It is believed that significant velocity overshoot effects are responsible for the high performance of Pseudomorphic HEMTs (PsHEMTs). The overshoot is associated with the low effective mass in the InGaAs channel and the large G - L (for G read Gamma) separation. Average channel electron velocities well in excess of 3.0x10⁷ cm/s have been predicted in Monte Carlo PsHEMT simulations. However, average electron velocities extracted form transconductance measurements of such devices are much lower, typically in the range 1.5 - 2.0x10⁷ cm/s. In this paper we analyse real device measurements by using Monte Carlo and drift diffusion simulations. We show clear evidence that the average velocity in the channel of a 200 nm PsHEMTs fabricated in the Nanoelectronics Research Centre of Glasgow University exceeds 3.0x10⁷ cm/s.

Introduction

PsHEMTs with InGaAs channels grown on GaAs or AlGaAs buffers have been studied extensively mainly because of their application in low noise MMICs [1]. Cut-off frequencies (f_T's) well in excess of 100 GHz have been measured in these devices [2,3]. In part this is due to hot electron velocity overshoot effects [4], enhanced by the low effective mass and the large G - L separation in the InGaAs channel [5]. When the carriers enter the high field channel region they travel some distance with an ensemble velocity higher than the saturation velocity before an equilibrium condition is established and the velocity saturates. The spatial velocity overshoot region is comparable to the carrier mean free path and in low doped GaAs this region extends to more than a quarter of a micron [5]. In In_xGa_1-xAs the spatial overshoot region is even larger which means that the carries will travel with velocities higher than the saturation velocity all the way through the typical 200 - 100 nm channel of the state-of-the art PsHEMTs. Monte Carlo simulations of PsHEMTs with 350 nm gate lengths predict that the average electron velocity in the channel under the gate are well above 3.0x10⁷ cm/s in normal operation conditions [6]. Similar high channel velocities are reported in [7] based on a hydrodynamic simulation of a 500 nm PsHEMT. However, average electron velocities extracted form transconductance measurements [8] of real devices are usually lower, typically in the range 1.5 - 2.0x10⁷ cm/s [9]. Although there are some explanations in the literature for why such discrepancies between the predicted and extracted effective velocity in HEMTs exist [10], they are based on Monte Carlo simulation itself without direct links to real fabricated and measured devices.

In this paper we use both Monte Carlo and drift diffusion simulations to analyse the characteristics of real PsHEMTs fabricated and measured in the Nanoelectronics Research Centre of Glasgow University. The analysis was carried out with the in-house compound FET simulator H2F which combines drift-diffusion and Monte Carlo modules in a same finite element simulation domain. Carefully considering the transport, the geometry and the parasitics effects in the simulation we show clear evidence that the average velocity in the channel of a 200 nm PsHEMT we have fabricated exceeds 3.0x10⁷ cm/s.

Device description

The layer structure of the p-HEMTs used to investigate the velocity overshoot phenomena is shown in Fig.1 [11]. Growth starts with a 100 period superlattice (impurity trap) to prevent the migration of impurities and defects from the semi-insulating GaAs substrate into the active device area. A 600 nm GaAs buffer separates the superlattice from the PsHEMT's channel and reduces the influence of the Fermi level pinning in the superlattice on the free carrier concentration in the channel. The 10 nm strained In_xGa_1-xAs channel is grown at 500 - 520°C. The low growth temperature allows the indium fraction x to be increased to 30% without noticeable strain relaxation. This increases the spacer/ channel conduction band offset and the G - L separation. The relatively thin (2.5 nm) Al_0.3Ga_0.7As spacer improves the carrier transfer efficiency at the cost of a slight mobility reduction as a result of the increased remote impurity scattering.

Figure 1: Vertical layer structure of the 200 nm PsHEMT under consideration.

The Si delta-doping is encapsulated between 3 and 2 monolayers GaAs. This reduces the diffusion of Si and the spreading of the delta-doping. The doping efficiency at the doping level of 7x10¹² cm^-3 is approximately 70%. The 10 nm Al_0.3Ga_0.7As Schottky layer is separated from the 5 nm Al_0.3Ga_0.7As recess etch stopper by a 2.5 nm GaAs buffer. The role of this buffer is to prevent deep oxidation of the Schottky layer in the recess region which leads to a degradation of the device. The overall separation between the channel and the gate is 21.5 nm. The heavily doped 30 nm GaAs cap layer screens the 2DEG in the region between the gate and the contacts from the negative charge of the electrons trapped on deep, acceptor type surface states.

The T-gate is fabricated by e-beam lithography using tri-layer PMMA/P(MAA-MMA)/PMMA resist. The gate recess was etched using damage free, selective SRIE procss [12]. Devices with gate length ranging from 120 to 320 nm were fabricated. A SEM cross section of a completed p-HEMT is shown in Fig.2. This device is designed with virtually a zero offset between the gate and the recess edge which, together with the high doing density at GaAs cap layer, eliminates the effects of the surface charge at the otherwise ungated sections of the recess. This removes the uncertainties related to the effect of the surface potential pinning in the simulations.

Figure 2: Cross sectional SEM view of a completed PsHEMT.

The measured transfer characteristics and gate voltage dependence of the dc transconductance at drain voltage V_D = 1.5 V for a 200 nm gate PsHEMT are presented in Fig.3.

Figure 3: Measured transconductance and transfer characteristics at V_D = 1.5 V.

Numerical Simulation

We use our Heterojunction 2D Finite element simulator H2F [13] to study the overshoot effects in the PsHEMTs described above. H2F is designed for modern submicometer MESFETs and HEMTs with an arbitrary gate and recess shapes. It allows precise description of the device geometry and supports Monte Carlo and Drift-Diffusion simulations in a same finite element simulation domain . The Galerkin finite element approach based on quadrilateral elements [14] has been adopted to solve Poisson's equation. The integration over quadrilateral elements during the finite element discretization is carried out by a linear isoparametric mapping of each element into a unit rectangle.

Monte-Carlo simulation in a single finite element is the building block of the Monte Carlo module in H2F [15]. Currently the simulator is restricted to n-channel compound FETs and in the Monte Carlo simulation only the trajectories of the electrons are followed in the solution domain. The particles are moved within a single element using a constant electric field. The linear isoparametric mapping from the finite element procedure is used to test the position of the particle with respect to the cell. On crossing a boundary, the particle is either transferred to a neighbouring cell, reflected, annihilated, etc. depending on the nature of the respective boundary. The linear isoparametric mapping is also used in the charge assignment process and in calculating the average electric field in each cell. The time of free-flight and subsequent scattering mechanisms are chosen using a standard self-scattering scheme. The scattering mechanisms currently implemented include: ionised impurity, acoustic phonon, piezo-electric, optical phonon and polar optic scattering with parameters adopted from different sources [16-18]. A non-parabolic three valley (G,L,X) conduction band model was used for the III-V materials.

Modelling the contacts at the left and right hand edges of the PsHEMTs poses some difficulties as little is known about the physical penetration of the ohmic contacts through the device layer structure. We have implemented an ohmic contact model which extends bellow the InGaAs channel. The number of particles in each material layer (subregion) in the contact region is fixed to the charge obtained by a 2D solution of the non-linear Poisson's equation before the beginning of the Monte Carlo simulation. The particles in each subregion are kept in thermal equilibrium using a standard ohmic contact procedure [19].

A generalised surface trap model in the simulator H2F includes acceptor and donor like traps with an arbitrary energy position. The model is self-consistently coupled to the Poisson equation in the Drift-Diffusion module of H2F. The Monte-Carlo module assumes a fixed surface charge which keeps the surface potential pinned to a value estimated from the drift-diffusion simulations at the same bias conditions.

The generation of the full I-V characteristics in the Monte Carlo simulations is accelerated by implementing a simple Single Programme Multiple Data (SPMD) strategy. The I-V curves are calculated in parallel on a Parsytec 8 node Power PC X-plorer parallel platform. This makes it possible to use the Monte-Carlo simulations in practical design work.

The vertical layer structure and the lateral dimensions of a 200 nm PsHEMT obtained from a cross-sectional SEM photograph of the device were introduced in the simulator. In Fig.4 a,b a section of the solution domain including the gate recess region is compared with the corresponding section of the SEM photograph. The distribution of the superparticles at V_G = 0 V and V_D=1.5 V is also given. The proper handling of the geometry is very important in the analysis of the overshot effects. Based on Monte Carlo simulation [10] it was clearly demonstrated that the major error in the experimental estimation of the effective channel velocity in deep submicrometer HEMT is introduced by neglecting the fringing effects which modify both the effective channel length and the gate-to source capacitance.

Figure 4: PsHEMT simulation. (a) Part of the MC simulation domain near the recess region; (b) The corresponding fragment of the SEM photograph.

We start our analysis of the 200 nm gate length PsHEMT with a Monte Carlo simulation. The simulated longitudinal electric field in the middle of the channel at V_G = 0 V and V_D = 1.5 V is plotted in Fig.5. The corresponding average electron velocity profile in the channel, outside the channel and the overall average velocity are plotted in Fig.6. The maximum velocity in the channel exceeds 5x10⁷ cm/s and the estimated average velocity in the channel was found to be 3.5x10⁷ cm/s. This is significantly higher than the value 1.65x10⁷cm/s inferred from the transconductance measurements of the same device.

Figure 5: Simulated longitudinal electric field in the middle of the channel at V_G = 0 V and V_D = 1.5 V.

Figure 6: Simulated average velocity in the channel region of the device at V_G = 0 V and V_D = 1.5 V.

In parallel with the Monte Carlo simulation we use the Drift-Diffusion module of H2F. The average velocity of 3.5x10⁷ cm/s obtained form the Monte-Carlo module was reinforced in the drift-diffusion simulation using the technique proposed in [20]. The I_D-V_G characteristics calculated by the drift-diffusion and the Monte Carlo modules are compared in Fig.7 for a device with 100 mm channel width. They are in surprisingly good agreement pointing out that in some design applications fast Monte Carlo calibrated drift-diffusion simulations can be useful. However both the Monte Carlo and the drift-diffusion results based on the above high average channel velocity are about 100 % above the measured current in the real device (see Fig. 7). This large discrepancy is due to the fact that the contact resistance and the series resistance introduced by the measurement equipment are not accounted for in the Monte Carlo and also in the drift-diffusion simulation. The simulations at this stage represent only the 'intrinsic' device. To allow for realistic comparison between the simulations and the measurements, the contact and the external series resistances should be carefully considered.

Figure 7: Comparison between the measured and calculated transfer characteristics at V_D = 1.5 V without correction for the external series resistances.

The effect of the series resistances

The introduction of a physically based contact resistance model in the simulations is practically impossible. The dynamics of transport between the metal and the semiconductor in the source and drain regions include tunnelling and thermionic emission processes. However, the metal and the semiconductor molecules diffuse across the interface causing a deviation of the band structure from that of the bulk. The direction of current flow near the contact greatly affects the contact resistance associated with the junction. The overall contact resistance includes the spreading resistance under the contact, current crowding effects and any resistance due to interfacial contamination. It is difficult to identify and separate the various components of the contact resistance and therefore the theoretically calculated junction characteristics of the ohmic metal-semiconductor contact often fail to reproduce the experimental data. The practical solution is to measure the contact resistance on specially designed control structures and to introduce it as a lump or distributed series resistance in the simulation.

The measurement equipment primarily designed for high frequency ac characterisation of PsHEMTs introduces additional series resistance in the measured dc characteristics. This series resistance should also be plugged in the simulation results to allow for a correct comparison with the experimental data.

In Drift-Diffusion simulations the combined contact and measurement equipment external series resistance can be introduced through the boundary conditions, modifying the potential at the contact by the voltage drop across this resistance. It is difficult to apply a similar procedure in the Monte Carlo simulations due to the stochastic nature of the instantaneous contact current. Here we use a simple algorithm to include the external to the Monte Carlo simulation contact and measurement equipment series resistances into the simulation results at a post processor stage. The voltages at the gate and drain electrodes are modified by the voltage drop across the source and drain external series resistances
and
, caused by the drain current I_D obtained in the Monte Carlo simulation of the intrinsic device. The mapping is given by

where V_D and V_G are the simulation drain and gate voltages respectively and V'_D and V'_G are the corrected drain and gate voltages required to maintain the same drain current through the intrinsic device when external series resistances are introduced. Nonlinear interpolation using bispline functions is performed on the new set of data to recover the transformed I-V curves.

The total series resistance of the PsHEMT under consideration was estimated from the I_D-V_G characteristics measured at low drain voltage (Fig.8). For positive gate voltages the current becomes independent of the gate voltage and is controlled only by the series resistance. At V_G = 0.5 V the total series resistance was found to be 12.38 ohms. This includes the access resistance of the regions between the gate and the contacts, the contact resistance and the measurement equipment resistance. The series resistances introduced to the source and the drain sides by the measurement equipment were found independently to be 0.2 and 2.78 ohms respectively. The access resistance of 3.2 ohms was estimated from the measured channel sheet carrier concentration and mobility. This leaves 6.2 ohms for the series resistances associated with the ohmic contacts. We can assume that the source and drain contacts are identical and therefore each will have a series resistance of 3.1 ohms. Thus the external to the Monte Carlo and the drift-diffusion simulations series resistances are R_CS = 0.2 + 3.1 = 3.3 ohms and R_CD = 2.78 + 3.1 = 5.88 ohms respectively.

Figure 8. Measured I_D-V_D characteristics at low drain voltage.

The effect of the post processor incorporation of the series resistances in the intrinsic device Monte Carlo simulation results is illustrated in Fig.9 The intrinsic device I_D-V_G characteristics, the modified with the contact and measurement equipment series resistances I_D-V_D characteristics, and the measured I_D-V_G characteristics are compared at V_G = 0 V. This figure highlights the significant influence of the series resistance on the device performance. It leads to a dramatic redaction in the drain current and the transconductance and shifts the knee voltage to higher drain voltages. The only positive effect is a slight reduction in the dc output conductance.

Figure 9: Comparison of Monte Carlo calculated and measured I_D-V_D characteristics at V_G=0V. The Monte Carlo result with post-processor incorporation of the external series resistance are also shown.

The external contact resistances and the series resistances of the measurement equipment estimated above were also introduced in the drift diffusion simulations fixing the average velocity in the channel to 3.5x10⁷ cm/s. The measured transfer characteristics at V_D = 1.5 V are compared are compared in Fig.10 with the drift-diffusion results and Monte Carlo results after the post processor incorporation of the external series resistance. The drift diffusion simulation shows good agreement with the measured transfer characteristics which indicates that the carriers in the channel of the fabricated and measured PsHEMTs really travel with velocities higher than 3x10⁷ cm/s. The Monte Carlo simulation results improve significantly but the current remains 10 - 15 % above the experimental values at high gate voltages. This is due to the fact that the Monte Carlo simulation predicts two times higher low field mobility in the region between the source contact and the gate compared to the measured 5000 cm²/V.s and hence underestimates the access resistance. Some of the scattering mechanisms that significantly affect the low field mobility in the PsHEMT channel are excluded from the Monte Carlo simulation. Among them are the remote impurity scattering, the surface roughness scattering and the alloy scattering mechanisms. The quantum effects are also ignored and in the simulation the channel is assumed to have the bulk material properties. The one-dimensional self-consistent Poisson-Schrodinger results for our layer structure show that the lowest energy level in the channel is approximately 100 meV above the bottom of the well which will reduce the effective AlGaAs/InGaAs barrier height and the charge transfer efficiency at high gate voltages. The maximum of the envelope function in the lowest band, and hence the maximum charge density, lies few nanometers into the well which reduces the gate-to-channel capacitance and weakens the gate control on the channel charge. We also point out the uncertainties associated with the material parameters for the binary materials and hence the tertiary materials [18].

Figure 10: Comparison between the measured and calculated transfer characteristics after the correction for the external series resistances.

Conclusions

In this paper we have demonstrated that the high overshoot velocities in the channel of short PsHEMTs predicted by Monte Carlo simulations are consistent with the measured characteristics of real fabricated devices if in the simulations all series resistances are accounted for and the 2D geometry effects carefully included. This helps to understand the discrepancy between theoretically predicted high nonequilibrium velocities in deep submicrometer Ps-HEMT and the average velocities that can be deduced from real device measurements. The series resistances are shown to play an important role in deteriorating the I-V chraratceristics of the modern PsHEMTs. The potential advantage of the massive velocity overshot in these devices can only be realised if special design measures are applied to reduce the fringing effects and the series resistance.

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