雪崩光电二极管(APD)
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雪崩光电二极管 （APD）探测器
百度文库
1
Avalanche Photodiode Detectors
The Multiplication Process
Avalanche Photodiode Designs Avalanche Photodiode Bandwidth Avalanche Photodiode Noise
2
3
4
5
6
7
8
The Multiplication Process
Measured values of ionisation coefficients e and h for some common semiconductor materials, plotted versus (1/E).
M = 1 / |1-(V-IR’)/VB|n
Where 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 typical 11 curves of M(V) for a silicon APD are shown in the figure.
APD Distance-Time Diagrams
Avalanche build-up shown on distance-time diagrams: a) k = 0, M=16; b) k = 0.37, M = 24 17
18
19
20
21
22
23
24
APD Noise
The value of the noise factor, F, and its variation with the multiplication factor, M, are clearly matters which bear on the optimisation 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 range of values of M. A theoretical treatment by McIntyre, yields the following more complex expressions. When the multiplication is initiated by electrons Fe = Me [ 1 - (1-k)(Me-1)2/Me2] When holes initiate the avalanche: Fh = Mh [ 1 + (1-k)/k .(Mh2-1)2/Mh2 ]
The first is the series resistance of the bulk semiconductor, RS, between the junction and the diode terminals. The second is the effect of the rise 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 terminal voltage, V, can usually be fitted to the form
12
13
14
APD Band width
In 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 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. In the n+-p--p+ type of APD illustrated previously the overall response is made up of three parts: – A) 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. Parts B) and C) represent delays additional to those experienced in a non-avalanching diode. 15
25
Comparation of the two theoretical curves：
F Mx And Fe = Me [1-(1-k)(Me-1)2/Me2]
26
27
9
The Multiplication Process
We 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 strength, 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 curves 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 h>e, while in gallium arsenide and indium phosphide the two coefficients are approximately the same. The ratio k = h/e is found to lie in the range 0.01 to 100. 10
APD Band width
The avalanche delay time, tA, is a function of the ratio of the ionisation coefficients, k. The 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 avalanche region (wA/se). We assume wA << w2. When k > 0, the avalanche develops in multiple passes across the avalanche region and at high levels of multiplication, with 0 < k < 1, tA MkwA/se The overall response time, , then becomes (w2 + MkwA)/se + (w2 + wA)/vsh And we should expect the (-3dB) bandwidth to be given approximately by f(-3dB) 0.44/ 16
The Multiplication Process - Experimental Behaviour
Two factors limit the increase of Me, the multiplication factor for the injected electrons 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->.
百度文库
1
Avalanche Photodiode Detectors
The Multiplication Process
Avalanche Photodiode Designs Avalanche Photodiode Bandwidth Avalanche Photodiode Noise
2
3
4
5
6
7
8
The Multiplication Process
Measured values of ionisation coefficients e and h for some common semiconductor materials, plotted versus (1/E).
M = 1 / |1-(V-IR’)/VB|n
Where 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 typical 11 curves of M(V) for a silicon APD are shown in the figure.
APD Distance-Time Diagrams
Avalanche build-up shown on distance-time diagrams: a) k = 0, M=16; b) k = 0.37, M = 24 17
18
19
20
21
22
23
24
APD Noise
The value of the noise factor, F, and its variation with the multiplication factor, M, are clearly matters which bear on the optimisation 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 range of values of M. A theoretical treatment by McIntyre, yields the following more complex expressions. When the multiplication is initiated by electrons Fe = Me [ 1 - (1-k)(Me-1)2/Me2] When holes initiate the avalanche: Fh = Mh [ 1 + (1-k)/k .(Mh2-1)2/Mh2 ]
The first is the series resistance of the bulk semiconductor, RS, between the junction and the diode terminals. The second is the effect of the rise 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 terminal voltage, V, can usually be fitted to the form
12
13
14
APD Band width
In 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 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. In the n+-p--p+ type of APD illustrated previously the overall response is made up of three parts: – A) 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. Parts B) and C) represent delays additional to those experienced in a non-avalanching diode. 15
25
Comparation of the two theoretical curves：
F Mx And Fe = Me [1-(1-k)(Me-1)2/Me2]
26
27
9
The Multiplication Process
We 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 strength, 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 curves 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 h>e, while in gallium arsenide and indium phosphide the two coefficients are approximately the same. The ratio k = h/e is found to lie in the range 0.01 to 100. 10
APD Band width
The avalanche delay time, tA, is a function of the ratio of the ionisation coefficients, k. The 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 avalanche region (wA/se). We assume wA << w2. When k > 0, the avalanche develops in multiple passes across the avalanche region and at high levels of multiplication, with 0 < k < 1, tA MkwA/se The overall response time, , then becomes (w2 + MkwA)/se + (w2 + wA)/vsh And we should expect the (-3dB) bandwidth to be given approximately by f(-3dB) 0.44/ 16
The Multiplication Process - Experimental Behaviour
Two factors limit the increase of Me, the multiplication factor for the injected electrons 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->.