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  Theory of Material types and Electric conduction

Intrinsic Un-doped Silicon:

At room temperature (that is, 27oC, 300oK), in intrinsic silicon a hole-electron pair is produced for each bond broken by the thermal agitation and number of free electrons, no, is equivalent to the number of free holes, po, in an un-doped material. Both holes and electrons take part in an electrical conduction procedure and therefore the term ‘bipolar semiconductor’. For intrinsic silicon, as the conducting charge carriers are produced in pairs, they have equivalent concentrations at any temperature and hence:

no = po = ni
nopo = ni2

This is termed as the Law of Mass Action.

At room temperature, (300oK), ni ≈ 1.5 x 1010/cm3

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Figure: Electron and Hole Generation in Intrinsic Silicon

n-Type Material:

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Figure: n-type Silicon Semiconductor

In this situation, the silicon is doped with impurity atoms containing five electrons in their outer shell. Four of such take part in covalent bonding of silicon crystal structure. The extra free electron originally occupies the donor energy level, Ed, just beneath the conduction band of silicon. At room temperature, almost all the electrons of the impurity atoms gain adequate energy to leave the donor level and enter the conduction band. Therefore the donor levels are almost all empty and do not take part in the conduction procedure. The number of electrons in conduction band in n-type material due to doping far exceeds such generated by thermal agitation of silicon. As a result, in n-type material, current conduction is mainly due to electrons in the conduction band. This is therefore to such an extent that the electron concentration in conduction band can be taken as equivalent to the doping concentration of n-type impurities present, that is, no ≈ Nd. Furthermore, the raised concentration of electrons in the conduction band as well raises the rate of carrier recombination in the doped material. Therefore, the concentration of holes in valence band of n-type material is much lower than in the case for un-doped material. Though, the Law of Mass Action still holds and hence, n0p0 = ni2.

p-Type Material:

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Figure: p-type Silicon Semiconductor

In this situation, the silicon is doped with impurity atoms containing only three electrons in their outer shell. Such all take part in covalent bonding of the silicon crystal, however for each impurity atom there is a vacant energy level, Ea, termed an acceptor level, just above the valence band of silicon. At room temperature, adequate electrons are excited from valence band to fill the acceptor levels. Therefore, the acceptor levels take no part in conduction process. The electrons excited into acceptor levels, though, leave behind an abundant supply of holes in the valence band and hence the number of holes exist far exceeds such generated by thermal agitation. As a result, in p-type material, current conduction is mainly due to the holes in valence band. The hole concentration in the valence band can, be taken as equivalent to the doping concentration of p-type impurities present in silicon, that is, po ≈ Na. Furthermore, the raised concentration of holes in valence band as well raises the rate of carrier recombination in doped material. Therefore, the concentration of electrons in conduction band of p-type material is much lower than the case for un-doped material. Again, n0p0 = ni2.

n-type material                                    p-type material

nopo = ni2                                                    nopo = ni2 

no ≈ Nd >> ni            majority carriers         po ≈ Na >> ni  

po ≈ ni2/Nd << ni     minority carriers          no ≈ ni2/Na << ni

The Effect of an Electric Field:

In the absence of some external influence other than temperature above 0oK, carriers experience thermal agitation only and move arbitrarily in the crystalline structure. There is no total flow of charge in any direction in the semiconductor, and therefore, no current flows via the material. The energy of carriers in a specific band is as well constant all through the material.

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Figure: Effect of an Electric Field on Energy Bands

Whenever an electric field is applied across the semiconductor, by using a battery or power supply for instance, an electrostatic force is exerted on the charge carriers in material. The carriers, as an outcome of the force they experience in the field, gain the electrostatic energy. This gives increase to a gradient in energy bands occupied by the carriers in the direction of electric field as shown in figure above.

As electrons will seek to occupy the lowest energy status accessible, they will move from positions of higher electrostatic energy to positions of lower energy. This gives mount to a total movement of carriers via the material and therefore sets up a flow of current. Electrons, since of their negative charge, will move in a direction opposite to electric field whereas holes will move in the direction of field. The current flow is, by convention, in the direction of electric field and is termed to as a drift current.

Carrier Mobility:

The total drift of carriers beneath the influence of an electric field depends on the relative ease with which they can move in the crystalline structure of the semiconductor. Carrier mobility is stated as the velocity with which a carrier will drift, on average, in the unit field strength of 1 Vm-1 and is as follows:

μn = (q τn)/m*e for electrons

μp = (q τp)/ m*p for holes
 
Where:

m*e and m*p are the effective masses of electrons and holes correspondingly.

τn and τp are the mean free times of carriers spent among collisions.

q is the magnitude of charge on the carrier.

Usually, the mobility of electrons in conduction band is somewhat bigger than that of holes in the valence band, that is, μn > μp and has units of m2V-1s-1.

Drift Current:

Whenever charge carriers drift in a uniform way across a piece of homogeneous semiconductor material, there is a constant and uniform flux of charge via the material. The charge flow per unit area is termed to as Charge Flux Density as shown in figure below.

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Figure: Charge Flux Density in an Electric Field

Where,

n and p are the respective charge carrier concentrations
q is the magnitude of charge on carriers
μn, μp are respective carrier mobilities
E is the electric field strength

Holes and Electrons will drift in opposite directions in a specific electric field. Though, as the charge on electron is negative, both holes and electrons will make positive contributions to conventional current specified in the direction of field. Whenever both flux components are integrated over the area A, of the semiconductor, then total drift current is obtained as:

Idrift = Jn drift + A = A Eq (n μn + p μp)

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