ELECTRON MOBILITY DEPENDENCE ON NEUTRON IRRADIATION FLUENCE IN HEAVILY IRRADIATED SILICON

1. Introduction

Silicon semiconductor detectors widely used in low-and high-energy physics, medicine and environmental applications are quite sensitive to radiation damage. Passage of an ionizing particle through a base material may cause defects of the crystal lattice: displacements (vacancies and interstitial Si atoms) and clusters, similar to tens-mm-size disordered structure inclusions due to knockouts of atoms from lattice sites [1]. The vacancies and interstitials lead to the formation of new trapping and recombination of carriers centres, as well as to a change in their effective (donor and acceptor) concentration, and could cause a transform of the oxygen clusters that are different in magnetic Czochralski (MCZ) and floating-zone (FZ) silicon [2, 3]. These processes at high irradiation doses significantly deteriorate the energy resolution of the radiation detectors and reduce their signal amplitude, that can be attributed to a decrease in the carrier lifetime and mobility, and can cause incomplete charge collection.

It was demonstrated [4] that the detector current under forward bias is larger than under reverse bias at the same voltage but the difference becomes smaller at higher fluence, and at 10¹⁷ neutron/cm² fluence the current equalizes. This result confirms the change in free carrier transport properties, and the investigation of mobility could be a key experiment to understand the change of properties in heavily irradiated silicon.

Main defects introduced by the high energy neutrons are clusters [1], the concentration of which is proportional to fluence. They are the main recombination centres in Si irradiated with neutrons, protons and pions [5], also this shows that the contribution of point defects is very small in Si irradiated by neutrons. As the free carrier reciprocal lifetime linearly increases if the hadron fluence increases at least over six orders of magnitude, it shows the existence of recombination centres that rapidly capture electrons and holes. It was proposed [6, 7] that the clusters could have the dipole properties which could also influence free carrier mobility. This was supported by imitating the damage created by a high-energy particle (HEP) after collision. Dipole structure HEP caused damage was obtained from simulations with the crystal TRIM (Transport of Ions In Matter) software [8], and it was shown that vacancy and interstitial enriched regions are spatially separated [9]. It was observed in agreement [10] with expectations that there was no change (within 5–10% errors) in mobility or saturation velocity for both electrons and holes in Si irradiated to 10¹⁴ cm^–2 fluence. The indications were found that in more heavily irradiated diodes the space charge density is nonuniform, and this excluded possibility to exploit the Hall effect to measure the mobility of carriers in more heavily irradiated Si. The investigation of Si samples irradiated to the similar and higher fluence confirmed this statement and demonstrated possibility to measure the mobility of carriers by magnetoresistivity effect that is less dependent on sample inhomogeneity than the Hall effect [11]. There a decrease of electron mobility was observed in Si irradiated to higher neutron fluence. In this work, the research has followed the same methodology to analyse the data in Si irradiated to extreme high fluence.

2. Experimental details

Two sets of microstrip silicon samples (43 µm width between strips, 10 mm length and 0.375 mm thickness) having an electron (phosphorus-doped) conductivity type were used in our experiments. More technical details may be found in our previous work [11] since this is the extension of investigation of the Si samples irradiated to higher neutron fluence. Magnetoresistance mobility μ_M in homogeneous crystals is related to the data obtained from the magnetoresistance effect measurements by the following relation [12]:

Here B is the applied magnetic induction, ρ₀ and ρ_B are the resistivity, and I₀ and I_B are the electric current with the magnetic field absent (0) and applied (B), respectively. The quadratic dependence of the magnetoresistance with magnetic induction was observed (Fig. 1).

Also, the relation of free carrier drift and magnetoresistance mobility given in [13] was taken into account: the factor for low magnetic field in bulk silicon irradiated to high fluence, i.e. Coulomb scattering, is equal to 2.43. Therefore the fitting of electron mobility data was performed by the relation according to the Matthiessen’s rule

and here μ_hon means the mobility of electrons in the undoped sample. The electron mobility limited by ionized impurity scattering was evaluated by the Conwell–Weisskopf formula [14]

where

The electron mobility limited by dipole scattering was evaluated by the formula [15]

the density of dipoles n₀, dipole length d₀, the effective Bohr radius a₀ = 4πε_s/m*e² = 30 Å = 0.53(ε_r/m_r) Å, where m* = m_rm₀ is the electron effective mass (m₀ being the electron rest mass), static dielectric constant ε_s = ε_r ε₀ = 11.9.

The electron mobility limited by cluster scattering without the dipole feature was evaluated by the relation [16]

where v is the thermal velocity of electron, the cross-section of cluster scattering S_clus = 10^–11 cm² and N_clus is the cluster concentration. This term depends on temperature as T^–1. For the electron mobility limited by phonon scattering the data from [17] was used: µ = 1/aT^2.42 and µ = 1400 cm^{2/Vs at 300} K.

3. Results

The magnetoresistance mobility was investigated in the silicon samples irradiated by neutrons to 1·10¹⁵–1·10¹⁷ neutron/cm² fluence at the Triga reactor (Ljubljana). The data was corrected to get the drift mobility values that were compared with a simulation which included all the above-presented scattering processes (Fig. 2). A choice of the contribution of different scattering processes started by fitting the mobility dependence on temperature that was very sensitive to contributions of different scattering processes, and the data corresponding to 300 K temperature was found and presented in Fig. 3. The following set of parameters was obtained:

1. The measured electron mobility in the non-irradiated sample with its value equal to 1200 cm²/Vs that was lower than given in [16] could be caused by scattering on ionized impurities, because Si was compensated. The ionized impurity concentration was found by Eq. (3), and its value was found to be 8·10¹⁴ cm^–3.

2. As the interaction and transform of the defects were neglected, the proposed concentration of radiation-induced defects was proportional to the neutron fluence. As the neutron irradiation created mostly clusters [1], it was proposed that at least 1% of neutrons created the ionized point defects.

3. The cross-section of cluster scattering was obtained equal to S_clus = 1.1·10^–15 cm².

4. The proposal of proportionality to the neutron fluence resulted in only one third of clusters having dipole properties.

These results are illustrated in Table 1.

Table 1. The partial contribution in the dependence of electron mobility on the fluence by the defects.

4. Discussion

The good correspondence of data obtained in the analysis of the dependence of different scattering processes on temperature, simulation of mobility dependence on neutron fluence and the experimental data showed that at least up to neutron fluence of 10¹⁶ cm² the defects did not interact. It was confirmed by the linear dependence of contribution of scattering by clusters and dipoles, which was dominating in defining the mobility value.

As proposed in [7], the dipoles could be the main recombination centres that provided the linear relation of fluence and lifetime [5]. The determined concentration of dipoles in the samples irradiated up to 1·10¹⁶ neutrons/cm³ permits evaluation of the free carrier recombination centre capture cross-section. As the lifetime follows the relation [18, 19]

where v_thermal is the electron thermal velocity, at 300 K equal to 10⁷ cm/s [20], σ is the capture of free carrier cross-section and M is the concentration of recombination centres. Here and above we follow an approximation that 10 neutron/cm² fluence creates 10 cluster/cm³ [1]. The experiment of slow neutron scattering obtained 2.5 times greater value [3]. The lifetime in Si irradiated to 10¹⁶ neutron/cm² fluence is equal to 0.42 ns [21], the concentration of recombination centres, i.e. dipoles, M = 3.3 ⋅ 10¹⁵ cm^–3, then the capture of free carrier cross-section is equal to σ = 7.2 10^–14 cm. It could be recognized being as a weak attractive centre.

The analysis of experimental data clearly shows that the applied model did not explain the mobility in the samples irradiated to the highest fluence. Therefore a new concept of carrier transport is needed. The measurement data was approximated by polynomial regression that is shown in Fig. 4, and the approximation was statistically correct (p = 0.0048).

The approximation curve demonstrated a tendency to change the Si conductivity nature. The Mott density [22] for excitons obtained n_Mott = 3.6 ⋅ 10¹⁷ cm^–3 that could be comparable for our case if a random distribution of the clusters is taken into account. As a conclusion could be the statement that Si irradiated above 10¹⁶ cm^–2 fluence (and up to 10²⁰ cm^–2 [3]) is a disordered material with the clusters.

Acknowledgements

This work, performed in the framework of the CERN-RD50 collaboration, has been funded by the Lithuanian Academy of Sciences for the Project CERN-RD50.

We are also grateful to AIDA Transnational Access for irradiations in the Triga reactor (Ljubljana).

References

STIPRIAI APŠVITINTO NEUTRONAIS SILICIO ELEKTRONŲ JUDRIO PRIKLAUSOMYBĖ NUO NEUTRONŲ ĮTĖKIO

J.V. Vaitkus, A. Mekys, Š. Vaitekonis

Vilniaus universiteto Fotonikos ir nanotechnologijų institutas, Vilnius, Lietuva