**3.3. Monte Carlo simulation of radiation transfer through photovoltaic detectors**

In order to understand the state of the semiconductor after irradiation, Monte Carlo simula‐ tions of radiation particles transfer through the material were performed. Monte Carlo simulation gets the answers by simulation of each individual particle and memorizing of certain aspects of their middle behavior. For simulation, FOTELP-2K10 and MCNP programs were used. FOTELP-2K10 is a program that gives the Monte Carlo simulation of the transport of photons, electrons, and positrons [39], while the MCNP (*Monte Carlo N-Particle*) is a general purpose software that can simulate the transport of neutrons, photons, electrons, or a combi‐ nation of neutron/photon/electron through arbitrary geometric configurations [40].

For this experiment, two Monte Carlo simulation were made, γ-photon transfer through the PIN photodiode and through the phototransistor. The simulations were done with the aim of understanding the processes occurring in the photodiode and phototransistor between gamma and neutron irradiation, i.e. to provide a review process, which is gamma radiation caused in a semiconductor since the final result of these processes represents the initial conditions for neutron irradiation that followed.

### *3.3.1. Monte Carlo simulation of gamma photon transport through a pin photodiode*

**Figure 13** presents a cross-section of a PIN photodiode used for the simulation.

**Figure 13.** Cross-section of a PIN photodiode [41].

The results of Monte Carlo simulations are shown in **Tables 1**–**5** and in **Figure 14**. **Table 1** shows the deposed energy per input particle in each zone of photodiode, where the zones are semiconductors area: *p+* (zone 1), *p* (zone 2), and *n+* (zone 4), and the pure semiconductor (zone 3). **Figure 14** shows the ratio of energy absorbed during each interaction in different layers per depth of semiconductors, i.e. each zone.


**Table 1.** Deposed energy per input particle obtained by Monte Carlo simulation using FOTELP-2K10.

**Figure 14.** Depth dose distribution in PIN photodiode obtained using FOTELP-2K10.

understanding the processes occurring in the photodiode and phototransistor between gamma and neutron irradiation, i.e. to provide a review process, which is gamma radiation caused in a semiconductor since the final result of these processes represents the initial conditions for

The results of Monte Carlo simulations are shown in **Tables 1**–**5** and in **Figure 14**. **Table 1** shows the deposed energy per input particle in each zone of photodiode, where the zones are

3). **Figure 14** shows the ratio of energy absorbed during each interaction in different layers per

(zone 4), and the pure semiconductor (zone

(zone 1), *p* (zone 2), and *n+*

**Zone Deposed energy (eV) Relative error (%)**

**Table 1.** Deposed energy per input particle obtained by Monte Carlo simulation using FOTELP-2K10.

 556 .77 0.165 257.78 0.255 293.31 0.239 1386.9 0.112

*3.3.1. Monte Carlo simulation of gamma photon transport through a pin photodiode*

**Figure 13** presents a cross-section of a PIN photodiode used for the simulation.

neutron irradiation that followed.

82 Radiation Effects in Materials

**Figure 13.** Cross-section of a PIN photodiode [41].

depth of semiconductors, i.e. each zone.

semiconductors area: *p+*

In order for a lattice atom to be displaced, a minimum amount of energy must be transferred to the target atom. This threshold energy is called the displacement energy *Ed* (*threshold displacement energy—TDE*) [42, 43]. By using molecular dynamics (*MD*) simulations, Perlado *et al*. [44] predicted TDE values, at 300 K, ranging from 42 to 112 eV for Si. Average TDE values of 93 eV for Si are suggested by El-Azab and Ghoniem from MD simulations [45].

In each zone of photodiode (**Table 1**), and in almost every layer (**Figure 14**) deposed energy per incident particle is high enough to move the atom, i.e. to create vacancy.

**Tables 2** and **3** show the probability of creating new photons and electrons per incident particle (photon) through individual interactions.


**Table 2.** Probability of creating new photons per incident particle (photon) obtained using MCNP.



**Table 3.** Probability of creating new electrons per incident particle (photon) obtained using MCNP.

Bremsstrahlung is the interaction that has the highest probability to generate new photons (**Table 2**), while the highest probability for creation have Auger electrons (**Table 3**).

**Tables 4** and **5** show the number of physical interactions in which are created or disappeared photons and electrons per input particle (per cell).


**Table 4.** Number of physical interactions in which are created or disappeared photons per incident particle (per cell) obtained using MCNP.


**Table 5.** Number of physical interactions in which are created or disappeared electrons per incident particle (per cell) obtained using MCNP.

Simulation results show that the number of interactions that result in a vacancy i.e. PKA (*primary knock-on atom*) are 10 to 1000 times higher than all other possible types of interaction (**Table 5**—shaded part). Among the total number of electrons caused by gamma radiation in all areas of photodiode, 78–80% is produced by PKA (in area 4 even up to 97%). This is an unequivocal sign that the gamma radiation caused a very large number of vacancies.

**Probability of creating new electrons Interaction that creates electrons**

**Table 3.** Probability of creating new electrons per incident particle (photon) obtained using MCNP.

From neutrons 0 0 0 0 0

P-annihilation 6.6667E-08 0 0 6.6667E-08 0 Pair production −3.333E-08 0 0 −3.333E-08 0 Photonuclear effect 0 0 0 0 0

Pair production 6.6667E-08 0 0 6.6667E-08 0

Photon Auger 0 3.3333E-08 3.3333E-08 1.3333E-07 0

p-annihilation −3,333E-08 0 0 −3.333E-08 0

Compton recoil 1.7967E-05 9.1000E-06 9.1667E-06 2.3833E-05 7.7333E-06 Photoelectric effect 2.2333E-06 1.4333E-06 1.8667E-06 1.5000E-06 1.1333E-06

Electron Auger 4.7667E-05 3.4133E-05 3.7300E-05 0 5.5800E-05 PKA 2.5647E-04 1.8663E-04 2.0543E-04 7.2073E-04 2.1520E-04

Total **3.2437E-04 2.3133E-04 2.5380E-04 7.4623E-04 2.7987E-04**

**Table 5.** Number of physical interactions in which are created or disappeared electrons per incident particle (per cell)

Bremsstrahlung 9.3333E-07 7.3333E-07 6.3333E-07 2.1333E-06 4.0000E-07 Capture of photons −2.233E-06 −1.433E-06 −1.867E-06 −1.500E-06 −1.133E-06

Electron x-rays 1.4333E-06 9.0000E-07 1.4667E-06 0 9.6667E-07 Total **1.6667E-07 2.0000E-07 2.3333E-07 6.6667E-07 2,3333E-07**

**Table 4.** Number of physical interactions in which are created or disappeared photons per incident particle (per cell)

**Physical interaction Area 1—***p+* **Area 2—***p* **Area 3—***i (intrinsic)* **Area 4—***n+* **Area 5—***Al contact*

(**Table 2**), while the highest probability for creation have Auger electrons (**Table 3**).

Bremsstrahlung is the interaction that has the highest probability to generate new photons

**Tables 4** and **5** show the number of physical interactions in which are created or disappeared

**Physical interaction Area 1—***p+* **Area 2—***p* **Area 3—***i (intrinsic)* **Area 4—***n+* **Area 5—***Al contact*

collision with impact electrons

5.3281E-07 Electrons knocked out in a

3.3333E-06 Auger photons 4.1667E-06 Auger electrons

photons and electrons per input particle (per cell).

obtained using MCNP.

84 Radiation Effects in Materials

obtained using MCNP.

In order for neutron irradiation of photodiodes (applied after gamma radiation) to cause intercenter charge transfer and tunneling supported by traps, as already mentioned, it is necessary for neutron radiation to form defects in a semiconductor (vacancies), which are close to each other, and to create a sufficient number of divacancies. As a relatively heavy and uncharged particles, neutrons, in a collision with the atoms of the crystal lattice, lead to the displacement of entire atoms from the lattice. This naturally causes the breaking and destruc‐ tion of the local lattice structure by displacing atoms and creating vacancies. Displaced atom is called interstitial because it takes place in the space between knots, and a pair of interstitial atom and vacancy is called Frenkel defect. If the energy of incident neutron is high enough, it can give sufficient energy to displaced atom, which can displace other atoms in the lattice. In the case of high-energy incident neutrons, this process has a cascade (avalanche) character. This requires quick energy neutrons from 10 keV to 10 MeV. At the end, all displaced atoms lose their excess energy and the heat balance in the grid established. Some of the atoms return to vacancies and reconstruct the structure of the local grid. Some of these atoms come together with dopants or impurity atoms and form stable electrically inactive defects, which do not contain recombination centers and trap. On the other hand, moving vacancies associate with impurity atoms, vacancies, and other donors forming temperature stable defects (complex defects) that represent recombination centers and trap centers. Since the mean energy of neutrons from a source in the experiment was 5.5 MeV, it follows that neutrons have sufficient energy to cause a cascading process of creating vacancies. Previously, gamma irradiation created a large number of vacancies, increasing the probability for vacancies, created by neutron irradiation, to be physically close to the preformed vacancy. Divacancies, formed like this, facilitate intercenter charge transfer supported by traps and provide increased generation of charge carriers and this, as already mentioned in Section 3.1., leads to partial reparation of semiconductor structure and increase the spectral response and the photocurrent of the photodiode.

#### *3.3.2. Monte Carlo simulation of gamma photon transport through a phototransistor*

**Figure 15** presents a cross-section of a phototransistor used for the simulation.

The results of Monte Carlo simulations are given in **Tables 6**–**8**. **Tables 6** and **7** show the probability of creating new photons and electrons per incident particle (photon) through individual interactions.

**Figure 15.** Cross-section of a phototransistor [41].


**Table 6.** Probability of creating new photons per incident particle (photon).


**Table 7.** Probability of creating new electrons per incident particle (photon).

According to the simulation results in any semiconductor field within the phototransistor, there was no interaction in which are created or disappeared photons. **Table 8** show the number of physical interactions in which are created or disappeared electrons per input particle (per cell).


**Table 8.** Number of physical interactions in which are created or disappeared electrons per incident particle (per cell).

In phototransistor, as in the photodiode, the largest number of integration caused by gamma radiation are vacancies (PKA) (**Table 8**—shaded part). When the semiconductor material, with structure like this, is exposed to neutron radiation, due to the nature of radiation, a number of new vacancies will be created together with those previously formed. The final result of both types of radiation action are divacancies. As already mentioned in Section 3.2, divacancies cause the increased generation of charge carriers through the two dominant effects [19]:


According to the results in **Table 8** the largest number of divacancies have creating in collector and the *n+* area of phototransistor, increasing the concentration of electrons in these areas. On the other hand, due to Compton scattering and Auger electron and increases the concentration of electrons in the base. The final result of these effects is increasing the transistors photocurrent after neutron irradiation (compared to its value after gamma irradiation), which is consistent with the results of the experiment presented in chapter 3.2.
