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PHS2011: CMP assignment solutions / feedback

This document is intended for feedback on your assignments. It is not a marking guide. However,

a satisfactorily complete answer would have included most of the underlined points.

Solar cell Composition: consists of a p-n junction with geometry such that light can penetrate into or

near the depletion region and with band gap such that light can excite electrons from thevalence band to the conduction band.

Function: to create a potential difference capable of charging a battery (generic energystorage device) upon being exposed to sunlight photovoltaic conversion.

Relevant band diagram(s) (reasonably labelled) Correct I-V curve (reasonably labelled).

A reasonably consistent description of the physics in terms of the band diagrams which explainsthe form of the I-V curve would be along the lines of the following:

Photons striking the material are able to excite electrons from the valence band to theconduction band. In a normal semiconductor, the electron-hole pair has a finite lifetime,an electron dropping back to fill the hole in short order. However, if this occurs within(or in close proximity to) the depletion region, the field will sweep the electron towardsthe n-type region (as it would for minority electrons reaching it from the p-type region)and the hole towards the p-type region. In these regions, these charges are majoritycarriers, and their de-excitation is no longer likely. This flow of charge produced in thisfashion is referred to as a photo-current.

The photocurrent through the resistive load produces a potential difference which forwardbiases the p-n junction. The behaviour of the p-n junction is thus the sum of the forward-bias current and the photocurrent (which are oppositely directed). This gives two limitingcases.

In the short-circuit condition, Rload = 0. Consequently, the current is the fullphotocurrent.

In the open-circuit condition, the resistance of the load is infinite, and no currentflows. This occurs at the photo-voltage Vopen-circuit, when the forward-biased currentexactly equals the photocurrent.

[Note: the photovoltaic effect is different to the photo-electric effect in which a photonleads to an electron being ejected from the material entirely.]

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Tunnel diode

Composition: a p-n junction in which the doping is very high (degenerately doped). Function: The I-V characteristic contains a negative resistance portion which makes these

diodes suitable for use in oscillators and amplifiers.

Relevant band diagrams (reasonably labelled) Correct I-V curve (reasonably labelled).

A reasonably consistent description of the physics in terms of the band diagrams which explains

the form of the I-V curve would be along the lines of the following: The impurity level in the n-type and p-type regions is very high (degenerate). The Fermi

level is thus within the conduction band in the n-type region, and within the valence band inthe p-type region: the top of the valence band in the p-type material is higher than the bottomof the conduction band in the n-type material.

The potential barrier is large, but the width of the depletion region reduces with increaseddoping (~100 in tunnel diodes): tunnelling across the barrier is possible. (Equilibrium in theabsence of fields is dominated by the equilibrium between tunnelling currents.)

For small positive bias, occupied energy levels in the conduction band of the n-type regionare adjacent to unoccupied energy levels in the valence band of the p-type region: there is anet tunnelling current from n-type to p-type regions.

The tunnelling current increases with increasing positive bias, until the energy of the topmostfilled level in the n-type region is level with the bottom of the band gap in the p-type region.As tunnelling only occurs when there are allowed levels of equivalent energy, the tunnellingcurrent drops off for further increase of the forward bias. Thus the I-V curve has a portion ofnegative gradient, where increase in bias V results in a decrease in current I.

The diffusion current has been steadily increasing with increasing forward bias, and for largeenough bias the diffusion current from n-type to p-type is the dominant current transfermechanism. From this point the p-n junction behaves as a normal diode.

Under reverse bias, a tunnelling current is always possible from the p-type region to the n-type region: the current increases monotonically and rapidly with reverse bias potential.

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Zener diode

Composition: a highly doped p-n junction Function: under reverse bias there is a sharp knee at which breakdown occurs. As the

breakdown voltage value can be tuned via the doping, it is of use in applications where a

sudden increase in current is required at a certain voltage. Examples include switches, voltagestabilizers, providing a voltage reference and protecting other diodes from voltage surges. Relevant band diagrams (reasonably labelled). Correct I-V curve (reasonably labelled).

A reasonably consistent description of the physics in terms of the band diagrams which explainsthe form of the I-V curve would be along the lines of the following:

Behaves as a standard diode under forward bias. At low reverse bias, there is a flow of minority electrons from the p-type region to the n-

type region, again as per a standard diode. However, for a large enough reverse bias, the energy of the top of the valence band in the

p-type region exceeds the energy of the bottom of the conduction band in the n-typeregion. The conditions are set-up where tunnelling might allow electrons from thevalence band in the p-type region to flow into the conduction band in the n-type region.

The doping is such that when the bands just overlap, the depletion region is a little toowide to readily allow tunnelling. Only when the reverse bias is further increased does thedepletion region narrow enough to allow tunnelling. Tunnelling therefore becomesallowed at a point where there is considerable overlap between electron-occupied levelsin the valence band of the p-type region and empty levels in the conduction band of the n-type region. The current becomes large rapidly beyond this point.

[Note: in terms of the mechanism, Zener breakdown is distinct from avalanche breakdown,where electron-hole pair formation (due to collisions of transiting electrons) in thedepletion region leads to an avalanche increase in current.]

Thermal e uilibrium

Reverse bias