Method of optimizing the EMI shielding and infrared transparency of GaAs IR windows

Abstract

A method of manufacturing a structurally competent, EMI-shielded IR window includes using a mathematical model that combines the Sotoodeh and Nag models to determine an optimal thickness and dopant concentration of a doped layer of GaAs or GaP. A slab of GaAs or GaP is prepared, and a doped layer of the same material having the optimal thickness and dopant concentration is applied thereto. In embodiments, the doped layer is applied by an HVPE method such as LP-HVPE, which can also provide enhanced GaAs transparency near 1 micron. The Drude model can be applied to assist in selecting an anti-reflective coating. If the model predicts that the requirements of an application cannot be met by a doped layer alone, a doped layer can be applied that exceeds the required IR transparency, and a metallic grid can be applied to improve the EMI shielding, thereby satisfying the requirements.

Claims

1. A method of designing and manufacturing an EMI shielded infrared (IR) window suitable for a specified application having specified size, transparency, and EMI shielding requirements, the method comprising: preparing a slab of GaAs or GaP according to the size requirement of the specified application, the slab having sufficient thickness to meet a structural competence requirement of the specified application; selecting a plurality of candidate parameter combinations comprising combinations of candidate dopant concentrations and candidate layer thicknesses for a doped conductive layer to be applied to the slab, the doped layer being a doped layer of GaAs if the slab is a GaAs slab, the doped layer being a doped layer of GaP if the slab is a GaP slab; applying a model to the candidate parameter combinations, thereby for each of the candidate parameter combinations estimating an IR absorption and a sheet conductivity of the doped conductive layer, wherein applying the model comprises: applying an empirical low field mobility model according to Sotoodeh, thereby estimating a carrier mobility of the doped conductive layer; calculating an estimated sheet resistance of the doped conductive layer according to the candidate parameters and the estimated carrier mobility; and applying a quantum mechanical defect scattering model of free carrier absorption based upon a relationship taught by Nag, thereby estimating the IR absorption of the doped conductive layer according to the candidate layer thickness and the estimated sheet resistance of the doped conductive layer; repeating the steps of selecting candidate parameters and applying the model thereto until an optimal combination of layer thickness and dopant concentration are determined; and if the model predicts that applying the doped semiconductor layer having the determined optimal combination of layer thickness and dopant concentration will meet the transparency and EMI shielding requirements of the specified application, applying the doped conductive layer to the slab according to the determined optimal combination of layer thickness and dopant concentration.

2. The method of claim 1, wherein the doped conductive layer is applied to the slab by a vacuum deposition process.

3. The method of claim 1, wherein the doped conductive layer is applied to the slab by hydride vapor phase epitaxy (HVPE).

4. The method of claim 3, wherein the doped conductive layer is applied to the slab by low pressure HVPE (LP-HVPE).

5. The method of claim 1, further comprising applying an anti-reflective (AR) coating onto the doped conductive layer.

6. The method of claim 5, wherein the method further comprises: applying a Drude model to estimate a real part of an index of refraction of the doped conductive layer; and selecting the AR coating at least in part according to the estimated real part of the index of refraction of the doped conductive layer.

7. The method of claim 1, wherein the slab is a GaAs slab, and preparing the slab includes growing the GaAs slab using HPVE.

8. The method of claim 7, wherein preparing the slab includes growing the GaAs slab using LP-HPVE.

9. The method of claim 7, wherein the doped conductive layer is applied to the slab as part of the HVPE process that is used to grow the slab.

10. The method of claim 1, wherein the method further comprises, if the model predicts that applying the doped semiconductor layer having the determined optimal combination of layer thickness and dopant concentration will not meet the transparency and EMI shielding requirements of the specified application: applying the doped conductive layer to the slab with a combination of layer thickness and dopant concentration that exceeds the transparency requirement of the application; and applying a metallic grid to the slab having a thickness and grid spacing sufficient to cause the combined metallic grid and doped semiconductor EMI shielding to meet both of the transparency and EMI shielding requirements of the specified application.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a graph presenting a comparison of measured values of carrier mobility for doped GaAs as a function of dopant concentration with predictions of the Sotoodeh model;

(2) FIG. 2 is a graph presenting a comparison of measured values of absorption for doped GaAs as a function of layer thickness with predictions of the Drude and Nag models for several values of sheet resistance;

(3) FIG. 3 is a graph comparing measured values of doped GaAs layers with predictions of the model included in the present disclosure, where sheet resistance is represented on the horizontal axis, layer thickness is represented on the vertical axis, and the percent absorption at 8 microns wavelength is indicated by the curved lines that separate approximate bands of absorption;

(4) FIG. 4 is a flow diagram illustrating an embodiment of the present disclosure; and

(5) FIG. 5 is a graph comparing the very high spectral transmission of GaAs grown by HVPE compared to the much lower transmission of typical commercial melt-grown GaAs, which exhibits high losses near 1 micron.

DETAILED DESCRIPTION

(6) The present disclosure is a method of manufacturing an IR window that is transparent over a wide range of IR wavelengths, and to which EMI-shielding is applied with minimal optical artifacts and loss of transparency.

(7) More specifically, the present disclosure is a method of manufacturing GaAs and GaP windows to which a doped layer of the same material is applied for EMI shielding.

(8) As noted above, implementing a GaAs or GaP IR window that is EMI shielded by applying a doped semiconductor layer faces at least two obstacles. First, because of the trade-off between IR transparency and EMI shielding, it is necessary to determine whether a doped semiconductor layer applied to a GaAs or GaP slab will be able to satisfy both the transparency and the EMI shielding requirements of a given application. Second, due to the complex dependence of the sheet conductivity on both the dopant level and the layer thickness, it is necessary to determine the optimal combination of these two parameters for a given application.

(9) The present disclosure overcomes both of these obstacles by accurately modeling the sheet conductivity and the IR transparency of a doped GaAs or GaP conductive layer as a function of the layer thickness and dopant level. By applying the model to a range of candidate layer thickness and dopant concentration values, it is possible to quickly determine the optimal combination of layer thickness and dopant concentration for a given application, and to determine whether these optimal thickness and dopant values will meet the requirements of the application. The desired window is then formed by applying a conductive layer, as determined using the model, to a GaAs or GaP slab, for example using an epitaxial method such as molecular beam epitaxy (MBE), metal-organic vapor phase epitaxy (MOVPE), metallo-organic chemical vapor deposition (MOCVD, organo-metallic vapor phase epitaxy (OMVPE), high vapor phase epitaxy (HVPE), or another vacuum deposition method.

(10) The disclosed model begins by applying the low field mobility model as taught by Sotoodeh et. al. (M. Sotoodeh, A. H. Khalid, and A. A. Rezazadeh, Journal of Applied Physics 87, 2890 (2000); doi:10.1063/1.372274) to estimate the carrier mobility that will result from a given dopant concentration.

(11) The empirical model estimates the low-field mobility ULF as a function of doping concentration N and temperature T according to the following empirical relationship:

(12) ${}_{LF}\left(N,T\right)={}_{\min }+\frac{{}_{\max }\left(300K\right){\left(300K/T\right)}^{{}_1}-{}_{\min }}{1+{\left(\frac{N}{N_{ref}\left(300K\right){\left(T/300K\right)}^{{}_2}}\right)}^{}}$

(13) Where .sub.min, .sub.max(300 K), N.sub.ref(300 K), , .sub.1, and .sub.2 are all fitted parameters.

(14) According to the model, .sub.max(T) is the low-field mobility at very low doping concentrations, .sub.min is the low-field mobility at very high doping levels, and N.sub.ref(T) is the doing concentration at which the mobility reduces to almost half of its maximum value at low doping.

(15) As reported by Sotoodeh et. al., for electrons in GaAs, the fitted parameters for GaAs are .sub.min=500 cm.sup.2/V s, .sub.max(300 K)=9400 cm.sup.2/V s, N.sub.ref (300 K)=6.010.sup.16 cm.sup.3, =0.394, .sub.1=2.1, and .sub.2=3.0.

(16) For holes in GaAs, the fitted parameters for GaAs are .sub.min=20 cm.sup.2/V s, .sub.max(300 K)=491.5 cm.sup.2/V s, N.sub.ref(300 K)=1.4810.sup.17 cm.sup.3, =0.38, .sub.1=2.2, and .sub.2=3.0.

(17) For electrons in GaP, the fitted parameters for GaAs are .sub.min=10 cm.sup.2/V s, .sub.max(300 K)=152 cm.sup.2/V s, N.sub.ref(300 K)=4.410.sup.18 cm.sup.3, =0.8, .sub.1=1.6, and .sub.2=0.71.

(18) For holes in GaP, the fitted parameters for GaAs are .sub.min=10 cm.sup.2/V s, .sub.max(300 K)=147 cm.sup.2/V s, N.sub.ref(300 K)=1.010.sup.18 cm.sup.3, =0.85, .sub.1=1.98, and .sub.2=0.0.

(19) With reference to FIG. 1, the present inventors verified the accuracy of the Sotoodeh model by comparing the predictions 100 of the model (using the Sotoodeh fitted parameters given above) with currently measured data 102 for GaAs. For the measured results 102, the thickness of the sheet was measured to within 3% accuracy. It can be seen in the figure that that the least-squares fit 104 to the data agrees well with the model prediction 100.

(20) Based on the predicted carrier mobility, the sheet resistance is then calculated according to R.sub.S=1/tqn, where Rs is the sheet resistance, t is the thickness of the sheet, q is the electron charge, is the carrier mobility, and n is the carrier concentration.

(21) The optical absorption of the doped layer is then predicted as a function of the IR wavelength and the sheet resistance using a quantum mechanical defect scattering model of free carrier absorption based upon a relationship taught by Nag (Nag, 1980) [B. R. Nag Electron Transport in Compound Semiconductors Springer-Verlag Berlin Heidleberg New York 1980, which is incorporated herein by reference for all purposes], especially chapter 9, table page 276. The Nag model provides expressions for five different scattering mechanisms by which IR photons are scattered by phonons or ionized impurities in a semiconductor. The scattering mechanisms and associated expressions for the absorption coefficient are as follows:

(22) Deformation Potential Acoustic Phonon:

(23) $/n=\frac{2\sqrt{2}{e}^2{E_1^2\left(m*k_{B}T\right)}^{1/2}\sinh \left(/2k_{B}T\right)K_2\left(/2k_{B}T\right)}{3{}^{3/2}{}_0{}^3{S}^{2}c{n}_r}$
Piezoelectric Acoustic Phonon:

(24) $/n=\frac{\sqrt{2}{e}^4\left(h_{pz}^2/s^2\right){\left(k_{B}T\right)}^{1/2}\sin \left(/2k_{B}T\right)K_1\left(/2k_{B}T\right)}{3{}^{3/2}{}_0{\mathrm{cn}}_r{m}^{*1/2}{}^2{}^2}$
Ionized Impurity (Neglecting Screening):

(25) $/n=\frac{N_j{Z}^2{e}^6\sinh \left(/2k_{B}T\right)K_0\left(/2k_{B}T\right)}{3\sqrt{2}{}^{3/2}{}^2{}_{0}c{n}_r{m}^{*3/2}{{}^3\left(k_{B}T\right)}^{1/2}}$
Nonpolar Optic Phonon:

(26) $/n=\frac{2\sqrt{2}{e}^2{D}_0^2{m^{*1/2}\left(k_{B}T\right)}^{3/2}{F}_{op}\left(z,z_{+},z_{-}\right)}{3{}^{3/2}{}^{4}c{n}_r{}_0{}^3}$$\mathrm{Where}{F}_{op}\left(z,z_{+},z_{-}\right)=\left[\sinh \left(z_{+}-z\right)z_{+}^2{K}_2\left(z_{+}\right)+\sinh \left(z_{-}+z\right)z_{-}^2{K}_2\left(.Math.z_{-}.Math.\right)\right]/\sinh \left(z\right)$$\mathrm{And}z=\left({}_0/2k_{B}T\right);z_{+}=\frac{\left({}_0+\right)}{2k_{B}T};z_{-}=\frac{\left(-{}_0\right)}{2k_{B}T}$
Polar Optic Phonon:

(27) $/n=\frac{\left(K^{-1}-K_s^{-1}\right)\sqrt{2}{e}^4{{}_l\left(k_{B}T\right)}^1/2F_{pop}\left(z,z_{+},z_{-}\right)}{4{}_{0}3{}^{1/2}{}_0{}^3{}^{3}c{n}_r{m}^{*1/2}}$$\mathrm{Where}{F}_{pop}\left(z,z_{+},z_{-}\right)=\left[\sinh \left(z_{+}-z\right)z_{+}{K}_1\left(z_{+}\right)+\sinh \left(z_{-}+z\right)K_1\left(.Math.z_{-}.Math.\right)\right]z_{-}/\sinh \left(z\right)$$\mathrm{And}z=\left({}_l/2k_{B}T\right);z_{+}=\frac{\left({}_l+\right)}{2k_{B}T};z_{-}=\frac{\left(-{}_l\right)}{2k_{B}T}$

(28) Variables in these equations are as follows: absorption coefficient, defined as the ratio of the power absorbed per unit length of the sample to the incident power m*effective mass of the carriers (in this case electrons) ncarrier densitymeasured for each sample after fabrication, or inferred from growth parameters E.sub.1acoustic phonon deformation potentialtaken from literature relative permittivitytaken from literature .sub.0permittivity of free spaceknown physical constant mass densitymeasured or known a priori Sspeed of sound in mediumtaken from literature Cspeed of light in vacuumknown physical constant n.sub.rrefractive indexmeasured or taken from literature h.sub.pzpiezo electric constanttaken from literature K.sub.1, K.sub.2modified Bessel functions of the second kind first order and second order respectivelyknown mathematical functions Kdielectric constantmeasured value taken from literature K.sub.sstatic dielectric constantmeasured value taken from literature N.sub.jcharged impurity number densitymeasured from growth process calibration Zcharge of impurityknown value D.sub.0nonpolar optical phonon deformation potentialtaken from literature .sub.0optical phonon frequencymeasured value taken from literature

(29) While the complete Nag model is presented above, the effects of the deformation potential acoustic phonon absorption and piezoelectric acoustic phonon absorption are expected to be negligible for GaAs and GaP. Because GaAs and GaP are both polar, it is expected that the polar optic phonon absorption will significant in both cases.

(30) It is notable that many different models exist that attempt to predict carrier mobility, sheet resistance, and resulting IR absorption. In many cases, these models either require that specific parameters of the semiconductor be carefully measured, or simply fail to agree closely with measured results. While the models that are included in the present disclosure also require accurate measurements of several material parameters, as noted above, most of these can be found readily in published literature and need not be measured specifically for input into the model.

(31) With reference to FIG. 2, the present inventors initially attempted to apply the Drude model 200 to predict IR absorption as a function of sheet resistance. The Drude model describes electrons as moving freely about a material until they are scattered by the lattice or by a defect. The probability of scattering is the same for all electrons and independent of the scattering mechanism and electron energy.

(32) To fully describe a material in the Drude model, the characteristic scattering time , the free carrier concentration N, the effective mass m*, and the high frequency dielectric constant (contribution from the valence electrons) are required. and m* are well established in literature. N and are determined from Hall effect measurements by relating =m*/q to the mobility , with the electron charge q. The Drude model then gives the dc conductivity .sub.0=N q , and the relative material permittivity:

(33) $={}_{}\left(\right)+\frac{i}{{}_0}\frac{{}_0}{1-i{m}^{*}/q}$

(34) The complex index of refraction according to the Drude model is given by =n+ik={square root over ()}, where .sub.0 is the permittivity of free space. In the longwave/low frequency limit, the absorption coefficient

(35) $=\frac{4k}{}$
with wavelength , depends on material properties such as

(36) $\frac{N{}^2}{m^{*2}}.$

(37) As can be seen in FIG. 2, however, the predictions of the Drude model 200 do not fit well with measured data 202. Instead, it can be seen in the FIG. that the measured absorption 202 as a function of layer thickness and at a wavelength of 8 microns fit well with the Nag model 100 of the present disclosure for sheet resistances of 2.5 /sq, 5 /sq, and 10 /sq.

(38) FIG. 3 illustrates a range of parameters that are accessible according to the present disclosure. Note, however, that the present disclosure is not limited to only the parameter ranges presented in the figure. The figure is essentially three-dimensional, with the sheet resistance presented on the horizontal axis, the layer thickness on the vertical axis, and the percent absorption at 8 microns wavelength indicated by the curved lines that separate approximate bands 300 of 0.1%, 0.5%, 1%, 2%, 5%, 10%, 20% and 50% absorption. Obviously, the absorption will vary continuously across the graph, with the indicated percentages being approximate averages for the spaces 300 between the curved lines. The stars 202 in the figure represent actual measured values at 8 microns.

(39) With reference to FIG. 4, according to the present disclosure a plurality of candidate combinations of dopant concentration values and layer thickness values are selected 400, and the model as presented herein is applied thereto 402. Depending on the model predictions for the initially considered combinations of parameter values, additional candidate combinations can be selected 400 and the model applied thereto 402. This process is repeated until an optimal parameter combination is determined 404 according to the requirements of a specific application.

(40) If the model indicates that the requirements of an application will be met by the optimal combination of parameters 406, then the window slab is manufactured and the optimal conductive layer applied thereto 408 as specified by the model.

(41) If, however, the model indicates that the requirements of the application will not be satisfied 406 even for the optimal choice of layer thickness and dopant concentration, then, in embodiments, a window is constructed by applying a doped layer to a slab for which the optical transparency exceeds the transparency requirement by some margin, even if the EMI shielding is not sufficient. In addition, a metallic grid layer is applied to the window to improve its EMI shielding 410. While the metallic grid results in some loss of transparency, sufficient transparency is maintained due to the margin provided by the doped layer, thereby meeting all requirements of the application.

(42) Due to the inverse dependence of skin depth on conductivity, the EMI shielding that is provided by a doped semiconductor layer will be strongest at the higher end of the EMI frequency range. In contrast, for a metallic grid having a given grid spacing, the EMI shielding will be strongest at the lower end of the EMI frequency range. Accordingly, for embodiments that include a metallic grid layer in addition to the doped semiconductor layer 410, the metallic grid will be significantly thinner and more widely spaced than would be required if the EMI shielding depended entirely on the metallic grid. As a result, any loss of transparency and optical artifacts introduced by the metallic grid are minimized.

(43) Embodiments further include applying an anti-reflective (AR) coating to the window on top of the conductive coating. In some of these embodiments, the Drude conductivity-based model is used to estimate the real part of the index of refraction of the doped GaAs or GaP layer, thereby providing a starting point for selecting a compatible AR coating material. While the Drude model was found to be a poor approximation of the IR absorption vs. sheet resistance for a conductive layer, the predictions according to the Drude model of the real part of the index of refraction of the doped layer corresponded well enough with measured values to provide a helpful starting point for determining an optimal AR coating material.

(44) In embodiments, for GaAs windows, the single crystal GaAs slab is grown using hydride vapor phase epitaxy (HVPE) rather than by vertical melt, thereby significantly improving the transparency of the GaAs, especially at wavelengths near 1 micron. In embodiments, the GaAs slab is grown using low-pressure HVPE (LP-HVPE) to obtain a maximum growth rate that is comparable to the growth rates of GaAs boules.

(45) With reference to FIG. 5, HVPE-grown GaAs windows 502 typically exhibit significantly lower absorption than melt-grown commercial off-the-shelf (COTS) crystals 500. In part, this is because GaAs grown using HVPE exhibits a greatly reduced concentration of impurities due to the use of ultra-high purity gas phase precursors. More importantly, native defects are reduced because the reduced growth temperatures of HVPE limit the solubility of excess arsenic that manifests itself as arsenic-on-gallium anti-sites. It is these so-called EL2 defects that tend to cause high absorption losses in conventional, melt-grown GaAs windows at wavelengths near one micron. In the illustrated example, a wafer approximately 1 mm thick grown vertically from melt and sliced from a boule transmits less than 35% at one micron, whereas a layer of similar doping and thickness grown by LP-HVPE transmits more than 50% at the same wavelength.

(46) The foregoing description of the embodiments of the invention has been presented for the purposes of illustration and description. Each and every page of this submission, and all contents thereon, however characterized, identified, or numbered, is considered a substantive part of this application for all purposes, irrespective of form or placement within the application. This specification is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of this disclosure.

(47) Although the present application is shown in a limited number of forms, the scope of the invention is not limited to just these forms, but is amenable to various changes and modifications. The disclosure presented herein does not explicitly disclose all possible combinations of features that fall within the scope of the invention. The features disclosed herein for the various embodiments can generally be interchanged and combined into any combinations that are not self-contradictory without departing from the scope of the invention. In particular, the limitations presented in dependent claims below can be combined with their corresponding independent claims in any number and in any order without departing from the scope of this disclosure, unless the dependent claims are logically incompatible with each other.