Physical based Schottky barrier diode modeling for THz applications

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1 Downloaded from orbit.dtu.dk on: Jan 6, 18 Physical based Schottky barrier diode modeling THz alications Yan, Lei; Krozer, iktor; Michaelsen, Rasmus Schandorh; Durhuus, Torsten; Johansen, Tom Keinicke Published in: Proceedings of the 13 IEEE International Wireless Symosium Link to article, DOI: 1.119/IEEE-IWS Publication date: 13 Document ersion Publisher's PDF, also known as ersion of record Link back to DTU Orbit Citation (APA): Yan, L., Krozer,., Michaelsen, R. S., Durhuus, T., & Johansen, T. K. (13). Physical based Schottky barrier diode modeling THz alications. In Proceedings of the 13 IEEE International Wireless Symosium IEEE. DOI: 1.119/IEEE-IWS General rights Coyright and moral rights the ublications made accessible in the ublic ortal are retained by the authors and/or other coyright owners and it is a condition of accessing ublications that users recognise and abide by the legal requirements associated with these rights. Users may download and rint one coy of any ublication from the ublic ortal the urose of rivate study or research. You may not further distribute the material or use it any rofit-making activity or commercial gain You may freely distribute the URL identifying the ublication in the ublic ortal If you believe that this document breaches coyright lease contact us roviding details, and we will remove access to the work immediately and investigate your claim.

2 Physical based Schottky barrier diode modeling For THz alications L. Yan 1,. Krozer, R. Michaelsen 1, T. Durhuus, T.K. Johansen 1 1 Deartment of Electrical Engineering, Technical University of Denmark, Kgs. lyngby, 8, Denmark Goethe University of Frankfurt am Main, Frankfurt an Main, 6349, Germany krozer@hysik.uni-frankfurt.de Abstract In this work, a hysical Schottky barrier diode model is resented. The model is based on hysical arameters such as anode area, Ohmic contact area, doing rofile from taxial (EPI) and substrate (SUB) layers, layer thicknesses, barrier height, secific contact resistance, and device temerature. The effects of barrier height lowering, nonlinear resistance from the EPI layer, and hot electron noise are all included accurate characterization of the Schottky diode. To verify the diode model, measured I- and C- characteristics are comared with the simulation results. Due to the lack of measurement data noise behaviors, simulated noise temerature is comared with the exerimental data found from the oen literature. Index Terms Schottky barrier diode, hysical based model, barrier height lowering, hot-electron noise. II. FEATURES OF THE MODEL Fig. 1 shows a cross-sectional view of a lanar Schottky-barrier diode. The metal-semiconductor contact is med on to of a lightly doed EPI layer. A highly doed SUB layer with low resistance is used to m the Ohmic contact. Modulation on deletion region lays a key role mixer and multilier oerations. Corresonding to its vertical structure, Fig. 1 also shows an equivalent circuit model of the diode. It includes two arts: 1) a unction which is reresented by a arallel network with nonlinear conductance and caacitance ) series imedance which reresents the contributions from the un-deleted EPI layer, SUB layer, and Ohmic contact. I. INTRODUCTION Recent advances in monolithic integrated membrane technology are making Schottky diode based mixer and multilier circuits ever more attractive [1]. Cometitive mixers use Suerconductor-Insulator-Suerconductor tunnel unctions oerating u to 1 THz and Hot Electron Bolometers oerating from 1 to 7 THz. However, both tyes of mixers must oerate at temerature below 4 K if sensitivity is stressed []. For commercial alications where cryogenic oeration is not ossible due to elevated sizes and costs, Schottky diode based technology oerating at room temerature is a good candidate. This work is a art of an eft to establish an accurate circuit model of a Schottky diode based on its hysical arameters. The advantage of using a hysical diode model is that the non-ideal features such as electron velocity saturation due to high electric field, barrier height lowering due to image ce, and excessive noise due to hot-electrons can be included. Furthermore, with a hysical device model, circuit designers can see the influence on the circuit ermance due to the different fabrication arameters examle anode area, doing rofile, and layer thickness. Those arameters are often used to otimize the Schottky diode characteristics some secific alications such as mixers or multiliers [3]. Fig. 1. The vertical structure of a Schottky barrier diode and the corresonding circuit model. The current transort mechanism of the hysical based model includes the contribution from field emission and thermionic field emission [4]. The series imedance of the diode due to the un-deleted region of the EPI layer, SUB layer, and Ohmic contact are calculated based on the anode and Ohmic contact area, deletion width, thickness and the associated conductivity of both EPI and SUB layers. For the SUB layer, the imedance due to current sreading and skin effect are considered [5]. The influence of dislacement current and charge carrier inertia effects [6] within the SUB layer are reresented by using a frequency deendent conductivity. The electron mobility is also a function of doing level, device temerature, and electrical field [7]. In this work, the calculation of

3 deletion layer, barrier height lowering, and hot-electrons noise imlementation are emhasized. A. Deletion width The variation of the deletion width is crucial circuit analysis, because the most imortant model roerties such as nonlinear conductance, caacitance, and resistance are all deendent on the deletion width. With the knowledge of doing levels and bias voltage, an aroximation of the deletion width can be calculated by w ( bi T ) (1) where N is doing level of the EPI layer, is the alied voltage on the diode unction, T is the thermal voltage, and ε is the ermittivity of GaAs material. bi reresents the built-in otential of the unction and is derived from the barrier height Ф B and the otential difference between Fermi level and bottom of the conduction band. Eq. 1 indicates that the deletion layer aroaching zero when = bi T, but there is always a hysical thin layer remaining and can be characterized by the Debye length L kt B D () Nq where k B is Boltzmann s constant. When the diode is reversely biased, Eq. 1 remains valid until the unch through voltage is reached where the EPI layer is comletely deleted. With the condition of w equal to the total thickness of the EPI layer T, the unch through voltage can be solved from Eq. 1 to be w tot T wsub w P ( ) LD m m where P( ) is a higher order olynomial function which makes a smooth transition between w and L D a large ward bias. = bi -3 T and m = bi - T is the lower and uer boundary of the transition region, resectively. With the knowledge of total deletion width and doing density of the EPI and SUB layers, the unction caacitance each layer can be derived from Eq. 6 and Eq. 7, resectively: dq d w C A A (5) SC, (6) d d w dq d w (7) SC, sub sub sub Csub A A d d wsub where A is the anode area and Q SC is the sace charge within the EPI and SUB layers. When the alied unction voltage is smaller than, the caacitances of C and C sub are connected in series. Fig. shows a tyical deletion width transition when the ward bias is aroaching flat band. The higher order olynomial avoids singularity of the caacitance function and results in a better convergence the circuit simulator. bi T T (3) When the alied reverse voltage is further increased, a very thin SUB layer will also be deleted. This deletion width can be calculated as w sub, ( ), sub The total deletion width of a Schottky diode is exressed as w tot =w +w sub. Deending on the alied unction voltage, w can be mulated as: tot (4) Fig. Calculated unction caacitance and deletion width from Eq. 5. The numerical results are based on the assumed values of T=3 [K], T =5 [m], N =1e+3 [m -3 ], N sub =4e+4 [m -3 ], T =8 [nm], T sub =5 [μm], and radius of anode contact a=.1 [µm]. B. Barrier height lowering Free electrons close to the barrier exerience an image ce, which lowers the Schottky barrier height a Schottky contact. This barrier lowering has an imact on current flow across the barrier. At a distance of x m the

4 barrier height lowering due to the image ce is aroximately qe q max Emax xm w ( bi T ) 8 (8) where K h T T K I e (11) h 3qk N A d B It can be seen that the excessive noise arises from the term of K h I, which has a ~I relationshi with the unction current. An effective value of.5~1 [s] is considered τ d in [8], but the direct calculation based on Eq. 1 shows a much smaller value. The comarison of noise temerature based on assumed and calculated τ d is shown in Fig. 4. The results in Fig. 4 indicate that the theoretical mulation has to be adusted by an emirical arameter, which reresents the imact of the technological rocess and its maturity. Fig. 3. Calculated barrier height lowering due to the image ce from Eq. 8. The numerical results are based on the assumed values of T=3 [K], T =5 [m], bi =.95 [], ε=1.16e-1 [F/m]. Fig. 3 shows effect of barrier height lowering due to different doing rofiles. The variation of the built-in otential bi is assumed to be small both doing levels. It indicates that the higher the doing, the more the barrier height is reduced. C. Hot-electron noise The noise sources within the Schottky diode are usually divided into three arts: 1) thermal noise from series resistance from the un-deleted EPI layer, SUB layer, and Ohmic contact; ) shot noise from conduction current through the unction; 3) excessive noise from hotelectrons. The derivation of hot-electron noise arises from electron energy and momentum balance equations [8]. The steady state solution of the equivalent noise temerature is exressed as * Te T ( q s de ) / 3kBm (9) where m * is the effective electron mass and E is the electrical field. τ s and τ d is the mean scattering and energy relaxation time GaAs material, which are defined by s * m / q / ( ) d (1) By inserting the electrical field calculated from the diode current, doing level, and low field electron mobility, T e can be re-mulated as Fig. 4. Calculated equivalent noise temerature from Eq. 9. Different τ d are considered the noise characterization. The numerical results are based on the assumed values of T=3 K, T =5 [m], N =e+ [m -3 ], τ s =.3 [s], ε=1.16e-1 [F/m], m * =.68m, m = 9.1e-31 [kg]. III. MODEL ERIFICATION To verify the hysical based diode model, the measured I- and C- characteristics from the fabricated Schottky diode at Chalmers and noise exerimental data from the oen literature are used. With the detailed knowledge of the Chalmers Schottky technology, the relevant diode arameters are set to be: T=3 [K], radius of anode contact a=.5 [µm], effective radius of Ohmic contact b=3.9 [µm], barrier height Ф b =1. [], N =5e+3[m -3 ], N sub = 5e+4 [m -3 ], T =48 [nm], N sub = [µm], and secific contact resistance ρ=5e-9 [Ωm ]. The comarison of I- characteristics an antiarallel diode air is shown in Fig. 5. The surface leakage low ward bias region(<.4 []) is modeled by a arallel resistor with a value of 33 [MΩ]. As shown, there is a good agreement between the measurement and simulation result. Fig. 6 shows the unction caacitance versus voltage the diode with an anode radius of.5 [μm]. The extracted caacitance data is not valid larger bias oints due to the short-circuited unction, and reverse bias region the diode model redicts a 3% lower

5 caacitance than the measurement, which might be due to a arasitic caacitance or originate from the extraction rocedure where the ad to ad caacitance is deembedded. Theree, an extra overlaing caacitance of.7 [ff] is added to the result from the hysical based model in Fig. 6. Fig. 7. The comarison of measured and simulated noise temerature at 1.5 GHz on (a) a Schottky diode with N =e+ [m -3 ], anode radius of 1.5 [µm], and Ф b =.99 [] (from [1]). Fig. 5. The comarison of measured and simulated currentvoltage characteristics an antiarallel diode air with an anode radius of.5 [µm]. the hysical model is lower than the measurements due to absence of a arasitic caacitance in the model. The noise behavior of the diode model is verified by the exerimental data from the oen literature. The good agreement verifies the noise sources imlemented in the model. ACKNOWLEDGEMENT The authors wish to acknowledge the assistance and suort of Terahertz and Millimetre-Wave Laboratory at Chalmers fabrication and measurement of the Schottky diodes. REFERENCES Fig. 6. The comarison of measured unction caacitance and simulation results a Schottky diode with an anode radius of.5 µm. The simulated noise temerature at 1.5 GHz is comared with measurement results from the oen literature [1]. τ d used in the calculation of hot-electron noise from Eq. 11 is increased by a factor of. In Fig. 7, a Schottky diode with arameters of a=1.5 [µm], N =e+ [m -3 ], and barrier height of.99 [] is used comarison. It shows that the simulated noise temerature agrees well with the measurement.. CONCULSION In this work, a hysical based Schottky diode model is resented. It includes features of barrier height lowering, nonlinear resistance from the EPI layer, and hot electron noise. The I- and C- measurements of from fabricated Schottky diodes agree well with simulation results from the hysical diode model. The redicted caacitance from [1] P.H. Sigel,.5THz GaAs Monolithic Membrane-diode Mixer, IEEE Trans. Microwave Theory & Tech., vol. 47, no. 5, , [] M.C. Gaidis, Sace-based Alications of Far-Infrared System, 8th International Conference on Terahertz Electronics., ,. [3] J.. Siles and J. Graal, Physics-Based Design and Otimization of Schottky diode Frequency Multiliers Terahertz Alications, IEEE Trans. Microwave Theory & Tech., vol. 58, no. 7, , 1. [4] F. Padovani and R. Stratton, Field and thermionic-field emission in Schottky barriers, Solid State Electron, vol. 9, no. 7, , [5] L. Dickens, Sreading Resistance as a Function of Frequency, IEEE Trans. Microwave Theory & Tech., vol. 15, no., , [6] T. Gonzalez et al, Microscoic analysis of electron noise in GaAs Schottky barrier diodes, in Journal of Alied Physics,1997, [7] C. Chang and H. Fetterman, Electron drift velocity versus electric field in GaAs, Solide State Electronics., , [8] H. Zirath, High-frequency noise and current-voltage characteristics of mm-wave latinum n-n(+)-gaas Schottky barrier diodes, in Journal of Alied Physics 1986, [9] A. Jelenski et al, New aroach to the design and the fabrication of THz Schottky barrier diodes, IEEE Trans. Microwave Theory & Tech., vol. 41, no. 4, , 1993.