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In this paper, we conducted a simulation of an indium-gallium-zinc oxide (IGZO)-based neuromorphic system and proposed layer-by-layer membrane capacitor (Cmem) optimization for integrate-and-fire (I&#x0026;F) neuron circuits to minimize the accuracy drop in spiking neural network (SNN). The fabricated synaptic transistor exhibited linear 32 synaptic weights with a large dynamic range <inline-formula> <tex-math notation="LaTeX">$(\sim 846$ </tex-math></inline-formula>), and an n-type-only IGZO I&#x0026;F neuron circuit was proposed and verified by HSPICE simulation. The network, consisting of three fully connected layers, was evaluated with an offline learning method employing synaptic transistor and I&#x0026;F circuit models for three datasets: MNIST, Fashion-MNIST, and CIFAR-10. For offline learning, accuracy drop can occur due to information loss caused by overflow or underflow in neurons, which is largely affected by Cmem. To address this problem, we introduced a layer-by-layer <inline-formula> <tex-math notation="LaTeX">${\mathrm{ C}}_{\mathrm{ mem}}$ </tex-math></inline-formula> optimization method that adjusts appropriate <inline-formula> <tex-math notation="LaTeX">${\mathrm{ C}}_{\mathrm{ mem}}$ </tex-math></inline-formula> for each layer to minimize the information loss. As a result, high SNN accuracy was achieved for MNIST, Fashion-MNIST, and CIFAR-10 at 98.42&#x0025;, 89.16&#x0025;, and 48.06&#x0025;, respectively. Furthermore, the optimized system showed minimal accuracy degradation under device-to-device variation.