Hooge Essay

726 Words 3 Pages
Hooge’s relationship is an empirical relationship based on a large collection of data obtained for flicker noise in semiconductors and metal films. According to this model, the PSD of flicker noise is given by,
S(f) = γHV
2
Ncf α
Where Nc = ncΩ is the number of free charge carriers in the specimen,nc is the charge carrier density and Ω is the volume of specimen.γH is the Hooges constant, a parameter which characterizes the noise levels of a particular system. The initial value of gamma is assumed as 2 ∗ 10−3
. Experimental evidence supporting this model is the noise signals in semiconductors, which are orders in magnitude larger than that of metals. But as evident from the experimental data, for various systems value of gamma deviates significantly
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For example, the noise in metallic films is a strongly dependent on temperature and the type of substrate, even when the number of charge carriers does not vary much. This observation cannot be explained by using Hooge’s relationship.
1.2.2 The McWhorter Model
According to this model, fluctuations in the surface density of electrons, which results into fluctuation in conductivity, arise from exchange of electrons between the surface layer and traps lying in the oxide layer covering the surface. The transfer of electrons took place via tunneling. Since the tunneling probability decreases exponentially with separation between surface and trap, so does the characteristic inverse relaxation time. This time is given by τ
−1 =
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resistance in disordered metals, variation in density of states in semiconductors and MOS structures. The noise resulting from these transitions has 1/f spectra.8
Figure 1.4: Two well potential of a two level tunneling system
The SNR associated with flicker noise is given by,
SNR = q ncΩ γHln( fmax fmin )
Where fmax and fmin are the limits of measurement frequencies. The SNR is independent of applied voltage or current. If 1/f noise dominates in an experiment, the accuracy cannot be improved by increment in circuit parameters viz. applied voltage or current. Also, the magnitude of flicker noise increases with decrease in volume of sample and hence it is a problem in miniaturization of electronic devices. Typically, the PSD of flicker noise increases linearly with square of applied voltage i.e. V
2 or with square of applied current (I
2
) throughout the region where
Ohms law is valid. This relationship is experimentally verified on metal films.
However for large currents the relationship does not hold. At high currents, the entire sample is overheated or the charge carriers become hot. However,

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