Optical and Other Measurement Techniques of Carrier Lifetime in Semiconductors

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1 International Journal of Otoelectronic Engineering 0, (: 5- DOI: 0.593/j.ijoe Otical and Other Measurement Techniques of Carrier Lifetime in Semiconductors Yeasir Arafat *, Farseem M. Mohammedy, M. M. Shahidul Haan Deartment of EEE, BUET, Dhaka, 000, Bangladesh Abstract In this aer, various methods for characterization of semiconductor charge carrier lifetime are reviewed and an otical technique is described in detail. This technique is contactle, all-otical and based uon measurements of free carrier absortion transients by an infrared robe beam following electron-hole air excitation by a ulsed laser beam. Main features are a direct robing of the exce carrier density couled with a homogeneous carrier distribution within the samle, enabling recision studies of different recombination mechanisms. The method is caable of measuring the lifetime over a broad range of injections ( cm -3 robing the minority carrier lifetime, the high injection lifetime and Auger recombination, as well as the transition between these ranges. Performance and limitations of the technique, such as lateral resolution, are addreed while alication of the technique for lifetime maing and effects of surface recombination are also outlined. Results from detailed studies of the injection deendence yield good agreement with the Shockley Read Hall theory, whereas the coefficient for Auger recombination shows an aarent shift to a higher value, with resect to the traditionally acceted value, at carrier densities below 0 7 cm -3. Data also indicate an increased value of the coefficient for bimolecular recombination from the generally acceted value. Measurement on an electron irradiated wafer and wafers of excetionally high carrier lifetimes are also discued within the framework of different recombination mechanisms. Keywords Carrier Lifetime, Electron-Hole Pair, Shockley Read Hall Recombination, Generation. Introduction With the decrease in feature size in semiconductor manufacturing, molecular contamination roblems are increased significantly[]. Recombination lifetime as well as diffusion length measurements have become ubiquitous in the semiconductor industry, because they are a good indicator of wafer contamination[]. When the defect densities in semiconductors are low, lifetime is one of few arameters that gives significant information about the lower concentration. No other technique can detect defect densities as low as cm 3 in a simle, contactle room temerature measurement. In rincile, there is no lower limit to the defect density determined by lifetime measurements[3]. It is for these reasons that the IC industry, largely concerned with uniolar MOS devices in which lifetime lays a minor role, has adoted lifetime measurements as a roce cleanline monitor [4]. Alongside this, recombination and generation lifetime as well as measurements of carrier diffusion lengths in semiconductors are also very crucial for hotovoltaic devices[5] which have recently become very attractive toic to researchers. * Corresonding author: arafat@eee.buet.ac.bd (Yeasir Arafat Published online at htt://journal.saub.org/ijoe Coyright 0 Scientific & Academic Publishing. All Rights Reserved The theory of electron-hole air recombination through recombination centers (tras was ut forth in 50s of the last century in the well-known works by Shockley-Read-Hall (SRH[6,7]. Here, we discu lifetimes, their deendence on semiconductor material and device arameters like energy level, injection level & surfaces and how lifetimes are measured. Different measurement methods can give widely differing lifetimes for the same material or device. In most cases, the reasons for these discreancies are fundamental and are not due to a deficiency of the measurement. The difficulty with defining a lifetime is that we are describing a roerty of a carrier within the semiconductor rather than the roerty of the semiconductor itself.. Theory There are two rincial categories of carrier lifetimes: recombination lifetimes and generation lifetimes. The concet of recombination lifetime r holds when exce carriers decay as a result of recombination. Generation lifetime g alies when there is a aucity of carriers, as in the sacecharge region of a reverse-biased device and the device tries to attain equilibrium. During recombination an electron-hole air ceases to exist on average after a time r, illustrated in Fig. (a. The generation lifetime, by analogy, is the time that it takes on average to generate an eh, illustrated in Fig. (b. Thus generation lifetime is a misnomer, since the creation of

2 6 Yeasir Arafat et al.: Otical and Other Measurement Techniques of Carrier Lifetime in Semiconductors an eh is measured and generation time would be more aroriate. Neverthele, the term generation lifetime is commonly acceted. When these recombination and generation events occur in the bulk, they are characterized by r and g. When they occur at the surface, they are characterized by the surface recombination velocity s r and the surface generation velocity s g, also illustrated in Fig.. Both bulk and surface recombination or generation occur simultaneously and their searation is sometimes quite difficult. Consisting of bulk and surface comonents, the measured lifetimes are always effective lifetimes. It is instructive to consider r and g in more detail before discuing lifetime measurement techniques. The exce ehs may have been generated by hotons or articles of energy higher than the band ga or by forward biasing a n junction. There are more carriers after the stimulus than before and the exce carriers return to equilibrium by recombination. Figure. Illustration of various recombination and generation mechanisms for a (a forward-biased and (b reverse-biased junction.. Recombination Lifetime and Surface Velocity The dearture of the carrier densities from their equilibrium values non-linearly controls the bulk recombination rate R. We consider a -tye semiconductor throughout this work and are chiefly concerned with the behavior of the minority electrons. Confining ourselves to linear, quadratic, and third order terms, R can be written as R A( n no + B( n ono + C ( n ono + Cn( n ono ( where n n o + Δn, o + Δ, n o, o are the equilibrium and Δn, Δ, the exce carrier densities. In the absence of traing, Δn Δ, allowing Eq. ( to be simlified to R A n+ B( o + n n+ C( o + o n+ n n ( + C n + n n+ n n ( n o o where some terms containing n o have been droed because n o << o in a -tye material. The recombination lifetime is defined as n r (3a R giving A+ B( o + n + C( o + o n+ n r (3b + C n + n n+ n ( n o o Figure. Variuos mechanisms: (a SRH (b radiative and (c Auger There are three main recombination mechanisms those determine the recombination lifetime: SRH or multihonon recombination characterized by SRH, radiative recombination characterized by rad and Auger recombination characterized by Auger. These mechanisms are illustrated in Fig.. The recombination lifetime r is determined according to the relationshi given below r (4 SRH + rad + Auger SRH Recombination: During SRH recombination, ehs recombine through dee-level imurities or tras, characterized by the density N T, energy level E T and cature cro-sections σ n and σ for electrons and holes, resectively. The energy liberated during the recombination event is diiated by lattice vibrations or honons, illustrated in Fig. (a. The SRH lifetime is given by[6] ( no + n+ n + n( o + + SRH (5 o + no + n where n,, n and are defined as ET Ei Ei ET n ni ex ; ni ex (6a n ; σnvthn (6b T σ vthnt Radiative Recombination: During this recombination, ehs recombine directly from band to band with the energy carried away by hotons as shown in Fig. (b. The radiative lifetime is[8] rad (7 B( o + no + n B is the radiative recombination coefficient. The radiative lifetime is inversely roortional to the carrier density because in band-to-band recombination both electrons and holes must be resent simultaneously. 3 Auger recombination: During Auger recombination, as illustrated in Fig. (c, the recombination energy is absorbed by a third carrier and the Auger lifetime is inversely roortional to the carrier density squared. The Auger lifetime is given by Auger C( o + o n+ n + Cn( no + no n+ n (8 C( o + o n+ n where C is the Auger recombination coefficient for holes

3 International Journal of Otoelectronic Engineering 0, (: 5-7 and C n for electrons. Values for radiative and Auger coefficients are given in Table. Table. Recombination Coefficients hole and electron densities (cm 3 at the surface. The interface tra density N it (cm is aumed constant in Eq. (3. If not constant, the interface tra density D it (cm ev must be integrated over energy with N it in these equations given by N it D it [9]... Recombination Lifetime and Level of Injections Equations (5 to (8 simlify for both low-level and high-level injection. Low-level injection holds when the exce minority carrier density is low comared to the equilibrium majority carrier density, Δn<< o. Similarly, highlevel injection holds when Δn>> o. The injection level is imortant during lifetime measurements. The aroriate exreions for low-level (ll and for high-level (hl injection become n SRH ( ll n n + + o (9 o SRH ( hl + n (9a where the second aroximation in the SRH (ll exreion holds when n << o and << o. rad ( ll ; rad ( hl (0 Bo B n Auger ( ll ; ( Auger hl ( Co ( C + Cn n The Si recombination lifetimes according to Eq. (4 are lotted in Fig. 3. At high carrier densities, the lifetime is controlled by Auger recombination and at low densities by SRH recombination. Auger recombination has the characteristic /n deendence. The high carrier densities may be due to high doing densities or high exce carrier densities. Whereas SRH recombination is controlled by the cleanline of the material, Auger recombination is an intrinsic roerty of the semiconductor. Radiative recombination lays almost no role in Si excet for very high lifetime substrates but is imortant in direct band ga semiconductors like GaAs. The bulk SRH recombination rate is given by σσ n vthnt ( n ni ( n ni R ( σn( n+ n + σ ( + ( n+ n + n( + The surface SRH recombination rate is σnsσ svth Nit ( n s s ni n ( n s s ni Rs (3 σns ( ns + ns + σ s ( s + s sn ( ns + ns + s ( s + s Where s n σ ns v th N it ; s σ s v th N it. The subscrit s refers to the aroriate quantity at the surface; s and n s are the Figure 3. Recombination lifetime versus majority carrier density for n-si with C n 0 3 cm 6 /s and B cm 3 /s Figure 4. Determination of bulk lifetime, surface recombination velocity and diffusion coefficient from lifetime measurements. Data from [0]

4 8 Yeasir Arafat et al.: Otical and Other Measurement Techniques of Carrier Lifetime in Semiconductors The surface recombination velocity s r is Rs sr (4a ns from eq. (3 n ( os + nos + ns sr (4b s n + n + n + s + + ( ( n os s s os s s The surface recombination velocity for low-level and high-level injection becomes n n sr( ll sn; sr( hl (5 s n + s + s + s ( ( n s os s os n s r deends strongly on injection level for the SiO /Si interface as shown in Fig Recombination Lifetime Measurements Techniques Recombination lifetime can be measured otically or electrically. The commonly used techniques are Otical Measurements: Photoconductance Decay (PCD, Quasi-Steady-State Photoconductance (QSSPC, Short-Circuit Current/Oen-Circuit Voltage Decay (SCCD/ OCVD, Photoluminescence Decay (PLD, Surface Photovoltage (SPV, Steady-State Short-Circuit Current (SSSCC, Free Carrier Absortion, Electron Beam Induced Current (EBIC etc. Electrical Measurements: Diode Current-Voltage, Reverse Recovery (RR, Oen-Circuit Voltage Decay (OCVD, Pulsed MOS Caacitor, Other Techniques. smaller the n roduct, the higher is the generation rate. R becomes negative and is then designated as the bulk generation rate G ni ni G R (6 n+ n g for n 0 with ET Ei Ei ET g ex + nex (7 The condition n 0 is aroximated in the scr of a reverse-biased junction. The quantity g, defined in Eq. (7, is the generation lifetime that deends inversely on the imurity density and on the cature cro-section for electrons and holes, just as recombination does. The generation lifetime can be quite high if E T does not coincide with E i. Generally, g is higher than r, at least for Si devices, where detailed comarisons have been made and g (50 00 r. When s n s < n i at the surface, we find from Eq. (3, the surface generation rate n n i Gs Rs ns (8 i g sn n s + where s g is the surface generation velocity, given by n sg (9 sn ex( ( Eit Ei + s ex( ( Ei Eit From Eqs. (4b and (9, for E it E i it is found that s r > s g. Generation lifetime is usually measured by electrical means such as Gate-Controlled Diode and Pulsed MOS Caacitor methods. 3. Methodology Of the various lifetime measurement methods, otical technique is stated in the following section. Figure 5. The surface recombination velocity s r versus injection level η as a function of σ s for N it 0 0 cm, os 0 6 cm 3, E Ts 0.4 ev, σ ns cm. Data from [].4. Generation Lifetime and Surface Velocity Every recombination roce of Fig. has a generation counterart. The inverse of multihonon recombination is thermal eh generation in Fig. (b. The inverse of radiative and Auger recombination are otical and imact ionization generation. Otical generation is negligible for a device in the dark and with negligible blackbody radiation from its surroundings. Imact ionization is usually considered to be negligible for devices biased sufficiently below breakdown voltage. However, imact ionization at low ionization rates can occur at low voltages and care must be taken to eliminate this generation mechanism during g measurements. Generation dominates for n < n i. Furthermore the 3.. Recombination Lifetime: Otical Measurements Consider a -tye semiconductor with light incident on the samle. The light may be steady state or transient. The continuity equation for uniform eh generation and zero surface recombination is [,3] nt ( nt ( G R G (0 t eff where Δn(t is the time deendent exce minority carrier density, G the eh generation rate and eff the effective lifetime. Solving for eff gives nt ( eff ( n ( G( t d n( t dt In the transient PCD method, with G(t << dδn(t/dt, the effective lifetime becomes eff (Δn -Δn(t/{dΔn(t/dt}. In the steady-state method, with G(t >> dδn(t/dt, the effective lifetime becomes eff (Δn Δn/G and in the QSSPC method, Eq. ( remains valid. Both Δn and G need to be known in the steady-state and QSSPC methods to determine the effective lifetime.

5 International Journal of Otoelectronic Engineering 0, (: 5-9 The exce carrier density decay for low level injection is given by Δn(t Δn(0ex(-t/ eff where eff is calculated as + Dβ ( eff with β found from the relationshi tan(βd/ s r /(βd. Here B is the bulk recombination lifetime, D the minority carrier diffusion constant under low injection level and the ambiolar diffusion constant under high injection level and d the samle thickne. Equation ( holds for any otical absortion deth rovided the exce carrier density has amle time to distribute uniformly, i.e., d << (Dt /. The effective lifetime of Eq. (0 is lotted in Fig. 5 versus d as a function of s r. For thin samles, eff no longer bears any resemblance to B, the bulk lifetime and is dominated by surface recombination. The surface recombination velocity must be known to determine B unambiguously unle the samle is sufficiently thick. Although the surface recombination velocity of a samle is generally not known, by roviding the samle with high s r, by sandblasting for examle, it is oible to determine B directly. However, the samle must be extraordinarily thick. Equation ( can be written as + (3 eff B s where s is the surface lifetime. B + π D + + (5 eff B a b c where a, b and c are the samle dimensions. It is recommended that the samle surfaces have high surface recombination velocities. The recommended dimensions and the maximum bulk lifetimes that can be determined through Eq. (3 for Si samles are given in Table. Table. Recommended Dimensions for PCD Samles and Maximum Bulk Lifetimes for Silicon Source: ASTM Standard F8 [4]. Photoconductance Decay: The hotoconductance decay lifetime characterization technique was roosed in 955 [5] and has become one of the most common lifetime measurement techniques. As the name imlies, ehs are created by otical excitation and their decay is monitored as a function of time following the ceation of the excitation. Other excitation means such as high-energy electrons and gamma rays can also be used. The samles may either be contactle (Fig. 7 or the measurement can be contacted with the current being monitored (Fig. 8. Figure 6. Effective lifetime versus wafer thickne as a function of surface recombination velocity. D 30 cm /s Two limiting cases are of articular interest: s r 0 gives tan(βd/ βd/ and s r gives tan(βd/ or βd/ π/, making the surface lifetime d d s( sr 0 ; s( sr (4 sr π D For s r 0, a lot of / eff versus /d has a sloe of s r and an intercet of / B, allowing both s r and B to be determined. For s r, a lot of / eff versus /d has a sloe of π D and an intercet of / B. Both examles are illustrated in Fig. 6. The aroximation s d/s r holds for s r < D/4d. Equations ( (4 hold for samles with one dimension much smaller than the other two dimensions, for examle, a wafer. For samles with none of the three dimensions very large, Eq. (3 becomes for s r Figure 7. PCD measurement schematic for contactle (a rf bridge and (b microwave reflectance measurements Figure 8. Schematic diagram for contact hotoconductance decay measurement

6 0 Yeasir Arafat et al.: Otical and Other Measurement Techniques of Carrier Lifetime in Semiconductors Quasi-Steady-State Photoconductance (QSSPC: In the QSSPC method the samle is illuminated with a flash lam with a decay time constant of several ms and an illumination area of several cm [7,9]. Due to the slow decay time, the samle is under quasi steady-state conditions during the measurement as the light intensity varies from its maximum to zero. The steady-state condition is maintained as long as the flash lam time constant is longer than the effective carrier lifetime. The timevarying hotoconductance is detected by inductive couling. The exce carrier density is calculated from the hotoconductance signal. The generation rate, required in Eq. (7.5, is determined from the light intensity measured with a calibrated detector. Semiconductors absorb only a fraction of the incident hotons, deending on the reflectivity of the front and back surfaces, oible faceting of those surfaces, and the thickne of the wafer. The value of the absortion fraction for a olished, bare silicon wafer is f 0.6. If the wafer has an otimized antireflection coating, f 0.9, while a textured wafer with antireflection coating can aroach f.36 The generation rate er unit volume G can then be evaluated from the incident hoton flux and the wafer thickne, according to where is the hoton flux density and the samle thickne. Auming the flash lam light decay is exonential in time, the generation rate is higher for eff < flash, the samle is in quasi steady-state during the measurement. Hence, the flash lam decay time must be sufficiently long for the QSSCP measurement to be valid. 4. Conclusions The microwave reflection or inductive couling hotoconductance decay technique is commonly used to measure carrier lifetime. Its key strength is the contactle nature and raidne and major weakne is the unknown surface recombination velocity. If the samle thickne can be changed, then both the bulk lifetime and the surface recombination velocity can be extracted. The quasi-steady-state hotoconductance method is a more recent method and has found wide accetance in the design of hotovoltaic devices. It measures the lifetime as a function of injection level in one ste but requires large samle area (several cm recluding high density maing. Surface hotovoltage technique is used to detect iron in -Si. The most common electrical recombination lifetime method is the oen-circuit voltage decay method. Measured r or L n mean little for thin layers, e.g., eitaxial layers on highly doed substrates, denuded zones on heavily reciitated substrates, or SOI films. Such layers are best characterized through generation lifetime characterization [6] which is commonly determined with the ulsed MOS caacitor. The Zerbst lot imlementation is the most common, but the current versus inverse caacitance is easier to interret because the doing density of the samle need not be known. Since g is measured in the sace-charge region of a reverse-biased device, it lends itself easily for the characterization of thin layers. Since the scr width can be varied by an alied voltage, it is oible to generate a g deth rofile, that is difficult to do with r measurements, because the measurement deth for r and L n measurements is the minority carrier diffusion length. ACKNOWLEDGEMENTS Authors of this aer would like to thank the Deartment of EEE, BUET, Dhaka-000, Bangladesh, for its various suorts during the rearation of this manuscrit. REFERENCES [] U.B. Godse, Simulations of removal of molecular contaminants from silicon wafer surface, PhD Thesis, UT Austin, December 0. [] P.Y. Yu, M. Cardona, Fundamentals of Semiconductors: Physics and Materials Proerties, 4 th ed., Sringer, 00. [3] S.M. Sze, K.K. Ng, Physics of semiconductor devices, 3rd ed., John Wiley & Sons, 007. [4] D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed., John Wiley & Sons, Inc., Hoboken, New Jersey, USA, 006. [5] M.C. Putnam, D.B.T. Evans, M.D. Kelzenberg, et al. 0 μm minority-carrier diffusion lengths in Si wires synthesized by Cu-catalyzed vaor-liquid-solid growth, Al. Phys. Lett., vol. 95, 009. [6] W. Shockley and W.T. Read, Statistics of the Recombinations of Holes and Electrons, Phys.Rev., vol. 87, , Set. 95. [7] R.N. Hall, Recombination Procees in Semiconductors, Proc. IEE, vol. 06B, , March, 960. [8] Y.P. Varshni, Band-to-Band Radiative Recombination in Grous IV, VI and III-V Semiconductors (I and (II, Phys. Stat. Sol., vol. 9, , Feb. 967; ibid. vol. 0,. 9 36, March 967. [9] D.J. Fitzgerald and A.S. Grove, Surface Recombination in Semiconductors, Surf. Sci., vol. 9, , Feb [0] S.K. Pang and A. 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7 International Journal of Otoelectronic Engineering 0, (: 5- [4] ASTM Standard F8-9, Standard Method for Measuring the Minority-Carrier Lifetime in Bulk Germanium and Silicon, 996. [5] D.T. Stevenson and R.J. Keyes, Measurement of Carrier Lifetimes in Germanium and Silicon, J. Al. Phys., vol. 6, , Feb [6] D.K. Schroder, B.D. Choi, S.G. Kang, W. Ohashi, K. Kitahara, G. Oosits, T. Pavelka, and J.L. Benton, Silicon Eitaxial Layer Recombination and Generation Lifetime Characterization, IEEE Trans. Electron Dev., vol. 50, , Aril 003.