1 3.1 Introduction to Semiconductors Y. Baghzouz ECE Department UNLV
2 Introduction In this lecture, we will cover the basic aspects of semiconductor materials, and the physical mechanisms which are at the centre of photovoltaic devices. These physical mechanisms are used to explain the operation of a p-n junction, which forms the basis of the greatest majority of solar cells An ingot of silicon, consisting of a single large crystal of silicon.
3 Semiconductors The atoms in a semiconductor are materials from either group IV of the periodic table, or from a combination of group III & V (III-V semiconductors), or II & VI (II-VI semiconductors). Silicon (Si) is the most commonly used semiconductor material as it forms the basis for integrated circuit (IC) chips. Most solar cells are also silicon-based. Other common semiconductors include Ge, GaAs, and CdTe. Section from the periodic table - Most common semiconductor materials shown in blue.
4 Silicon Atom Si - Silicon (14 th element) is a "semiconductor" or a "semi-metal," and has properties of both a metal and an insulator. Silicon has 14 electrons. The outermost four electrons, called valence electrons, play a very important role in the photoelectric effect. These electrons have certain energy levels, based on the number of electrons in the atom, which is different for each element in the periodic table. In a crystalline solid, a silicon atom shares each of its four valence electrons with each of four neighboring atoms. In a regular structure, each atom is surrounded by 8 electrons.
5 Bond Structure The bond structure of a semiconductor determines the material properties of a semiconductor. The electrons surrounding each atom in a semiconductor are part of a covalent bond, (i.e., two atoms "sharing" a single electron). The electrons in the covalent bond are held in place by this bond and hence they are localized to region surrounding the atom. However, only at absolute zero are all electrons in a bonded arrangement (insulator). At elevated temperatures, these electrons can gain enough energy to escape from their bond (conductor). At room temperature, a semiconductor has enough free electrons to allow it to conduct limited current (semiconductor).
6 Band gap The most important parameters of a semiconductor material for solar cell operation are: the band gap; the number of free carriers available for conduction; the "generation" and recombination of free carriers in response to light shining on the material. The presence of the bond introduces two distinct energy states for the electrons. The lowest energy position - bound state. If the electron has enough thermal energy to break free of its bond, then it is in a - free state. The electron cannot attain energy values intermediate to these two levels; it is either at a low energy position, or it has gained enough energy to break free and therefore has a certain minimum energy. This minimum energy is called the "band gap" of a semiconductor. Formation of "free" electron and hole when an electron can escape its bond.
7 Band Gap The space left behind by the electrons allows a covalent bond to move from one electron to another, thus appearing to be a positive charge moving through the crystal lattice. This empty space is commonly called a "hole", and is similar to an electron, but with a positive charge. The free electrons and resulting holes are called carriers. The band gap of a semiconductor is the minimum energy required to move an electron from its bound state to a free state where it can participate in conduction. The band structure of a semiconductor gives the energy of the electrons on the vertical axis and is called a "band diagram". The lower energy level of a semiconductor is called the "valence band" (EV) and the energy level at which an electron can be considered free is called the "conduction band" (EC). The band gap (EG) is the distance between the conduction band and valence band.
8 Intrinsic Carrier Concentration The thermal excitation of electrons from the valence band to the conduction band creates free carriers in both bands. The concentration of these carriers in intrinsic materials (semiconductor with no added impurities) is called the intrinsic carrier concentration, n i. n i is the number of electrons in the conduction band or the number of holes in the valence band in the intrinsic material. n i depends on the band gap and on the temperature of the material. A large band gap will make it more difficult for a carrier to be thermally excited, hence n i is low for materials with a high band gap. Alternatively, increasing the temperature makes it more likely that an electron will be excited into the conduction band, which will increase n i. T0 T1 > T0 T2 > T1
9 Intrinsic Carrier Concentration in Si At 300 K, the generally accepted value for the intrinsic carrier concentration of silicon is n i = 1.01 x /cm 3 . An empirical fit to the measured data over the range 275 K to 375 K is given by: where T is in deg. K. While the intrinsic carrier concentration is normally quoted at 300 K, solar cells are usually measured at 25 C where the intrinsic carrier concentration is 8.6 x 10 9 /cm 3. Temp. conversion: [K] = ([ F] ) 5 9 [K] = [ C]  Sproul A.B., Green M.A., "Improved Value for the Silicon Intrinsic Carrier Concentration from 275 to 300K", J. Appl. Physics., 70,
10 Doping It is possible to shift the balance of electrons and holes in a silicon crystal lattice by "doping" it with impurities. Atoms with one more valence electron than silicon (e.g., phosphorous) are used to produce "n-type" material, which adds electrons to the conduction band. Atoms with one less valence electron (e.g. boron) result in "p-type" material where the number of electrons trapped in bonds is higher, thus increasing the number of holes. In doped materials, there is always more of one type of carrier than the other. The type of carrier with the higher concentration is called a "majority carrier", while the lower concentration carrier is called a "minority carrier."
11 Doping In a typical semiconductor, there might be /cm 3 majority carriers and 10 6 /cm 3 minority carriers. The ratio of minority to majority carriers is less than one person to the entire population of the planet. Minority carriers are created either thermally or by incident photons. N P
12 Equilibrium Carrier Concentration The number of carriers in the conduction and valence band with no externally applied energy source is called the equilibrium carrier concentration. For majority carriers, the equilibrium carrier concentration is equal to the intrinsic carrier concentration plus the number of free carriers added by doping the semiconductor. Under most conditions, the doping of the semiconductor is several orders of magnitude greater than the intrinsic carrier concentration, such that the number of majority carriers is approximately equal to that due to doping.
13 Equilibrium Carrier Concentration At equilibrium, the product of the majority and minority carrier concentration is constant, and this is mathematically expressed by the Law of Mass Action: where n i is the intrinsic carrier concentration and n 0 and p 0 are the electron and hole equilibrium carrier concentrations. Intrinsic material Material doped moderately with group V Material heavily doped with group V
14 Absorption of Light Photons incident on the surface of a semiconductor will be either reflected from the top surface, absorbed in the material, or transmitted through the material. For photovoltaic devices, reflection and transmission are typically considered loss mechanisms as photons which are not absorbed do not generate power. If the photon is absorbed, it will raise an electron from the valence band to the conduction band. A key factor in determining if a photon is absorbed is the energy of the photon. Photons falling onto a semiconductor material can be divided into three groups based on their energy compared to that of the semiconductor band gap:
15 Absorption of Light E ph < E G : Photons with energy E ph less than the band gap energy E G interact only weakly with the semiconductor, passing through it as if it were transparent. E ph = E G : Photons have just enough energy to create an electron hole pair and are efficiently absorbed. E ph > E G : Photons with energy greater than the band gap are strongly absorbed. The number of light-generated majority carriers are often orders of magnitude less than the number of majority carriers already present in the solar cell due to doping. Hence, the number of majority carriers in an illuminated semiconductor does not alter significantly. The number of photo-generated minority carriers outweighs the number of minority carriers existing in the solar cell in the dark. Therefore, the number of minority carriers in an illuminated solar cell can be approximated by the number of light generated carriers.
16 Absorption Coefficient The absorption coefficient determines how far into a material light of a particular wavelength can penetrate before it is absorbed. The absorption coefficient depends on the material and also on the wavelength of light which is being absorbed (see next slide). Notes: The absorption coefficient is not constant and depends strongly on wavelength Light which has energy below the band gap does not have sufficient energy to dislodge an electron. Consequently this light is not absorbed.
17 Absorption coefficient of common semiconductor materials 300 o K)
18 Absorption Coefficient Notes: (cont,) For photons which have an energy very close to that of the band gap, the absorption is relatively low since only those electrons directly at the valence band edge can interact with the photon to cause absorption. As the photon energy increases, there are a larger number of electrons which can interact with the photon and result in the photon being absorbed. For photovoltaic applications, the photon energy greater than the band gap is wasted (as heat) since electrons quickly move back down to the band edges.
19 Absorption Depth The dependence of absorption coefficient on wavelength causes different wavelengths to penetrate different distances into a semiconductor before most of the light is absorbed. The absorption depth is defined as the inverse of the absorption coefficient. The absorption depth is a useful parameter which gives the distance into the material at which the light drops to about 36% (or 1/e) of its original intensity. High energy light (blue) is absorbed within a few microns, while low energy (red) is absorbed after a few hundred microns. The blue photons are absorbed very close to the surface but most of the red photons are absorbed deep in the device
20 Absorption depth of common semiconductor materials 300 o K)
21 Generation Rate The generation rate gives the number of electrons generated at each point in the device due to the absorption of photons. Neglecting reflection, the amount of light which is absorbed by a material depends on the absorption coefficient (in cm -1 ) and the thickness of the material. The intensity of light at any point in the device can be calculated according to the equation below: where α is the absorption coefficient (in cm -1 ), x is the distance (in cm) into the material at which the light intensity is being calculated; and I 0 is the light intensity at the top surface.
22 Generation Rate Assuming that the loss in light intensity (i.e., the absorption of photons) directly causes the generation of an electron-hole pair, then the generation G in a thin slice of material is determined by finding the change in light intensity across this slice. Consequently, differentiating the previous equation will give the generation rate at any point in the device: G x = αi e α 0 where I 0 = photon flux at the surface (photons/unit-area/sec.); α = absorption coefficient; and x = distance into the material. For photovoltaic applications, the incident light consists of a combination of many different wavelengths, and therefore the generation rate at each wavelength is different. The net generation is the sum of the generation for each wavelength.
23 Generation Rate The generation as a function of distance for a standard solar spectrum (AM 1.5) incident on a piece of silicon is shown below. Note: there is an enormously greater generation of electron-hole pairs near the front surface of the cell, while further into the solar cell the generation rate becomes nearly constant.
24 Recombination Any electron which exists in the conduction band is in a meta-stable state and will eventually fall back to a lower energy position in the valance band. When the electron falls back down into the valence band, it removes a hole. This process is called recombination. There are three basic types of recombination in the bulk of a single-crystal semiconductor. Radiative recombination; Shockley-Read-Hall (SRH) recombination Auger recombination.
25 Radiative Recombination Radiative recombination is the recombination mechanism that dominates in direct bandgap semiconductors, (e.g., LEDs). However, most terrestrial solar cells are made from silicon, which is an indirect bandgap semiconductor and radiative recombination is extremely low and usually neglected. The key characteristics of radiative recombination are: An electron directly combines with a hole in the conduction band and releases a photon; The emitted photon has an energy similar to the band gap, hence only weakly absorbed such that it can exit the piece of semiconductor.
26 SRH Recombination Recombination through defects, also called Shockley-Read-Hall, occurs only in defective materials. It is a two-step process. An electron moves into an energy state in the forbidden region (which is introduced through defects or deliberately added, i.e., doping) and releases energy. The electron and hole then recombine, further releasing energy in the form of heat or photons. The rate at which a carrier moves into the energy level in the forbidden gap depends on the distance of the introduced energy level from either of the band edges. Recombination is less likely if an energy is introduced close to either band edge, Energy levels near mid-gap are very effective for recombination.
27 Auger Recombination An Auger Recombination involves three carriers. An electron and a hole recombine, but rather than emitting the energy as heat or as a photon, the energy is given to an electron in the conduction band. This electron then thermalizes back down to the conduction band edge. Auger recombination is most important in heavily doped materials.
28 Carrier Lifetime The minority carrier lifetime is a measure of how long a carrier is likely to stay around for before recombining. Stating that "a silicon wafer has a long lifetime" means that minority carriers generated in the bulk of the wafer by light or other means will persist for a long lifetime before recombining. The "minority carrier lifetime" of a material is the average time which a carrier can spend in an excited state after electron-hole generation before it recombines. The lifetime τ is related to the recombination rate R by: where Δn is the minority carriers concentration.
29 Diffusion Length Minority carrier diffusion length is the average distance a carrier can move from the point of generation until it recombines. The minority carrier lifetime and the diffusion length depend strongly on the type and magnitude of the recombination processes in the semiconductor. For many types of silicon solar cells, SRH recombination is the dominant recombination mechanism. This recombination rate will depend on the number of defects present in the material, so that as doping the semiconductor increases the rate of SRH recombination will also increase. In addition, since Auger recombination is more likely in heavily doped materials, the recombination process is itself enhanced as the doping increases. The method used to fabricate the semiconductor wafer and the processing also have a major impact on the diffusion length.
30 Diffusion Length The diffusion length L is related to the carrier lifetime τ as follows: where D is the diffusivity of the material in m²/s. In silicon, the lifetime τ can be as high as 1 msec., and the diffusion length L is typically µm.
31 Surface Recombination Any defects or impurities at the surface of the semiconductor promote recombination. Since the surface of the solar cell represents a severe disruption of the crystal lattice, the surfaces of the solar cell are a site of particularly high recombination. The high recombination rate in the vicinity of a surface depletes this region of minority carriers. A localized region of low carrier concentration causes carriers to flow into this region from the surroundings with higher concentration regions. Therefore, the surface recombination rate is limited by the rate at which minority carriers move towards the surface. The dangling bonds at the surface of semiconductor cause a high local recombination rate.
32 Surface Recombination The defects at a semiconductor surface are caused by the interruption to the periodicity of the crystal lattice, which causes dangling bonds at the semiconductor surface. The reduction of the number of dangling bonds, and hence the recombination, is achieved by growing a layer on top of the semiconductor surface which ties up some of these dangling bonds. This reduction of dangling bonds in known as surface passivation.
33 Movement of Carriers in Semiconductors Electrons in the conduction band and holes in the valence band are considered "free" carriers in the sense that they can move throughout the semiconductor crystal. The carrier moves in a random direction before colliding with a lattice atom. Once the collision takes place, the carrier moves away in a different random direction. There is no net motion of carriers unless there is a concentration gradient or an electric field. The diagram to the right has 1,000 scattering events. The net movement of the carrier is typically very small.
34 Diffusion The constant random motion of carriers can lead to a net movement of carriers if one particular region has a higher concentration of carriers than another region. When this happens, a carrier gradient exists between the highconcentration region and the low-concentration region. Carriers flow from the high-concentration region to the lowconcentration region. This carrier flow is called "diffusion. The rate at which diffusion occurs depends on the speed at which carriers move and on the distance between scattering events. Since raising the temperature will increase the thermal velocity of the carriers, diffusion occurs faster at higher temperatures. One major effect of diffusion is that it evens out carrier concentrations in a device, such as those induced by generation and recombination, without an external force being applied to the device. Diffusion equations are complex!
35 Mobility and Drift Transport In the absence of an electric field, carriers move a certain distance at a constant velocity in a random direction. However, in the presence of an electric field, there is an acceleration in the direction of the electric field if the carrier is a hole or opposite to the electric field if the carrier is an electron. The acceleration in a given direction causes a net motion of carriers. The direction of the carrier is obtained as a vector addition between its direction and the electric field. The net carrier movement in the presence of an electric field is characterized by the mobility. Transport due to the movement of carriers in an electric field is called "drift transport". Drift transport equations are complex!
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