1 Introduction 2 The Haynes-Shockley Experiment

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pick up the AC component corresponding to the minority carriers’ pulse. The push button is to be switched on for a short period fo time during the taking of measurements to prevent overheating of the semiconductor sample due to the DC component. a. Change the polarity of the 27 V battery to determine the type of minority charge carriers in the sample under investigation. b. Make sure that the trace height is proportional to the laser beam intensity which means that the oscilloscope vertical deflection is proportional to teh number of the minority charge carriers passing under the detector. This is done by simultaneously reducing the light intensity using the film screen supplied and increasing the gain of the oscilloscope by the same factor. The pulse obtained should match exactly the original pulse. c. Record the distance d between the points A and C, the corresponding values of the drift time t d , the pulse height and its full width at half maximum. Conduct this analysis of the trace profile every 0.5 mm from the collection point C. The micrometer range is ∼ 10 mm, so you will be able to get 19 or 20 experimental points. d. Plot the graph of t d versus d and determine the drift velocity v d from the graph. e. Calculate the minority charge mobility, µ h . The diffusion current for charge carriers (electrons or holes) is related to the concentration gradient according the the diffusion equation J = eD δn δx (11) Note that this is just a restatement of equations (5) and (6). The diffusion current can also be written J = env diff (12) where v diff is the diffusion velocity with which the pulse is broadened with time. From the above relations we can find an expression for the diffusion coefficient: D = nv diff δn δx The diffusion velocity is defined as the pulse broadening per unit time: . (13) v d iff = x f − x i t f − t i (14) where x f and x i are the half-widths of the pulse in meters at teh final and intial instants t f and t i respectively. The oscilloscope unfolds the pulse along the time axis and hence it measures the half-width of the pulse t p in seconds. Since the pulse passes the collection point C with the drift velocity v d one can see that the width of the pulse x is related to its time width t p as monitored by the oscilloscope at the point C according to the relation x = v d t p . For two successive moments t f and t i we have respectively x f = v d t pf and x i = v d t pi , so 4
x f − x i = v d (t pf − t pi ) (15) = v d ∆t p (16) where ∆t p = t pf − t pi is the change in the time half-width between the successive travel times t i and t f . Then v diff = x f − x i t f − t i = v d∆t b ∆t (17) where ∆t = t f − t i . Assume that the charge concentration is an approximately linear function of the distance from the central part of the pulse. Then δn δx ≃ n x (18) where n is the mean concentration and x = v d t p is the half-width. Combining the equations (13) and (17) yields D = (v d ) 2 t p∆t p ∆t . (19) In this equation ∆t p is the change in the time half-width during the time interval ∆t, whereas t p is the average time half-width of teh pulse within the time interval ∆t. That is, t p = ¯t p = (t pf +t pi ) 2 . Then te quantity t p ∆t p = (t pf +t pi )(t pf −t pi ) 2 = ((t pf ) 2 −(t pi ) 2 ) 2 = ∆(tp)2 2 , so that the diffusion coefficient can be presented in the form D = (v d ) 2 ∆(t p) 2 2∆t (20) You should note that this expression is obtained by assuming that the concentration gradient is constant. That is, the recombination rate is not taken into account. In general, we have to introduce the a constant, a, which takes these effects into account: D = a(v d ) 2 ∆(t p) 2 ∆t (21) where for our sample and arrangement the constant a = 0.242. f. Plot the graph of the squares of the half-widths of the pulses observed on the oscilloscope, (t p ) 2 versus their corresponding delay times t d , and use the slope of the resulting straight line to calculate the diffusion constant. g. Compare your result with that given by the Einstein relation (equations (9) and (10)). The pulse area 5
Page 1 and 2: 1 Introduction PART III LABORATORIE
Page 3: D e = kT e µ e (9) and D h = kT e
Page 7 and 8: (ii) valence band (iii) conduction
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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