2.3 Injection Mechanisms
2.3.6 Radiation-induced carriers
The interactions of high energy particles and photons with electronic devices can lead to deterioration and failure.18,37 Applications in which circuitry can be exposed to radiation include space modules, nuclear reactors, and military equipment. A famous example the Telstar communication satellite which failed in 1962 after passing through the Van Allen belts, a torus of energetic charged particles around earth.
There are two main mechanisms leading to device failure when an oxide-based device is exposed to radiation. First, high energy particles such as neutrons can collide with the nuclei of the lattice atoms and induce displacement damages. These defects can be permanent and if they are located in the active region, they will reduce carrier lifetime.
Second, energetic radiation can result in the generation of electron-hole pairs throughout the structure. Excess carriers in the dielectric can then be trapped, modifying the device properties, and ultimately lead to breakdown.
As, high energy photons do not lead to displacement damage, their use in a controlled environment corresponds to an accelerated technique that can be used to study the prop- erties of a gate dielectric in the presence of excess carriers, very much like the methods previously described.
There are three different mechanisms leading to ionization of a material by photons, they are illustrated in Figure 2.14. The one that dominates for a particular radiation source is defined by the energy of the photons. Photons with energies of a few electron-volts, corre- sponding to the band offsets between the gate oxide and the metal or the semiconductor, can inject carriers in the dielectric. When the photon energy exceeds the one of the oxide band-gap ( 9 eV for amorphous SiO2), they directly generate electron-hole pairs in the oxide by mean of the photo-electric effect. A photon then interacts with an electron and promotes it to the conduction band of the material as its energy is entirely absorbed. In a Compton scattering event, which occurs at higher photon energies, only some of the energy of the incident photon is transferred to the electron, and it can produce several electron-hole
Figure 2.14: Schematic representation of ionization processes in silicon dioxide. After Gwyn.18
pairs until it is completely absorbed. When the energy of the incident photon exceeds 1.02 MeV, it can interact with the Coulomb field of the nuclei and induce an electron-positron pair, the photon is then completely annihilated.
In the case of 10 eV VUV (vacuum ultra-violet) and 10 keV X-ray photons, electron-hole pairs are the result of the photo-electric effect. However, the details of the process are very different for these two radiation sources. As the energy of VUV photons barely exceeds the one of the SiO2 band-gap, they are absorbed within 10 nm of the oxide and they can only promote electrons from the top of the valence band to the bottom of the conduction band. X-rays however are energetic enough to span several microns and knock electrons out of the core shells of atoms. The subsequent transition of electrons from the outer shells to the core shells, generate additional X-rays. Since the binding energy of a core electron is of the order of 1 keV, most of the absorbed photon energy (≥ 9 keV) is transferred to
the kinetic energy of the emitted secondary electron. The secondary electrons generated by X-rays can then induce electron-hole pairs themselves by progressively losing their excess energy to the lattice. So, an absorbed 10 keV photon will ultimately lead to the generation about a thousand times more electron-hole pairs than a 10 eV photon, because of secondary processes.
Table 2.1: Constants for interactions between 10 keV photons and electrons.38,39,40
Quantity SiO2 Si 4H-SiC Al Mo Au
Ma,γ (cm2/g) 19.3 34.5 24.9 28.9 90.1 123.0
dEe−/dx(eV/nm) 4 - - - - -
Epair (eV) 18 3.63 7.5 x x x
The details of the device structure, the X-ray photon mass attenuation coefficient (Ma,γ
in cm2/g), the secondary electrons stopping power (dEe−/dx in eV/nm), and the average energy required to induce ionization (Epair in eV), determine the total amount of generated electron-hole pairs within a given oxide thickness. The average energy Epair required by high energy particles to induce an electron-hole pair is always larger than the band-gap.
This is because of momentum conservation and phonon interactions. In SiO2, Epair 18 eV. Some other constants are listed in Table 2.1. Using the mass attenuation coefficient Ma,γ, one finds that the penetration depth of 10 keV photons in SiO2 is about 220 μm. It can be shown that in a free-standing 50 nm oxide, approximately 2 X-ray photons out of 10,000 will be absorbed; each of the induced secondary electrons will generate electron-hole pairs. In a real device, the contribution from secondary electrons coming from the gate metal and the semiconductor need to be counted. If the structure consists of a 50 nm thick Al gate, on top of the 50 nm oxide grown on Si, the total amount of induced electron-hole pairs will approximately double.
Figure 2.15: Fractional yields of electron-hole pairs generated in SiO2 by various radiation sources.37
The unit used to define the energy absorbed by a material per unit mass is the rad (radiation-absorbed dose). One rad corresponds to 100 erg/g (1 erg = 10−7 joules). Note that a transistor in a earth satellite passing repeatedly through the Van Allen belts could absorb approximately 1 Mrad per year. Radiation setups are calibrated so that the parame- ter that defines the desired exposure time isR, the absorbed dose rate in SiO2[rad(SiO2)/s].
The generation rate of electron-hole pairs (in cm−2 s−1) in a free standing SiO2 thin film (<220 μm) is then given by
rpair = ρoxxox R
Epair (2.43)
where ρox is the density of the oxide (about 2.3 g/cm3) and xox is the oxide thickness.
Accordingly, if one chooses to deposit 1 Mrad(SiO2) in the structure mentioned above (Al/SiO2/Si), it will induce about 1×1014 pairs/cm2, when accounting for the doubling of the rate due to secondary electrons from the metal and the semiconductor.
When a bias is applied on the gate during irradiation, the electric field in the oxide ξox
will induce a current by separating electrons and holes, and by driving them to opposite electrodes. The fractional yieldFy is the fraction of pairs that do not recombine. As shown in Figure 2.15, Fy depends on the type of radiation and on the field. The current density is then
JRAD = 2qFyrpair (2.44)
If the Al/SiO2/Si structure is biased such that ξox= 1.5 MV/cm and the absorbed dose rate from 10 keV X-rays is given by R = 500 rad/sec, rpair [from Eq.2.43] is approximately 2.5×1010 pairs/sec and Fy (from Figure 2.15) is about 0.7. Using an extra factor of 2 because of the secondary electrons from the metal and the semiconductor, Eq.(2.44) yields JRAD 20 nA/cm2 in good agreement with experimental values.18