List of Figures
 

Figure 1.1 Gain per amplifier stage and output power of amplifiers with HEMTs, HBTs, and other FETs.

 

Figure 2.1 Schematic cross section of a High Electron Mobility Transistor (HEMT). Depending on the use of GaAs or AlGaAs for the buffer layer the HEMT is called single heterojunction HEMT (SH­HEMT) or double heterojunction HEMT (DH­HEMT) respectively.

 

Figure 2.2 Lattice constant versus band gap of the most important semiconductors. The bold line represents the AlGaAs/InGaAs system. The lattice constant of GaAs and AlAs are very similar whereas the lattice constant of InGaAs is significantly larger for all In contents.

 

Figure 2.3 Conduction band diagram of a delta doped HEMT. The Fermi level E_F and the quantum energy level E_e of the electrons in the channel are indicated by the dashed line.

 

Figure 2.4 Electron drift velocity in GaAs, InAs and InGaAs bulk material versus electric field. III-V semiconductors typically exhibit a local maximum in the v(E) characteristics. The velocity is increased with the In content in the whole range of electric field.

 

Figure 2.5 Critical thickness (bold line) of a GaAs/In_xGa_1-xAs/GaAs single quantum well according to the theory of Matthews and Blakeslee. Empty symbols represent samples with low dislocation density and filled symbols samples with high dislocation density. Samples with moderate dislocation density are indicated by the asterisks.

 

Figure 2.6 Schematic conduction band diagram of an InGaAs quantum well with AlGaAs barriers. For the energy difference of an electron to surmount the barrier the change in E_g due to strain as well as the quantum levels of electrons in the channel have to be taken into account.

 

Figure 2.7 Conduction band offset of an unstrained and strained Al_0.2Ga_0.8As/In_xGa_1­xAs/Al_0.2Ga_0.8As quantum well. Electron quantum level for the quantum wells along the critical thickness (dashed line). Effective conduction band offset DE_{C eff} according to Figure 2.6 (bold line).

 

Figure 3.1 Equivalent circuit model for parameter extraction. It includes the intrinsic device, the series resitances to all three terminals as well as the parasitic capacitances and inductances of the contacting network.

 

Figure 3.2 Total capacitance of HEMTs versus gate width at V_DS=2.0V. The capacitances are calculated using (12) with measured g_m and f_T of devices with gate widths L_w= 80, 180, 360 µm. For all V_GS a linear fit can be found. The intercept determines the constant part of C_tot, i. e. C_PG + C_PG.

 

Figure 3.3 Definition of voltages and capacitances of a FET.

 

Figure 4.1 Schematic conduction band diagram of the heterojunction between an InGaAs channel and an AlGaAs barrier. The effective barrier height DE_C is lowered by dE_C due to tunneling of electrons through the energy barrier.

 

Figure 4.2 Schematic conduction band diagram and electron distribution in the channel of a delta doped DH­HEMT. The wave of the electron distribution obtained from quantum mechanical considerations extends several nano meters into the barrier layers.

 

Figure 4.3 Carrier temperature along the channel of a HEMT obtained implicitly by DD simulation (bold line) and directly by HD simulation (dashed line).

 

Figure 4.4 Driving force along the channel of a HEMT obtained by DD simulation (bold line) and by HD simulation (dashed line).

 

Figure 5.1 SEM photograph of a HEMT. The ohmic source and drain contacts can be identified by the alloy penetrating into the cap layers whereas the Schottky gate contact builds a sharp interface.

 

Figure 5.2 Schematic cross section of the simulated HEMT_ref. The region for which different models are investigated are indicated by the hatched areas.

 

Figure 5.3 Measured and simulated transfer characteristics. The simulations are performed with the nominal layer structure and a interface model with and without tunneling.

 

Figure 5.4 Measured and simulated transfer characteristics. The simulations are performed with different geometric contact models. Either with source and drain contacts directly on the channel or source and drain only on top of the cap layers.

 

Figure 5.5 Measured and simulated transconductance. The simulations are performed with different geometric contact models. With source and drain contacts directly on the channel and source and drain only on top of the cap layers.

 

Figure 5.6 Current density of the HEMT geometry with directly contacted channel at V_DS = 2.0 V and V_GS = 0.5 V. In addition to the current conducted through the cap a large fraction is conducted directly from source through the channel to the drain. The geometry is not in linear scale.

 

Figure 5.7 Current density of the HEMT geometry with contacts only on top of the cap layer at V_DS = 2.0 V and V_GS = 0.5 V. All electrons from the channel which contribute to I_D have to be partially conducted in AlGaAs layers. The geometry is not in linear scale.

 

Figure 5.8 Schematic cross section of a power HEMT with different thickness of undoped supply layer.

 

Figure 5.9 Measured and simulated transfer characteristics of two devices which differ only in their thickness of undoped AlGaAs supply layer between the ohmic contacts and the channel.

 

Figure 5.10 SEM picture of the contact metals of a HEMT from the backside with removed semiconductor. A gate finger as well as alloyed ohmic contacts on both sides are shown. Some remaining GaAs can be observed by the lighter spots on source and drain.

 

Figure 5.11 Measured transfer characteristics and transconductance of a DH-HEMT. The characteristics can be divided into five regions, each owing to a major physical effect.

 

Figure 5.12 Measured and simulated transfer characteristics for different transport models. Circles indicate DD in all layers, squares HD in the channel and DD in the remaining layers, and triangles HD in the channel and supply layer, DD in the remaining layers.

 

Figure 5.13 Electron velocities in the channel at V_DS = 2.0 V and V_GS = 0.0 V with a hydrodynamic (bold line) and drift diffusion transport model (bold dashed line) in the channel. The electron velocity in the supply layer at V_DS = 2.0 V and V_GS = 0.8 V with a hydrodynamic and drift diffusion transport model is indicated by the thin bold line and thin dashed line, respectively.

 

Figure 5.14 Measured and simulated transconductance for different transport models. Circles indicate DD in all layers, squares HD in the channel and DD in the remaining layers, and triangles HD in the channel and supply layer, DD in the remaining layers.

 

Figure 5.15 g_{m max int} versus the equilibrium sheet carrier density n_s0.

 

Figure 5.16 g_{m max int} versus the electron low field mobility for different gate lengths.

 

Figure 5.17 g_{m max int} versus the saturation velocity of the electrons in the channel.

 

Figure 5.18 g_{m max int} versus the gate length.

 

Figure 5.19 g_{m max int} versus the gate to channel separation.

 

Figure 5.20 Electron velocities in the channel at V_DS = 2.0 V and V_GS = 0.5 V. The bold line indicates a reference simulation with v_sat = 1.1 * 10⁵ ms^-1, b = 0.9, and t_w = 0.18 ps. In the simulation indicated by symbols one parameter is changed.

 

Figure 5.21 Electron velocities in the channel calculated by Monte Carlo and mixed DD/HD simulations at V_DS = 2.0 V and V_GS = 0.5 V.

 

Figure 5.22 Simulated transfer characteristics with different parameters governing. A change in the tunnel coefficients B_i has a similar effect on the transfer characteristics than a change in the t_w of the HD model in the channel.

 

Figure 5.23 Gate capacitance extracted from S­parameter measurements and mixed DD/HD simulations using a quasi static approximation at V_DS = 2.0 V. An increase in electron velocity reduces C_G but increases I_D. This way the electron velocity can be separated from the electron concentration.

 

Figure 5.24 Measured output characteristics of HEMT_ref. The characteristics with the highest current is obtained for V_GS = 1.0 V. The remaining curves are separated by DV_GS = 0.2 V.

 

Figure 5.25 Measured (lines without symbols) and simulated (lines with circles) output characteristics of HEMT_ref. The characteristics with the highest currents are obtained for V_GS = 1.0 V. The remaining curves are separated by DV_GS = 0.2 V.

 

Figure 5.26 DC and pulsed measurement of output characteristics of a power HEMT taken from [64].

 

Figure 6.1 Most important design parameters for HEMTs which are defined by the process technology.

 

Figure 6.2 SEM photograph of a HEMT with a gate structure produced by a side wall spacer technology. The cross section of the gate can be characterized by the distances L_G, L_T, d_T and d_G.

 

Figure 6.3 Principle steps of a sidewall spacer process.

 

Figure 6.4 SEM photograph of a gate cross section obtained by EBL (NTT [71]).

 

Figure 6.5 Conduction band diagram and the electron distribution in the channel of a HEMT biased near the threshold voltage V_T.

 

Figure 6.6 Schematic cross section of a low noise SH­HEMT with homogeneously doped supply layer. The parameters investigated in this section are d_GC, L_G, L_R, and e_r.

 

Figure 6.7 Measured and simulated transfer characteristics of HEMT A and HEMT B at V_DS = 2.0 V

 

Figure 6.8 Measured and simulated transconductance of HEMT A and HEMT B at V_DS = 2.0 V

 

Figure 6.9 Simulated C_G of HEMT A and HEMT B at V_DS = 2.0 V

 

Figure 6.10 Measured (bold line without symbols) and simulated transfer characteristics of HEMT C with the nominal d_GC (circles) and d_GC - 1.7 nm (triangles) at V_DS = 2.0 V

 

Figure 6.11 Measured (bold line without symbols) and simulated transconductance of HEMT C with the nominal d_GC (circles) and d_GC - 1.7 nm (triangles) at V_DS = 2.0 V

 

Figure 6.12 Simulated C_G of HEMT A (squares) and HEMT C (circles) at V_DS = 2.0 V

 

Figure 6.13 Measured (bold line without symbols) and calculated f_T with simulated (squares) and extracted (triangles) C_G and g_m at V_DS = 2.0 V

 

Figure 6.14 Measured (filled symbols) and simulated (open symbols) DC output conductance g_o versus the gate length at the bias point V_GS = 0.2 V and V_DS = 2.0 V

 

Figure 6.15 Measured (filled squares) and simulated f_T versus L_G for a passivated HEMT with e_r = 7 (filled circles) and e_r = 0 (open circles) at V_GS = 0.2 V and V_DS = 2.0 V

 

Figure 6.16 Simulated gate capacitance C_G vs. gate length L_G for two different e_r at V_DS = 2.0 V, I_D = 160 mA/mm.

 

Figure 6.17 Simulated f_T versus L_R for a passivated HEMT with e_r = 7 (filled symbols) and e_r = 0 (open symbols) at V_GS = 0.2 V and V_DS = 2.0 V

 

Figure 6.18 Simulated f_T and f_max versus L_R for a passivated HEMT with e_r = 7 (circles) and e_r = 1 (squares) at V_GS = 0.2 V and V_DS = 2.0 V

 

Figure 6.19 Amplifier circuit with a HEMT biased at V_DS and V_{GS DC}. Additionally an RF input signal is applied. The HEMT is driving a 50 W load resistor and a network with the impedance Z.

 

Figure 6.20 Measured DC output characteristics of HEMT_ref. With a DC bias of V_{DS, DC} = 3 V and V_{GS DC} = 0.35 V and a sinusoidal input signal with GHz I_D/V_DS characteristics over time in plane AA' (Figure 6.19) can be obtained by circuit simulation with the HP software MDS. The largest trajectory is obtained for an input signal amplitude of 0.3 V the smallest for 0.01 V.

 

Figure 6.21 Schematic cross section of the simulated power DH­HEMTs with double recess. The shape of the T­gate is characterized by L_G, L_T, d_T and d_G. e_{r 1} and e_{r 2} account for a certain passivation dielectric.

 

Figure 6.22 Simulated (bold line without symbols) and measured (line with symbols) transfer characteristics for V_DS = 2.0 V.

 

Figure 6.23 Simulated (bold line) and measured (line with symbols) transconductance g_m at V_DS = 2.0V.

 

Figure 6.24 Electric field distribution in the channel at V_DS = 10.0 V._max is shifted from the drain end of the gate to the end of the double recess if the conductivity of the channel is increased by increasing V_GS.

 

Figure 6.25 Electric field distribution in the channel at V_DS = 10 V and V_GS = 0.8 V. To reduce _max the thickness of the recessed cap has to be such that  is equally distributed under the recess.

 

Figure 6.26 The reduction of _max at V_DS = 10 V and V_GS < V_T goes along with a reduction of g_m at the active bias point V_DS = 2.0 V and V_GS = 0.4 V. A strong increase of C_G leads to a reduced f_T for small L_R.

 

Figure 6.27 Maximum electric field in the channel versus the thickness of the recessed cap d_DR for an open channel bias point (V_DS = 10 V, V_GS = 0.8 V). Parameter is the length of that recess L_DR.

 

Figure 6.28 Maximum transconductance g_m versus the thickness of the recessed cap d_DR at V_DS = 2.0 V and V_GS = 0.4 V. Parameter is the length of that recess L_DR.

 

Figure 6.29 Gate capacitance C_G versus the thickness of the recessed cap d_DR at V_DS = 2.0 V and V_GS = 0.4 V. Parameter is the length of that recess L_DR.

 

Figure 6.30 Current gain cut-off frequency f_T versus the thickness of the recessed cap d_DR at V_DS = 2.0 V and V_GS = 0.4 V. Parameter is the length of that recess L_DR.

 

Figure 6.31 Simulated and measured current gain cut-off frequency f_T at V_DS = 2.0 V, I_D = 160 mA/mm.

 

Figure 6.32 Simulated gate capacitance C_G vs. gate length L_G for two different e_r at V_DS = 2.0 V, I_D = 160 mA/mm.

 

Figure 6.33 Electric field of the simulated HEMT in true scale at V_DS = 2.0 V, V_GS = 0.4 V.

 

Figure 6.34 Capacitances C_G, C_GS, C_GD, and the ratio C_GS /C_GD as a function of passivation thickness.

 

Figure 6.35 Simulated gate capacitance C_G vs. gate length L_G for two different e_r at V_DS = 2.0 V, I_D = 160 mA/mm.

 

Figure 6.36 Parameters to investigate the influence of the gate cross section on C_G.

 

Figure 6.37 Simulated gate capacitance C_G and current gain cut-off frequency f_T for L_G = 220 nm and different gate cross sections (V_DS = 2.0 V, V_GS = 0.4 V). All calculations for L_T = 800 nm.

 

Figure 6.38 Schematic cross section of the investigated millimeter wave HEMT.

 

Figure 6.39 Simulated (lines without symbols) and measured (lines with symbols) transfer characteristics of two millimeter wave HEMTs with different recess depths.

 

Figure 6.40 Simulated (lines without symbols) and measured (lines with symbols) transconductance of two millimeter wave HEMTs with different recess depths.

 

Figure 6.41 Simulated g_m and V_T versus d_GC. Both g_m and V_T is almost linear dependent on d_GC for the given range of d_GC.

 

Figure 6.42 Simulated g_m and V_T versus L_G for devices with d_GC = 10 nm and d_GC = 13 nm. Both the g_m and f_T characteristics are non linear due to short channel effects.

 

Figure 6.43 Simulated g₀ versus L_G. g₀ is underestimated due to a DD model in the buffer layer and disregarding impact ionization in the simulation. The principle dependence on L_G is simulated very realistically.

 

Figure 6.44 Simulated f_T versus L_G for two different d_GC. The characteristics reveal a cross over for d_GC = 10 nm and d_CG = 13 nm for both passivated and unpassivated devices.

 

Figure 6.45 Simulated C_G versus L_G for d_GC = 10 nm and d_GC = 13 nm. To deduce the parameters A₁, A₂, and A₃ for both d_GC the passivated and unpassivated case is shown.

 

Figure 6.46 Dependence of g_m, C_G, and f_T on d_GC. The strong increase of C_G with a reduction of d_GC almost compensates the improvements in f_T. Only a moderate increase is obtained.

 

Figure 6.47 f_T versus d_GC for different assumptions on the gate capacitance. For e_r = 7 the characteristics of Figure 6.46 is obtained. e_r = 1 represents unpassivated devices. The slope of the characteristics is even positive if only the contribution of C_G dependent on L_G is considered.

 

Figure 6.48 f_T and f_max versus L_R for passivated and unpassivated devices. The maximum of f_max is reached for significant larger values of L_R due to the larger impact of C_GD on f_max than on f_T.

 

Figure 6.49 f_T and f_max versus d_P. Only a moderate increase in f_T and f_max is obtained for a reduction of d_P from 700 nm to 200 nm. If the passivation is removed in regions with high electric field the increase in both f_T and f_max is much more significant.

 

Figure 6.50 Contributions to C_GS due to backside doping (dots), channel (short dashes) and upper barrier doping (long dashes).

 

Figure 6.51 Simulated and extracted C_GS of the investigated millimeter wave HEMT at V_DS=3.0 V.

 

Figure 6.52 Simulated C_GS of the same HEMT but with different backside doping at V_DS=3.0 V.

 

Figure 6.53 Layout of the measured VCO with buffer amplifier.

 

Figure 6.54 Measured f_osc of the VCO versus the tuning voltage V_GS and the extracted C_GS of the HEMT used in the VCO.

   
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