Defects Creation

When charged particles traverse semiconductor devices, three main processes occur:

• Displacement due to non-ionizing energy loss (NIEL). When the primary particle scatters on a lattice atom, transferring enough energy to displace it, a vacancy and a primary knock-on atom (PKA) is formed. As long as, the kinetic energy of the PKA is sufficiently high, further displacements take place. The rest of the energy is dissipated by phonon creation. At high energies, nuclear reactions occur, producing

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activation. The so-called self-annealing process takes place. These rearrangements are partially influenced by the presence of impurities in the initial material, forming complex defects. Thermally stable defects influence the electric properties of the semiconductor, and thus detector operation.

• Ionization - this process creates electron-hole pairs and is used for radiation detec-tion.

• Trapping - In insulators or wide-band gap semiconductors, the material does not return to its initial state, if the electrons and holes produced are trapped and could not be re-emitted at the operating temperature. Thus, space charge is created, which affects detector operation.

The evaluation of the non-ionizing energy-loss component is performed by computing the flux-weighted displacement cross-section D(Φ, E), also called the average displacement Kinetic Energy Released per unit Mass (KERMA). For a given particle flux Φ(E), D(Φ, E) is defined by Equation 7.1

D(Φ, E) =

where D(E) is the damage function describing the macroscopic cross section σ_k(E) for a specific particle interaction out of the various reactions within the solid:

D(E) = 

k

σ_k(E) 

dE_rf_k(E, E_r)P (E_r) (7.2) with f_k(E, E_r) being the probability for an incident particle of energy E to produce a recoil energy E_r via a reaction of type k, and the function P (E_r) being the part of the recoil atom of energy E_r deposited by displacements. P (E_r) is called the Lindhard partition function.

The NIEL hypothesis states that the damage created in a semiconductor material is directly proportional to the non-ionizing energy loss independent of the type of impinging particle or the type of interaction. For radiation-hardness studies of silicon detectors, D(E) (expressed in MeVmb), is commonly normalized according to the ASTM standard [ASTM]

to the displacement cross section of damage produced by a 1 MeV neutrons, quoted to be 95 MeVmb. Using the N IEL scaling hypothesis, the damage efficiency of any particle type and flux of a given kinetic energy E_k, can be described by the hardness factor k, defined by Equation 7.3

k(Φ_k) = D(Φ_k)/D1MeV n(95MeV mb) (7.3) However, such a normalization is only valid for silicon. For any other material including diamond, the damage function will be different. The NIEL for diamond damage functions have been calculated in the past for proton and pion interaction [Laz99], and more recently by a group of the University of Karlsruhe for neutrons and protons of kinetic energies

7.1. Non-Ionizing Energy Loss and Radiation Damage to Diamond 95 ranging from 5 MeV to 5 GeV [Boe07]. A modified FLUKA code was used, where nuclear elastic and non-elastic processes are implemented to calculate the fragment and the recoil production rates over the kinetic energy range of the impinging primary particles. The secondaries have been used as an input to the SRIM simulation software [Zie85], which calculates the lattice damage of diamond caused by slow-down fragments, as well as, PKA produced by multiple elastic Coulomb scattering. Theoretical details of damage production in solids can be found in the pioneering work of Kinchin and Pease [Kin52].

In Figure 7.1 the NIEL damage cross-sections of diamond (Right panel) are compared to silicon data (Left panel) [Huh02], both plotted versus the energy of the incoming particles.

Figure 7.1: NIEL damage cross-sections for protons and neutrons as a function of the incoming particles energy after [Boe07]: (Left panel) silicon, (Right panel) diamond.

As shown in Figure 7.1, the damage cross sections are commonly lower for diamond than for silicon over the full range of the explored energies. Below 100 MeV, the cross sections for charged particles are dominated by Rutherford scattering, which increases rapidly at low energies. Due to the Z²/E² dependence, the radiation hardness of diamond is expected to be a factor 3.6 higher than that of silicon in this energy region. For energies higher than 100 MeV, heavier nuclear recoils are created in the silicon case (A_Si = 28), leading to an amount of N IEL larger by a factor of ten.

The concentration of the primary-radiation induced defects (CPD) in an irradiated material can be calculated using the N IEL data as proposed by [Laz98] from the following relation:

CP D(E_k) = ρ

2E_d(N IEL) (7.4)

where E_k is the kinetic energy of the incident particle, (N IEL) is the corresponding N IEL value in [keV cm²/g], ρ is the material density in [g/cm³] and E_d is the threshold energy

d

37.5 eV, E_d¹¹¹ = 45.0 eV, E_d¹¹⁰ = 47.6 eV [Koi92]. In diamond, conversion from NIEL expressed in [MeVmb] to [keV cm²/g] can be made according to:

100 MeV mb ×¹⁰_{M eV}^3keV × ¹⁰⁻²⁷_mb^cm2 ×

mole(C) 12.01g

×

6.022×10²³ mole(C)

= 5.018 keV cm²/g, (7.5)

Taking the calculated NIEL values from Figure 7.1, relation 7.4, and the conversion pre-sented in Equation 7.1.1, the CP D value after the hadron irradiation discussed in this work is estimated for 26 MeV protons, giving a CP D^{26MeV p}= 282 cm⁻¹ and for∼20 MeV neutrons CP D^{20 MeV n}= 47 cm⁻¹

Care must be taken comparing the calculated concentration of primary defects with the experimentally measured defect density. Due to self-annealing processes, a large ratio of the primary induced defect anneals out during the irradiation. The comparison, done by [Mai98] between calculations (TRIM, GEANT) and experimental data for neutron and electron irradiated diamond suggest, that at RT more than 90 % primary created defects may recombine already during irradiation.