Nuclear Engineering

Solid State Detector

In the previous lectures gas has been considered as detection medium and three different gaseous detectors have been discussed. Now let us ask a question: is it possible to use solid as a detection medium? If possible, then do we achieve any advantage over gas detectors?

Among various solids, semiconductors (like Si, Ge) have been used in a significantly to design solid state detectors (SSDs). Recently, compound semiconductors with higher energy band gap are also used as SSDs for specific applications. Although semiconductor detectors are more costly in terms of availability, processing and design as compared to gas detectors, they are widely used for charged and gamma particle spectroscopy because of very good energy resolution. The energy required to produce one electron-positive ion pair is almost 10 times less than that of gas ionization detector. Recently, nuclear scientists are making detectors combing semiconductor and gas detectors with a very special design to determine energy and position of the particles.

In the rest part of this lecture, the basic physics behind semiconductors, making a semiconductor junction and designing a semiconductor detector is discussed.

Let us start from the basic discussion on intrinsic and extrinsic semiconductor and semiconductor junction.

What is an intrinsic semiconductor?

Intrinsic semiconductor is basically a pure semiconductor, where valance band is completely filled and conduction band* is empty at absolute zero. At this condition, Fermi level # lies exactly in the middle of the band gap. Electrons can cross the band gap and reach to conduction band when temperature of the material is enhanced. In this case a hole is formed at the place from where electron has left and therefore, the number of electrons in the conduction band is exactly equal to the number of holes in the valance band. If n is the concentration of electrons in the conduction band and p is that of valance band, then from the equilibrium condition,

n_i = p_i ———— (m2.28)

where subscript i stands for intrinsic. The electron and hole density at room temperature are 1.5 x 10¹⁰ cm^-3 in Si and 2.4 x 10¹³ cm^-3 in Ge respectively. Considering ^~10²² atoms/cm³ in these materials one can see only 1 in 10⁹ Ge and 1 in 10¹² Si atoms are ionized. Now let us ask a question ‘what is the transport process of the carriers so generated’? Contrary to the metallic conductor, where negatively charged electrons are the only charge carriers, both negatively charged electrons and positively charged holes contribute to the conductivity of the intrinsic semiconductor

Under the application of an electric field both the electrons and holes undergo a net migration. The motion will be the combination of a random thermal velocity and a net drift velocity parallel to the direction of the applied field. Electrons move preferentially in an opposite direction to the electric field vector while hole moves in the same direction. The drift velocities of electrons and holes can be represented by

where, E is the magnitude of the applied electric field, μ_e and μ_h are the mobilities of the electrons and holes respectively. Increase in electric field causes increase in drift velocity, which eventually attains saturation value and becomes independent of electric field. Many semiconductor detectors are operated at electric field values sufficiently high to result in saturated drift velocity for the charge carriers. Physically, saturation occurs because of the proportional fraction of the kinetic energy acquired by the electrons and holes are drained by collision with the lattice atoms. Because the saturated velocities are of the order of 10⁷ cm /sec, the time required collecting the carriers over typical dimensions of 0.1 cm or less will be around 10 ns. Semiconductor detectors are therefore be fastest-responding of all radiation detector types. The typical values of mobilities of electrons and holes in Si are 1350 cm² /Vs and 480 cm ²/Vs, respectively. The mobilities, of course determine the current in a semiconductor. Since the current density J = ρv, where ρ is the charge density and vthe velocity, J in a pure semiconductor is given by

Moreover, J = σE, where σ is the conductivity, given by the relation

This also gives the resistivity which is just inverse of σ. The following example shows the resistivity of intrinsic Si at room temperature.

Example m2.1

Find the resistivity of intrinsic Si at room temperature.

From intrinsic to extrinsic semiconductor:

Let us now go from intrinsic to extrinsic semiconductors, their fabrication and basic properties. In intrinsic semiconductor crystals, the number of holes equals the number of electrons in the conduction band. The number of either of these charge carriers can be preferentially increased by adding impurities in it. Suppose that we incorporate few arsenic atoms in a silicon crystal. Arsenic atoms have five electrons in their outermost shells, silicon atoms have four. These shells have the configurations 4s²4p³ and 3s²3p²respectively. When an arsenic atom replaces a silicon atom in silicon crystal, four of its electrons participate in covalent bonds with nearest neighbors. The fifth electron requires little energy ^~0.05 eV to be detached and move around inside the crystal. As shown in Fig. m2.17, arsenic as an impurity in silicon provides energy levels just below the conduction band. Such levels are known as donor levels, and the substance is called n-type semiconductor because electric current in it is carried by negative charges. The Fermi level also rises from the mid position of the energy gap due to the presence of the donor levels.

FIGURE m2.17 Doping of As in a silicon crystal provides donor levels in the normally forbidden band, producing an n-type semiconductor.

Now, if a trivalent atom gallium (Ga) is incorporated in a silicon crystal different characteristic occurs. The configuration of outer most electron shell of Ga is 4s²4p, and their presence leaves vacancies called holes in the electron structure of the crystal (Fig. m2.18). We see that Ga as an impurity in silicon provides energy levels called acceptor levels, just above the valance band and the Fermi energy lies below the middle of the energy gap. This is known as p-type semiconductor.

FIGURE m2.18 Doping of Ga in a silicon crystal provides acceptor levels in the normally forbidden band, producing a p-type semiconductor.

The amount of dopant used is generally very small with typical concentration being on the order of 10¹³ atoms/cm³ . Since the atomic concentration of Si and Ge is of the order of 10²² atoms/cm³ , this implies impurity is of only a few parts per billion. Regardless of the type of dopant, the concentration of electrons and holes obey a simple law of mass action at thermal equilibrium. If n is the concentration of electrons and p is the concentration of holes, then their product is

where n_i is the intrinsic concentration. Since the semiconductor is neutral, the negative and positive densities must be equal, so that

where N_D and N _A are donor and acceptor concentrations. In an n-type material, where N A =0 and n>>p, the electron density is therefore

i.e. the electron concentration is approximately the same as dopant concentration. Then the minority carrier concentration is

Therefore, the conductivity and resistivity of an n-type material becomes

An analogous result is found for p-type material.

From Extrinsic Semiconductor to Semiconductor Junction:

Now let us see how these extrinsic semiconductors are used to make a semiconductor junction and use them in real device like semiconductor detector. The function of semiconductor detectors depends on the formation of good semiconductor junction. For this purpose, one method for example is to diffuse sufficient p-type impurities into one end of a homogeneous bar of n type material so as to change that end into a p-type semiconductor. When a pn-junction is formed there is an initial diffusion of holes towards the n-region and similar diffusion of electrons into p-region due to difference in the concentration. The diffusing electrons fill up holes in the p-region while the diffusing holes capture electrons on the n-side, which eventually result in charge build-up to occur on either side of the junction. Since the p-region is injected with extra electrons it thus becomes negative while the n-region becomes positive. This creates an electric field gradient across the junction, which halts the diffusion process leaving a region of immobile space charge as shown schematically in Fig. m2.19 (a). The corresponding electronic energy level is shown in Fig. m2.19 (b).

FIGURE m2.19 (a) Schematic diagram of an np junction, (b) diagram of electronic energy levels showing creation of a contact potential V₀

The region of changing potential is known as depletion zone or space charge region devoid of all mobile charge carriers. Any electron-hole created or entering in this zone will be swept out by the electric field. The width of the depletion zone, which depends on the concentration of n and p impurities, is very much important for detection purpose. The width (d) of the depletion zone can be calculated from simple electrostatic equations and can be shown to be equal to¹

Where N_A and N_D are concentration of acceptor and donor impurities, e is the electronic charge and e is the dielectric constant of the medium. Because of its electrical configuration, the depletion layer also has certain capacitance,

where A is the area of the depletion zone and d is the width. For an unbiased junction the width of depletion region is very small and therefore stopping of high-energy particles is not possible. Due to small width of this zone the capacitance C is also quite high and hence increases the noise of the detector. Therefore, a reverse bias i.e. a negative voltage to the p-side and positive voltage to the n-side has to be applied in order to increase the depletion depth. This is illustrated in Fig. m2.20.

FIGURE m2.20 Semiconductor junction with and without reverse bias indicating broadening of depletion zone.

This voltage attracts the holes in the p-region away from the junction and similarly for the electrons in the n-region resulting an enlargement of the depletion zone. The Higher the external voltage, the wider the depletion zone. The higher external voltage will also provide efficient charge collection, which is otherwise very small for only intrinsic field. A simple calculation based on above equations shows that for n-type silicon a depletion layer greater than 1 mm can be obtained under a reverse bias of 300 V. This is a great improvement over a few tens of microns in an unbiased junction.

In order to collect charges produced by radiation, electrodes must be attached to the two sides of the junction. To make a direct ohmicmetallic contact to the semiconductor is practically difficult as a junction extending to the semiconductor is formed. To prevent this formation, a heavily doped (typically ^~10²⁰ atoms/cm³ ) layer of n⁺ or p⁺ materials is used between the semiconductor and the metal leads.

The average energy (w) needed to create electron-hole pair is much smaller as compared to gas ionization detector. Like gases, the average energy at a given temperature is found to be independent of the type and energy of the radiation and depends only on the type of material. Due to low values of average energy, the number of charge carriers will therefore be almost an order of magnitude greater in these materials than in gases, and hence semiconductor detectors provide much higher resolution (i.e. lower FWHM in energy peak) . The typical values of average energies for Si and Ge are shown in Table m2.1.

Table m2.1 Average energy for electron-hole creation in Si and Ge .

Average energy (eV)	For Si	For Ge
300 K	3.62	——–
77 K	3.81	.96

If the incident radiation of energy E is totally stopped in the depletion region, then E/w no. of electron-hole pair should be created. Considering the collection efficiency to be ε , a charge ε E/w will be collected on the electrodes. The observed voltage V on the electrode is then

where, C is the capacitance of the depletion region as shown earlier. It is clear from the above relation that the signal varies linearly with E. Moreover, since w is independent of particle type, the response is also independent of type of radiation. Now, if the depletion zone is smaller than the range of the radiation, it is clear then that a nonlinear response should be expected since the full energy is not totally deposited in the sensitive volume. In this case, instead of total energy, the energy loss DE is measured, which is a nonlinear function of E. Generally, semiconductor detectors are highly efficient (intrinsic efficiency ^~100 %) for charged particle as only very few particles will fail to create ionization in the sensitive volume. The sensitivity is of course limited by the noise generated from leakage current in the detector and from the associated electronic circuitry. A second source is thermally generated electron-hole pairs originating from recombination and trapping centers in the depletion layer.

Semiconductor Junction as Radiation Detector:

Now we will see how the semiconductor junction is used as radiation detector. Semiconductor detectors can be fabricated in different process and configurations such as diffused junction detectors, surface barrier detectors, ion-implanted diode detectors, fully depleted detectors, passivated planar detectors etc. Here we shall discuss only about solid state surface barrier detectors (SSBD), the most widely used for charged particle detection. The basic design of this type of detector is the formation of semiconductor-metal junction, usually n-type semiconductor with gold and p-type semiconductor with aluminium. The junction so formed is known as Schottky barriers, where the depletion zone extending entirely into the semiconductor side. The depletion depth in a surface barriers detector can be calculated using Eqn. m2.37 and for high resistivity silicon, depths of ^~5 mm can be achieved. Generally SSB detectors are made at room temperature by first etching the silicon surface and then depositing a thin layer (^~ 40 mg/cm² ) of gold by evaporation. In this process, it is also necessary to allow the surface to oxidize slightly before deposition. The junction is then mounted in an insulating ring with metallized surfaces for electrical contact.

Surface barrier detectors are generally of two types – fully depleted and partially depleted. For fully depleted detectors, a gain in the collection time of charges can be obtained resulting in a faster signal risetime. In case of partially depleted detectors, an increase in bias also extends the depletion zone and thus the distance over which charges must be collected. SSBD’s are very sensitive to surface contamination and care must be taken to keep the surface clean. If the detector is used in the vacuum chamber, attention must be paid to the possibility of presence of oil from the vacuum pump being deposited on the surface. There are suitable devices such as foreline trap, LN2 trap, oil mist eliminator etc. to get rid of these problems.

Nuclear Engineering

Nuclear Engineering

Curriculum

Solid State Detector

Modal title