Moss-Burstein effect 莫斯-布尔斯坦效应

MOSS-BURSTEIN EFFECT (Expt. B1O) The Moss-Burstein effect results from the Pauli Exclusion Principle and is seen in

semiconductors as a shift with increasing doping of the band-gap as defined as the

separation in energy between the top of the valence band and the unoccupied energy

states in the conduction band. The shift arises because the Fermi energy (EF) lies in the

conduction band for heavy n-type doping (or in the valence band for p-type doping). The

filled states therefore block thermal or optical excitation. Consequently the measured

band gap determined from the onset of interband absorption moves to higher energy (i.e.

suffers "a blue shift").

Provided that the effective masses of the valence and conduction bands are known

reasonably accurately and it is assumed that the curvature and position of the bands are

independent of the doping, the shift in energy can be used as an accurate and contactless

method of determining the carrier concentration in the sample.

Where:

And Eg is the band gap found with undoped samples.

Note that the equations overleaf assume that the optical transition of an electron from

the valence band to the conduction band is "vertical"; i.e. that the photon wavevector (k

= 2π/λ) is small compared with that of the electrons at the Fermi energy (kF = (3π2)1/3).

Conduction Band

Heavy holes

Light holes

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vcFgvcFgmmEEmmkEhf111

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ccFFCheck that you agree with this assumption taking λ (in air) as 3 microns, the refractive

index of InAs as 3.5 and n = 1024 m-3. By performing the following experiment, and assuming that the conduction and valence

band effective masses are mc = 0.03m0 and mv = 0.4m0 respectively, calculate the carrier

concentration (n) for the doped samples provided (the effective mass at the conduction

band edge is 0.024m0. At the Fermi energy concerned the appropriate effective mass has increased by 50%).

EXPERIMENT

You are provided with a Spex monochromator, a globar source with a germanium

lens, a light chopper, lead selenide and lead sulphide photodetectors and a "Phase

Sensitive Detector" which enhances and amplifies the signal and suppresses noise.

A PC is also available for equipment control and data processing. See Figure 1 for a

schematic of the experimental set-up. Check the zero setting of the monochromator. If the grating were perfectly positioned

it would act as a mirror for all wavelengths at a dial setting of 0000. You will almost

certainly find that the maximum reflection occurs at a slightly different dial reading. Add or subtract this small "zero error" when you calculate the true wavelength. Use

the "mirror" setting to align your source and detector. Provided that you are using

the germanium lens you will not get any diffracted radiation through the

spectrometer until a dial reading of about 3000 is reached and you should obtain a

maximum signal on your detector at a dial reading of about 4000. Remember that the

grating equation is m λ = a sin θ so that you may get second order (m = 2) radiation

through the monochromator at dial settings greater that 6000 (assuming that the Ge

lens cuts in at 3000). Assume that the grating scale is linear in wavelength and that the

wavelength in microns is 6x10

-4 of the dial reading; i.e. that a dial reading of 4000

corresponds to a wavelength of 2.4μm.

Take several 'background' recordings with no sample in place in order to PSD PC

Monochromator Light source and lens

Light chopper

Sample Detector

Figure 1 - Diagram to show the experimental set-up familiarise yourself with the equipment and in order that background features due

to atmospheric absorption may be at least partially removed by ratioing the

transmission with the sample in place with the “background” values.

The 'background' spectrum is limited by the band gap absorption of the Ge lens at

short wavelengths and by the cut-off for intrinsic excitation of the photodetectors

at long wavelengths. Estimate the band gaps of Ge, PbS and PbSe from the

respective background spectra.

Observe the effect of changing the slit-widths on the monochromator on the

atmospheric features at wavelengths at 4.2μm and 2.7μm.

You are given four epitaxial films of InAs of thickness of a few microns grown on

GaAs substrates. One sample is undoped and the others have been fairly heavily doped

with silicon donors. Taking great care, place each metal sample mount in turn over the detector iris in order to take a transmission spectrum. On no account touch the surface of the semiconductor samples as they are very fragile.

The GaAs substrates do not absorb significantly in the wavelength range concerned.

However both the InAs epitaxial film and the GaAs substrate have high refractive

indices and reflect quite strongly. You should be able to observe Fabry-Perot interference fringes from the epitaxial film at wavelengths which are too long for the