Quantum Efficiency Determination of Unbiased Silicon Photodiode and Photodiode Based Trap Detectors

Rev.Adv.Mater.Sci.90 21(2009) 90-98 Ö. Bazkir

QUANTUM EFFICIENCY DETERMINATION OF UNBIASED SILICON PHOTODIODE AND PHOTODIODE BASED TRAP DETECTORS

Özcan Bazkir TUBITAK-UME, Optics Laboratory, Gebze/KOCAELI, Turkey

Received: April 7, 2008

Abstract. This work describes the determination of both internal and external quantum efficiency, QE, of unbiased silicon photodiodes (p+-n) to be used as a light detection element in the trap detectors, which are in general used as the optical responsivity transfer standard. The internal QE values of silicon photodiodes and of trap detectors were calculated from experimentally measured responsivity and reflectance values with an uncertainty at the order of 10-3 and 10-4%. By applying a QE model that is based on the photodiodes electrical parameters like recombination velocity, diffusion length, diffusion coefficient, absorption coefficient, etc. the internal QE values were ex- trapolated to 400-1100 nm range. The variations in reflectance and responsivity due to the surface non-homogeneities of photodiodes were also analysed and their effects on QE were calculated approximately at the order of 10-4%.

1. INTRODUCTION ing layer thickness, doping level, etc., have been considered as the important parameters that cause The quantum efficiency is defined as a degree of the reduction of QE below the unity [2]. effectiveness of the incident radiant flux for pro- The silicon-based photodiodes generally have ducing measurable parameters like temperature, been produced in such a way that their internal QE current, etc. in a detector [1]. Depending on the is close to unity especially in the visible region of portion of light that takes part in formation of these electromagnetic spectra [3]. However, due to the effects, it can be defined either as internal QE or loss mechanisms mentioned above there expected external QE. The internal QE for a photodiode is to be some deflections from unity, which are called the number of electron hole pairs created per ab- internal QE deficiency. In order to take these loss sorbed photons; whereas, the external QE is the mechanisms into account and to calculate QE, number of number of electron hole pairs created some mathematical modes have been developed per incident photons [1]. by Geist [4], Geist et al. [5], Gentile et al. [6], The QE is in general expressed as a function L.Kreinin et al. [7], N. Bordin et al. [8], Alejendro et of one of the parameters like wavelength, absorp- al. [9] tion coefficient, frequency, etc. At a certain wave- In this work both the internal QE and the exter- length if the incident photons are completely ab- nal QE of the silicon photodiodes were studied. sorbed and all the generated minority carriers con- Moreover, effects of the surface reflectance and tribute to the current, then the QE at that particular responsivity non-homogeneities on the QE were wavelength is said to be unity. Optical reflection analyzed. losses, carrier recombinations, defects, passivat- Corresponding author: Ozcan Bazkir, e-mail: [email protected]

Fig. 1. Laser based responsivity and reflectance measurement set up.

2. QUANTUM EFFICIENCY con photodiodes. The main parameters of the set up are; laser source, and laser power stabilizer Incident radiant flux on a photodiode undergoes system (LPS) and detection system. Measure- reflectance, absorbance and transmittance events. ments were done using fixed He-Ne (632.8 nm) The percentage of the incident photons that con- and tuneable Ar-Ion (488 and 514.5 nm) lasers. tribute to photocurrent is defined as external QE LPS system was used to compensate the fluctua- and is given by: [1,9,10] tions in the lasers output intensities. This system also has a spatial filter system which functions for Rhc EQEafλ = . generating a geometrically well-defined Gaussian λ (1) q beam to be incident on the photodiode. Using this system diameter of laser beams were adjusted to where R is the responsivity of a photodiode which 3 mm (1/e2 points) and the fluctuations in their is given as the measured current per incident ra- power were reduced to approximately 0.006%. diation power, c is the velocity of light in vacuum, q The responsivity measurements of photodiodes is the electron charge, λ is the wavelength of light and h stands for the Planck’s constant. and trap detectors are shown in the Fig. 2. Curve 1 shows experimental responsivity for the photodiode Some portion of light beam will be reflected from obtained by comparing with a reference standard the photodiode surface. The percentage of contri- whose responsivity is traceable to electrically sub- bution of remaining photons to photocurrent or to stituted cryogenic radiometer system described in the reflectance ρ corrected external QE, which is our previous works [11,12]. A reflectance unit was called internal QE, is given as [1,9,10]: added to responsivity measurement system that Rhc EQE enables us to measure the reflectance of photo- IQEafλ = = . (2) diodes at the same laser wavelengths. In this sys- qλρa11− f a − ρf tem, the stabilized laser beam was aligned to incident a point close to the rim of a mirror so as to get 3. EXPERIMENTAL the small angle between the incident and the reflected beam. This prevents the effects that can The optical measurement set up shown in Fig. 1 arise due to polarization dependence of reflectance was used to measure the responsivity, R of the sili- [13]. The detector under measurement and the 92 Ö. Bazkir

Fig. 2. Optical responsivity and reflectance values of silicon photodiode. Reflectance values of Si-trap are multiplied with 10 to display on the same graph.

Fig.3. Variation of responsivity values over the surface of silicon photodiodes.

reference reflectance standard were placed on a measurements of diode reflectance and spectral rotating and translating stages respectively and the responsivity, the effects of surface non-uniformity reflected beams were measured separately using on these parameters and thereby on QE were ana- silicon photodiode based trap detector. The mea- lyzed by measuring the spatial variation of photo- sured reflectance values are shown in Fig. 2, Curve diodes. In the responsivity measurement set up, 2. Fig.1, the photodiodes were mounted on X-Y trans- Substituting those values into Eq. (2) we get lation stage, which was driven by PC-controlled step the internal QE values. The repeated measure- motors. Using power stabilized He-Ne laser (632.8 ments of responsivity and reflectance indicated that nm) beam having spot size of 1.0 mm diameter, the uncertainty in the internal QE is of the order of the spatial uniformities were investigated by scan- 10-3 and 10-4%. This variation has been related to ning the surface of photodiodes with a step length the spatial non-uniformity of light source and de- of 1.0 mm. The spatial variations of about 10-4% tector active area (illuminated area). Since the in- were observed within the 10 mm diameter on the ternal QE measurements consist of simultaneous surface of photodiodes, Fig. 3. Quantum efficiency determination of unbiased silicon photodiode and photodiode based trap... 93

Fig. 4. Spectral reflectance measurement set up. A: Aperture, FM; Flat Mirror, SM: Spherical Mirror, CM: Cylindrical Mirror, OSF: Order Sorting Filter, D; Detector; Si: Silicon, RS; Reference Standard.

Fig. 5. Absorption and generation of electron hole pairs in silicon photodiode structure.

The QE values of a silicon photodiodes, which the lamp stable to within few tenths of a percent are the most widely used detector within the spec- over a measurement period. The monochromatic tral range from 400 to 1100 nm, obtained in this beam emerged from monochromator system was way are limited to only certain laser wavelengths. collimated and directed to the photodiode surface The whole values within this range from 400 nm to and reference standard respectively. Reflected 1100 nm were obtained by applying the model de- beams from the photodiode surface and reference scribed in Section 4. standard were collected in the integrating sphere The surface reflectance looses of silicon pho- separately and these signals were recorded using todiodes within the range from 400 nm to 1100 nm silicon photodiode trap detector. were measured using double monochromator system consisting of collimator, integrating sphere, lock 4. MODELING OF QUANTUM in amplifier and detector system as shown in Fig. EFFICIENCY 4. As a light source a flat tungsten filament quartz halogen lamp was used and it was operated at a In this work, we examined the internal QE of the constant current mode, which kept the output from photodiode whose structure as shown in Fig. 5 has 94 Ö. Bazkir thin p layer (p<

dnp photodiode. By considering the electric field in the JnqEqD=+µ , (3b) nnnd x neutral n region as zero and also by taking into account only steady state condition, the first term where the first terms are drift currents which arise in the left hand side of Eq. (5a) vanishes. Thus we from electric field E at the space charge region, have and second terms are diffusion currents due to concentration gradient of carriers, D and µ are 2 p,n p,n ∂ p hole (electron) diffusion constant and mobility re- D n +−=GR 0, (6) p ∂ 2 spectively. x The photon flux inside the photodiode varies The generation G and recombination R rate exponentially with distance generate electron hole parameters in Eq. (6) were defined by considering pairs. Some of these carriers undergo recombina- that the generation rate of electron and hole pairs tion and do not contribute to current. Thus, the inside the photodiode in the both depletion and n variation of these carriers inside the photodiode, regions vary exponentially as a function of absorp- α ρ α -α which is called continuity equation, are given as tion coefficient as G = (1 - )F0 e . Recombina- [14,15] tion rate in Si photodiode, which have indirect band gap, is defined by the local energy levels within the pxtafaf,d+− t pxt , A d x = band. We used recombination rate defined by Hall, (4a) Read, and Shockley and made an assumption that Fxaf−+ Fx add xAt f +−b G RAxtg dd, ppptrap energy level is at the mid gap, so for low injec-

tion we have R= (pn-pn0)/tp [16,17]. Having defined nxta ,d+− tf nxta ,f A d x = the G and R parameters in Eq. (6) and the bound- ary conditions (a- the back surface recombination a f −+a f +−a f (4b) Fxnn Fxdd xAt G nn RAxt dd, velocity is Sb and at x=H it has the relation SbDpn=- D dp /dx. b- there is no recombination in the p and where the terms in the left hand side are time rate p n of change of carriers in Adx volume element, the depletion regions, then at x=D, Dpn=0) the varia- first terms in the right hand side are the change in tions of minority carriers, Eq. (7) in n side of photo- the photon flux, G and R are generation and re- diode can easily be obtained with a simple math- combination of carriers. ematical algebra. Using the relation between current density and αρτaf− 1 F0 p photon flux for electron and holes Jn,p= ± qF and pp−= ⋅ nn0 − α 2 also substituting Eqs. (3a) and (3b) into Eqs. (4a) 1 Lp and (4b) we get the following equations. D 2D x x |RL −χ −+αD O −χ − |U L L L L −α (7) SM −++eeeeepppP p x V ∂p ∂ 2 p ∂p |M ξ P ξ | n =−+−D n Eµ n GR, (5a) TN Q W ∂t p ∂x 2 p ∂x pp with

HD− ∂ ∂2 ∂ F I n n n Dp L −−ααD H p =++−D p Eµ p GR. (5b) χα=+GS Jeep −−af S De, ∂ n ∂ 2 n ∂ nn H b K b t x x Lp Quantum efficiency determination of unbiased silicon photodiode and photodiode based trap... 95

Fig. 6. Absorption coefficient of silicon photodiode as a function of wavelength.

HD− H F I − D L L 12/ ξατ=−GS +p JeSDeLDpp −b −g ,. =b g H b K p ppp Lp → Using pn=pn(x) Ip=-qADpdp/dx relation the generated current due to minority carriers in the n side of photodiode can be obtained.

The current generated within the depletion region was also calculated by considering Eq. (3a) and Eq.(5a), with no recombination of electron-hole pairs as

1− e −αD I =+const. . (9) d α

The total current generated within photodiode is the sum of currents in Eqs. (8) and (9). The internal QE of photodiode is the generated current divided by photon flux absorbed by the photodiode. α In Eqs. (8) and (9), is the absorption coefficient, Sb is the back surface recombination velocity, Lp is the diffusion length of holes, D and H are the thicknesses depletion region and n side of photodiode respectively. To solve these equations, the absorption coefficient of silicon photodiode needs to be calculated. The remaining parameters can be obtained by fitting the calculated quantum efficiency measurements to the measured ones. The optical absorption coefficient is related to the imaginary part of index of refraction k by α(ω) = 4πk/λ [18]. It is obvious that to calculate absorption coefficient the imaginary part of index of refraction k is 96 Ö. Bazkir

Fig. 7. Internal quantum efficiency of silicon photodiode at different beam diameters.

needed. For the photodiode used in this work this coefficient, as a function of wavelengths was de- parameter was obtained after determining the op- termined as shown in Fig. 6. tical phase angle using reflectance measurements With the substitution of absorption constants we at normal incidence of light and Kramers–Kronig get the internal QE. The QE values were then cor- relations [18]. Using Fresnell’s equations, the in- rected by using reflectance looses as given in Eq. dex of refraction k as functions of experimentally (2) and they were fitted to the measured values by measured reflectance R(ω) and phase angle θ(ω) adjusting diffusion coefficient, diffusion length, between incident and reflected flux can be ex- thickness of photodiode, and back surface recom- pressed as [19] bination velocity. The modeled QE values as a function of wavelength at different beam diameters for 2 R sin θ both silicon and silicon based trap detectors are = k . (10) shown in the Figs. 7 and 8. Reflectance values of 12+−RRcos θ silicon based trap detectors were taken from our By using Kramers–Krönig dispersion relations previous work [11]. between the real and imaginary parts of complex The responsivity of photodiodes, which allows function lnr = ln|r|+iθ, the phase angle θ(ω) is given one to determine how much detector signal will be by [20] available for a specific application, are defined by the diode surface reflectance and the QE is ex- ∞ 1 ωω− d pressed as [22] θωaf= z ln 0 lnR afωω d . 0 (11) 2π ωω+ d ω 0 0 enλ R=−1 ρλaf IQE af λ , (12) This equation indicated that after having mea- hc sured experimentally R(ω) it is possible to calcu- λ late θ(ω). The methods used for the reflectance where e is the elementary charge, is the wave- measurements and the calculations of phase angle length in vacuum, h is the Planck constant, c is the are described in [21]. Using the calculated phase speed of light in vacuum, n is the refractive index ρ λ angle values obtained from Eq. (11) the imaginary of medium, ( ) is the reflectance of trap detector λ part of refraction index k and therefore absorption and IQE( ) is the internal QE of detector. Quantum efficiency determination of unbiased silicon photodiode and photodiode based trap... 97

Fig. 8. Internal quantum efficiency of silicon based trap detectors at different beam diameters.

Fig. 9. Responsivity of silicon and silicon based trap detectors.

The units of responsitivity are either amperes/ 5. CONCLUSION watt (alternatively milliamperes/milliwatt or micro- In this work both measurement of quantum effi- amperes/microwatt, which are numerically the ciency of silicon photodiode at the laser wave- same) or volts/watt, depending on whether the lengths and the theoretical approach that are used output is an electric current or a voltage. In the Fig. for modelling of quantum efficiency were described. 9 responsivities of photodiodes and trap detectors In the measurement part; responsivity, reflectance, are displayed. 98 Ö. Bazkir surface homogeneity, effects of beam diameter [8] N. Bordin, L.Kreinin and N. Eisenberg // Solar were discussed at the power stabilized (~10-5) la- Energy Materials and Solar Cells 63 (2000) ser wavelengths. In the theoretical part, variation 247. of internal quantum efficiency of silicon photodiode [9] A.Ferrero, J.Campos, A.Pons and A.Corrons having a very thin p layer (p<