"XBn" Barrier Photodetectors for High Sensitivity and High Operating Temperature Infrared Sensors

Transcription

1 "XBn" Barrier Photodetectors for High Sensitivity and High Operating Temperature Infrared Sensors Philip Klipstein Semiconductor Devices, P O Box 2250, Haifa 31021, ISRAEL philip_k@scd.co.il ABSTRACT A barrier photodetector is a device in which the light is absorbed in a narrow bandgap semiconductor layer whose bands remain essentially flat or accumulated at the operating bias so that all carrier depletion is excluded. In a conventional photodiode below a threshold temperature T 0, typically K for MWIR devices, the dark current is due to Generation-Recombination (G-R) centres in the depletion layer. In a barrier detector, the absence of depletion in the narrow bandgap semiconductor ensures that the G-R contribution to the dark current is negligible. The dark current in the barrier detector is thus dominated by the diffusion component, both above and below T 0. Therefore, at a given temperature below T 0, a barrier detector will exhibit a lower dark current than a conventional photodiode with the same cut-off wavelength. Alternatively, for a given dark current, a barrier detector will operate at a higher temperature than a conventional photodiode, provided that this temperature is below T 0. Device architectures are presented for barrier detectors with photon absorbing layers based on InAs 1-x Sb x alloys and type-ii InAs/GaSb superlattices (T2SL). The thermionic and tunneling components of the dark current are analyzed and shown to be negligible for typical device parameters. An operating temperature of ~150K is estimated for a MWIR barrier detector with f/3 optics and a cut-off wavelength of 4.2µ. Keywords: Shockley-Read-Hall, Generation-Recombination Current, Diffusion Current, Dark Current, Infrared Detector, High Operating Temperature, Focal Plane Array, Indium Arsenide Antimonide, Type II Superlattice 1. INTRODUCTION The maximum operating temperature of a solid state infrared detector is usually determined by its dark current, which increases exponentially with temperature. In standard MWIR photodiodes operating under conditions of backgroundlimited performance (BLIP) this dark current is almost universally produced by so called Generation-Recombination (G-R) centres (also known as Shockley-Read-Hall traps) in the depletion region of the device. A reverse bias applied to the diode activates these G-R centres which provide energy levels close to the middle of the bandgap that reduce the amount of thermal energy needed to excite an electron out of the valence band or into the conduction band approximately by a factor of two. As a result, electron-hole pairs are generated that are immediately removed by the r EGR kbt electric field of the depletion region. The G-R current typically varies with temperature as ~ Te where E GR is roughly equal to half the zero temperature semiconductor bandgap, r ~1.5 and k B is Boltzman's constant. In 2003, a new type of heterostructure device was proposed, in which no depletion layer exists in any narrow bandgap region [1]. This device is similar in some respects to that proposed by White in 1983, in which two narrow gap semiconductors surround a p-type wide bandgap semiconductor and in which a barrier only exists in the conduction band [2]. A related device was also proposed by Maimon and Wicks in 2006 to which they gave the name nbn where "n" stands for the doping in identical narrow gap semiconductors and "B" stands for the Barrier [3]. In all cases one of the narrow gap semiconductors constitutes a contact layer for biasing the device and the other is the photon absorbing layer whose thickness should be comparable to the absorption length of light in the device, typically several microns. The main difference between the device in ref. 1, which will be referred to below as an XBn device, and the other devices is that the doping profile in the barrier region is tailored to ensure that the bands in the narrow bandgap photon absorbing layer are flat right up to the barrier or else contain a narrow accumulation layer immediately next to the Infrared Technology and Applications XXXIV, edited by Bjørn F. Andresen, Gabor F. Fulop, Paul R. Norton, Proc. of SPIE Vol. 6940, 69402U, (2008) X/08/$18 doi: / Proc. of SPIE Vol U-1

2 barrier. Since there is no depletion, the G-R contribution to the dark current is essentially totally suppressed. The dark current is then limited r Ediff kbt to the diffusion contribution which typically varies as ~ Te in which E diff is roughly equal to the zero temperature semiconductor bandgap and r ~ 3, (although other r-values are possible). In conventional diodes operating in the MWIR wavelength range, the diffusion current at 77K is typically several orders of magnitude lower than the G-R current, while at room temperature it is several orders greater. T 0 is defined as the "cross-over" temperature at which the diffusion and G-R currents are equal. Figure 1 shows a typical Arrhenius plot of the dark current in a conventional diode. The lower portion has a slope which is roughly half that of the upper portion. When multiplied by Boltzman's constant, the slopes essentially correspond to the activation energies for G-R and diffusion limited behaviour respectively. The dashed line is an extension of the high temperature diffusion limited behaviour to temperatures below T 0. It represents the behaviour of an XBn barrier device in which there is no G-R current. At temperatures below T 0, an XBn device offers two important advantages. First, it should exhibit a higher signal-to-noise ratio than that of a conventional diode operating at the same temperature. This is depicted by a vertical arrow in figure 1. Second, an XBn device will operate at a higher temperature than a conventional diode with the same dark current. This is depicted by a horizontal arrow in figure 1. As shown below, the G-R current increases with reverse bias while the diffusion current does not. Thus T 0 is raised as the bias is increased and these advantages become more pronounced. In addition, since the dark current of the XBn device is insensitive to bias, the nonuniformity in an array of XBn detectors should be smaller than in a conventional detector array. XBn devices should also be simpler to fabricate since passivation is usually easier to achieve in the wider bandgap material used for the barrier than in the narrow gap materials used for conventional diodes. This should also contribute to better uniformity in detector arrays. In the next section, the principles of the XBn barrier device are presented, including examples based on two different material systems: InAs 1-x Sb x alloys and type-ii InAs/GaSb superlattices. This is followed by an estimation of the criteria on barrier width and height necessary for successful device operation. It is shown that these criteria are easily met for the materials in question. In the following section the crossover temperature, T 0, and the operating temperature T OP, are estimated for MWIR standard and XBn devices respectively, in each case with f/3 optics and a cut-off wavelength of 4.2µ. The ratio of the dark currents in standard and XBn devices at 77K is also evaluated. In the final section the main conclusions are summarized. Log I XBn (high temperature) XBn (high sensitivity) T 0-1 Standard diode 1 / T Figure 1: Schematic Arrhenius plot of the dark current in a standard diode (solid line) and in an XBn device (dashed line). Open circle shows the operating point of a standard diode while solid circles show operating points for the XBn device with improved sensitivity or higher operating temperature. 2. "XBn" BARRIER PHOTODETECTORS Figure 2 shows the band profile of a barrier detector grown on a GaSb substrate in which the contact, barrier and photon absorbing layers are made from p-type GaSb, n-type AlSb 1-x As x and n-type InAs 1-y Sb y respectively. For x~y~0.09 all layers are closely lattice matched and the cut-off wavelength of the photon absorbing layer at 150K is ~4.2µ [4]. Using notation analogous to that introduced by Maimon and Wicks, the device in figure 2 will be termed C p B n n, where C stands for "contact", B for "barrier" and the subscripts indicate the doping in the C- and B-layers. C is used when the contact is made from a different material than the photon absorbing layer. The photon absorbing layer is always n-type and so is denoted simply by its doping, as in the Maimon and Wicks notation. These symbols are written under the relevant layers in figure 2. In figure 2 a reverse bias is applied to maintain the Fermi-level in the contact above that in the photon absorbing layer. For an analogous C n B n n device, the diagram would look similar but the Fermi level in the contact would be near the conduction band instead of the valence band and a higher bias would be applied. The band bending in the contact layer would also be confined to a narrow electron accumulation layer next to the barrier instead Proc. of SPIE Vol U-2

3 n-type AlSb 1-x As x of the wider depletion layer of the p-doped case. In what follows the generic name "XBn" will be used for a barrier detector where X can stand for C n, C p, n, or p. p-type GaSb E(p) F V bias n-type InAs Sb 1-y y φ V C p B n n E C E(n) F E V Figure 2: Band profile for a C p B n n device made from GaSb / AlSb 1-x As x / InAs 1-y Sb y when biased to an operating voltage below the maximum possible value, V Max, defined in the text. The bands in the InAs 1-y Sb y photon absorbing layer are flat except very close to the barrier where they are accumulated. There is no depletion in this layer in contrast to the depletion that exists in both barrier and contact layers. The band profile in figure 2 can be understood as follows. Donor levels are located in energy just below the conduction band edge of the n-type barrier layer and they are all ionized (i.e. they are empty), because all of their donated electrons can reduce their energy substantially by residing in the ionized acceptor states of the contact layer and in an electron accumulation layer inside the photon absorbing layer next to the barrier. The barrier is therefore fully depleted and the donor states receive a positive charge. This is consistent with Poisson's equation and the positive curvature of the bands (i.e. the second derivative of energy with respect to position is positive). The number of negative charges in the accumulation layer plus the number of ionized acceptors in the contact layer is equal to the number of positive ionized donors in the barrier layer. As the bias is increased, electrons transfer from the accumulation layer to the contact layer where they create more ionized acceptors. A maximum bias is reached, V Max, where the bands in the photon absorbing layer are totally flat and the accumulation layer then vanishes. The operation of the C p B n n device of figure 2 as a photodetector is similar to the operation of a standard photodiode. Photons enter from the right hand side of the InAs 1-y Sb y photon absorbing layer where they are converted to electron-hole pairs. The holes diffuse to the barrier layer where they are excited over the small barrier in the valence band of height, φ V, shown in figure 2. φ V is the difference in energy between the flat valence band edge in the photon absorbing layer and the lowest point of the curved valence band edge of the barrier layer. The holes are then removed to the contact by the electric field that they encounter at the contact-barrier junction. On reducing the bias, the device should continue to operate efficiently until a minimum reverse bias of magnitude, V MIN, is reached. Usually this will be when the barrier, φ V, exceeds about 3k B T OP, where T OP is the operating temperature. The spike in the valence band due to the electron accumulation layer next to the barrier can probably be ignored since it is very thin ( Å) so that holes should be able to tunnel through it easily. In any case the spike is removed completely for a bias of V MAX. A range of biases exists therefore, V MAX > V > V MIN, where the bands in the photon absorbing layer are flat or accumulated and minority carriers generated by photon absorption can transfer relatively unimpeded to the contact layer. This is the condition for an operating photodetector with no G-R contribution to the current. On the other hand if the bias is increased beyond V MAX, the depletion in the barrier layer will start to extend into the photon absorbing layer. Under these conditions the G-R contribution to the dark current will start to increase rapidly, especially when the band p-type AlSb As 1-x x V bias Figure 3: Band profile for a C p B p n device which is the same structure as in figure 2 but with a p-type barrier. The InAs 1-y Sb y photon absorbing layer is depleted close to the barrier. Proc. of SPIE Vol U-3

4 bending in the photon absorbing layer exceeds E F (n) E t 3k B T OP where E F (n) is the quasi Fermi level in the photon absorbing layer and E t is the energy of the trap level responsible for the G-R current. In order to avoid depletion in the narrow bandgap photon absorbing layer the barrier in figure 2 has been doped n-type. The equivalent profile for a C p B p n device with a p-type barrier is shown in figure 3. The p-n junction is now on the right hand side of the barrier layer and its depletion region extends into the photon absorbing layer where positive ionized donors are created. On the left hand side of the barrier the band bending is due to a hole accumulation layer at the contact-barrier interface. The positive charge in these two regions is balanced by an equal negative space charge inside the fully depleted p-type barrier layer due to its acceptors which are all ionized. For a C n B p n device the band diagram would look the same as in figure 3 but the Fermi level in the contact would be near the conduction band instead of the valence band and a higher bias would be applied. The band bending in the contact layer would also be more extended due to the fixed positive space charge of ionized donors. It is possible to conceive of variations of the device in figure 2, such as C n B n n devices made from InAs 1-y1 Sb y1 / AlSb 1-x As x / InAs 1-y2 Sb y2 or SL1/ AlSb 1-x As x / SL2, in each case grown on a GaSb substrate, in which all layers are doped n-type and SL1, SL2 are two type II superlattices with different bandgaps. The band profile under bias is shown in figure 4 for the case of InAs 1-y Sb y. This is a unipolar device and it offers a particularly simple architecture for a two colour detector if layers with different bandgaps can be used on each side of the barrier layer which have only a small valence band offset with respect to the barrier ( 1, 2 <3k B T OP ). Different colours are then detected according to the bias direction [2, 5]. For InAs 1-y Sb y the cut-off wavelengths will roughly be in the MWIR µ range, while for superlattices both MWIR and LWIR atmospheric windows can be covered. If the same layers are used on each side of the barrier a single colour nbn device is created. An nbn device with InAs n-layers (y 1 = y 2 = 0) grown on an InAs substrate and with an AlAsSb barrier of unspecified doping type was demonstrated in 2006 by Maimon and Wicks at an operating temperature of 230K with a full 2π steradians field of view [3]. At this temperature the cut-off wavelength was about 3.3µ. As discussed below, T 0 in InAs diodes is unlikely to exceed 230K and a value of T 0 =170K was reported by Astakhov et al. for Be-ion implanted devices [6]. Therefore while not a proof of a higher operating temperature due to the use of an nbn architecture, the report of Maimon and Wicks does demonstrate the first operation of a unipolar device as a photodetector. A type II superlattice nb p n device with a 5.2µ cut-off wavelength was reported recently by Rodriguez et al [7]. Again operation of the unipolar device as a photodetector was demonstrated, although the current deviated from the expected diffusion limited value below temperatures of about 160K, possibly due to perimeter leakage, and the device was not background limited (BLIP). Two open questions remain concerning the above implementations of nbn and C n B n n devices. First, for the case of InAs 1-y Sb y n-layers, is it possible to achieve an unimpeded path for the holes? Second, if a type II superlattice is used for the n-layers, are the holes mobile enough to be collected before they recombine? According to Vurgaftman et al. [8] a band offset 2 ~150meV, is expected for InAs 1-y Sb y / AlSb 1-x As x junctions lattice matched either to E F,L E G1 V bias 2 1 E G2 E F,R E C E V Figure 4: Band profile for a C n B n n device made from InAs 1-y1 Sb y1 / AlSb 1-x As x / InAs 1-y2 Sb y2 when biased to an operating voltage below the maximum possible value, V Max, defined in the text. The bands in the more positively biased InAs 1-y Sb y photon absorbing layer are flat except very close to the barrier where they are accumulated. There is no depletion in this layer in contrast to the depletion that exists in the barrier layer. An accumulation layer also exists in the more negatively biased InAs 1-y Sb y contact layer. Proc. of SPIE Vol U-4

5 InAs (y=0, x~0.18) or to GaSb (y~x~0.09). A barrier, depicted 2 in figure 4, might therefore exist that could impede hole flow at low biases. Although a photocurrent has been reported by Maimon and Wicks in their InAs / AlSb 1-x As x nbn device [3], a very narrow barrier of 100nm was used and the photocurrent was measured at a bias of 0.5V, where a relatively high electric field existed at the barrier/contact junction that might have allowed tunneling through the 2 hole barrier if it was present. Photocurrent measurements at smaller bias voltages on devices with thicker barriers have yet to be reported. For the case of the type II superlattice, the barriers, 1 and 2 in figure 4 can be reduced essentially to zero by choosing the correct aluminium concentration in a lattice matched Ga 1-x Al x Sb 1-y As y barrier. However, in the case of the superlattice the hole diffusion length is expected to be very small due to the narrow width of the first heavy hole miniband of the superlattice. Therefore the Quantum Efficiency (QE) may be depressed due to holes recombining in the photon absorbing layer before they can reach the electric field in the depletion region of the barrier. Rodriguez et al [7] estimate a maximum QE of 40% at 4.5µ in their nbn device under optimum conditions of minimum optical losses and complete absorption of the light. This value indicates that the QE is not depressed strongly although it is lower than expected for a device with an n-type absorbing layer. Due to the above uncertainties, it seems probable that for an efficient MWIR XBn detector, a C p B n n device or a C n B n n device based on GaSb / AlSb 1-x As x / InAs 1-y Sb y remains the most promising prospect at the moment. However a thorough investigation of the nbn device may show it to be equally good. In the next section the conditions on barrier height and width will be discussed in detail for both C p Bn and nbn devices based on an InAs 1-y Sb y photon absorbing layer. 3. BARRIER PROPERTIES In order for a barrier device to work in the diffusion limit, it is necessary to ensure that the currents due to thermionic emission over the barrier or tunneling through the barrier are negligible in comparison to the diffusion current. Figure 5 shows a schematic band profile of a C p Bn device based on GaSb / AlSb 1-x As x / InAs 1- ysb y under flat band conditions with a cut-off of ~4.3µ. The inset shows the profile of an equivalent nbn device. A value of 80meV is shown for the valence band offset, which is slightly lower than the value discussed above and given in reference [8], but the results presented below are not very sensitive to this difference. GaSb E C = 1060 AlSb As AlSb As The current density due to thermionic emission is given by the Richardson formula [9]: J TE = h * 2 4 π em kb 2 / kt B T e φ 3 (1) where φ is the energy difference between the top of the barrier and the Fermi energy in the contact layer and m * is the conduction band effective mass in the contact layer at energies close to the top of the barrier layer. Planck's constant is denoted h, and e is the charge of an electron. For a given value of the conduction band offset, E C, at the contact/barrier heterojunction, φ will be larger in a C p Bn device than in an nbn device, as can be seen in figure 5. The calculated thermionic currents for E G C= V bias InAs InAs Sb Sb Figure 5: Band profile of C p Bn device based on GaSb / AlSb 0.92 As 0.08 / InAs 0.91 Sb 0.09 under flat band conditions. Energies are shown in mev. Inset: Flat band profile for equivalent nbn device (these would be the actual profiles for very low p-doping in the barrier). The barrier for thermionic emission discussed in the text is φ. Proc. of SPIE Vol U-5

6 Current density (A/m 2 ) 1.E+04 1.E+00 1.E-04 1.E-08 1.E-12 1.E-16 1.E-20 1.E-24 1.E-28 1.E-32 1.E-36 1.E-40 CBn nbn Conduction band offset, E c (ev) Figure 6: Current due to Thermionic Emission calculated as a function of the conduction band offset between contact and barrier, E C. The broken horizontal line is the photocurrent at f/8 and a quantum efficiency of 70% for a photon absorbing layer with the bandgap given in figure 5. will we used here and it is written as: both nbn and C p Bn devices at an operating temperature of 150K are shown in figure 6 as a function of E C. A value of m * =0.2m 0 was used, which is greater than the band edge effective mass in order to allow for nonparabolicity. The results are not critically dependent on the exact mass value used since it only appears in the prefactor of equation (1). Also shown as a horizontal line in figure 6, is the photocurrent at f/8 and a cut-off wavelength of 4.3µ in the InAsSb layer. From figure 6 it can be seen that the thermionic currents are below the photocurrent for all values of E C in the C p Bn device and for E C >0.35eV in the nbn device. Since E C ~1eV and ~2eV respectively for the C p Bn and nbn devices shown in figure 5, the thermionic current is many orders of magnitude smaller than the photocurrent in both cases. Using equation (9) of ref [10], the formula for the tunnel current density through a barrier takes a particularly simple form at zero temperature. Since the temperature dependence of the tunnel current is negligible, this form J Tunn * 2 ememit η = I (2) 2 3 π h Real * where I is the transmission coefficient of the barrier and m is the emit effective mass of the carriers incident on the barrier. η is the maximum energy of the incident carriers relative to the nearest band edge. For the C p Bn device depicted in figure 5, values will be used of m*~ 0.14m 0, corresponding to electrons from the valence band of GaSb tunneling from the left in figure 5, and η ~ 0.22eV, corresponding to the overlap energy between filled valence states on the left and empty conduction states on the right. m 0 is the free electron mass. In the appendix, a formula is derived for the energy dispersion of the barrier material, k (E), in the vicinity of the bandgap. For energies, E, within the bands, the wavevector k is real. For energies in the bandgap it is imaginary and can be written k = iq. In the simplest approximation, the transmission coefficient in equation (2) can then be written: I ~exp( qz). Figure 7 shows k plotted as a function of energy for an AlSb 0.92 As 0.08 barrier. In the band overlap region of figure 5, the corresponding q-values of figure 7 are in the range < q < m -1. Taking the smaller value as the most extreme case (i.e. with the largest tunneling contribution), figure 8 shows the calculated tunnel current density as a function of barrier width, based on equation (2) * with I ~ exp( qz) and the above values of m and η. Results for * the nbn device are also shown in figure 8 using m emit =0.023 and η = 0.032eV which are appropriate to an InAsSb emitter with a doping of ~ cm -3 (in the nbn device, η is just the Fermi energy relative to emit Energy (ev) Energy (ev) Imag Wavevector ( 2π/a) Wavevector (in units of 2 /a ) E C E V Real Figure 7: Energy dispersion for energies spanning the bandgap of AlSb 0.92 As 0.08, calculated from equation (A2). The wavevector is real for energies above the conduction band edge E C, or below the valence band edge, E V, and is imaginary otherwise (a = Å and 2π / a = m -1 ). Proc. of SPIE Vol U-6

7 the conduction band edge). The lines in figure 8 for the two devices are very similar because the smallest tunneling wavevector, q, is the same in both cases. Also shown as a horizontal broken line in figure 8 is the photocurrent at f/8 and a cut-off wavelength of 4.3µ as for figure 6. It can be seen that for barrier thicknesses greater than a few hundred angstroms the tunnel current is negligible compared with the photocurrent. Even for more realistic band-profiles which consider the band bending due to doping and bias, such as those of figures 2 and 4, the huge difference between the photocurrent and the calculated tunnel current for barrier widths of >1000Å shows that in all typical cases the tunnel current will be negligible. A treatment similar to the above can also be applied to a device based on a type II superlattice. In this case the lattice matched barrier (x~0.2) is made from Ga 1-x Al x Sb 1-y As y and the barrier bandgap is then slightly greater than that of GaSb. The valence band can be made essentially continuous. The parameters for GaSb will be taken as the worst case (smallest barrier) and a bandgap of 0.25eV is assumed for the photon absorbing and contact layers in a MWIR nbn detector. On this basis and assuming a continuous valence band, the conduction band offset is E C > 0.55eV. For this range of E C, figure 6 shows that the thermionic current is at least several orders of magnitude below the photocurrent and may be considered negligible. A calculation of the tunnel current can also be carried out using the GaSb parameters for the barrier. The worst case for tunneling is when the bandgap of the photon absorbing and contact layers in an nbn detector is small, as in a LWIR nbn detector. For this case with a tunneling energy of just 0.1eV above the valence band of the barrier, the smallest tunneling wavevector is, q~ m -1. For this value of the tunneling wavevector, the tunnel current and photocurrent (at f/8 and 70% QE) are equal for a barrier width of ~700Å. Therefore for typical barrier widths of a thousand angstroms or more, the tunnel and thermionic currents in detectors based on superlattices may be considered negligible, as for detectors based on InAs 1-y Sb y alloy. Having established the principles of barrier diodes, a final step is to estimate the likely temperature range of an XBn detector. 4. TEMPERATURE OF OPERATION General expressions for the diffusion and G-R limited currents in an ideal, p + n diode [11] are given below by equations (3) and (4): diff L NCNV p EG J ~ e β Diff ND τ p0 (3) J GR Ldep NN v c 2 = e 2 τ τ (4a) p0 n0 Current Density (A/m 2 ) 1.E+08 1.E+04 1.E+00 1.E-04 1.E-08 1.E-12 1.E-16 L dep ~ L dep 1 EG 4( Vbi V) EG 2( Vbi V) β E G Barrier Thickness (A) Figure 8: Current due to tunneling calculated as a function of the barrier thickness. The broken horizontal line is the photocurrent at f/8 and a quantum efficiency of 70% for a photon absorbing layer with the bandgap given in figure 3. (4b) Proc. of SPIE Vol U-7

8 in which β ~ 1/k B T, E G and N D are the bandgap and n-doping in the photon absorbing layer, V is the forward bias, V bi is the built-in voltage of the junction, L p is the hole diffusion length and L dep is the depletion width. Equations (3) and (4) contain the standard semiconductor parameters N C, N V, which in S.I units can be written as: 21 ( ) NCV, = meh, m0 T where m e, m H are the effective masses of the electron and hole and m 0 is the free electron mass. The electron and hole G-R lifetimes are τ n0 =1/N t σ n and τ p0 =1/N t σ p, where N t is the trap density and σ n, σ p are the respective capture cross-sections. These lifetimes may take different values inside or outside the depletion region and this difference has been noted by the use of primes in equations (3) and (4). In equation (4b) L' dep is the active portion of the depletion region where the conduction band bending relative to the n-side quasi Fermi level and the valence band bending relative to the p-side quasi Fermi level are each greater than half the bandgap. The expression in equation (4b) is an approximation based on the assumption that the G-R trap energy is at mid-gap which is sufficiently accurate for the purposes of the current model. The value of the crossover temperature, T 0, between G-R and diffusion limited behaviour in a standard p + n diode can be estimated using equations (3) and (4), by solving the equation: J GR (T 0 ) = J Diff (T 0 ). This leads to an equation of the form: E /2k T 0 p0 p0 n0 where τ, τ are the G-R lifetimes in the active portion of the depletion region and p0 n0 1.5 G B 0 T e τ τ τ τ is the hole G-R lifetime in the photon absorbing layer. The G-R lifetimes in n-type InSb were shown to vary p0 inversely with the free carrier concentration, with the electron G-R lifetime being much smaller than the hole G-R lifetime due to the donor like character of the G-R centre [12]. The hole lifetime in the photon absorbing layer, τ, is p then equal to the hole G-R lifetime, τ, and τ << τ, τ < τ. These properties will be assumed to be the case p0 n0 p0 p0 p0 below in InAs 1-y Sb y with 0 < y < 1. Assuming τ p0τ n0 τ p0 ~300nS, and taking fairly typical values for the other parameters: DP = Lpτ = 30 cm 2 /s (hole diffusion coefficient), ε p s =15 (semiconductor dielectric constant), ev bi = E G 0.03eV and V = - 0.1V, the solutions for T 0 at two different carrier concentrations are shown in figure 9 as a function of the semiconductor bandgap. The dependence of the effective masses on bandgap has been ignored since it has a negligible influence and values of m e /m 0 =0.023 and m h /m 0 =0.4 have been used. Reducing the lifetime parameter, τ τ τ, by a factor of 10 only increases the value of T 0 by about 10% over the whole bandgap range, so the p0 n0 p uncertainty over the value of this parameter is not too critical. In figure 9 the theoretical estimate of T 0 is compared against the experimental results reported for In 0.99 Al 0.01 Sb in ref. [13] (solid circle), for InAs 1-y Sb y alloys with y ~ in refs. [14] and [15] (solid squares), and for InAs in ref [6] (open diamond). The agreement for the solid symbols is seen to be quite reasonable, justifying the estimate used for the lifetime parameter. In the case of InAs, the activation energy obtained in ref [6] for the diffusion current was 0.384eV which is about 55meV lower than the accepted zero temperature extrapolation of the variation of the bandgap of InAs with temperature [4]. It is possible that stress, or some other cause such as damage due to the Be-ion implantation, result in a reduction of the effective bandgap. If this is the case, the open diamond in figure 9 can be shifted to the left by ~55meV which then results in quite good agreement with the theoretical estimate of T 0. Alternatively, the G-R centres in InAs may behave differently than in InSb and have a larger value of the lifetime parameter. This might also account for the experimental value of T 0 lying below the value predicted in figure 9. T0(K) 50 N=2e16 N=2e Bandgap (ev) Figure 9: Calculated variation of the crossover temperature, T 0, between G-R and diffusion limited behaviour, in a p + n diode as a function of the bandgap, for two different donor concentrations (shown in the inset in units of cm -3 ). The parameters used in the calculation are given in the text. Experimental results are shown as a solid circle (ref. 13), solid squares (refs. 14 and 15), and an open diamond (ref 6). Proc. of SPIE Vol U-8

9 Temperature (K) T 0 _ T OP 1.E+14 1.E+15 1.E+16 1.E+17 N D (cm -3 ) Figure 10: Comparison of the calculated crossover temperature, T 0, in a conventional p + n diode and the operating temperature T OP, in an XBn detector, both having a photon absorbing layer of InAs 0.91 Sb 0.09 with a cut-off wavelength of 4.2µ (bandgap of 0.295eV), as a function of the donor concentration. The parameters used in the calculation are given in the text. Based on equations (3) and (4) an estimation can be made of the performance of a MWIR XBn detector made from InAs 0.91 Sb 0.09 alloy lattice matched to a GaSb substrate. As mentioned above, at ~150K the cut-off wavelength is 4.2µ. An f-number of f/3 and a quantum efficiency of 70% will be assumed. The operating temperature, T OP, can be estimated from equation (3), based on the required dark current in the detector, J XBn. This current will be taken to be 10% of the photocurrent. It represents a typical value based on the requirement that a detector array should have a spatial noise that is less than or equal to the temporal noise, and is a function of the raw non-uniformity of the pixels and the stability of the cooler. On this basis the operating temperature is then given by: T E k en N D C V P OP = G Bln NDJXBn τ p0 (5) Figure 10 compares the T 0 value calculated in figure 9 for a cut-off wavelength of 4.2µ (bandgap =0.295eV) with the value of T OP estimated from equation (5), both as a function of the donor concentration in the photon absorbing layer. In figure 10 the values of the parameters used are the same as those given above and in addition, the hole lifetime has been taken to be τ p0 ~500nS [15]. It should be noted that for high doping levels in the range N D ~ cm -3 both the hole diffusion coefficient and the hole lifetime should vary as N D -1 since the dominant scattering mechanism will be ionized impurity scattering and an inverse dependence of the lifetime on doping was demonstrated in ref. [12]. Thus the square root in equation (5) can be taken to be roughly constant. Since it is also included inside the logarithm term any residual variations, such as its variation with temperature, should have only a weak effect and will be ignored. From figure 10 a number of deductions about a MWIR XBn detector based on InAs 0.91 Sb 0.09 can be made. First, since the operating temperature is smaller than the crossover temperature, T 0, the device will exhibit a higher operating temperature than a standard diode detector, as depicted by the horizontal arrow in figure 1. Second, it should be possible to achieve an operating temperature of ~150K for doping in the photon absorbing layer in the region of cm -3. It may even be possible to increase the operating temperature further by increasing the doping beyond cm -3, since in an XBn detector increasing the doping in the photon absorbing layer has no effect on the thickness of the depletion region whose thickness is determined essentially by the barrier width. To increase the doping above cm -3 in a standard diode detector would rapidly lead to Zener breakdown since the depletion width reduces with doping. At very high doping the performance of the XBn detector will eventually be limited by the reduction of the hole diffusion length and by the increase of the effective bandgap for photon absorption due to the Moss Burstein effect [16], which will start to become significant for doping levels above about cm -3 (where a two band k.p model can be used to show that the effective bandgap is increased by about 20meV). Finally the advantage of XBn devices for reducing the detector noise at low temperatures is estimated. This is depicted by the vertical arrow in figure 1. From equations (3) and (4) it follows that the ratio of GR current to diffusion current is: JGR 1 N L D Dep τ p0 = (6) J 2 n D τ p0τ n 0 Diff i p Proc. of SPIE Vol U-9

10 This is equal to the ratio of dark currents in a standard and an XBn detector. Using the parameters given above, the ratio of currents at 77K has a typical value of , depending on the doping level and the exact value of the lifetime parameter. The main contribution comes from the ratio N D /n i which is very large at low temperatures. 5. SUMMARY AND CONCLUSIONS The concept of the XBn barrier detector has been presented. The detector behaves optically like a narrow bandgap detector but electrically like a wide bandgap device. The G-R contribution to the dark current is essentially totally suppressed by ensuring that the bands in the narrow bandgap photon absorbing layer are flat or accumulated and that all depletion is confined to a wide bandgap barrier layer and in some cases also to a negatively biased contact layer. A number of different architectures have been discussed. In these cases, "X" stands for C p or C n, if the material used in the Contact or C-layer has a different bandgap to that used in the n-type photon absorbing layer. The subscript denotes the Contact doping. "X" stands for p or n if the same material is used in both the "x"-type contact and n-type photon absorbing layers. Materials with suitable band alignments for XBn detectors have been demonstrated in which InAs 1-y Sb y alloy or a type II InAs/GaSb superlattice is used for the photon absorbing layer. The former is appropriate to the MWIR wavelength region only and the latter to both the MWIR and LWIR wavelength regions. In order to avoid depletion in the narrow bandgap photon absorbing layer the barrier should be doped n-type. Although not discussed here, the n-doping can also be concentrated in a delta-doping layer at the junction between the photon absorbing layer and the barrier layer if a p- type barrier is used [1]. Without delta doping, the use of a p-type barrier will cause depletion into the photon absorbing layer. Unless the photon absorbing layer is doped very high and the barrier layer is very thin or has a very low doping level, this depletion may be severe enough to cause a significant G-R current. A thick barrier is preferable for low detector capacitance, while it is not always possible to achieve a low and stable level of doping in the barrier if there is a high background acceptor level. The two important requirements for XBn devices, namely negligible thermionic and tunnel currents, have been justified for typical barrier parameters in devices based both on InAs 1-y Sb y alloy and type II InAs/GaSb superlattice materials. Significant advantages of XBn detectors are that they can offer a lower dark current or a higher operating temperature than a standard detector, provided that the crossover temperature, T 0, between G-R and diffusion limited behaviour in the standard detector is sufficiently high. Since the dark current in the XBn detector is diffusion limited it should also be much less sensitive to reverse bias, which is an important feature for reducing spatial noise in array detectors. The crossover temperature, T 0, and the operating temperature, T OP, have been estimated for MWIR standard and XBn detectors with f/3 optics based on an InAs 0.91 Sb 0.09 photon absorbing layer with a cut off wavelength of 4.2µ. An XBn operating temperature of ~ 150K should be feasible. Since this operating temperature is less than the crossover temperature, the XBn detector will operate at a higher temperature than a standard detector made from the same absorbing material. The C n B n n architecture offers a very simple structure for a two colour device, particularly if the narrow bandgap layers are based on a type II superlattice. Another important advantage of the XBn device architecture is that processing and passivation should be substantially easier than in a conventional diode made from the same photon absorbing material, especially in array detectors which contain many thousands of diodes and a reliable and uniform process is critical. The barrier can be used as an etch stop layer and its wide bandgap provides a natural way to isolate the individual diodes in an array. Passivation, which is still a substantial problem for LWIR devices should be significantly easier since it will be carried out on the wide bandgap material of the barrier instead of the narrow bandgap photon absorbing material. APPENDIX: CALCULATION OF THE BARRIER TRANSMISSION COEFFICIENT The transmission coefficient for tunneling through the barrier in figure 5, I, may be derived from the two band k.p Hamiltonian of the barrier material [17, 18]. The Hamiltonian may be written: Proc. of SPIE Vol U-10

11 ( 1 ) ( 2 ) H = I E h 2m z + I E h 2m z + iσ 2 3 P z (A1) + C V y where z is the growth direction, E C and E V are the energies of the conduction and valence band edges, I ( ) = I ± σ 2, I is the unit matrix and ± z σ z, σ y are Pauli spin matrices. The sign and phase of the off-diagonal elements depends on the definition of the s and 3/2, 1/2 basis states used and so may differ from those in similar Hamiltonians quoted by other authors. The interband coupling parameter P, is related to the k.p energy E P, by 2 2 the formula: E = 2m P h. The effective masses m P 0 1 and m 2 are given in terms of the band edge electron mass m C and the valence band Luttinger parameters, γ 1 and γ 2 as follows: m m = m m 2E 3E and ( γ γ ) C P G m m = E 3E. Plane wave solutions for the Hamiltonian exist with wavevectors given by [18]: P G 2 m mm ( E E ) ( E E ) 2E ( E E ) ( E E ) 2E 4( E E )( E E ) V C P V C P C V k± = m m m m m 3 ± + + h m m m m 3 mm m (A2) Solutions of equation (A2) with the positive sign are close to the Brillouin zone boundary, and for the cases considered here where the product mm 1 2 is negative, they are imaginary and so decay extremely fast. They have negligible influence and for the present purposes may be ignored. Solutions of equation (A2) with the negative sign are imaginary in the bandgap region and real outside and these represent the real dispersions of the conduction and valence states. In the bandgap of the barrier, we write k 2 = q 2 and the transmission coefficient is then given in the simplest approximation by I ~exp( qz). This is based on the assumption that the order of magnitude of the transmission coefficient is determined by the exponential term and that the prefactor will be of order unity. The exact solution for the transmission coefficient can be determined by transfer matrix techniques and is quite complicated [18]. For the present purposes the simpler form should be sufficient. The following parameter values have been used to calculate the dispersion in figure 7: E P =18.9eV, E G =2.3 ev, m C /m 0 =0.14, γ 1 =5.07 and γ 2 =1.16. These values are appropriate to an AlSb 0.92 As 0.08 barrier and are based on weighted averages of the data given in [8] for AlSb and AlAs. Note that if the mass terms of equation (A1) are ignored, as in ref [17], this results in an overestimation of q by about 15%. The error due to ignoring the mass terms reduces considerably for barriers with a smaller bandgap such as GaSb. ACKNOWLEDGEMENTS The author would like to acknowledge useful discussions with Dr, Igor Szafranek, Dr. Eliezer Weiss and Dr. Yael Oiknine-Schlesinger. REFERENCES 1 P.C. Klipstein, "Depletionless Photodiode with Suppressed Dark Current " Int. Patent Publication no: WO 2005/ A1 (13 January 2005) 2 Anthony White, "Infra Red Detectors" USA Patent 4,679,063 (7 July 1987) 3 S. Maimon and G. W. Wicks, Appl. Phys. Lett. 89, (2006) 4 M. A. Marciniak, R. L. Hengehold, Y. K. Yeo, and G. W. Turner, J. Appl. Phys. 84, 480 (1998) 5 A. Khoshakhlagh, J. B. Rodriguez, E. Plis, G.D Bishop, Y.D. Sharma, H.S. Kim, L.R. Dawson and S. Krishna, Appl. Phys. Lett. 91, (2007) Proc. of SPIE Vol U-11

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