We report experimental results on the low-frequency noise in GaN/AlGaN transistors fabricated under different conditions and evaluate different methods to extract the effective trap density using the McWhorter model. The effective trap density is found to be below 10^{19} cm^{−3} for some of the wafers. This trap density is of the same order of magnitude as that reported in Si MOSFETs with a high-k dielectric. One of the structures manifested about two orders of magnitude higher noise level. These measurements correlate with the results of secondary ion mass spectroscopy and terahertz electroluminescence measurements which indicated a ∼30% higher concentration of uncompensated oxygen in this structure. Effective trap density extracted from noise measurements is proven to be a very sensitive figure of merit parameter for the GaN/AlGaN field effect transistors and material quality assessment.

The low frequency noise in GaN-based field effect transistors (FETs) has been studied for more than 20 years (see Refs. 1–7 and references therein). In the majority of publications, the amplitude of the 1/*f* noise is characterized by the Hooge parameter *α _{H}* =

*S*/

_{I}*I*

^{2}

*× N × f*.

^{8}Here,

*S*/

_{I}*I*

^{2}is the relative spectral noise density of the drain current fluctuations,

*N*is the total number of carriers in the channel, and

*f*is the frequency. Although there is no theory behind this formula, it is a simple and convenient way to characterize the amplitude of noise and compare the noise level of different devices. The value of the Hooge parameter reported in publications in GaN/AlGaN high electron mobility field effect transistors (HEMTs) is within the range

*α*≅ 10

_{H}^{−1}–10

^{−5}.

^{1,2,5,6,9,10}However, the Hooge parameter in GaN/AlGaN HEMTs usually depends on the gate voltage, i.e., on the electron concentration in the channel. Therefore, it is not clear how to choose the electron concentration (gate voltage) to compare noise in different HEMTs.

Another method to characterize noise in FETs is based on the McWhorter model of noise in Si MOSFETs.^{11,12} In this model, the 1/*f* noise originates from the tunneling of electrons from the channel to oxide and their capture at different distances from the channel.

The mechanism of noise in GaN/AlGaN transistors can be quite similar. Electrons can tunnel from the channel to the AlGaN barrier layer or to the GaN and be captured there by the traps. The McWhorter model allows to calculate the trap density responsible for the 1/*f* noise, which is a good figure of merit for the noise amplitude and HEMT quality. However, there are just a limited number of publications where the trap density in GaN/AlGaN transistors was estimated based on the McWhorter model and compared with the other FETs.^{7,13,14}

In this work, we study the 1/*f* noise in GaN/AlGaN HEMTs fabricated under different conditions, evaluate different methods to extract the trap density, and compare the results with Si MOSFETs.

The epistructures were grown on a high-resistivity GaN:C buffer formed either on a c-axis sapphire (Al_{2}O_{3}) or on semi-insulating (SI) 6H poly-type SiC substrate by the metalorganic chemical vapor deposition (MOCVD) method. The unintentionally doped (UID) GaN layers were grown at the pressure of *P* = ∼100, ∼200, and ∼300 Torr for the wafers #TG2219, #TG2196, and #Hx2688, respectively, with the compensation of growth temperature for the pressure change. The sequence of layers and their parameters are shown in Table I. The molar fraction, x, of the Al content and the thickness of the Al_{x}Ga_{1−x}N barrier were obtained from X-ray diffraction measurements.

Wafer layer . | #TG2196 . | #TG2219 . | #Hx2688 . |
---|---|---|---|

SiN_{x} cap | No | No | 1 nm |

GaN cap | No | 1 nm | 2 nm |

Al_{x}Ga_{1−x}N barrier | 25 nm | 27 nm | 19 nm |

x = 0.20 | x = 0.23 | x = 0.25 | |

AlN spacer | 1 nm | 1 nm | 0.8 nm |

UID-GaN | 500 nm | 500 nm | 1000 nm |

GaN:C | 1000 nm | 1000 nm | 1300 nm |

Substrate | Al_{2}O_{3} | Al_{2}O_{3} | SiC |

Wafer layer . | #TG2196 . | #TG2219 . | #Hx2688 . |
---|---|---|---|

SiN_{x} cap | No | No | 1 nm |

GaN cap | No | 1 nm | 2 nm |

Al_{x}Ga_{1−x}N barrier | 25 nm | 27 nm | 19 nm |

x = 0.20 | x = 0.23 | x = 0.25 | |

AlN spacer | 1 nm | 1 nm | 0.8 nm |

UID-GaN | 500 nm | 500 nm | 1000 nm |

GaN:C | 1000 nm | 1000 nm | 1300 nm |

Substrate | Al_{2}O_{3} | Al_{2}O_{3} | SiC |

The Ohmic and Schottky contacts were fabricated at the FTMC using the Ti/Al/Ni/Au (30/90/20/100 nm) and Ni/Au (25/200 nm) metal stacks, respectively. The Ohmic contacts formed using the rapid thermal annealing method in a nitrogen ambient demonstrated a resistance *R _{c}* ∼ 1 Ω mm. More details about the fabrication of contacts can be found in Refs. 15 and 16.

A specific transistor design was chosen in order to avoid the mesa etching step and minimize the process flow to two photolithography procedures. In this design, a square-shaped drain contact is surrounded by a rectangular double gate and double source electrodes. The optical microscope pictures of the transistor and its main dimensions are shown in Fig. 1(a).

The current-voltage characteristics and noise were measured at room temperature on a wafer using a probe station. The noise spectra were measured as a function of the drain, *V _{D}*, and gate,

*V*, voltages with the source grounded. The voltage fluctuations,

_{g}*S*, from the drain load resistance

_{v}*R*= 1–10 kΩ were analyzed with a dynamic signal analyzer. The short-circuit current fluctuations were calculated in the usual way as

_{L}*S*=

_{I}*S*[(

_{v}*R*+

_{L}*R*)/(

_{d}*R*)]

_{L}R_{d}^{2}, where

*R*is the differential drain to source resistance obtained from the experimental current-voltage characteristics.

_{d}The devices were characterized by a ∼6 orders of magnitude on/off ratio and a small gate leakage current. The subthreshold slope was within the range of *η* = 1.5–2.

The noise spectra had the form of 1/*f ^{α}* noise with

*α*= 0.95–1.05 without a noticeable contribution of the generation-recombination noise. In the linear regime, the spectral noise density of the drain current fluctuations,

*S*, was always proportional to the current squared. The dependences of noise on the gate voltage swing (

_{I}*V*−

_{g}*V*) in the linear regime at frequency

_{t}*f*=

*10 Hz for the representative devices are shown in Fig. 2 (*

*V*is the threshold voltage). They have the usual shape for the FETs. At a high gate voltage, the noise slightly increases with the gate voltage increase manifesting the contribution of the contact noise.

_{t}^{17}At a lower gate voltage, noise decreases with the gate voltage increase steeper than 1/(

*V*−

_{g}*V*)

_{t}^{2}. Although the McWhorter model predicts the 1/(

*V*−

_{g}*V*)

_{t}^{2}slope, the steeper dependences are often observed. There are several possible reasons for that: (i) influence of the drain and source access resistances; (ii) dependence of the trap density on energy; and (iii) contribution of the correlated mobility fluctuations.

In the McWhorter model, the spectral noise density of the drain current fluctuations *S _{I}*/

*I*

^{2}is given by

^{12}

where *k* is the Boltzmann constant, *T* is the temperature, *N _{t}* is the effective trap density,

*f*is the frequency,

*WL*is the channel area,

_{g}*n*is the concentration, and

_{s}*γ*is the attenuation coefficient of the electron wave function under the barrier, usually taken equal to 10

^{8}cm

^{−1}.

In many publications^{18,19} Eq. (1) is complemented by another term for the correlated mobility fluctuations. Mobility fluctuations and correlated mobility fluctuations are indeed the possible mechanisms of noise. However, the relative contribution of the mobility fluctuations is difficult to define. Therefore, we do not include the mobility fluctuations in our analysis and name the *N _{t}* value in Eq. (1) “the effective trap density.”

Equation (1) does not take into account the drain and source access resistances, which are the sum of the contact resistance and resistance of the ungated parts of the channel. Even if the access resistances have a negligible contribution to noise, they still affect the noise properties of the device. First, at nonzero access resistance, the voltage drop on the channel is smaller than the drain voltage. Second, the source access resistance provides a negative feedback to the gate. As a result, the drain current noise is smaller than it would be at zero access resistance, and the correct calculation of the trap density requires the knowledge of this value.

Fluctuations of the current at nonzero access resistance can be written as

where *σ _{t}* is the total conductance of the transistor including access resistances,

*V*

_{g}_{0}is the gate voltage, and

*R*is the source access resistance [see Fig. 1(b) for the equivalent circuit and notations]. The first term in the brackets,

_{S}*δσ*, describes the fluctuations of the channel conductivity due to physical processes, for example, fluctuations of the number of carriers,. The second term describes the negative feedback provided by the fluctuations of the current and corresponding voltage fluctuations on the source access resistance.

_{t}The derivative d*σ _{t}*/

*dV*

_{g0}can be expressed using the internal transconductance g

_{m0}= dI/dV

_{g0}:

Here, *σ _{Ch}* = 1/

*R*is the channel conductance, and

_{Ch}*R*and

_{S}*R*are the source and drain access resistances.

_{D}Combining Eqs. (2) and (3), the expression for the current fluctuation can be written in the following form:

From Eq. (4), it is easy to find how the relative spectral noise density of drain current fluctuations relates to the channel conductance fluctuation spectral noise density:

Here, $S\sigma Ch/\sigma Ch2$ is the relative spectral noise density of the channel conductance fluctuations. If the access resistance is negligible in comparison with the channel resistance, the relative spectral noise density of the current fluctuations is equal to $S\sigma Ch/\sigma Ch2$. In the opposite case of high access resistance, one needs to calculate $S\sigma Ch/\sigma Ch2$ using Eq. (5) and find the trap density as

Another way to estimate the effective trap density is using the input gate voltage noise *S _{Vg}* = (

*S*/

_{I}*I*

^{2})/(

*g*/

_{m}*I*)

^{2}. Here,

*g*=

_{m}*K × g*is the external transconductance, which can be easily measured. The expression for the coefficient

_{mo}*K*, which relates the internal and external transconductances, can be found in Ref. 20, for example. It can be expressed exactly as the term in the square brackets in Eq. (5). Therefore, the input gate voltage

*S*“does not depend” on the access resistance.

_{Vg}From Eqs. (1) and (5) and the expression for the internal transconductance in the linear regime, *g _{m}*

_{0}

*= CμV*(

_{Ch}*W*/

*L*), it is easy to obtain the well-known expression for the input gate voltage noise:

where *q* is the electron charge and *C* is the gate capacitance per unit area. Since *S _{Vg}* does not depend on the access resistance, it can be used directly to calculate the effective trap concentration without knowing the access resistance. Note also, that in accordance with the McWhorter model,

*S*does not depend on the carrier's concentration in the channel, i.e., on the gate voltage.

_{Vg}Figure 3 shows the gate voltage dependence of the effective trap density for the HEMTs fabricated on different epitaxial structures and calculated using Eq. (7). Although all the three wafers were fabricated by a similar technology and have similar layer parameters, the effective trap densities, *N _{t}*, in these structures are quite different. Particularly, the effective trap density at a high gate voltage for the #TG2219 structure is about two orders of magnitude higher than that for the other two structures.

In order to find out what is specific in this wafer, we characterized all the wafers by secondary ion mass spectroscopy (SIMS) and compared the results with the previously published data on the terahertz electroluminescence of impurities.

Special surface-cleaning procedures were employed before the SIMS measurements. This enabled a determination of the doping level well below 10^{17} cm^{−3}. Table II shows the oxygen, silicon, and carbon impurity concentrations in the UID GaN layers obtained by the SIMS technique. Oxygen and silicon act as donors in GaN, and carbon is a compensating acceptor.^{21–23} As follows from Table II, the #TG2219 structure has the highest concentration of uncompensated donors (*N _{D}* −

*N*). Just this structure is characterized by the highest effective trap density,

_{A}*N*. Although we cannot state that these particular donors (oxygen or silicon) are responsible for the high noise level, a higher concentration of the uncompensated donors leads to a higher conductivity and a lower quality of the layer. Traps, which are responsible for the high noise level, might be associated with the defects which accompany these donor dopants. However, these defects cannot be directly observed by the SIMS.

_{t}Wafer . | Oxygen, N × 10_{D}^{16} cm^{−3}
. | Silicon, N × 10_{D}^{16} cm^{−3}
. | Carbon, N × 10_{A}^{16} cm^{−3}
. |
---|---|---|---|

#TG2196 | 2.0 ± 1.0 | 0.9 ± 0.6 | 1.4 ± 0.2 |

#TG2219 | 2.5 ± 1.1 | 1.0 ± 0.7 | 1.1 ± 0.2 |

#Hx2688 | 2.1 ± 1.2 | 1.0 ± 0.8 | 1.3 ± 0.2 |

Wafer . | Oxygen, N × 10_{D}^{16} cm^{−3}
. | Silicon, N × 10_{D}^{16} cm^{−3}
. | Carbon, N × 10_{A}^{16} cm^{−3}
. |
---|---|---|---|

#TG2196 | 2.0 ± 1.0 | 0.9 ± 0.6 | 1.4 ± 0.2 |

#TG2219 | 2.5 ± 1.1 | 1.0 ± 0.7 | 1.1 ± 0.2 |

#Hx2688 | 2.1 ± 1.2 | 1.0 ± 0.8 | 1.3 ± 0.2 |

The terahertz electroluminescence of impurities at the cryogenic temperature was studied in Refs. 24 and 25 for the same #TG2196 and #TG2219 structures (marked as U26 and U28, respectively). Indeed, the electroluminescence spectroscopy indicated a ∼30% higher oxygen peak intensity in the #TG2219 wafer, which is characterized by the highest noise level. This result agrees with the SIMS measurements indicating that either oxygen or the other accompanying trap levels are responsible for the high noise in this structure. The possible reason for the lower quality of this wafer is the small pressure during the growth, i.e., 100 Torr contrary to 200 and 300 Torr for other wafers. It is known that lowering of the growth pressure deteriorates the material properties.^{26}

The concentration of oxygen in the UID-GaN layer of the #TG2219 wafer is higher than that in other wafers just by a few tens of percent. Meanwhile, the noise amplitude and the corresponding effective trap density differ in an order of magnitude or more, indicating that a minor change in technology might induce a high increase in the trap density which is responsible for the noise. Therefore, noise measurements are a very sensitive method for the assessment of the epistructure technology and the material quality.

Contrary to the McWhorter model prediction, the effective trap density for some devices slightly decreases with the gate voltage increase reflecting the *S _{Vg}* dependence on

*V*. As it was discussed several times, this effect can be due to the contribution of the correlated mobility fluctuations

_{g}^{19}which are not taken into account in this estimate. Another reason is the dependence of the trap density on the energy. Since the main contribution to noise comes from the traps near the Fermi energy, the gate voltage dependence of noise reflects the energy profile of the effective trap density.

At a high gate voltage, the trap density in two of the studied GaN/AlGaN HEMTs is below 10^{19} eV^{−1} cm^{−3} (see Fig. 2). Similar or higher values of the effective trap density are often found in Si MOSFETs with a high-k dielectric.^{27–29}

In conclusion, the effective trap density was extracted from the low frequency noise measurement of GaN/AlGaN field effect transistors. The extraction method based on the McWhorter model and input gate voltage noise allowed us to take into account the effect of the access resistance on the output noise. The effective trap density can be as low as below 10^{19} eV^{−1} cm^{−3}, which is of the same order of magnitude as in Si MOSFETs with a high-k dielectric. It was found that the high effective trap density correlates with SIMS and terahertz electroluminescence spectroscopies, which reveal a slightly higher concentration of uncompensated donors in GaN in one of the epitaxial structures. The noise level and effective trap density in this structure is orders of magnitude higher confirming that noise is a very sensitive parameter for the material quality and technology of GaN/AlGaN HEMT structures.

The work was supported by the “International Research Agendas” program of the Foundation for Polish Science cofinanced by the European Union under the European Regional Development Fund (No. MAB/2018/9) and by the National Science Centre, Poland allocated on the basis of Grant Nos. 2016/22/E/ST7/00526 and UMO-2017/27/L/ST7/03283. The research at the Terahertz Photonics Laboratory at Vilnius was supported by the Research Council of Lithuania (Lietuvos mokslo taryba) under the “TERAGANWIRE” project (Grant No. S-LL-19-1). The research was also partially supported by the Foundation for Polish Science through the TEAM project POIR.04.04.00-00-3D76/16 (TEAM/2016-3/25).