1、1雪崩光电二极管雪崩光电二极管（APDAPD）探测器）探测器2nThe Multiplication ProcessnAvalanche Photodiode DesignsnAvalanche Photodiode BandwidthnAvalanche Photodiode NoiseAvalanche Photodiode Detectors3456789Measured values of ionisation coefficients e and h for some common semiconductor materials, plotted versus (1/E).The M
2、ultiplication Process10The Multiplication ProcessnWe may define ionisation coefficients for electrons and holes, e and h respectively, as the probability that a given carrier will excite an electron-hole pair in unit distance. The coefficients increase so rapidly with increasing electric field stren
3、gth, that it is often convenient to think in terms of a breakdown field, EB, at which avalanche excitation becomes critical, say becomes of the order 105 106 m-1. Graphs of e and h versus electric field are plotted for a number of semiconductors known to be of interest as detector materials. The cur
4、ves refer to room temperature. As the temperature increases, the ionisation coefficients decrease, because the greater number of scattering collisions reduces the high-energy tail of the carrier energy distribution and hence reduces the probability of excitation. In some materials e h, in others he,
5、 while in gallium arsenide and indium phosphide the two coefficients are approximately the same. The rationk = h/enis found to lie in the range 0.01 to 100.11The Multiplication Process - Experimental BehaviournTwo factors limit the increase of Me, the multiplication factor for the injected electrons
6、 and hence I as the applied voltage approaches the breakdown voltage, VB, at which the values e and h satisfy the condition for breakdown, that is M-.nThe first is the series resistance of the bulk semiconductor, RS, between the junction and the diode terminals.nThe second is the effect of the rise
7、in temperature resulting from the increased dissipation as the current rises. This reduces the values of e and h and raises the breakdown voltage. It also increases the rate of thermal generation of carriers and hence the dark current. Multiplication factors measured as a function of the applied ter
8、minal voltage, V, can usually be fitted to the form M = 1 / |1-(V-IR)/VB|nWhere R = RS +RTh is the sum of the series resistance, RS, and an effective resistance, RTh, which derives from the rise in temperature. The index, n, is a function of the detailed design and the material of the diode. Some ty
9、pical curves of M(V) for a silicon APD are shown in the figure.1213142022-5-151516nIn this section we avoid a detailed analysis of the consequences of sinusoidal modulation of the incident light but concentrate instead on the response of an APD to an optical pulse. The full theory, which has much in
10、 common with the theory of IMPATT and TRAPATT oscillators is complex, so we limit the discussion to the general physical principles and to estimate the order of magnitude of an bandwidth limitation. nIn the n+-p-p+ type of APD illustrated previously the overall response is made up of three parts: A)
11、 the electron transit time across the drift region, (ttr)e = w2/se, B) the time required for the avalanche to develop, tA, C) the transit time of the last holes produced in the avalanche back across the drift space, (ttr)h = w2/sh.nParts B) and C) represent delays additional to those experienced in
12、a non-avalanching diode.17APD Band widthnThe avalanche delay time, tA, is a function of the ratio of the ionisation coefficients, k.nThe distance-time diagrams to follow give a graphic illustration of this. When k = 0, the avalanche develops within the normal electron transit time across the avalanc
13、he region (wA/se). We assume wA 0, the avalanche develops in multiple passes across the avalanche region and at high levels of multiplication, with 0 k 1,tA MkwA/senThe overall response time, , then becomes (w2 + MkwA)/se + (w2 + wA)/vshnAnd we should expect the (-3dB) bandwidth to be given approxim
14、ately byf(-3dB) 0.44/ 18APD Distance-Time DiagramsAvalanche build-up shown on distance-time diagrams: a) k = 0, M=16; b) k = 0.37, M = 241920212223242526APD NoisenThe value of the noise factor, F, and its variation with the multiplication factor, M, are clearly matters which bear on the optimisation
15、 of the optical receiver. For purposes of system evaluation the approximation:F Mx Has often been used. The index, x, typically takes on values between 0.2 and 1.0 depending on the material and the type of carrier initiating the avalanche. As we will see, F Mx, may be reasonably valid over a limited
16、 range of values of M.nA theoretical treatment by McIntyre, yields the following more complex expressions. When the multiplication is initiated by electronsFe = Me 1 - (1-k)(Me-1)2/Me2 When holes initiate the avalanche: Fh = Mh 1 + (1-k)/k .(Mh2-1)2/Mh2 27nComparation of the two theoretical curves： F Mx And Fe = Me 1-(1-k)(Me-1)2/Me2282022-5-1529
