SEMICONDUCTOR MATERIAL AND DEVICE CHARACTERIZATION

Transcription

1 SEMICONDUCTOR MATERIAL AND DEVICE CHARACTERIZATION

2 SEMICONDUCTOR MATERIAL AND DEVICE CHARACTERIZATION Third Edition DIETER K. SCHRODER Arizona State University Tempe, AZ A JOHN WILEY & SONS, INC., PUBLICATION

3 7 CARRIER LIFETIMES 7. INTRODUCTION The theory of electron-hole pair (ehp) recombination through recombination centers (also called traps) was put forth in 952 in the well-known papers by Hall and Shockley and Read 2. Hall later expanded on his original brief letter. 3 Even though lifetimes and diffusion lengths are routinely measured in the IC industry their measurement and measurement interpretation are frequently misunderstood. Lifetime is one of few parameters giving information about the low defect densities in semiconductors. No other technique can detect defect densities as low as cm 3 in a simple, contactless room temperature measurement. In principle, there is no lower limit to the defect density determined by lifetime measurements. It is for these reasons that the IC community, largely concerned with unipolar MOS devices in which lifetime plays a minor role, has adopted lifetime measurements as a process cleanliness monitor. Here, we discuss lifetimes, their dependence on material and device parameters like energy level, injection level, and 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 discrepancies are fundamental and are not due to a deficiency of the measurement. The difficulty with defining a lifetime is that we are describing a property of a carrier within the semiconductor rather than the property of the semiconductor itself. Although we usually quote a single numerical value, we are measuring some weighted average of the behavior of carriers influenced by surfaces, interfaces, energy barriers, and the density of carriers besides the properties of the semiconductor material and its temperature. Lifetimes fall into two primary categories: recombination lifetimes and generation lifetimes. 4 The concept of recombination lifetime τ r holds when excess carriers decay Semiconductor Material and Device Characterization, Third Edition, by Dieter K. Schroder Copyright 2006 John Wiley & Sons, Inc. 389

4 390 CARRIER LIFETIMES s r sg V F t r V R p t g p L n n-type n-type E c E c E v E v Recombination Generation (a) (b) Fig. 7. (a) Forward-biased and (b) reverse-biased junction, illustrating the various recombination and generation mechanisms. as a result of recombination. Generation lifetime τ g applies when there is a paucity of carriers, as in the space-charge region (scr) of a reverse-biased device and the device tries to attain equilibrium. During recombination an electron-hole pair ceases to exist on average after a time τ r, illustrated in Fig. 7.(a). The generation lifetime, by analogy, is the time that it takes on average to generate an ehp, illustrated in Fig. 7.(b). Thus generation lifetime is a misnomer, since the creation of an ehp is measured and generation time would be more appropriate. Nevertheless, the term generation lifetime is commonly accepted. When these recombination and generation events occur in the bulk, they are characterized by τ r and τ 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. 7.. Both bulk and surface recombination or generation occur simultaneously and their separation is sometimes quite difficult. The measured lifetimes are always effective lifetimes consisting of bulk and surface components. Before discussing lifetime measurement techniques, it is instructive to consider τ r and τ g in more detail. Those readers not interested in these details can skip these sections and go directly to the measurement methods. The excess ehps may have been generated by photons or particles of energy higher than the band gap or by forward biasing a pn junction. There are more carriers after the stimulus than before, and the excess carriers return to equilibrium by recombination. A detailed derivation of the relevant equations is given in Appendix RECOMBINATION LIFETIME/SURFACE RECOMBINATION VELOCITY The bulk recombination rate R depends non-linearly on the departure of the carrier densities from their equilibrium values. We consider a p-type semiconductor throughout this chapter 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 n o ) + B(pn p o n o ) + C p (p 2 n p 2 o n o) + C n (pn 2 p o n 2 o ) (7.)

5 RECOMBINATION LIFETIME/SURFACE RECOMBINATION VELOCITY 39 where n = n o + n, p = p o + p, n o, p o are the equilibrium and n, p the excess carrier densities. In the absence of trapping, n = p, allowing Eq. (7.) to be simplified to R A n + B(p o + n) n + C p (po 2 + 2p o n + n 2 ) n + C n (n 2 o + 2n o n + n 2 ) n (7.2) where some terms containing n o have been dropped because n o p o in a p-type material. The recombination lifetime is defined as τ r = n (7.3) R giving τ r = A + B(p o + n) + C p (Po 2 + 2p o n + n 2 ) + C n (n 2 o + 2n (7.4) o n + n 2 ) Three main recombination mechanisms determine the recombination lifetime: Shockley- Read-Hall (SRH) or multiphonon recombination characterized by τ SRH, radiative recombination characterized by τ rad and Auger recombination characterized by τ Auger.Thethree recombination mechanisms are illustrated in Fig The recombination lifetime τ r is determined according to the relationship τ r = τ SRH + τ rad + τ (7.5) Auger During SRH recombination, electron-hole pairs recombine through deep-level impurities or traps, characterized by the density N T, energy level E T, and capture cross-sections σ n and σ p for electrons and holes, respectively. The energy liberated during the recombination event is dissipated by lattice vibrations or phonons, illustrated in Fig. 7.2(a). The SRH lifetime is given by 2 τ SRH = τ p(n o + n + n) + τ n (p o + p + p) p o + n o + n (7.6) Phonon E c E T Photon E v Excited Carrier (a) (b) (c) Fig. 7.2 Recombination mechanisms: (a) SRH, (b) radiative, and (c) Auger.

6 392 CARRIER LIFETIMES where n, p, τ n,andτ p are defined as ( ET E i n = n i exp kt τ p = ) ( ; p = n i exp E ) T E i kt (7.7) ; τ n = (7.8) σ p v th N T σ n v th N T During radiative recombination ehps recombine directly from band to band with the energy carried away by photons in Fig. 7.2(b). The radiative lifetime is 5 τ rad = B(p o + n o + n) (7.9) B is the radiative recombination coefficient. The radiative lifetime is inversely proportional to the carrier density because in band-to-band recombination both electrons and holes must be present simultaneously. During Auger recombination, illustrated in Fig. 7.2(c), the recombination energy is absorbed by a third carrier and the Auger lifetime is inversely proportional to the carrier density squared. The Auger lifetime is given by τ Auger = C p (p 2 o + 2p o n + n 2 ) + C n (n 2 o + 2n o n + n 2 ) C p (p 2 o + 2p o n + n 2 ) (7.0) where C p is the Auger recombination coefficient for a holes and C n for electrons. Values for radiative and Auger coefficients are given in Table 7.. Equations (7.6) to (7.0) simplify for both low-level and high-level injection. Lowlevel injection holds when the excess minority carrier density is low compared to the equilibrium majority carrier density, n p o. Similarly, high-level injection holds when TABLE 7. Recombination Coefficients. Semiconductor Temperature (K) Radiative Recombination Coefficient, B (cm 3 /s) Auger Recombination Coefficient, C (cm 6 /s) Si [0] C n = , C p = 0 3 [ D/S] Si 300 C n + C p = [ B/G] Si [0] Ge [5] C n = , C p = GaAs [8 S/R] C n = , C p = [6] GaAs [8 t Hooft] C n = , C p = [8 S/R] GaP [5] InP [7] C n = , C p = [6] InSb [5] InGaAsP [8] C n + C p = [9]

7 RECOMBINATION LIFETIME/SURFACE RECOMBINATION VELOCITY 393 n p o. The injection level is important during lifetime measurements. The appropriate expressions for low-level (ll) and for high-level (hl) injection become τ SRH (ll) n ( τ p + + p ) τ n τ n ; τ SRH (hl) τ p + τ n (7.) p o p o where the second approximation in the τ SRH (ll) expression holds when n p o and p p o. A more detailed discussion of injection level is given by Schroder. 2 τ rad (ll) = ; τ rad (hl) = (7.2) Bp o B n τ Auger (ll) = ; τ C p po 2 Auger (hl) = (7.3) (C p + C n ) n 2 The Si recombination lifetimes according to Eq. (7.5) are plotted in Fig At high carrier densities, the lifetime is controlled by Auger recombination and at low densities by SRH recombination. Auger recombination has the characteristic /n 2 dependence. The high carrier densities may be due to high doping densities or high excess carrier densities. Whereas SRH recombination is controlled by the cleanliness of the material, Auger recombination is an intrinsic property of the semiconductor. Radiative recombination plays almost no role in Si except for very high lifetime substrates (see τ rad in Fig. 7.3), but is important in direct band gap semiconductors like GaAs. The data for n-si in Fig. 7.3 can be reasonably well fitted with C n = cm 6 /s. However, the fit is not perfect and detailed Auger considerations suggest different Auger coefficients. 3 The bulk SRH recombination rate is given by 2 R = σ nσ p v th N T (pn n 2 i ) σ n (n + n ) + σ p (p + p ) = (pn n 2 i ) (7.4) τ p (n + n ) + τ n (p + P ) leading to the SRH lifetime expression (7.6). The surface SRH recombination rate is R s = σ ns σ ps v th N it (p s n s n 2 i ) σ ns (n s + n s ) + σ ps (p s + p s ) = s n s p (p s n s n 2 i ) s n (n s + n s ) + s p (p s + p s ) (7.5) t r (s) s s s 0 6 t SRH = s 0 7 SRH Auger 0 8 n-si n (cm 3 ) Radiative Fig. 7.3 Recombination lifetime versus majority carrier density for n-si with C n = cm 6 /s and B = cm 3 /s. More detailed Auger considerations suggest C n = n Data from ref. and 3. t rad

8 394 CARRIER LIFETIMES s r (cm/s) 0 2 s ps = 0 7 cm cm h Fig. 7.4 s r versus injection level η as a function of σ ps for N it = 0 0 cm 2, p os = 0 6 cm 3, E Ts = 0.4 ev,σ ns = cm 2. Data from ref. 5. where s n = σ ns v th N it ; s p = σ ps v th N it (7.6) The subscript s refers to the appropriate quantity at the surface; p s and n s are the hole and electron densities (cm 3 ) at the surface. The interface trap density N it (cm 2 )is assumed constant in Eq. (7.5). If not constant, the interface trap density D it (cm 2 ev ) must be integrated over energy with N it in these equations given by N it kt D it. 4 The surface recombination velocity s r is From Eq. (7.5) s r = R s n s (7.7) s r = s n s p (p os + n os + n s ) s n (n os + n s + n s ) + s p (p os + p s + p s ) (7.8) The surface recombination velocity for low-level and high-level injection becomes s n s p s r (ll) = s n (n s /p os ) + s p ( + p s /p os ) s n; s r (hl) = s ns p (7.9) s n + s p s r depends strongly on injection level for the SiO 2 /Si interface as shown in Fig GENERATION LIFETIME/SURFACE GENERATION VELOCITY Each of the recombination processes of Fig. 7.2 has a generation counterpart. The inverse of multiphonon recombination is thermal ehp generation in Fig. 7.(b). The inverse of radiative and Auger recombination are optical and impact ionization generation. Optical generation is negligible for a device in the dark and with negligible blackbody radiation from its surroundings. Impact ionization is usually considered to be negligible for devices

9 RECOMBINATION LIFETIME OPTICAL MEASUREMENTS 395 biased sufficiently below their breakdown voltage. However, impact ionization at low ionization rates can occur at low voltages, and care must be taken to eliminate this generation mechanism during τ g measurements. From the SRH recombination rate expression in Eq. (7.4), it is obvious that generation dominates for pn < n 2 i. Furthermore the smaller the pn product, the higher is the generation rate. R becomes negative and is then designated as the bulk generation rate G for pn 0 with G = R = n 2 i τ p n + τ n p = n i τ g (7.20) ( ET E i τ g = τ p exp kt ) ( + τ n exp E ) T E i kt (7.2) The condition pn 0 is approximated in the scr of a reverse-biased junction. The quantity τ g, defined in Eq. (7.2), is the generation lifetime 6 that depends inversely on the impurity density and on the capture cross-section for electrons and holes, just as recombination does. It also depends exponentially on the energy level E T.The generation lifetime can be quite high if E T does not coincide with E i. Generally, τ g is higher than τ r, at least for Si devices, where detailed comparisons have been made and 2, 6 τ g (50 00)τ r. When p s n s <n 2 i at the surface, we find from Eq. (7.5), the surface generation rate G s = R s = s n s p n 2 i s n n s + s p p s = n i s g (7.22) where s g is the surface generation velocity, sometimes designated as s o (see note in Grove 7 ), given by s g = s n s p s n exp((e it E i )/kt ) + s p exp( (E it E i )/kt ) (7.23) For E it = E i,wefinds r >s g from Eqs. (7.8) and (7.23). 7.4 RECOMBINATION LIFETIME OPTICAL MEASUREMENTS Before discussing lifetime characterization techniques, we will briefly give the relevant equations for the common optical methods. More details are given Appendix 7.. Consider a p-type semiconductor with light incident on the sample. The light may be steady state or transient. The continuity equation for uniform ehp generation and zero surface recombination is 8 n(t) t = G R = G n(t) τ eff (7.24) where n(t) is the time dependent excess minority carrier density, G the ehp generation rate, and τ eff the effective lifetime. Solving for τ eff gives τ eff ( n) = n(t) G(t) d n(t)/dt (7.25)

10 396 CARRIER LIFETIMES In the transient photoconductance decay (PCD) method, with G(t) d n(t)/dt τ eff ( n) = n(t) (7.26) d n(t)/dt In the steady-state method, with G(t) d n(t)/dt τ eff ( n) = n (7.27) G andinthequasi-steady-state photoconductance (QSSPC) method, Eq. (7.25) obtains. Both n and G need to be known in the steady-state and QSSPC methods to determine the effective lifetime. The excess carrier density decay for low level injection is given by n(t) = n(0) exp( t/τ eff ) where τ eff is = + Dβ 2 (7.28) τ eff τ B with β found from the relationship tan ( ) βd = s r 2 βd (7.29) where τ B is the bulk recombination lifetime, D the minority carrier diffusion constant under low injection level and the ambipolar diffusion constant under high injection level, s r the surface recombination velocity, and d the sample thickness. Equation (7.28) holds for any optical absorption depth provided the excess carrier density has ample time to distribute uniformly, i.e., d (Dt) /2. The effective lifetime of Eq. (7.28) is plotted in Fig. 7.5 versus d as a function of s r, showing the dependence on d and s r. For thin samples, τ eff no longer bears any resemblance to τ B, the bulk lifetime, and is dominated by surface recombination. The surface recombination velocity must be known to determine τ B unambiguously unless the sample is sufficiently thick. Although the surface recombination velocity of a sample is generally not known, by providing the sample with high s r,by t eff (s) s r = 0 cm/s t B = s d (cm) Fig. 7.5 Effective lifetime versus wafer thickness as a function of surface recombination velocity. D = 30 cm 2 /s.

11 RECOMBINATION LIFETIME OPTICAL MEASUREMENTS 397 sandblasting for example, it is possible to determine τ B directly. However, the sample must be extraordinarily thick. Equation (7.28) can be written as = + (7.30) τ eff τ B τ S where τ S is the surface lifetime. Two limiting cases are of particular interest: s r 0 gives tan(βd/2) βd/2 and s r gives tan(βd/2) or βd/2 π/2, making the surface lifetime τ S (s r 0) = d 2s r ; τ S (s r ) = d2 π 2 D (7.3) For s r 0, a plot of /τ eff versus /d has a slope of 2s r and an intercept of /τ B, allowing both s r and τ B to be determined. For s r, a plot of /τ eff versus /d 2 has a slope of π 2 D and an intercept of /τ B. Both examples are illustrated in Fig The approximation τ S = d/2s r holds for s r <D/4d. 250 /t eff (s ) slope: s r = cm/s intercept: t B = 6.65 ms /d (cm ) (a) / t eff (s ) slope: D = 36.5 cm 2 /s intercept: t B =.05 ms /d 2 (cm 2 ) (b) Fig. 7.6 Determination of bulk lifetime, surface recombination velocity, and diffusion coefficient from lifetime measurements. Data from ref. 9.

12 398 CARRIER LIFETIMES Equations (7.28) (7.3) hold for samples with one dimension much smaller than the other two dimensions, for example, a wafer. For samples with none of the three dimensions very large, Eq. (7.30) becomes for s r = ( + π 2 D τ eff τ B a + 2 b + ) (7.32) 2 c 2 where a, b, andc are the sample dimensions. It is recommended that the sample surfaces have high surface recombination velocities, by sandblasting the sample surfaces, for example. 20 The recommended dimensions and the maximum bulk lifetimes that can be determined through Eq. (7.32) for Si samples are given in Table 7.2. The time dependence of the carrier decay after cessation of an optical pulse is a complicated function, as discussed in Appendix We show in Fig. 7.7 calculated excess carrier decay curves with the time dependence ( n(t) = n(0) exp t ) (7.33) τ eff According to Eq. (7.30) the effective lifetime is τ eff = τ B + τ S = τ B + Dβ 2 (7.34) TABLE 7.2 Recommended Dimensions for PCD Samples and Maximum Bulk Lifetimes for Si. Sample Length (cm) Sample Width Height (cm cm) Maximum τ B (µs) n-si Maximum τ B (µs) p-si Source: ASTM Standard F28. Ref n(t)/ n(0) 0. s r = 0 6 cm/s t B = 0 4 s Time (s) Fig. 7.7 Calculated normalized excess carrier density versus time as a function of surface recombination velocity. d = 400 µm, α = 292 cm.

13 RECOMBINATION LIFETIME OPTICAL MEASUREMENTS 399 where β is determined from Eq. (7.28), which has a series of solutions for βd/2inthe ranges 0 to π/2, π to 3π/2, 2π to 5π/2, and so on. For each combination of s r, d, and D, wefindaseriesofβ values, giving a series of τ S. One way to solve Eq. (7.29) is to write it as β m d 2 ( ) sr (m )π = arctan β m D (7.35) where m =, 2, 3,... and solve iteratively for β m. The higher order terms decay much more rapidly than the first term. Hence, the semi-log curves are non-linear for short times and then become linear for longer times. From Eq. (7.33), the slope of this plot is Slope = d ln( n(t)) dt = ln(0)d log( n(t)) dt = τ eff (7.36) Taking the slope in the linear portion of the plot gives τ eff. To be safe, one should wait for the transient to decay to about half of its maximum value before measuring the time constant Photoconductance Decay (PCD) The photoconductance decay lifetime characterization technique was proposed in and has become one of the most common lifetime measurement techniques. As the name implies, ehps are created by optical excitation, and their decay is monitored as a function of time following the cessation of the excitation. Other excitation means such as highenergy electrons and gamma rays can also be used. The samples may either be contacted with the current being monitored or the measurement can be contactless. In PCD, the conductivity σ σ = q(µ n n + µ p p) (7.37) is monitored as a function of time. n = n o + n, p = p o + p and we assume both equilibrium and excess carriers to have identical mobilities. This is true under low-level injection when n and p are small compared to the equilibrium majority carrier density, but not for high optical excitation, because carrier-carrier scattering reduces the mobilities. In some PCD methods the time-dependent excess carrier density is measured directly; in others indirectly. For insignificant trapping, n = p, and the excess carrier density is related to the conductivity by n = σ q(µ n + µ p ) (7.38) A measure of σ isameasureof n, provided the mobilities are constant during the measurement. A schematic measurement circuit for PC decay is shown in Fig We follow Ryvkin for the derivation of the appropriate equations. 24 For a sample with dark resistance r dk and steady-state photoresistance r ph, the output voltage change between the dark and the illuminated sample is V = (i ph i dk )R (7.39)

14 400 CARRIER LIFETIMES Pulsed Light Sample L Area A r dk, r ph i dk, i ph R DV R DV V o V o Fig. 7.8 Schematic diagram for contact photoconductance decay measurements. where i ph, i dk are the photocurrent and the dark current. With Equation (7.39) becomes g = g ph g dk = r ph r dk (7.40) V = r 2 dk R gv o (R + r dk )(R + r dk + Rr dk g) (7.4) where g = σ A/L. According to Eq. (7.4), there is no simple relationship between the time dependence of the measured voltage and the time dependence of the excess carrier density. There are two main versions of the technique in Fig. 7.8: the constant voltage method and the constant current method. The load resistor R is chosen to be small compared to the sample resistance in the constant voltage method, and Eq. (7.4) becomes V R gv ( o + R g R gv o V ) (7.42) V o For low-level excitation ( gr or V V o ) V g n; the voltage decay is proportional to the excess carrier density. For the constant current case, R is very large, and V (r2 dk /R) gv o + r dk g r dk gv o ( rdk R V V o ) (7.43) For r dk g or V /V o r dk/r, V g n again. For the measurements in Fig. 7.8, the contacts should not inject minority carriers and the illumination should be restricted to the non-contacted part of the sample to avoid contact effects or minority carrier sweep-out. The electric field in the sample should be held to a value E = 0.3/(µτ r ) /2,whereµ is the minority carrier mobility. 20 The excitation light should penetrate the sample. A λ =.06 µm laser is suitable for Si. One can also pass the light through a filter made of the semiconductor to be measured to remove the higher energy light. The carrier decay can also be monitored without sample contacts, allowing for a fast, non-destructive measure of n(t), using the rf bridge circuit of Fig. 7.9(a) or the microwave circuit of Fig. 7.9(b) in the reflected or transmitted microwave mode. 27 Low surface recombination velocities can be achieved by treating the surface in one of several ways. Oxidized Si surfaces have been reported with s r 20 cm/s. 28 Immersing

15 RECOMBINATION LIFETIME OPTICAL MEASUREMENTS 40 Pulsed Laser Laser or Strobe Lamp Wafer in HF or Iodine Bias Light Wafer Signal Processing (a) Microwave Oscillator (b) Circulator Detector Signal Fig. 7.9 PCD measurement schematic for contactless (a) rf bridge and (b) microwave reflectance measurements. a bare Si sample in one of several solutions can reduce s r even below this value. For example, immersion in HF has given s r = 0.25 cm/s for high level injection. 29 Immersing the sample in iodine in methanol has given s r 4cm/s. 22 Low temperature silicon nitride deposited in a remote plasma CVD system has yielded s r 4 5 cm/s. 30 The contactless PCD technique has been extended to lifetime measurements on GaAs by using a Q- switched Nd:YAG laser as the light source. 3 By using inorganic sulfides as passivating layers, surface recombination velocities as low as 000 cm/s were obtained on GaAs samples. In the microwave reflection method of Fig. 7.9(b), the photoconductivity is monitored by microwave reflection or transmission. Microwaves at 0 GHz frequency are directed onto the wafer through a circulator to separate the reflected from the incident microwave signal. The microwaves are reflected from the wafer, detected, amplified, and displayed. In the small perturbation range, the relative change in reflected microwave power P /P is proportional to the incremental wafer conductivity σ 33 P P = C σ (7.44) where C is a constant. The microwaves penetrate a skin depth into the sample. Typical skin depths in Si at 0 GHz are 350 µm forρ = 0.5 ohm-cm to 2200 µmforρ = 0 ohm-cm. Skin depth is discussed in Section.5.. Consequently, a good part of the wafer thickness is sampled by the microwaves and the microwave reflected signal is characteristic of the bulk carrier density. The lower limit of τ r that can be determined depends on the wafer resistivity. Lifetimes as low as 00 ns have been measured. If a resonant microwave cavity is used, it is important that the signal decay is indeed that of the photoconductor and not that of the measurement apparatus. When the cavity is off resonance the system response is very fast, while an on-resonance cavity results in a large increase in the system fall time. 34