EE495/695Introduction to

Semiconductors I

Y. BaghzouzECE Department

UNLV

Introduction• Solar cells have always been

aligned closely with other electronic devices.

• 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.

Semiconductor Structure • Semiconductors are made up of

individual atoms bonded together in a regular, periodic structure to form an arrangement whereby each atom is surrounded by 8 electrons.

• An individual atom consists of a nucleus made up of a core of protons (positively charged particles) and neutrons (particles having no charge) surrounded by electrons.

• The number of electrons and protons is equal, such that the atom is overall electrically neutral.

• The electrons occupy certain energy levels, based on the number of electrons in the atom, which is different for each element in the periodic table.

structure of a semiconductor

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 and is the most mature technology. →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.

Silicon (Si) Atom

• Most solar cells are made from silicon (14th element). Silicon is a "semi-conductor" 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.

• In a crystalline solid, a silicon atom shares each of its four valence electrons with each of four neighboring atoms.

Bond Structure of Si• 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 the region surrounding the atom. However, only at absolute zero temperature 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).

Band Gap• 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.

• 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.

Formation of "free" electrons and holes when an electron can escape its bond.

Band Diagram• Most important parameters of semiconductor

material for solar cell operation:– the band gap; – the number of free carriers (free electrons

and resulting holes) available for conduction;

– the "generation" and “recombination” of free carriers in response to light shining on the material.

• 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 that gives the energy of the electrons on the y-axis and is called a "band diagram".

• The lower energy level of a semiconductor is called the "valence band" and the energy level at which an electron can be considered free is called the "conduction band".

• The band gap is the distance between the conduction band and valence band.

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, ni.

• ni is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.

• ni 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 ni is lower in higher band gap materials.

– Alternatively, increasing the temperature makes it more likely that an electron will be excited into the conduction band, which will increase ni .

T0

T1> T0

T2> T1

Intrinsic Carrier Concentration

• At 300 K the generally accepted value for the intrinsic carrier concentration of silicon, ni = 1.01 x 1010 /cm3 [1].

• An empirical fit to the measured data over the range 275 K to 375 K is given by:

where T is in deg. K.• Question: find the intrinsic carrier concentration of Si at 25

°C and at 95 °F.

[1] Sproul A.B., Green M.A., "Improved Value for the Silicon Intrinsic Carrier Concentration from 275 to 300K", J. Appl. Physics., 70, 846-854 1991.

[K] = ([°F] + 459.67) × 5⁄9

[K] = [°C] + 273.15

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.

Doping• The type of carrier with the higher concentration is called a "majority

carrier", while the lower concentration carrier is called a "minority carrier."

• In a typical doped semiconductor, there might be 1017/cm3 majority carriers and 106/cm3 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

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.

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 ni is the intrinsic carrier concentration and n0 and p0 are the electron and hole equilibrium carrier concentrations.

Intrinsic material

Material doped moderately with group V

Material heavily doped with group V

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:

Absorption of Light– Eph < EG : Photons with energy Eph less than the band gap

energy EG interact only weakly with the semiconductor, passing through it as if it were transparent.

– Eph = EG : Photons have just enough energy to create an electron hole pair and are efficiently absorbed.

– Eph > EG : 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.

Absorption Depth• Different wavelengths penetrate

different distances into a semiconductor before most of the light is absorbed.

• 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

Absorption depth of common semiconductor materials (@ 300o K)

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 I0 is the light intensity at the top surface.

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:

where I0 = 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.

xeIG αα −= 0

Generation Rate• The generation as a function of cell depth 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.

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.

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.

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.