Characterization of Carrier Lifetime

Characterization of Carrier Lifetime

1. Characterization of Carrier Lifetime Presentation as part of internal assessment in course Semiconductor Processing & Characterization M.Tech Solar, PDPU. Presented to Prof. Manoj Kumar Presented by Aditya Soni ( 17MSE001 ) Jay Joshi ( 17MSE005 ) Mrunmayee Unawane ( 17MSE016 )

2. Carrier Lifetimes – Why Measure them In IC Industries, Carrier lifetime determines the performance of devices. It is a sensitive measure of material quality and cleanliness. It gives information about low defect densities as low as 1o 9 to 1o 11 cm -3 4/27/2018 In Solar Cells, Carrier lifetime of minority carriers determines performance of the solar cell. Longer the minority carries retain the energy corresponding to the conduction band, higher their probability to cross the SCR and contribute in conduction. Band diagram of Solar Cell under illumination.

3.   Carrier Lifetimes – What are they Recombination lifetime : Excess carriers decay by recombining is the average time after which the electron goes back in the valence band and recombines with it’s hole.   4/27/2018 E v E c     𝑅−𝐺 𝐶𝑒𝑛𝑡𝑒𝑟𝑠 E v E c Band to Band recombination SRH Recombination Auger recombination E v E c

4. Carrier Lifetimes – What are they Generation lifetime : In case of lack of carriers, electron-hole pairs are generated. is the average time after which the electron hole pair is generated. Misnomer - Generation Time.   4/27/2018 Thermal Generation Optical Generation Impact Ionization generation E v E c E f T = o K T > o K E v E c   An carrier with enough kinetic energy can knock a bound electron out of its bound state and promote it to a state in the conduction band, creating an electron-hole pair.

5. Recombination lifetime Recombination rate, In case of Low-Level Injection,   4/27/2018 , for n-type , for p-type          

6. Recombination lifetime 4/27/2018       𝑁 𝑇 = 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑣 𝑡ℎ = 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝜎 𝑝 = 𝑐𝑎𝑝𝑡𝑢𝑟𝑒 𝑐𝑟𝑜𝑠𝑠-𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 ℎ𝑜𝑙𝑒𝑠 𝜎 n = 𝑐𝑎𝑝𝑡𝑢𝑟𝑒 𝑐𝑟𝑜𝑠𝑠-𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 electrons 𝑛 = 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑝 = ℎ𝑜𝑙𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑛 o = 𝑒𝑞𝑢𝑖𝑙𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑒 − 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑝 o = 𝑒𝑞𝑢𝑖𝑙𝑙𝑖𝑏𝑟𝑖𝑢𝑚 ℎ + 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 Δ 𝑛 = 𝑒𝑥𝑐𝑒𝑠𝑠 𝑒 − 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝛥𝑝 = 𝑒𝑥𝑐𝑒𝑠𝑠 ℎ + 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛      

7. Recombination lifetime 4/27/2018    

8. Recombination lifetime   Recombination lifetime versus majority carrier density for n-Si with &  

9. Generation lifetime 4/27/2018   E 𝑇 = Energy Level E i = Intrinsic Energy Level    

10. Optical Methods Different methods available Photoluminescence method (PL) Free carrier absorption (FCA) Photoconductance Decay (PCD) Short circuit current / open circuit voltage decay (SCCD / OCVD) Surface Voltage Steady state short circuit current method (SSSCC) Electron beam induced current (EBIC) Quasi steady state photoconductance (QSSP)

11. Photoluminescence Method Near band gap emission is used. The pulse height discriminator is necessary to block electrical pulses produced by thermal and other nonphotonic sources. Different types of Photodetectors Photomultiplier tubes detector (impulse response of about 300ps) Microchannel plates detector (impulse response of about 30ps) Fig – Experimental Setup Time Amplitude Converter Pulse Height analyzer

12. Photoluminescence Method Advantages Non contact method Also can be used for determining the composition of compound Semiconductors, such as by using shallow emission or deep level emissions   Fig – Experimental Setup Time Amplitude Converter Pulse Height analyzer

13. Photoluminescence Method Disadvantages Costly equipment required Not so accurate for the characterization of indirect band gap semiconductors Not a bulk characterization technique Only a thin, near surface region can be investigated. Error can occur if the photon recycling happens Fig – Experimental Setup Time Amplitude Converter Pulse Height analyzer

14. Photon recycling Basically, it is the recapturing of photon It may give you the carrier lifetime well above the theoretical value It could be corrected by adding the photon recycling factor in the final equation   E v E c

15. Free Carrier Absorption Excess carrier density = Here, = cross sectional area d = sample thickness = incident beam intensity = = = absorption coefficient Where, Laser generation rate   Detector Amplifier Oscilloscope

16. Free Carrier Absorption Detector Pump Laser Selection From experiments, it is observed that a yttrium-aluminum-garnet (YAG) laser operating at = 1.06 m is ideally suited for Si wafers (around 350 m thick) because of its low absorption coefficient. Pulse duration must be kept below the shortest expected lifetime in the sample, minimum beam size should be at least a few carrier diffusion lengths in diameter.   Amplifier Oscilloscope

17. Free Carrier Absorption Probe Laser Selection long wavelengths toward the IR range are preferable and the choice is often set by laser availability. As probe lasers, HeNe lasers are traditionally used at operating wavelengths of 3.39, 1.3, or 0.632 m, depending on band gap. Also, relatively intense lasers (high temperature) have become available offering increased measurement speed, although care must be taken not to affect the carrier dynamics by heating.   Detector Amplifier Oscilloscope

18. Free Carrier Absorption Detection Electronics Reduction of noise is the priority here. To reduce noise, oscilloscopes with minimum bandwidth is selected. Digital oscilloscope is preferred over the analog because of the provision of digital averaging. Detector Amplifier Oscilloscope

19. Free Carrier Absorption Advantages Non contact method Suitable for bulk lifetime measurements Able to measure through very different sample structures and semiconductor materials Disadvantages Surface recombination decreases the accuracy Thus, it is accurate in short carrier lifetimes (for example, indirect-band-gap semiconductors. At low carrier concentration, the optical absorptivity reduces. Thus, it is difficult to measure for minority charge carriers. Detector Amplifier Oscilloscope

20. Photoconductance decay Methodology = G – R = G - (Continuity equation) For PCD, G(t) << Therefore, = - (We need to find )  

21. Photoconductance decay Methodology Conductivity can be given by, Where, are the mobility of electrons and holes q is the charge of electron n = & p = For equilibrium, = Therefore, (We need to find )  

22. Photoconductance decay Here, is the voltage change between the dark and the illuminated sample. & are photocurrent and dark current. Conductivity = (We need to find )  

23. Photoconductance decay For constant voltage, the above equation can be written as Form this equation, we get .  

24. Verdict Versatile techniques. Can be used for several different conductors. Non contact method, which means simple or no sample preparation. You may get an error in the calculation if carrier trapping is dominant. They require comparatively complex experimental setup.

25. Electrical Measurement Techniques Diode-based: Open-circuit voltage decay ( ) Reverse-recovery ( ) Pulsed MOS capacitor method ( ): Inversion method   4/27/2018

26. Electrical Measurement Techniques Pulsed MOS capacitor method (τ g ): Deep depletion method and Zerbst plot Current-capacitance 4/27/2018

27. Open-Circuit Voltage Decay (OCVD) Fig a. Plot of the decay of Voc with time The carriers decay exponentially, due to recombination given by The open‐circuit voltage decay (OCVD) goes approximately as:      

28. The open‐circuit voltage decay (OCVD) goes approximately as: Experimental Setup & Output:   Fig b. Circuit diagram for the OCVD experiment Fig c. A typical Voc plot when the solar cell is repeatedly turned ON and OFF

29. Open Circuit Voltage Decay Solar cell in in μ s OCLI 1400 18 Solarex 4800 5 Semicon 1000 25 Solar cell OCLI 1400 18 Solarex 4800 5 Semicon 1000 25 Data taken from “Measurement of Minority Carrier Lifetime in Solar Cells from Photo-Induced Open-circuit Voltage Decay by JOHN E. MAHAN”

30. Reverse Recovery (RR) Fig a. Circuit Schematic Fig b. Plot of reverse recovery of a solar cell under transient condition V(t) V(f) V t t i(t) I(f) -Ir ts  

31. Concept of MOS Capacitor Fig a: Structure of MOS Capacitor   Total Capacitance C is given by,

32. Carrier Distribution in MOS Structure Accumulation Depletion Inversion

33. C-V Characteristics of a MOS Structure Characteristic of structure at a- Low Frequency b- High Frequency c- High Frequency with pulsed bias Methods are based on return of pulsed MOS to equilibrium from Accumulation towards depletion Inversion towards depletion

34. Deep depletion method The MOS receives voltage pulses, going from equilibrium to deep depletion: the capacitance is observed as the MOS comes back to equilibrium via thermal generation of carriers. Fig a. The C–VG and C − t behavior of an MOS-C pulsed into deep depletion.

35. Zerbst plot

36. Current-capacitance Advantages: Does not require differentiation of experimental data Doping concentration need not be known Measurement time required is less Fig a. Current Vs Inverse Capacitance Plot

37. Conclusions Electrical Measurements methods are technically simple as they are based on current, voltage and capacitance methods. Recombination lifetimes are best measured by optical methods, while generation lifetimes prefer the MOS capacitor method, especially for thin layers like epitaxial layers.

38. The recombination lifetime τ r is shown in Fig. and given by, Determine σ p NT and C for device ( i ) and σ p NT and B for device (ii). v th = cm/s.   Problem

39. Problem 1 For device ( i ), Also from 2 points we get the equations, Solving these we get  

40. Problem 2 For device (ii), Also from 2 points we get the equations, Solving these we get  

41. The effective recombination lifetime is shown in fig. As a function of wafer thickness; all samples have identical τ B and s r . Determine τ B and s r .   Problem 3

42. From the given equations, we can write, from the two points on the graph, we can obtain two equations, which gives us, S r = 1080 cm/s and = 2.09x10 -5 s   Problem 3

43. Problem 4 Is it possible to determine Ln when d < L n ? The term was calculated and plotted versus 1 /α as a function of L n using the equation shows a good linear fit to the calculated data for d ≈ 4 L n as expected, but beyond that there is poor linearity and the simple analysis does not work.  

44. Problem 4 Constant voltage SPV plots exact equation, approximate equation. s r 1 = 104 cm/s, s r 2 = 104 cm/s, D n = 30 cm2 / s, V SPV = 10 mV, R = 0 . 3, n po = 105 cm−3, d = 500 μm. where the approximation holds for high s r 2 . The equation has a 1 /α intercept that is neither the sample thickness d nor Ln . It is obvious from these figures that the diffusion length cannot be reliably determined when L n exceeds the sample thickness.

45. The recombination lifetime τ r is shown in Fig. and given by, is plotted in Fig as a function of impurity density N T . Determine σ n and s r . v th = 10 7 cm/s.   Problem 5

46. From the given equations, we can write, from the two points on the graph, we can obtain two equations, which gives us, S r = 7.76 cm/s and = 9.97x10 -15 cm 2   Problem 5