Chapter 1. Ionizing radiation effects on MOS devices and ICs

Transcription

1 Chapter 1 Ionizing radiation effects on MOS devices and ICs The interaction of radiation with matter is a very broad and complex topic. In this chapter we try to analyse the problem with the aim of explaining, at least qualitatively, the more important aspects which are essential for a physical comprehension of the degradation observed in MOS devices and circuits when they are irradiated. In section 1.1 we introduce the effects of the interaction of various kind of particles with matter, in 1.2 the effects in the MOS devices, in 1.3 the consequent degradation of the MOS transistor electrical parameters. In section 1.4 we introduce Single Event Effects, phenomena induced in a device or a circuit by the impact of a single particle or ion. 1.1 Radiation-matter interaction The manner in which radiation interacts with solid materials depends on the type, kinetic energy, mass and charge of the incident particle and the mass, atomic number and density of the target material. We divide for simplicity the particles in two groups: charged particles (section 1.1.1) and neutral particles (section 1.1.2) [Bou93, Bra93, Sch94] Charged particles The principal characteristic of charged particles is that they interact mainly through Coulomb attraction or repulsion with the electronic clouds of the target atoms. The charged particles of interest are protons, heavy ions and electrons. Protons give origin to the following phenomena: Coulomb interaction, which can induce ionization or atomic excitation (the latter for protons energy < 100 kev); Collisions with the nuclei, which can cause their excitation or displacement; Nuclear reaction, which can occur for protons energies higher than 10 MeV. Heavy ions give origin, qualitatively, to phenomena similar to those induced by protons. Electrons, which can be present in the radiation environment or be produced by interaction of other particles with the material, can interact in two different manners, namely: 35

2 Coulomb interaction, which can induce, as in the case of protons, ionization or atomic excitation; Scattering with the nuclei, which can cause their displacement if the energy of the incoming electron is high enough and if enough energy is transferred to the nucleus; When electrons decelerate in the target material, they also loose energy by emitting Bremsstrahlung, which is composed by X-rays Neutral particles Neutrons and photons differ from the charged particles because they do not experience the Coulomb force. Neutrons are divided, depending on their energy level, into slow (E < 1 ev), intermediate and fast (E > 100 kev), and give origin to three different phenomena of interaction with the atomic nuclei: Nuclear reactions: the incident neutron is absorbed by the nucleus, which afterwards emits other particles (protons, α particles, γ photons). It is possible that nuclear fission can occur; Elastic collisions: the incident neutron collides with the nucleus and continues its path. If the energy given to the nucleus is sufficient, displacement of the nucleus can occur, and the displaced nucleus can in turn cause ionisation or nuclear displacement; Inelastic collisions: the phenomenon is similar to the previous one, but in addition there is excitation of the nucleus, which afterwards decays, emitting gamma rays. The relative probability of these phenomena depends strongly on the neutron energy. Slow neutrons give origin mainly to nuclear reactions or elastic collisions, fast neutrons mainly to elastic collisions. For very high energies the inelastic collisions dominate. Photons interact with matter in the three different ways described below and shown in figure 1.1: Photoelectric effect, in which the incident photon ionizes the target atom and is completely absorbed. In addition, as the photoelectric electron is emitted, an electron in an outer orbit of the atom will fall into the spot vacated by the photoelectron, causing a low energy photoelectric photon to be emitted; Compton effect, in which an electron of the target atom is set free and a photon is emitted. The energy of the incident photon is divided between the two products of the interaction; 36

3 Creation of electron-positron pairs. The incident photon is completely annihilated. This phenomenon never happens for energies of the incident photon less than MeV. This value increases with decreasing atomic mass Z (figure 1.2). The probability of these three effects changes with the energy and also strongly depends on the atomic number of the target, as shown in figure 1.2. The photons used in the radiation test of this work were 10 kev X-rays (which interact with silicon mainly by photoelectric effect) and gamma rays emitted by a 60 Co source with an energy around 1.25 MeV (with interact with silicon mainly by Compton effect). Figure 1.1: Schematic drawing of three processes through which photons interact with material: a) photoelectric effect, b) Compton scattering and c) pair production [Sch94 (p. 15)]. Figure 1.2: Relative importance of the photoelectric effect, Compton scattering and pair production as a function of photon energy [Sch94 (p. 16)]. 37

4 Summarizing the effects of both charged and neutral particles on matter, they can be grouped in two classes: ionization effects and nuclear displacement. These phenomena may be caused directly by the incident particle or from secondary phenomena induced by it, and represent the overwhelming majority of the events which happen in the irradiated matter. They are present with different proportions depending on the type of incident particle. Neutrons, which are neutral and massive particles, give origin mainly to nuclear displacement, whereas photons and electrons are responsible for ionization effects. Ionization in a semiconductor or insulating material creates electron-hole pairs. The number of pairs created is proportional to the quantity of energy deposited in the material, which is expressed through the total absorbed dose. For this reason, to study the effect of ionization in a material, we can disregard the type of particle used during the irradiation test, having already carefully chosen particles whose main phenomenon of interaction is ionization, and refer only to the quantity of energy deposited in the material. Atomic displacement gives origin to a neighboring interstitial atom and vacancy, which together are called a Frenkel pair. In silicon dioxide at room temperature 90% of the Frenkel pairs recombine within a minute after the end of the irradiation. This phenomenon has therefore a limited importance in our case. To study the displacement damage, neutrons sources are generally used, characterised by a quantity called neutron fluence. In the total dose radiation tests carried out for this work we used mainly X or gamma rays. This choice was due to the fact that, as it will be better explained later, MOS transistors (figure 1.3) are almost entirely insensitive to displacement damage, since they are devices whose conduction is based on the flow of majority carriers 1 below the SiO 2 -Si interface, a region which does not extend deep in the silicon bulk. Figure 1.3: Simplified structure of an n-channel MOS transistor [Tsi99, p. 35]. The conductive channel flowing between source and drain is underneath the SiO 2 -Si interface. 1 A major effect of displacement damage is the reduction of the minority carriers life time in the semiconductor bulk. 38

5 1.2 Radiation effects in the materials of a MOS transistor As already mentioned above, MOS transistors are more sensitive to ionization than to displacement damage. The part of the MOS structure (figure 1.3) which is sensitive to ionizing radiation is the silicon dioxide. When a ionizing particle goes through an MOS transistors [fig. 1.4 (1)], electron-hole pairs are generated. In the gate (metal or polysilicon) and in the substrate the electron-hole pairs quickly disappear, since these are materials of little resistance. On the contrary in the oxide, which is an insulator, electrons and holes have different behaviours, as their mobilities differ by five to twelve orders of magnitude. A fraction of the radiation-induced electron-hole pairs will recombine immediately after being created. The electron-hole pairs which do not recombine are separated in the oxide by the electric field [fig. 1.4 (2)] and, for example in the case of a positive bias applied to the gate, the electrons drift to the gate in a very short time (order of picoseconds) whereas the holes move towards the SiO 2 -Si interface [fig. 1.4 (3)] with a very different characteristic transport phenomenon, which will be described in section Close to the interface, but still in the oxide, some of the holes may be trapped, giving origin to a fixed positive charge in the oxide [fig. 1.4 (4)]. The generation, transport and trapping of holes in the oxide will be treated in more detail in section Ionizing radiation also induces the creation of traps at the SiO 2 -Si interface [fig. 1.4 (5)]; this topic will be treated in section Figure 1.4: Schematic illustration of the effects induced by ionizing radiation in an MOS device, when the gate is positively biased. 39

6 1.2.1 Generation, transport and trapping of holes in SiO 2 As stated before, the mobility in silicon dioxide is a lot higher for electrons than for holes; for electrons the typical mobility at room temperature is 20 cm 2 V -1 s -1. For holes the mobility depends strongly on the temperature and on the electric field, and varies from 10-4 to cm 2 V -1 s -1. This means that for a 10 nm gate oxide thickness and an electric field of 10 6 V/cm, for example, the electrons which do not recombine immediately with holes exit the oxide in less than a ps. For this reason, and also because in the best oxides the ratio between trapped holes and trapped electrons is between three and six orders of magnitude, in the following discussion the transport and trapping mechanisms will be treated only for holes Generation and recombination of electron-hole pairs in SiO 2 [Sch94, Mcl89] To calculate the number of the electron-hole pairs generated we must first of all know the total amount of energy deposited in the matter by the incident particles. This amount is related to their LET 2 (Linear Energy Transfer), which expresses the linear transfer of energy to the material by the incident particles. The LET depends on the nature and on the energy of the incident particles and on the absorbing material, and is expressed by LET 1dE = (1.1) ρ dx where ρ is the mass per unit volume expressed in kg/m 3 and de/dx is the mean energy transferred to the material per unit path length. The LET is measured in J m 2 kg -1 or, more practically, in MeV cm 2 mg -1. Once the LET and the total deposited energy are known, the number of generated electron-holes pairs is obtained by dividing the total deposited energy by the energy necessary to create an electron-hole pair, which in the SiO 2 is equal to 17±1 ev [Ben86]. A few picoseconds after the generation, there is a partial recombination of the generated pairs. The percentage of recombined pairs depends on the LET of the incident radiation and on the electric field applied to the oxide. The dependence from the LET can be qualitatively understood considering that particles with a higher LET will leave along their path a denser column of pairs, and the recombination probability is proportional to the density. To better quantify the density of pairs two parameters are used: r t, called thermalization distance, which represents the initial separation between a hole and its 2 In the case of photons, the energy transmitted to the target is expressed by the absorption coefficient, since the LET is used only for charged particles. We talk again of LET of the charged particles generated by the photons in the material. 40

7 corresponding electron after they reach thermal energy, and λ, which is the mean separation between electron-hole pairs. In silicon dioxide, r t is evaluated to be of the order of 5-10 nm. λ is inversely proportional to the LET. If the LET of the incident radiation is high enough such that λ is substantially smaller that r t (for example for an LET greater than 100 MeV cm 2 g -1 λ is smaller than 1 nm), we can imagin having a dense column of pairs with a diameter r t. In this case a model which is called "columnar model" is used. In the opposite case (i.e. LET smaller than 10 MeV cm 2 g -1 and thus λ bigger than 10 nm) the "geminate model" is used. Many models have been proposed for the transition region between the columnar and the geminate models, which are a lot more complex. Taking into account that the transition between the two models is gradual, they are sufficient for our purposes. These models are able to explain the curves shown in figure 1.5, where the fraction of non recombined pairs as a function of the applied electric field is plotted for several kind of particles. It can be noted that, in all cases, increasing the electric field leads to a decrease in the recombination phenomenon. In the case of photons emitted by a cobalt source or a 10 kev X-rays source it is interesting to note how much the electric field in the oxide (perpendicular to the SiO 2 -Si interface) and therefore the gate bias conditions during irradiation can influence the fractional yield: with a zero electric field 70% (for gamma rays) or 90% (for X-rays) of the generated pairs recombine after the generation. Increasing the electric field these percentages go down to zero. Figure 1.5: Fraction of non recombined electron-hole pairs (fractional yield) in the silicon dioxide as a function of the applied electric field for several different kinds of incident radiation. 41

8 Transport of holes in SiO 2 [Sch94, Mcl89, Ben86, Sha91, Boe85] The holes which do not recombine start to drift, due to the electric field, towards the SiO 2 -Si interface (we suppose that the gate is biased positively). This transport phenomenon is quite anomalous, since there is a very wide distribution (many decades) of hole transit times through the oxide. The transport phenomenon can last up to several seconds at room temperature, a lot more at lower temperatures (for example, if T = 80 K it can last several tens of thousand of seconds). The study of dispersive transport phenomena is silicon dioxide led to the description of the transport of holes in SiO 2 by a model based on the concept of small polaron hopping. This mechanism, which matches very well with experimental results, is based on the strong interaction V(x) (1) (2) between the hole and the lattice (or the atom network for (a) a disordered solid). The interaction gives origin to a (1) (2) distortion of the lattice, close to the hole, which lowers (b) the energy of the system. In practice, the carrier polarizes + the surrounding medium, and this polarization then interacts back on the carrier. If the interaction is (1) (2) sufficiently strong, with a large distortion of the lattice in + (c) TUNNELING the immediate vicinity of the carrier, then the carrier TRANSITION becomes localized at a particular site. In this way the (1) (2) effective mass of the hole is increased. The carrier which (d) is, in practice, self-trapped, is called small polaron. The + mechanism of charge transport via small polaron hopping is depicted in figure 1.6. When an initially empty localized trap site [fig. 1.6 (a)] captures a carrier (a hole, in our case), the total potential V of the system is lowered by a distortion of the lattice around the trap site [fig. 1.6 (b)]. X Figure 1.6: The polaron hopping transport phenomenon. The hole "digs" a potential well for itself, i.e. is selftrapped. When the hole moves through the insulator, it carries with it the potential well arising from the distortion of the lattice, i.e. the polaron is moving. The transition of the hole between two nearby sites occurs via the intermediate state shown in fig. 1.6 (c), which is thermally activated by the thermal fluctuations of the system. These momentarily bring the electronic energy levels of the two sites into coincidence, so that the hole can tunnel from the state (1) to the state (2). The final state of the system is shown in figure 1.6 (d). The transition probability is essentially given by the product of two factors. The first is the spatial overlap integral of the wave functions of the two sites, which governs the tunneling transition between the two sites. The second is the probability of creating the thermally 42

9 activated state showed in figure 1.6 (c). The activation energy of this state is supplied by the phonons, and is then related to the temperature: the higher the temperature, the faster the transport phenomenon. This transport mechanism can be mathematically described by a model called CTRW (continuous-time random walk), which has been developed to describe generally the dispersive transport phenomena in a disordered solid. This model perfectly agrees with the polaron hopping transport phenomenon, and moreover is able to explain an interesting characteristic of the transport of holes in the silicon dioxide, which is the universality of its time response with respect to the temperature, electric field in the oxide and oxide thickness. This means that if we plot the charge which exits the oxide as a function of time (in logarithmic scale) we obtain a curve which does not vary in shape but only translates horizontally changing one of the three parameters mentioned above. An example is shown in fig Figure 1.7: Variation of the flat band voltage (normalized to its value just after the end of the irradiation) as a function of the time (scaled to t 1/2 ). The plot shows the universality of the time response of the holes transport with respect to the electric field. The measurements have been performed at constant temperature (79 K) and constant gate oxide thickness (96.5 nm) [Mcl87]. The variation of the flat band voltage (whose value is related to the amount of radiation induced positive charge in the oxide) normalized to its value just after the end of the irradiation [ V fb (t)/ V fb (0 + )] is plotted as a function of the time. The logarithmic time scale is scaled for each curve to the value t 1/2, for which V fb (t)/ V fb (0 + )=0.5. In this way we can see the good agreement between the theoretical prediction of the CTRW model (solid line in fig. 1.7) and the experimental data for different values of the oxide electric field. In these measurements the temperature and the gate oxide thickness were constant; similar results can be obtained varying one of these two parameters. All this is of course 43

10 valid for oxides which do not trap holes (which we can call "radiation hardened"). The trapping of holes in the oxide would make difficult to study the transport phenomenon. We will treat the trapping of holes in non radiation hardened oxides in the next section. To conclude this section we report the formula which link the characteristic time scale of the holes transport process in the oxide (t s ) to the temperature (T), the electric field in the oxide (E ox ) and the oxide thickness (t ox ) t s = t 0 s t a ox 1/ α exp 0 qae kt ox /2 (1.2) where q and k are respectively the electronic charge and the Boltzmann constant, a is the average hopping distance in the electric field direction, 0 and t 0 s are two constants and α is the principal parameter of the CTRW model, linked to the disorder in the solid and determined by the detailed microscopic transport process. In the case of holes in the silicon dioxide, α = It is interesting to note that the characteristic time scale of the holes transport process in the silicon dioxide varies with the fourth power of the oxide thickness and decreases exponentially with the electric field and the temperature Positive charge trapped in SiO 2 [Mcl89, Boe85, Mcw90] When the radiation-induced holes have completed the crossing of the oxide, they can be trapped close to the SiO 2 -Si interface or to the SiO 2 -gate interface. This phenomenon generally dominates over other radiation-induced phenomena, such as for example the trapping of electrons in silicon dioxide. As will be seen later, the trapping of holes in the oxide gives origin to a negative threshold voltage shift V ox which is not sensitive to the surface potential in the silicon and which can stay for a period of time varying from milliseconds to years. The amount of trapped charge is proportional to the number of defects in the silicon dioxide. For this reason one of the fundamental steps for the fabrication of radiation hardened technologies is the control of the gate oxide quality. Various techniques have been used in the past to determine the position of hole traps in the oxide. One of these is, for example, the etch-back technique 3, which allowed the observation that hole traps are generally located near the interfaces (SiO 2 -Si or SiO 2 -Gate), within a few nanometers from the interface. When a hole reaches this region, depending on the mean trap density N ht and on their hole capture cross-section σ ht, it will be trapped or not. The fraction ƒ T of trapped holes, on which V ox depends, can be expressed as 3 In an etch-back experiment a MOS capacitor is first irradiated to accumulate charge in the oxide traps. The gate electrode is then removed, and the oxide layer is carefully removed stepwise by etching. At each step, the trapped charge remaining in the oxide is determined from C-V measurements. 44

11 f T = N ht σ ht X (1.3) where X is the width of the trap distribution. Depending on the quality of the oxide, typical values for N ht are cm -3 [Gro66, Hug83, Ait77], and is independent of the electric field. The hole capture cross-section σ ht typically varies from few to few cm 2 [Boe86]. The electric field dependence is proportional to E -1/2. With these values, taking X 5 nm, we obtain for f T values between 0.01 and 1. This means that, depending on the oxide quality and on the electric field, the fraction of trapped holes varies from 1% to 100%. The non trapped holes which reach the SiO 2 -Si interface (in the case of positive gate bias), will recombine with electrons coming from the silicon. Moreover these electrons may tunnel from the surface into the oxide and recombine with trapped holes, giving origin to a tunnel-effect-based annealing. The tunnel annealing, which tends to reduce the amount of positive charge trapped in the oxide, is helped by two other phenomena. The first is electrons generated within the trapped holes distribution. Depending on the local density of trapped holes n ht and the cross-section σ r of the capture of an electron by a trapped hole, an electron can recombine with a trapped hole. The importance of this phenomenon increases with the total dose, and is one of the effects which contributes to the saturation of V 4 ox. The second consists of electrons in the oxide valence band which, having a sufficient thermal energy to jump into the oxide, recombine with holes trapped in the oxide (thermal annealing). The tunnel annealing has an almost logarithmic temporal behavior. This is a consequence of the tunnel effect probability, which is exponentially decreasing with the distance from the SiO 2 -Si (or SiO 2 -gate) interface (p tun e -βx ). At a given instant t the electrons recombine with holes which are at a distance X(t) from the interface, where X(t) is expressed as [Man83, Ben85, Ros69, Mcl76] 1 X(t) = 2β ln t t 0 (1.4) where β is a parameter related to the height of the potential barrier and 1/t 0 is the frequency at which the electrons try to cross it. The hole-removal process by tunnel annealing can therefore be seen as a front of electrons moving with a speed v = 1.15/β per decade 5 in 4 The saturation of the threshold voltage shift component due to the holes trapped in the oxide was observed experimentally. V ox does not increase linearly with the dose, and its value tends to saturate at high doses. 5 v= dx(t) dx(t) = ln10 = ln10 = d(log t) d(ln t) 2β β 10 45

12 time (generally v varies from 0.2 to 0.4 nm per decade). We can understand then why the number of neutralized holes and the neutralization rate strongly depend on the spatial distribution of the traps in the oxide, which in turn strongly depends on the fabrication process. If the traps distribution were uniform, the reduction of trapped holes at a given instant due to the tunnel annealing will be proportional to X(t), and so will be V ox. In reality, it is difficult to find exactly this logarithmic behaviour, since the trap distribution is not uniform but decreases very sharply moving away from the interfaces. The tunnel annealing becomes more effective as the electric field increases, since in this way the potential barrier which has to be crossed by the electrons is lower. The thermal annealing can be explained starting from the emission probability p em of an electron from the oxide valence band to the trap where the hole is trapped. p em is equal to AT 2 e -qφ/kt, where φ is the difference in energy between the trap and the valence band and A is a constant which depends on the trap capture cross-section and others parameters. From this expression we can note that thermal annealing strongly depends on T and does not depends on the spatial distribution of the traps. For the tunnel annealing the spatial distribution of the traps in the oxide is important, whilst for the thermal annealing it is the distribution in energy of the traps which matters. These have to be close enough to the valence band. This distribution can be studied with isochronal techniques, which consist of measuring the fraction of recombined holes after heating the device for constant time periods but at temperatures progressively increasing or with isothermal techniques by measuring this fraction following its time evolution at constant temperature, for a range of temperatures. As in the case of the tunnel annealing, we can imagine the hole removal process by the thermal annealing as a front of electrons moving in the oxide energy gap from the valence band to the conduction band. At a given instant t the position φ(t) of the front with respect to the valence band is equal to kt ln(at 2 t). From this expression it can be seen that the thermal annealing temporal behavior is also logarithmic Radiation induced traps at the SiO 2 -Si interface [Win89] Another effect of radiation on MOS devices is the increase by several orders of magnitude of the trap density at the interface SiO 2 -Si [fig. 1.4 (5)]. This phenomenon has been studied for many years, and is not fully understood yet, even though several models have been developed to explain the phenomenon, taking into account the dependencies on several parameters, such as electric field, time, temperature and total dose. The radiation induced traps have an energy between the valence and conduction bands of the silicon. Experiments indicate that the major part of the traps present above midgap 46

13 are acceptors whilst traps below are donors 6. For this reason both for n- and for p-channel MOS transistors the threshold increases (in absolute value) after irradiation due to the creation of new interface traps. As an example let us take an n-channel transistor working in inversion: the acceptor-like traps in the upper part of the gap, being below the Fermi level, will be filled by electrons and then negatively charged, making necessary an higher gate voltage to have the same channel inversion (i.e. the threshold voltage is higher). It can be found in the literature (see for example [Lai81, Mcw88]) that sometimes acceptor-like traps are found below midgap and donor-like above. We will explain how this does not (qualitatively) influence the threshold voltage shift after irradiation. Figure 1.8 shows the energy levels close to the interface SiO 2 -Si and the charge state of the traps. The three situations differ from the position of the Fermi level. The traps whose presence is certain are indicated by an asterisk. In the first situation we have the Fermi level in the middle of the energy gap. In this case the presence of donor-like traps above midgap and acceptor-like traps below should not give origin to particular effects if these traps are in equal number in the two halves of the energy gap. But the more interesting situations are the second and the third, since these represent respectively an n-channel transistor and a p-channel transistor working in inversion. In these cases we can see that the presence of the traps whose presence is doubtful does not affect qualitatively the effects already given by the traps whose presence is certain. To provide a more precise quantitative explanation it would be necessary to know the exact energetic distribution of the trap densities. These quantities are very difficult to measure and can vary significantly from one technology to another. The models which have been developed to describe the creation of radiation induced interface states can be divided into three groups, depending on the most important cause behind the phenomenon, which can be: Direct creation of the traps by radiation; Generation of traps directly due to hole trapping close to the surface; Trap creation due to secondary phenomena. The direct creation of traps by radiation was excluded by experiments where the thin metallic gate of several MOS structures was irradiated under vacuum with ultraviolet rays (which have little penetration). The light was all absorbed in the first layers of oxide without reaching the SiO 2 -Si interface. With a positive bias applied to the gate a generation of traps at the interface was still observed, similar to the situation where highly energetic 6 A donor trap releases an electron when it passes from below to above the Fermi level. Donor traps are neutral when full and positively charged when empty. An acceptor trap captures an electron when it passes from above to below the Fermi level. Acceptor traps are neutral when empty, negatively charged when full. 47

14 (i.e. highly penetrating) gamma rays were used. These experiments not only confirm that the number of traps created directly by radiation is negligible, but also that a precursor phenomenon of the interface traps build-up is the creation of electron-hole pairs and the subsequent transport of holes in the oxide. Φ S = Φ N-channel P-channel B E C E i E V * * Acc. Don. Acc. Don. E C N * Acc. - * Acc. N + Don. N Don. + - N E F E i E V * Acc. Don. - N E F E C E i E V * Acc. Don. N + E F Figure 1.8: Charge of the traps at the SiO 2 -Si interface as a function of the position of the Fermi level E F at the interface. The N letter indicates that the traps are neutral, the symbols + and indicate charge. The traps indicated by an asterisk are those which are definitely present in that part of the energy gap. The energy levels are shown close to the SiO 2 -Si interface, the horizontal direction does not represent a physical direction in the MOS structure (i.e. these are not band diagrams). Also the second hypothesis of direct generation of traps by hole trapping close to the surface was proved to be wrong by experiment, which showed that the time evolution of the interface traps build-up was slower than the one of the hole transport in the oxide. The models based on secondary phenomena subsequent to the generation of electronhole pairs are then the most likely to be true. The one which is more convincing, in our opinion, is the model proposed by Winokur and McLean [Win79, Mcl80], which employs two different stages. In the first hydrogen ions are set free from the radiation-generated holes which are moving towards one of the two oxide surfaces. Hydrogen atoms and other impurities are present in the oxide, due to the methods used to process it, and these make it non perfectly stoichiometrical. In the second stage, hydrogen ions move towards the SiO 2 - Si interface (in the case, for example, of positive gate bias) where they give origin to new states which serve as traps. This model explains why the build-up of interface states is slower than the transport of holes in the oxide, since the ions have a lower mobility, and why the amount of generated traps is lower if the gate is negatively biased. In this case only hydrogen ions generated very close to the SiO 2 -Si interface will give origin to traps. The model also explains why at low temperature there is practically no trap generation, since the ions are "frozen" in the oxide. The model on the other hand fails to explain the decrease of the number of generated traps with the electric field (experimental results showed a proportionality to E -1/2 ). One would in fact expect that for higher fields the holes could set 48

15 free more hydrogen atoms, and therefore there would be more traps. Shaneyfelt and others were able to explain this inconsistency, and developed a model which is called (HT) 2 (Hole-Trapping/Hydrogen-Transport) [Sha90, Sha92]. In this model, for a positive gate bias, holes drift towards the SiO 2 -Si interface and are then trapped close to the interface. When they are trapped, hydrogen ions are released, which afterwards move towards the interface where they react and give origin to the traps. In this way the temporal evolution of the interface trap generation will again be determined by the hydrogen ions, but the electric field dependency will be decided by the hole capture cross-section, which is proportional to E -1/2 (section ). This model, at least for dry oxides, is also supported by the experimentally observed independence of the interface traps temporal build-up from the gate oxide thickness. If such a dependence existed it would imply that the hydrogen ions are created in the entire volume of the oxide and not only close to the surface. Some experiments showed that there is a proportionality between the gate oxide thickness and the number of generated traps; this can be explained by the fact that the number of generated holes is proportional to the thickness. The two previously explained models the one from Winokur and McLean and the (HT) 2 although different in detail, are the two which are best able to explain a large number of experimental observations. What is not yet clear is if the hydrogen atoms are released everywhere in the oxide or only close to the interface, or again a mixture between the two solutions. To conclude this section it is also important to note that the radiation induced interface trap generation is strongly dependent on the processing steps of MOS devices, and that at room temperature there is generally not a significant annealing of the generated traps. 1.3 Consequences of radiation on the electrical parameters of a MOS transistor In this section we present the consequences of hole trapping in the oxide and of interface traps generation on the electrical parameters of a MOS transistor, namely the threshold voltage V T, the subthreshold current and the leakage current, the carrier mobility µ and the transconductance g m Threshold voltage shift The threshold voltage of a MOS transistor changes when the device is irradiated. The change V T is given by the sum of two contributions, V ox and V it, which are related to 49

16 the hole trapping in the silicon dioxide and to the charge state of the interface traps respectively. Threshold shift due to the oxide charges The charges trapped in the oxide give origin to a shift in the flat-band voltage 7, and therefore in the threshold voltage, which can be expressed as [Mul86 (p. 401)] V ox 1 x = C t ox t ox 0 ox ρ (x) dx (1.5) where t ox is the gate oxide thickness, C ox is the capacitance per unit area and ρ(x) is the charge distribution in the oxide per unit volume as a function of the distance from the gateoxide interface x. The first observation one can make from this expression is that the voltage shift due to this contribution is negative when the charge is positive (as it is in the reality, see section ). This can easily be understood qualitatively: for a p-channel transistor, for example, the positive charge trapped in the oxide repels the holes in the channel. This means that to re-create the same inversion condition one will need to apply a more negative potential to the gate, i.e. the threshold voltage is lower (higher in absolute value). Another important consideration indicated by (1.5) is that the effect of the oxide charge on the voltage shift is weighted by its position in the oxide: the closer the charge to the SiO 2 -Si interface, the bigger the threshold voltage shift. If we assume, for example, to have a charge distribution close to the gate-sio 2 interface, of constant density A [C/cm 3 ] for x<w and equal to zero for W<x<t ox (the x axis is normal to the gate, directed from the gate to the silicon and with the origin on the gate-oxide interface), the threshold voltage shift will be 2 A W Vox = (1.6) 2 ε ox where ε ox is the silicon dioxide permittivity. If we suppose to have a similar charge distribution in the oxide but this time close to the SiO 2 -Si instead of the gate-sio 2 interface (i.e. the charge distribution is zero for 0<x<t ox -W and is equal to A for t ox -W<x<t ox ), the voltage shift will be 7 The flat-band voltage is the voltage that has to be applied to the gate in order to have flat energy bands inside the silicon. 50

17 2 A W t ox Vox = ε W ox (1.7). We can see that in (1.7) we have an additional multiplicative factor > 1 (since t ox >W) which is not present in (1.6), and thus V ox is indeed larger for charge distributions closer to the SiO 2 -Si interface. From (1.6) and (1.7) one can also note that the voltage shift increases with the square of the width W of the charge distribution, although this effect is mitigated in (1.7) by the reduction in the multiplicative factor. Threshold shift due to the charges at the oxide-silicon interface The threshold voltage shift component associated with the radiation induced interface states V it can be treated as before. Since the charge distribution can be considered bidimensional it can simply be expressed as V it =- Q it /C ox where Q it is the difference of the charge (per unit area) which fills the interface states after and before irradiation. V it can have positive or negative values. As mentioned in section we assume that the traps above midgap are acceptor-like and those below are donor-like. This means that for an n-channel transistor (for example), where the Fermi level in the silicon close to the silicon-oxide interface lies between E i and E c (fig. 1.9), the acceptor-like traps which are below the Fermi level will be negatively charged, and then the threshold voltage shift will be positive. Similarly for a p-channel the threshold voltage shift will be negative (i.e. the threshold increases, in absolute value, both for an n-channel transistor and for a p-channel). qφ S Charged acceptors SiO 2 o o o o Silicon Neutral acceptors Neutral donors N-channel transistor qφ Β E C E i E F E V Ionized donors qφ S SiO 2 Silicon o o Neutral acceptors Neutral donors P-channel transistor qφ Β E C E F E i E V Figure 1.9: Energy bands diagrams in the silicon for an n-channel and a p-channel transistors. The diagrams show the behaviour of the interface traps in two typical cases (gate bias, referred to the substrate, positive for the n-channel transistor and negative for the p-channel). The interface states increase is a slower phenomenon than the build-up of positive charge in the oxide. For this reason, V it can start to play a role later than V ox. This can also explain why the threshold voltage shift for n-channel transistors as a function of the total dose or the annealing time can be negative at the beginning and become positive in a second time (this effect is known as rebound). The slower temporal evolution of the 51

18 radiation-induced interface states also plays an important role in the an annealing of the irradiated circuits, since this will decrease V ox but will probably increase V it both for n- channel and for p-channel transistors, affecting in this way the bias conditions of the circuit. Separation of the two threshold voltage shift contributions The measured threshold voltage shift V T is the sum of the two previously described contributions V ox and V it. To understand the behaviour of both the trapped oxide charge and the interface traps it is interesting to separate the measured threshold voltage shift for the two contributions. There are several ways of doing that. Our preference, also due to its simplicity, goes to the method described by McWorther and Winokur [Mcw86], based on the variation of subthreshold slope before and after irradiation. The drain current of an MOS transistor below threshold (i.e. for values of the surface potential Φ S comprised between Φ B and 2Φ B, where Φ B is the Fermi potential in the semiconductor bulk, fig. 1.9) varies exponentially with V GS. The plot of the drain current (log scale) as a function of the gate-source voltage is therefore a straight line. The slope of this line is called subthreshold slope, and its inverse, called subthreshold swing, can be expressed as [Sze81 (p. 447)] kt C d + Cit S = ln (1.8) q Cox where C d and C ox are the capacitances per unit area respectively of the depletion region in the silicon and of the gate oxide. C it is the capacitance associated with the charges trapped in the interface states, and is the term which varies with irradiation, since C it =q D it and D it is the variation of the interface state density, expressed in V -1 cm -2. kt/q ln10 at room temperature has the value 60 mv/decade, which is the minimum theoretical value for the subthreshold swing. The subthreshold swing variation as a function of the radiation induced variation in the interface state density can be expressed as kt q q D C it S = ln10 (1.9) ox The quantity S (which is positive for both n-channel and p-channel transistors, since the effect of radiation is always to increase the interface state density) is easy to measure, leading to an estimation of D it. The interface state density distribution is supposed to be constant in the energy gap, at least close to the intrinsic energy level, both before and after irradiation. This is justified by the (1.8), since S does not vary with V GS (and then Φ S ) in 52

19 the subthreshold region for values of Φ S close to the middle of the energy gap 8. To extract V it =- Q it /C ox from D it, we have to integrate D it over the energy gap to obtain Q it and then V it. The integral Q = q D dφ (1.10) it gap it S with the conventions indicated in fig. 1.9 has always a positive value, but then has to be taken with its sign for p-channel transistors and with the opposite for n-channel. Up to now we have made the following hypothesis: The interface states density is constant close to the band gap centre both before and after irradiation (i.e. also the difference between after and before irradiation is constant); The interface states are acceptor-like above midgap and donor-like below it. With these assumptions the integral of D it for Φ S varying in the energy gap (close to midgap) is simplified greatly. D it is constant and can be taken out of the integral. The extremes of integration are Φ B and 2Φ B, since for Φ S =Φ B the Fermi level starts to charge negatively the first acceptors for the n-channel transistors (or positively the first donors for the p-channel's), and for Φ S =2Φ B the threshold condition is reached; beyond that, the surface potential is fixed at 2Φ B. The result of (1.10) is then Q it = q D it Φ B (1.11). Since V it =- Q it /C ox, using (1.11) and (1.9) we can write ΦB Vit = S (1.12). kt ln10 q Knowing S and V T we are then able to calculate the threshold voltage shift given by the interface trapped charges V it, and also V ox. This is very useful when we want to have information on the quality of the oxide and of the oxide-silicon interface and also if we want to study the annealing of the holes trapped in the oxide and of the interface states. 8 The interface states distribution as a function of the energy in the energy gap can be found in the literature, and is almost constant close to the centre of the gap [Poi84, Sze81 (p.385)]. 53

20 1.3.2 Increase of subthreshold and parasitic currents The "off-state" current in a MOS transistor is defined as the current which flows from drain to source when V GS = 0, and is sometimes referred to as "leakage current". In an irradiated n-channel transistor two effects lead to an increase in the "off-state" current: the increase of the subthreshold current and the generation of parasitic currents. These phenomena can be critical for many applications, as for example when the transistor is used as a switch Increase of the subthreshold current The increase in the subthreshold current is related to two factors, illustrated in fig The first is the decrease of the threshold voltage. The pre-irradiation solid line in fig shifts towards the y axis (V T goes from V T1 to V T2 ) and becomes the dotted line after irradiation. The second is the radiation-induced decrease of the subthreshold slope; due to this effect the dotted line in figure 1.10 becomes the solid one after irradiation. The subthreshold current which before irradiation was I 1 becomes therefore I 2 due to the threshold voltage shift and then I 3 due to the subthreshold slope decrease. log I D After irradiation Pre-irradiation I 3 I 2 I 1 0 V T2 V T1 V GS Figure 1.10: Increase of the subthreshold current in a n-channel transistor given by a decrease in the threshold voltage and in the subthreshold slope. Up to now we have supposed that the radiation-induced threshold voltage shift of an n-channel transistor is negative. This was especially true in technologies with a relatively thick gate oxide (roughly >10 nm). For these technologies the negative contribution to the threshold voltage shift given by the holes trapped in the oxide was generally higher than the positive one given by the charged interface states. After the end of the irradiation and some annealing the situation can change, since there is a decrease (in absolute value) of V ox due to the tunnel and thermal annealing (section ) and an increase of V it due to the slow interface traps build-up (section 1.2.2). For deep submicron technologies the gate oxide is so thin that the contribution V ox can be smaller than V it. This is due to two 54

21 facts. The first is that there is a smaller volume where one can generate holes. The second is that the annealing of the trapped holes plays an important role already during irradiation. To summarise, it is difficult to predict the sign of the radiation-induced threshold voltage shift in an n-channel device. If it becomes positive, it can help in compensating for the decrease in the subthreshold slope, i.e. the subthreshold current might not increase after irradiation. This can be checked only with measurements on the technology of interest Increase of the parasitic currents Another contribution to the post-irradiation off-state current in a standard n-channel transistor is given by the creation of two parasitic paths under the region called "bird's beak 9 " (figure 1.11) or, further away from the device, underneath the thick oxide. In all the different technologies we have measured, with minimum gate length from 0.7 µm to 0.25 µm, this contribution to the total leakage current dominated over that one due to the subthreshold current. Figure 1.11: Schematic illustration of the parasitic transistors which are in parallel to the main transistor and of the parasitic leakage paths in the bird's beak region or underneath the field oxide which connects the source and the drain [Gai95]. 9 The bird's beaks are present in CMOS technology when the isolation between devices is done employing local oxidation of silicon (LOCOS). In deep submicron technologies this isolation has been replaced by shallow-trench isolation (STI). It can be found in the literature that this new kind of isolation does not eliminate the post-irradiation leakage paths [Sha98]. 55

22 The parasitic paths shown in figure 1.11 are easily created by the radiation since the oxide in these regions is thick, and is therefore able to trap a large amount of holes. A qualitative representation of this phenomenon can be the following: the parasitic transistor can be represented as a parallel combination of several transistors with width W and roughly the same L of the main transistor, but with increasing gate oxide thickness when going towards the field oxide. When the gate oxide of these parasitic transistors increases, the gate capacitance C ox = ε ox /t ox decreases, the threshold voltage increases (since it varies with 1/C ox ) and the current decreases. This situation is represented in figure 1.12, where the characteristics of the parasitic transistors in parallel are shown. The threshold voltage of the parasitic transistor can be of the order of several volts, but since their gate oxide is rather thick the threshold voltage shifts can also be of the same order of magnitude. Moreover the parasitic transistors with higher threshold voltages will have the higher shifts, having the thicker gate oxides (figure 1.13). The shape after irradiation of the I D vs V GS characteristic strongly depends on the total dose absorbed and on the quality and type of the oxide. Two examples are shown in figure log I D Main transistor Parasitic transistors characteristics moving during irradiation Figure 1.12: Curves representing the drain current of the main transistor and of the parasitic transistors before irradiation. The curves of the parasitic transistors move during irradiation. V GS log I D log I D V GS Figure 1.13: Two possible examples of the effects on the main transistor of the shift of the parasitic transistor characteristics caused by the irradiation. Note that the parasitic transistor with the higher threshold voltage shift (i.e. thicker gate oxide) is the one which moves further. V GS 56