CHAPTER 2 WORKING PRINCIPLE OF HEMTs
2.3 Basic model of GaN HEMTs
The first report on the fabrication and operation of AlGaN/GaN heterojunction FETs, also called HEMTs, was by Khan et al. in 1993. Figure 2.8 shows the cross-
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Figure 2.8: A planar gate AlGaN/GaN based HEMT structure.
The basic level analysis of the I-V characteristics of a HEMT is similar to a Metal-Oxide- Semiconductor FET (MOSFET) using a gradual channel approximation [26] taking into account two variations:
• According to equation 2.8, the charge carriers Ns can be modulated by altering the built-in field in the barrier. The surface potential ΦP in equation (2.8) is written as:
ΦP= ΦPQ + VS (2.9)
• The pinch-off voltage (Vp) is defined for the case that Ns equals zero (see also Figure 2.9b). This can be derived by replacing equation (2.9) in equation (2.8) and setting it to zero noting that EF (Ns) equals zero at pinch-off, yielding:
T = TUV *!W ,− ?. >=0.. -.<. & "*, ,!-./01-
=0.. -.
(2.10)
where TUV *!W , is the built-in voltage, and is equal to ФXU−∆YZFGHHIJH/LGM
[ , and is
defined by the gate and heterostructure material parameters. Thus Vp for a given GaN HEMT can be changed by changing dbarrier as will be shown later in chapter 3 for LM-
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Figure 2.9: Schematic of HEMT band diagram under the gate (a) in case of no applied gate voltage ΦP equals the contact potential ΦPQ (left), and (b) ΦP is controlled by the gate voltage, as shown here for the case of a pinched-off channel (right).
Now following the gradual channel approximation as in a MOSFET, the drain- source current (IDS) can be written as:
\]X = ^ 2X_`2
2 abT2X− T c. T]X−
T]X
2 d
(2.11)
where CGS is the gate-source capacitance and given by:
2X = <=0.. -.> _2`2 =0.. -.
(2.12) where WG and LG are the gate width and gate length respectively.
The saturation drain current (IDSS) can be obtained by deriving equation (2.11)
with respect to VD and setting it to zero yielding:
\]XX= ^ 2X_`2
2 bT2− T c
(2.13) and thus the transconductance (ef) in the saturation region is a function of 1/LG,
expressed by: ef =>\>T]XX 2 = ^ 2X _2 `2 bT2− T c (2.14)
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However, these equations represent the long channel approximation and are valid only in the constant mobility regime where the electron velocity is below the saturation velocity. Due to the high mobility in GaN HEMTs, the saturation velocity can be reached even for small drain biases and hence the device will operate in the velocity saturation mode. IDSS can be then written using a two-piece linear approximation [27] as:
\]XX≈ _2 2XbT2− T ch#0! (2.15)
and the transconductance is expressed by:
ef = _2 2Xh#0! (2.16)
thus the linear dependence of the transfer characteristics on VG, in contrast to long
channel devices. Moreover, the cut-off frequencies of the device, neglecting extrinsic parameters, can be approximated by [26]:
i! ≈2j( ef 2X+ 2]) (2.17) and if0k= ef 2j 2Xl4(nX+ n + n2) oep+ ef@ 2]2XNq (2.18)
which for the case of small resistances can be reduced to:
if0k≈ l8jni!
2 2]
(2.19)
The natural way to increase the device cut-off frequencies in GaAs HEMTs is to aggressively scale down the device dimensions [28] in addition to better channel confinement [29]. From equation (2.17) and (2.14), it can be seen that ft is inversely
proportional to LG (neglecting the parasitic capacitances), thus reducing LG would yield
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MOSHEMTs [26]. In the case of GaN HEMTs, the lateral field at the drain side makes the effective gate length asymmetric, and in total larger than the metallurgical gate length [30]. Thus to maintaining a certain aspect ratio LG / dbarrier to keep the internal field
distribution the same, down scaling of the barrier is also required. A universal minimum aspect ratio of 15 was found to be a limit to avoid short channel effects by simulation of AlGaN/GaN HEMTs and observed experimentally in [31]. For power amplifiers, increased operation frequency has another limitation on the output power due to current collapse effect that will be discussed separately.
For linear operation of a class-A amplifier the output power (Pout) can be estimated as [32]:
"V!=18 \]XrGs@T]X|uvw − Tx,--N
(2.20) where Vknee is the knee voltage defined at the onset of current saturation.
Before discussing the power performance of GaN HEMTs, it is necessary to describe the breakdown mechanisms, in on-state and in off-state. The breakdown occurs through an increased gate leakage current in on-state. The gate leakage mechanisms in GaN HEMTs are dominated by trap-assisted tunneling and these traps can be located at the barrier/GaN interface or in the barrier due to un-intentional barrier doping or can be due to defects. A general expression of the tunneling current between the gate contact and the source contact across the barrier, conducted by the 2DEG is given by:
yz = ?{|-}(B) (2.21)
where JT is the tunneling current density, n is the electron concentration, |- is the electron
velocity and T(E) is the transmission probability. Equation (2.21) is sufficient to describe the main features of the gate diode characteristics shown in Figure 2.10.
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In forward bias direction, increasing the gate voltage modulates the barrier height making a flat band condition in the barrier. T(E) in eqn. (2.21) will then decrease but is counter balanced by an increase in the electron concentration in the channel. However, since |- increases with voltage, JT will eventually increase, until sufficiently high enough
leakage current destroys the gate contact.
The same behavior is expected but here when reverse biasing the gate, T(E) will be increasing, counter balanced by a decreasing electron concentration and the reverse leakage current will increase up to the point where the channel is pinched-off.
The on-state breakdown and reverse bias leakage current are vertical field phenomena up to pinch-off and the surface properties will dominate the HEMT behavior once the channel is pinched-off. The diode characteristics exhibit a current limiter behavior and the leakage current is conducted laterally at the surface of the barrier, through hopping mechanism after pinch-off. At this stage, off-state breakdown will occur through an avalanche mechanism, occurring at the high field region at the gate edge toward the drain. A maximum of IDSmax.VBR should be targeted to maximize the power.
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Figure 2.10: Schematic of gate diode characteristics for a single barrier HEMT. The leakage current in the forward direction follows a tunneling mechanism, and similarly in the reverse bias direction up to channel pinch-off, where the characteristics resemble a current limiter.
GaN HEMTs faces two types of limitations, technological limitations and intrinsic limitations. There are several solutions that can be addressed to overcome the technological limitations such as, design modifications, recesses, barrier or buffer doping, cap layers, field plates, gate dielectrics, which can be applied to all polar heterostructures regardless of the composition. On the other hand, the intrinsic limitations, namely the current collapse and self heating, apply to all heterostructures (regardless of composition) and cannot be eliminated but rather compromised by controlling the high field region near the gate, by optimizing the surface electronic conditions, and designing an efficient heat management solution.
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