2 Instituto de FÃsica de LÃquidos y Sistemas Biológicos (IFLYSIB). CONICET â UNLP â ... the carriers lifetime, will modify the electric behavior of the device. .... particles strike the device. .... Spectroscopy Group of Physics Department. Comisión ...
STUDY OF SEMICONDUCTOR DEVICES EXPOSED TO SPATIAL RADIATION G. DOMINGO YAGÜEZ 1, D. N. VILLARRAZA 1, M. A. CAPPELLETTI 1 y E. L. PELTZER y BLANCÁ 1,2 1 Grupo de Estudio de Materiales y Dispositivos Electrónicos (GEMyDE) Departamento de Electrotecnia Facultad de Ingeniería de la Universidad Nacional de La Plata 2 Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB) CONICET – UNLP – CIC CC 91, 1900, La Plata ARGENTINA
Abstract: - The present work aims at the study of physical processes that take place in electronic devices exposed to spatial radiation. The modelling and simulation of electronic devices is done by means of numerical algorithms. By using the coupled Poisson and Continuity equation we have obtained the description of the behavior of electronic devices numerically. The effects of the radiation studied in the present work are the atomic displacement damages and the ionization caused by an incident charged particle. Key-Words: - Modelling - Simulation – Radiation - Displacement damages – Ionization – PIN photodiode
1 Introduction The present work shows the analysis of the behavior of a PIN semiconductor device, exposed to spatial radiation. Our aim is to determine how their operation properties are affected on such circumstances. The physical processes that happen in the semiconductors devices, can be described through models and simulations by means of numerical algorithms. The reliableness of electronic devices that are in some system in orbit is constantly threatened by the effects of the characteristic radiation of the environment in which they are moving. The main radiation sources are: the particles coming from the Sun, the cosmic rays and the particles trapped in the Van Allen´s belts, as neutrons (n), electrons (e-), protons (p+) and heavier ions. Mainly, two types of damages can affects to the PIN photodiodes (the present study is focused on such devices) when they are exposed to the radiation: ionization and atomic displacement damages. The first one, generate electron-hole pairs along the path of the incident charged particle inside of the semiconductor. It is a transitory damage, because it disappears shortly after the particle strike. In opposition, displacement damages (dislocations of atoms from their normal lattice position) cause alterations in the periodicity of the lattice, originating
energy levels located in the forbidden band of the semiconductor. As consequence of this, atomic displacement damages, which produce a decrease in the carriers lifetime, will modify the electric behavior of the device. The last, are considered permanent damages, because their effects can be present for periods longer than one year. The modelling and simulation of electronic devices are achieved with the development of the computer codes, which involve equations representing their physical behavior. The resolution of these equations in a numeric way, allows us to obtain a prediction of the electric characteristics of the device irradiated under different operation conditions, making it possible to research the consequences of the permanent and non-permanent damages. The development of electronics and microelectronics is based on two fundamental pillars. On one hand, the study of materials and their microscopic properties, nowadays makes it possible to carry out the analysis of them from the theoretical point of view with an incredible precision in the predictions of their properties. On the other hand, the study of devices by means of the modelling and simulation, allow us to obtain results with the same precision. Without doubt, the computer simulation codes have become indispensable tools practically in all the
branches of the science. Their importance has gone growing continually and nowadays they are applied in every integrated circuits and semiconductor devices designs. It is also necessary to highlight the utility of these codes as educational tools. It can be mentioned some applications that put in evidence the great importance of the study using simulations: • understanding of the physical operation principles by means of the calculation and visualization of magnitudes such as: potential, electric field, current density, carrier concentration, among others; • improvement of the design of devices for the optimization of their behavior in specific applications; • analysis of fail and rupture mechanisms; • quantification of physical characteristics that are difficult to measure; • obtaining of analytic models of devices either in balance or under different operational conditions: DC, AC or transitory; • research of structures not yet developed, avoiding test and error’s cycles in the production of prototypes. The advantages in such procedure is the economy on the time and material resources. The first analysis in our work was carried out with a PIN photodiode exposed to radiation of neutrons (n), electrons (e-), protons (p+) and oxygen ions. In Fig. 1 we can appreciate a simplified outline of the PIN and the incident radiation.
(3) where V is the electrostatic potential; ∈ is the dielectric permittivity of the material; q is the electron charge; p and n are the concentrations of are the holes and electrons; Nd+ and Naconcentrations of donor and acceptor ionized impurities; Jn and Jp represent the current densities of electrons and holes respectively; and R is the net recombination-generation rate. The expression used to describe the current density is: (4) where x indicates carrier type (n for electrons and p for holes); µ x is the mobility; D x is the diffusion coefficient; and E is the electric field. In (4), the first term on the right member refers to the drift currents (carrier movement as a consequence of the electric field) and the second term refers to the diffusion currents (carrier movement as a consequence of a gradient in the carrier concentrations). In our analysis it is considered that the temperature is constant in the whole device, that is the reason why the currents generated by gradients of temperature are not taken into account. The carrier mobility µ following term:
x
is described by the
(5)
Fig. 1. Simplified scheme of a PIN photodiode.
2 Development The basic model that governs the electric behavior of the semiconductors consists of three coupled and not linear partial differential equations. The first one is the Poisson’s equation (1) that relates the variations of the electric potential with the spatial charge density, and the other two are the continuity equations for both electrons and holes ((2) and (3)), that describe the time evolution of the carrier concentrations due to transport and recombinationgeneration processes: (1) (2)
where, µxLI represents the mobility due to two different scattering mechanisms: first one, by means of thermal vibrations of the crystal’s atoms; second one, by means of ionized impurities. The parameter µxLIE takes into account the µxLI factor and the saturation of the carrier drift speed for high electric fields; νxsat is the saturation speed in the material; and the value of the constant βx is 2 for electrons and 1 for holes. Several carrier generation and recombination mechanisms exist in the semiconductors, each one has a model that describes its physical behavior. The thermal recombination-generation process via traps is represented by the Shockley-Read-Hall equation (6).
(6) where nint is the intrinsic carrier concentration; n1 and p1 depend on the energy level of traps; and τn and τ p are the mean lifetimes of electrons and holes respectively, whose models are described later. The other process considered is the impact ionization, which is a mechanism of carrier generation, and it is represented by (7).
Due to that the incident particle goes loosing energy inside of the material of the device, and considering known the spectral distribution of the incident radiation, the minority carrier mean lifetime can be written as: (10)
where 'y' is the perpendicular distance to the device surface; initial
(7) where αn and αp are the ionization rates of electrons and holes, which have an exponential dependence with the component of the electric field E in the direction of the current flow. Finally, for the mean lifetimes of carriers, the used expression comes from a the fitting of a experimental data curve (8).
(8) In this formula can be observed the dependence of τ x with the impurities concentrations. The rate at which the electric properties of the materials are degraded in an radiation environment is usually formulated in terms of the damage coefficient. The degradation of the minority carrier lifetime can be expressed as:
(9) In this equation and are the lifetimes values before and after irradiation; φ is the particle fluence; and Kr is the damage coefficient for the mean lifetime. In general, the damage coefficients in semiconductors depend on the following parameters: type and energy of the incident particle, kind of material, resistivity, types and concentration of impurities, injection level, temperature and elapsed time after irradiation.
is the total fluence on the device; is the relative frequency of particles with energies in the range around Einitial;
is the relative frequency of occurrence of a certain LET deviation from its mean value; and K is the constant of damage displacement, which depends on the type and energy of the incident particle. For the transitory analysis of the ionization effects caused by the incidence of a charged particle, it is considered that the particle uses its energy in the creation of carriers in the neighborhood of its path. The concentration of created carriers is given by (11).
(11) where 'd' is the distance traveled by the particle; LET is the energy used in ionization per length unit; Ei is the necessary energy for the creation of carrier pairs (~3,6 eV for Si); and σ is the cross section of the incident particle (~1 µm2 for protons in Si). Since it is impossible to find an exact analytic solution for the system obtaining from the previous equations, the problem is solved by special numeric techniques. The most appropriate for this case is the finite differences method. The simulation codes developed solve the basic semiconductors equations in one and two dimensions with the appropriate contour conditions. Firstly, a mesh is defined over the simulation domain, and the equation system is normalized and discretized. Then, in each point the electrostatic potential V and the carrier concentrations n and p are calculated by means of an iterative numeric method (Gummel Method) [1]. This successively improves the estimation of V, n and p in a self consistent way until it arrives to the final solution. The Gummel Method, in each iteration, solves separately the equations (1),
(2) and (3), introducing in each step the solution of the previous step. We should finally mention that it has not been considered the effects that take place in the metalsemiconductor junctions of the device.
can be seen in Fig. 2 and Fig. 3, is justified by the rise in the carrier concentration (mainly in the intrinsic layer) that is shown in Fig. 5. The last fact is due to an increment in the thermal carrier generation rate, what is deduce from equations (6) and (9). 10-4
3 Results
1 MeV 10-6
Dark current [A]
A PIN photodiode had been studied under different kinds of radiation, using the carrier generationrecombination processes presented above. In first place, it has been analyzed the increase in the carrier thermal generation rate due to the displacement damages introduced when sub-atomics particles strike the device. The parameters used for the simulated diode are: lp = 2.25 µm, lI = 25.5 µm and ln = 2.25 µm; Na = 5 · 1017 cm-3, NI = 1013 cm-3 (donnors) and Nd 5 · 1017 cm-3; τno = 3.95 · 10-4 s and τpo = 3.52 · 10-4 s.
500 keV 10 MeV
10-8
100 MeV
10-10
spectrum 10-12 108
1010 1012 Fluence [p/cm 2]
1014
Fig. 3. Dark current for protons at several energies. Proton flux [p/cm 2/day/MeV]
In this case, a one-dimensional model was used, based on the characteristics of the device and the kind of radiation (uniform and perpendicular to the surface). This allows to save computational resources compared to bi or tri-dimensional systems, without loosing too much precision. Some results obtained by the simulations are shown in Fig. 2, for a bias of –20 V, when the photodiode is irradiated with neutrons, electrons, protons and oxygen ions at 10 MeV.
105 104 103 102 100
102 Energy [MeV]
-4
10
Fig. 4. Proton spectrum used in the simulation.
p+
O ions
Dark current [A]
10-6
n 20
10-10
10-12 108
10
12
14
10 10 10 Fluence [particles/cm 2]
16
10
Fig. 2. Dark current for 10 MeV n, e-, p+ and O ions.
In Fig. 3 it is shown the effects produced by protons of several energies. It was also analyzed the behavior for irradiations of protons with the spectrum presented in Fig. 4. In Fig. 5 it is shown the electron concentration as a function of the length in the PIN diode, for several fluences of 10 MeV protons. The increment in the reverse current with the fluence that
Electron concentration [cm -3]
e-
10-8
15 10e14 p+/cm2 10e12 p+/cm2
10
0 p+/cm2
5
0 0
5
10 15 20 Distance [um ]
25
Fig. 5. Electron concentration through the device, for a number of 10 MeV proton fluences.
30
In the analysis of the ionization effects produced by the strike of a charged particle, transitory bidimensional simulations were done. Fig. 6 shows the current pulses produced as a consequence of the incidence of protons at a different energies. It was verified that the area under the curves (collected charge) agree with the created charge in the photodiode depletion layer. In the series of Fig. 7 appears the hole distribution for several times, where it can be seen the changes caused by the incidence of a single 1 MeV proton. 25
Current [uA]
20 10 MeV
15 10
1 MeV 5 100 MeV 0 0
0.5
1 Tim e [ns]
1.5
2
Fig. 6. Current pulses produced by 1 Mev, 10 MeV and 100 MeV protons.
In order to establish a comparison between simulated and empiric data, it was simulated the experience done by Onoda et al. [2]. This experience is based in the irradiation of the PIN photodiode described below, with 15 MeV oxygen ions. The results obtained are shown in Fig. 8 and Fig. 9. The PIN parameters are: lp = 0.2 µm, lI = 8.5 µm and ln = 3.3 µm; Na = 1017 cm-3, NI = 8 · 1012 cm-3 (donnors) and Nd = 1017 cm-3. It was also simulated a PIN photodiode exposed to 14 MeV neutron irradiation. The results show extraordinary concordance with experimental measurements done by Kalma and Hardwick [3].
Fig. 7. Hole concentration through the device (plane in which the particle impacts) at several times.
4 Conclusions
Current density [uA/cm2]
200 1e10 cm-2 150 4e10 cm-2
100
50
7e10 cm-2
0 0
5
10 15 Reverse bias [V]
20
Fig. 8. Dark current density for 1010, 4 · 1010 and 7 · 1010 particles/ cm2 for 15 MeV oxygen ions. (Solid line belongs to the present work, triangles belongs measured data).
Acknowledgment: We grateful to Dr. A.J. Kreiner, Head of the Nuclear Spectroscopy Group of Physics Department. Comisión Nacional de Energía Atómica (CNEA) for his colaboration in the experimental phase of this work..
Current density [uA/cm2]
200
150
In this work it has been successfully developed and implemented numeric algorithms for the simulation of semiconductor devices. The codes numerically solve the Poisson’s equation and the continuity equations for one and two dimensions, jointly with the current densities, mobilities, recombinationgeneration processes and mean lifetimes models. This tool allows to predict the behavior of several kinds of devices under different operation conditions (stationary and transitory regimes), and it is useful in the device analysis, design and optimization, and in education purposes. The results obtained with our codes, applied to a silicon PIN photodiode exposed to neutron and oxygen ion radiations, shows a great agreement with experimental data.
simulated data measured data
100
50 0 6 10
8
10
10 10 Fluence [ions/cm2]
Fig. 9. Dark current as a function of 15 MeV oxygen ions fluence. (Solid line belongs to the present work, triangles belongs measured data).
References: [1] H. Gummel, A self-consistent iterative scheme for one-dimensional steady-state transistor calculations, IEEE Transactions on Electron Devices, Oct 1964, 455-465. [2] S. Onoda, T. Hirao, J.S. Laird, H. Mori, H. Itoh, Y. Wakasa, T. Okamoto, Y. Koizumi, Displacement damage degradation of ion-induced charge in Si pin photodiode. [3] A.H. Kalma, W.H. Hardwick, IEEE Trans. Nucl. Sci. 32,4195 (1978).
