# I. Introduction ince its invention in 1979 [1], IGBT has been considered a preferred switching device in power electronic systems and significantly improved the quality of life of people. Specially 90% of low voltage products (600V to 1700V) are being occupied by IGBTs. Compared to the first and second generation of NPT IGBTs, the device performance using latest thin film technology has been improved by introducing various doping concentrations in the Carrier Storage Region (CSR), specially known as SPT technology [2] or field stop concept [3]. The advantages of the first two generations have been combined by this technology, resulting in evolution of further generations [4][5][6]. Different doping profiles have significant effects on the base charge distribution of NPT IGBTs, which can be thoroughly studied by proper estimation of doping concentration in the effective base region (CSR) of IGBT. In recent times, high doping profile has been considered as a matter of concern in the steady-state and transient operation of IGBT. However, with the modern IGBT structure having highly doped CSR, a MOSFET-like behaviour has been seen at low collector-emitter voltage when the gate is fully turned on [7]. Actually increasing the base doping concentration can reduce the on-state loss while maintaining the desirable blocking voltage. But too high doping may affect the injection efficiency of p-emitter and result in some undesirable effects [8], which need to be avoided. This has caused considerable interest in modeling of base doping profile in DC linked type circuits [9] as well as motor drive applications [10]. However, the accurate and effective study of IGBT requires proper modeling of doping profiles in the CSR with systematic estimation technique. This paper introduces the idea of doping profile modeling in the base through investigation into the transient characteristics of IGBTs. The steady state minority carrier concentration is proposed through a parabolic profile [11]. Using this profile, an analytical model is derived for explaining transient base charge decay during turn-off. Fourth order Runge-Kutta (RK4) method is used to validate the model over a wide range of doping concentration. Finally being consistent with the practical results, base doping profile is investigated through turn-off base charge distribution on different time instances. # II. Turning of Operation of Igbt During the turn-off operation of IGBT the gate voltage is kept less than the threshold voltage. It is assumed that the anode voltage is kept constant during the current decay, but it may be different from the anode voltage of the steady state. Fig. 1 shows the cross section schematic of IGBT half cell and Fig. 2 shows the schematic diagram of excess minority carrier distribution for two doping profiles, Low-doped Base (LDB) and High-doped Base (HDB). The figure shows charge distribution for immediately before (steady state) and after the channel current has been removed. It can be seen that the minority carrier holes decreases quickly to zero after switching in case of LDB, resulting in a large depletion region. This causes the effective base width (W) smaller than the ambipolar diffusion length (L). On the other hand, the HDB causes the carrier reduction much slower after turn-off, causing a smaller depletion region. In this case the effective base width is not very small compared to the total base width (WB), resulting in W being comparable or even larger than L. So the transient operation is very much dependent on the base doping profile. # III. Expression for Transient base Charge The main foundation of the previously established models was based on the assumption that W must be much smaller than L, which corresponds to LDB. But these models are inefficient in case of other doping profiles and thus fail to optimize power in NPT and PT IGBTs. The proposed model takes this into account and provides consistent results in all base doping concentrations. The initial expression for time independent minority carrier concentration is assumed by taking parabolic approximation in the hyperbolic function W x L p x P W L ? ? ? + ? ? ? ? = ? ? + ? ? ? ? where P 0 is minority carrier concentration at the collector-base junction, W is effective base width, L is ambipolar diffusion length and x is the distance from emitter to collector region. Using this assumption in the ambipolar diffusion equation and integrating the equation with boundary conditions x=0;p= P 0 and x=W;p=0, a time dependent expression for minority carrier concentration is found in the previous work [11]. 5 2 3 0 2 2 2 ( ) ( , )4 ( ) 5 4 (6 ) 6) 12 P W x P x t L W x L W L W ? ? ? = ? + ? ? + ? ? 2 2 0 2 2 2 2 1 1 12 3 4 (P W L W D W t W L W L W ? ? ? ? + ? 5 2 3 ( ) 4 ( )5W x L W x ? ? ? ? + ? ? ? ? 3 4 5 2 2 0 2 2 2 1 (6 ) 6 6 20 ( 6) P W x x x L W W D t W L W ? ? ? + + ? + ? ? ? + ? ? 0 2 2 2 2 1 (6) P W D t W L W ? + ? + 3 4 5 2 2 2 2 ( 6 ) (2 6 ) 6 12 20 x x x W W L W L W ? ? ? ? ? + ? ? ? ? 2 2 2 2 0 2 2 2 2 1 20 6 5 6 12 P x W L W L W D t L W L W ? + ? ? ? + ? 2 2 2 0 2 2 2 1 10 10 ( 6) P xW W W L D t L W ? ? ? ? + 2 2 0 0 0 2 2 2 20 20 6 P x P x L W W P W L W L ? ? + ? + + ? ? + ? ? 2 2 2 2 2 0 2 2 2 2 2 20 1 12 3 .....(2 ) 20 6 12 P L W W W L W W D t L W L L W ? ? ? ? + ? ? ? ? ? ? ? ? ? + ? ? ? ? ? where D is ambipolar diffusivity. Integrating the excess carrier concentration with respect to x having limit of zero to W and then multiplying by charge (q) and area (A), an expression for stored base charge is found W t W t Q t qAP L ? ? = ? ? ? ? ? The charge decay rate relates to the electron current at emitter -base junction through the following expression ???? Using the quasi-equilibrium simplification and assuming high-level injection of the holes into the base, an expression for transient base charge decay is found ??.. .... (5) where I sne is the emitter electron saturation current and ? HL is high level excess carrier lifetime. For W<