogen atoms are singly coordinated. An example of a coordination defect where the bonding state is different from the ideal one is the three-fold coordinated silicon with a dangling bond. This type of defect therefore has the distinguishing characteristic of either a paramagnetic spin or an electric charge, which sets it apart from the electronic states of the ideal network. As it was already mentioned above, in common with most other covalent amorphous semiconductors, the overall shapes of the valence and conduction bands of a-Si: H are hardly different from a smoothed crystalline density of states. The most significant difference between the crystal and amorphous phases comes at the band edges where the disorder creates 14 te l-0 09 22 99 4, v er si on 1 1 Ja n 20 14 1 a-Si:H and its applications a tail of localized states extending into the gap. The width of the tail depends on the degree of disorder and on the bonding character of the states. The localized tail states are separated from the extended band states by the mobility edge [24]. Information on band tails is generally obtained from photoemission and absorption data [25-28]. The photoemission data provide some direct information on the density of states N(E) in the band tails, but the results are limited by the low sensitivity and energy resolution of the experiment. The density of states can be determined only to about 5-10% of the peak density in the band, with an energy resolution of 0.05-0.1 eV, after careful correction for the experimental resolution. Both band edges are found to have an approximately linear energy dependence of N(E) over an energy range of about 0.5 eV from the band edges and down to a density of about 3·10 cmeV. The density of states deep in the band gap of good quality aSi:H is no more than 10—10 cm eV[19], so that another 5-6 orders of magnitude of sensitivity are needed to describe the band tails properly. A typical density of states consists of the following terms [29]: 1. a free electron conduction band DOS for E ≥ EC: