1 Introduction 2 The Haynes-Shockley Experiment

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A = Ht b , (22) where H is the pulse height. It is possible to use this quantity to determine the lifetime of the minory charge carriers, τ. Assume that when excess carriers are present, the rate of recombination is proportional to the excess carrier concentration. That is, − ∂n ∂t ∝ n. (23) The minus sign indiates that, as t increases, the excess concentration decreases. We can integrate the above equation to give n(t) = n 0 e ( −t τ ) . (24) Here, τ is the time required for the number of excess carriers to drop to 1/e times their original value. We call this characteristic time the lifetime of the minority charge carriers. The pulse area is proportional to the excess charge concentration, so it follows the same form as equation (24) above: Hence, A(t) = A 0 e ( −t τ ) . (25) ln A(t) = ln A 0 − t τ ln e (26) = ln A 0 − 1 τ .t (27) h. Plot the graph of the logarithm of the pulse area A versus the drift time t d . i. From the graph, find the lifetime of the minority charge carriers, τ. 3 Optical Characterisation and Band Gap of Materials References - the optical properties handout and kittel... So far we have used the electrical properties of semiconductors to help characterise them, but the electronic structure of materials can also be investigated by considering their optical properties. Light incident on a sample may be reflected, absorbed and/or transmitted. Each of these processes is governed by the electronic structure of the material. For example, the dominant absorption mechanism in semiconductors and insulators is usually the excitation of an electron from the valence to the conduction band across the forbidden band gap. (a) Before proceeding, make sure that you understand the following terms: (i) band gap 6
(ii) valence band (iii) conduction band (iv) direct transition (v) indirect transition (vi) crystalline material (vii) amorphous material You should provide an explanation of each of them in your log book. (b) Based on your results from section (2), discuss the mechanism of charge recomination in direct and indirect band semiconductors. 3.1 Background The complete optical characterisation of a solid both in bulk and thin film form involves a knowledge of its complex refractive index: N ∗ = n − jk (28) where j = √ −1. Here, n is the real part of the refractive index. This should already be a familiar concept. It is important in the design of optical components as it is this quantity which primarily determines the refracting power of lenses etc. It is also important when designing anti-reflection coatings, optical fibres and modern electro-optical devices. The imaginary or loss part of the refractive index, k, is crucial in the determination of the absorption properties of materials. In practice, this quantity when measured as a function of frequency can give a direct measure of the band gap of solids. As mentioned above, when light strikes a sample it may be absorbed, reflected or transmitted (see figure (We define a transmission coefficient, given by and a reflection coefficient, T = I T I 0 , (29) R = I R I 0 . (30) Here, I 0 is the intensity of the incident lifht, I T is the intensity of the transmitted light and I R is the intensity of the reflected light. Optical absorption is usually defined in terms of an absorption coefficient, α, such that I T = (I 0 − I R ) e −αd . (31) Here (I 0 − I R ) is the intensity of the light that actually propagates into the crystal (with second order corrections for reflections from the back face and from repetitive crossings of the crystal as a result), and d is the thickness of the sample. The absorption coefficient is in turn related to the imaginary part of N ∗ by 7
Page 1 and 2: 1 Introduction PART III LABORATORIE
Page 3 and 4: D e = kT e µ e (9) and D h = kT e
Page 5: x f − x i = v d (t pf − t pi )
Page 9 and 10: By monitoring the absorption coeffi
Page 11 and 12: 3.4.2 Loading Samples On the right
Page 13: You can find a rough value for the

1 Introduction 2 The Haynes-Shockley Experiment

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