2.4 MOS Capacitance
2.4.4 Capacitance-Voltage measurements
Capacitance can be measured in various conditions.18 One can probe it as function of frequency and deduce theDit from the time dependence of the interface response (conduc- tance method) or one can compare a CV curve at a given frequency to an ideal simulated curve and extract the parameters (Terman’s method). Here, a third method is described:
simultaneous high-frequency (AC) and low-frequency (quasi-static) CV measurements. It is known as the hi-lo technique; the setup is illustrated in Figure2.19(a).
A constant amplitude small AC signalVacis added to a DC oneVdc, so that the gate bias is given byVg =Vdc+Vac. The sweep of the DC bias is performed in a staircase fashion. It will be shown later that the limit of the technique comes from the AC angular frequencyωac and from the DC ramp rate ΔVdc/τdc. A vector ammeter measures the resulting current.
The total current density (in A/cm2) isJac+Jdc.
Figure 2.19: (a) MOS CV measurement system; the voltmeter and ammeter measure both the magnitude and the phase of the signal. (b) Simultaneous Ch (continuous line) andCq (dotted line) measured as a function of voltage.8
The definition of the capacitance is
C = Q
Vg (2.49)
The quasi-static capacitance Cq can be extracted from the displacement current resulting from a small change inVdc.
Cq = ΔQ ΔVdc =
τdc
0 Jdcdt
ΔVdc (2.50)
and the high-frequency capacitance Ch can be extracted from the amplitude of the AC signal
Ch = dQ/dt
dVac/dt = Jac
dVac/dt = Jac∗
Vac∗ ωac (2.51)
whereJac∗ and Vac∗ are respectively the amplitude of the AC current density and the ampli- tude of the AC bias.
A typical set of high and low frequency curves is shown in Figure 2.19(b) for p-type silicon. The reason whyCh does not reach inversion is that the frequencyωac is typically 1 MHz, much faster than the generation rate. As explained earlier, in the case of wide band- gap semiconductors, even Cq does not reach inversion. In any case, the Dit is extracted
from the CV behavior in the depletion regime where the two curves are different because of the response time of the switching states. Indeed, as the bias is swept from accumulation to depletion, the traps emit their charges when the Fermi level at the interface crosses the corresponding energy in the band-gap. This emission affects the displacement current and, therefore Cq, but since those interface states do not subsequently fill and empty, they are not detected in Ch. At a given DC bias, the energy band bending (qφbs) at the interface is the same for Cq and Ch, and their difference reveals the Dit value at the corresponding energy. Indeed,
1 Cq
= 1
Cox
+ 1
qDit+s/xd (2.52)
and similarly for the high frequency capacitance 1
Ch = 1 Cox
+ 1
s/xd (2.53)
which leads to the density of interface states at a given level
Dit = 1 q
1 Cq − 1
Ch +xd s
−1
− s
qxd (2.54)
The value of the corresponding trap energy, and the value of the depletion layer length, can be calculated using Berglund’s method.42
Finally, it should be noted that the emission time of the traps on which the hi-lo method is based also sets the limit of the technique. Indeed, in a n-type material, for energy levels very close to the conduction band the emission time is so fast that charges can follow the high frequency signal and the two capacitances are therefore equal. And for deep levels, the emission time is so long that the traps cannot follow the DC signal and therefore do not empty. Subsequently, there is an energy window in which the method is valid; the upper limit (deep states) is set by the ramp rate ΔVdc/τdc and the lower limit (shallow sates) is set by the frequency ωac. These limits can be calculated for n-type materials using the
expression for the emission time of an electron
τn = 1 σnvtNc
exp
Ec−E
kbT (2.55)
where σn is the capture cross section of an electron by an interface trap,vt is the thermal velocity of an electron, Nc is the density of states in the conduction band,Ec is the energy of the conduction band edge, and E is the energy level in the gap. At room temperature, the assumed valid window is between 0.2 eV and 0.6 eV from the band edges for a ramp rate of 0.1 V/s and a 1 MHz frequency. At 300◦C, this window is between 0.7 eV and 1.9 eV.43 Therefore, the complete energy gap of wide band-gap semiconductors can be probed by measuringDit at different temperatures (see Figure 2.20).
Figure 2.20: Emission time constants at 23◦C and 350◦C of traps with different capture cross-sections. Ec-E is the energy within the gap measured from the conduction band edge. Low-frequency (LF) and high-frequency (HF) limits of the hi-lo CV techniques are indicated. Courtesy of Sarit Dhar.
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PART TWO
STUDIES ON THE PROPERTIES AND THE RELIABILITY OF THE SiO2/SiC INTERFACE
Chapter III: Pressure dependence of SiO2 growth kinetics on SiC 82 Chapter IV: Impact of nitrogen incorporation on electron trapping 103 Chapter V: Impact of nitrogen incorporation on hole trapping 113 Chapter VI: Dependence of interface properties on nitrogen density 127 Chapter VII: Accelerated oxide breakdown on implanted surfaces 154
CHAPTER III