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PRELAB Read the theory section below. Calculate the photon wavelength in nm corresponding to a photon energy equal to the theoretical band gap energy of S1.121 eV and GaAs, 1.422 eV. These will be used to set the monochromator.

Theory section is below for the equations

THEORY One of the most important characteristics of a semiconductor is its band gap energy Eg Whereas an electron in an isolated atom has discrete energy levels, an electron in a semiconductor crystal has energy bands separated by ranges of forbidden energies called energy gaps. The outermost band in a semiconductor is the conduction band. Each electron energy level (state) in the conduction band typically has a very low probability of occupancy. The second outermost band is the valence band. Each electron energy level in the valence band typically has a very higlh probability of occupancy. An electron in an isolated atom can be sent to a higher energy level by photon absorption if the photon energy is equal to the difference in energy between the higher energy level and the energy level where the electron came from, Similarly, in order to excite an electron from the valence band to the conduction band, the photon energy must be at least the energy of the band g ap Ep 2 Eg This is the condition for photon absorption. If the photon energy is greater, it can be absorbed by an electron deeper in the valence band or it can send the electron higher into the conduction band This is illustrated in Fig. 1. If the photon energy is less, it cannot be absorbed. Since a photon that is not absorbed is transmitted, the condition for photon transmission through the wafer is therefore A plot of photon intensity transmitted through a semiconductor wafer as a function of photon energy will be high at low photon energies and abruptly drop to zero at energies above the band gap energy. This is a classic method for determining the band gap energy of a semiconductor The photon energy Ep can be determined from its wavelength 2,

where h is Plancks constant and c is the speed of light in vacuum. We will measure the light intensity in watts as a function of wavelength. The light source is a 55 W quartz haloger ISOLATED ATOMS SOLIDS DISCRETE ENERGY LEVELS CONDUCTION BAND PHOTON ENCE BAND PHOTON E2-E1 PHOTON WILL BE ABSORBED IF E FEpEg PHOTON WILL BE ABSORBED Fig. 1 - photon absorption automotive bulb, which emits a continuous blackbody spectrum. The transmission coefficient for the wafer at a particular wavelength is defined by The power at a particular wavelength with or without the wafer intercepting the light beam is measured at the exit slit of the monochromator using the optical power meter with a Ge detector The Ge detector is sensitive at long enough wavelengths to measure the wavelengths transmitted through Si or GaAs wafers. Direct and indirect band gap A more complete picture of the energy levels of a semiconductor crystal can be viewed by plotting the energy levels as a function of electron momentum - see the text or e.g. energy bands tend to curve parabolically upward (because the kinetic energy K and the valence energy bands tend to curve parabolically downward. In such a diagram, the energy gap is the minimum energy between the valence band and the conduction bands. If the minimum in the conduction band energy is at the same momentum as the maximum in the valence band energy, the semiconductor is said to have a direct band gap. Such materials can be used to make LEDs or LASER diodes. The reason is that a single photon is emitted when an electron goes from the conduction to the valence band. If the minimum in the conduction band energy does not coincide

with the maximum in the valence band energy, the semiconductor is said to have an indirect band gap. Such materials cannot be used to make LEDs and include the most common semiconductors Si and Ge. In an indirect material, an electron transition from the minimum of the conduction band to the top of the valence band must necessarily involve a change in momentum. The intensity of light I through a semiconductor of thickness z depends on the absorption coefficient a, defined by I = 10e-z z where lo is the light intensity incident on the wafer. The intensity ratio is related to the transmission coefficient,-= T, and therefore α~(-1 置) An analysis of the density of states near the edges of the band gaps shows (see wiki link above) that for a direct band gap material Io and for an indirect band gap Consequently, we can conclude that for a direct band gap material, a plot of (v sE, for Ep near Eg will yield a straight line with horizontal intercept Eg. Similarly, for an indirect band gap material, a plot of (-1 f)1/2v sEp for Ep near Eg will yield a straight line with intercept Eg. These results can be used to quantitatively determine the band gap energy of a semiconductor

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h c 3u Es 11 07. 27 m -7 1 9

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