Effects on Diamond Bulk Properties

Figure 7.3 shows the electron re-trapping probability in diamond at RT as a function of the activation energy for defects located within the band-gap. Two regions are distinguished:

the so-called ’hot’ and ’cold’ regions. In the hot region, shallow defects dominates, and generate an almost continuous exchange of carriers between conduction band (CB) and the trapping level. The cold region, where the emission probability is low is dominated by deep defects. In this case the trapped charge could not be effectively re-emitted to the CB.

Symmetrical processes take place for holes excitation to valence band (VB) maximum.

In general, the energy levels of primary-radiation induced defects (vacancies and inter-stitials) are located close to the mid-gap of the semiconductor [Kin52], giving rise to the following phenomena: change of the dark current with increasing fluence (caused by the creation of generation-recombination centers), change of the effective doping concentration at large fluences, and finally, decrease of the carrier lifetimes due to an increased trapping probability at radiation-induced defects.

2.5

Figure 7.3: The re-trapping probability as a function of the activation energy of trapping center for diamond at RT. The Fermi levels of intrinsic silicon E_F^Si and diamond E_F^D are indicated in the graph. In the case of silicon, the radiation induced defects are located mainly in the ’hot’ region, leading at first to an increase of the leakage current of the detector, whereas defects induced in diamond are located mainly in the ’cold’ region with a low probability of re-emission.

Dark current When the band-gap of a semiconductor is relatively narrow (like e.g., for silicon at RT - 1.2 eV), radiation-induced defects are activated at RT, acting as generation-recombination centers. Thus a strong linear increase of the dark current is observed for this material at increased fluence [Fur06]. On the other hand, since the irradiation causes the creation of deep defects levels within the energy gap, of a wide band-gap material like diamond, such defects do not contribute to the dark current, but result in trapping centres located well below 1 eV. The dark conductivity of intrinsic wide-bandgap materials is usually governed by native dominant defects with relatively low activation energy. Thus radiation induced deep defects may lead to a partial compensation of shallow states. Consequently, the leakage current in such materials may be decreasing with increasing irradiation fluence.

Effective doping concentration - N_{ef f} Vacancies in diamond can be considered as amphoteric impurities, acting as deep donors as well as acceptors, since their charge state depends on the position of the Fermi level [Bas01]. In high purity intrinsic IIa diamond, where the Fermi level is close to the mid-gap, neutral mono-vacancies are the major defect after irradiation. Thus, no change of the effective dopant concentration is expected after irradiation. However, as soon as free carriers are produced by ionizing radiation, the neu-tral mono-vacancies V⁰ can trap the excess carriers becoming charged. As it was shown in [Neb01] and [Pu01], neutral mono-vacancies can be positively V⁺ (hole trapping) and negatively charged V⁻ (electron trapping), respectively. Charged mono-vacancies give rise

7.1. Non-Ionizing Energy Loss and Radiation Damage to Diamond 99 to space charge changing N_{ef f} and also (as it was suggested in [Bas01]) they can form delocalized energy bands. Hereby, the charge conduction takes place due to electron (hole) activation from an occupied donor (acceptor) to a nearest-neighboring occupied donor (ac-ceptor). This conductivity mechanism is characterized by extremely low mobilities and thermal activation energies ranging from 0.35 to 1.15 eV (depending on the vacancies con-centration). These effects may lead to the detector polarization, and consequently, to a deterioration of the charge transport within a biased device.

Charge carrier trapping after irradiation The lifetime of the charge carriers decreases inversely to the defect concentration. Exposing the semiconductor to a high particle fluence new defects are successively introduced. Therefore the lifetime of the excess charge carriers can be written as:

1

τ_e,h = 1

τ_intr + 1

τ_ind (7.6)

where τ_intr is the charge carriers lifetime of non-irradiated device given by Equation 3.23, and τ_ind is the charge carriers lifetime limited by defects introduced by NIEL during the irradiation and can be written as:

τ_ind∝ 1

Φ_pβ_p (7.7)

where Φ_p is the applied fluence, and β_p ≡ dNp/dΦ_p is the primary defects creation rate.

According to Equation 7.7, a linear decrease of τ_e,h with increasing particle fluence is ex-pected in the irradiated material . An important consequence of this Matthiesen’s scaling rule is the fact that radiation damage will be much more pronounced in a perfect material (like scCVD diamond) than in defective materials (like pcCVD diamond). Since, for low fluences the concentration of radiation-induced defects is often lower than the concentration of native impurities, the radiation damage effect is ’masked’.

Trapped charge can be re-emitted from a trap e.g., due to thermal or optical excitation.

The probability of thermal excitation P (τ_d) dependents exponentially on the temperature as described by:

τ_d= 1

σ· vth· NCB · exp(−∆E/kT ) (7.8) where N_CB is the density of states in the CB, ∆E is the activation energy, k is the Boltzmann constant, and T is the absolute temperature.

Due to the relatively narrow band gap of silicon, the fraction of thermally re-emitted charge is high at RT. This leads to a highly increased leakage current and to a change of N_{ef f}. Consequently, the charge collection in silicon detectors is decreased mainly by the reduction of the diode’s depletion zone and not by the charge trapping itself. In silicon the charge loss due to the trapping starts to be important only above Φ_{1MeV neq} ≈ 1 × 10¹⁵ n/cm² [Fur06].

For diamond the probability of re-emission at RT is small. Thus after exposure of a dia-mond detector containing deep trapping centers to the ionizing radiation, a partial recovery of the charge collection efficiency is observed - which is the so-called priming phenomenon or Lazarus effect known from cryogenic silicon. However, according to the Shockley-Read-Hall

sample dimensions [mm] electrodes (diameter = 2.9 [mm]) BDS14 4 × 4 × 0.49 Cr(50 nm) Au(100 nm) annealed EBS3 3.5 × 3.5 × 0.377 Cr(50 nm) Au(100 nm) annealed BDS13 4 × 4 × 0.473 Cr(50 nm) Au(100 nm) annealed s256-05-06^∗ 4 × 4 × 0.38 Al(100 nm)

(^∗)damaged surfaces

recombination (SRH) model, when the density of passivated traps increases, the probability of recombination of trapped charge increases as well. Thus, full passivation of deep traps is never possible.